mathematics unit plan std. 5

MATHEMATICS UNIT PLAN

SETEMBER

Week One: Routines and procedures

Week two

Subject: Mathematics

Topics: Missing Numbers in Addition, Missing Numbers in Subtraction, Missing Numbers in Multiplication, Missing Numbers in Division,

Previous Knowledge:

Students are able to read and write numbers up to million, and have been introduced to a number line in lesson 9.

Objectives:

Through use of direct instruction, Class discussion and practice, students will be able to:

Lesson 031. Use subtraction to find a missing addend in an addition problem.2. Check their answer to a missing number in an addition problem by using the answer in place of

the letter in the original problem.3. Find the missing minuend in a subtraction problem by adding the subtrahend and the difference.4. Find the missing subtrahend in a subtraction problem by subtracting the difference from the

minuend.5. Check their answer to a missing number in a subtraction problem by using the answer in place of

the letter in the original problem.Lesson 046. Use division to find a missing factor in a multiplication problem.7. Find the missing dividend in a division problem by multiplying the divisor and the quotient.8. Find the missing divisor in a division problem by dividing the dividend by the quotient.Lesson 059. Take steps in order from left to right in a problem with more than one addition or subtraction

step.10. Take steps in order from left to right in a problem with more than one multiplication or division

step. 11. Do the work within parentheses first when solving a problem with more than one step.12. Identify and use the associative property of addition and the associative property of

multiplication.13. Perform the operations above the bar and below the bar before dividing in a division problem

with a bar.

Concepts:

- We can find a missing addend by subtracting the known addend from the sum.Example: 12 + m = 31 - solution: 31 – 12 = 19, therefore the m = 19

- We can find a missing minuend (first number in a subtraction problem) by adding the other two numbers. Example: w – 16 = 24 – solution 16 + 24 = 40, therefore w = 40

- We can find a missing subtrahend (second number in a subtraction problem) by subtracting the difference from the minuend. Example: 236 – y = 152 – solution 236 – 156 = 84, therefore y = 84

- We can find a missing factor by dividing the product by the known factor. Example: A x 6 = 72 – solution: 72 ÷ 6 = 12, therefore A = 12

- We can find the missing dividend (the number inside the division box) by multiplying the other two numbers. We can find either the divisor or quotient (the numbers outside the box) by dividing.

- When there is more than one addition or subtraction step within a problem, we take the steps in order from left to right. In this problem we first subtract 4 from 9. Then we add 3. 9 – 4 + 3 = 8

- If a different order of steps is desired, parentheses are used to show which step should be taken first. In the problem below, we first add 4 and 3 to get 7. Then we subtract 7 from 9. 9 – (4 + 3) =2

Skills:

- Ordering mathematical operations- Finding missing numbers in multiplication and division- Finding missing numbers in addition and subtraction.- Using appropriate vocabulary for mathematical arithmetic operations.

Attitudes:

- Awareness that math is used in our daily life.- Appreciation for numbers. - Respect for others and their ideas. - Cooperation as students work in groups.

Teaching/Learning Strategies:

Day One

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Present and addition problem to students.- Have them cover one addend and then the next with their fingers.- Discuss with students what steps they would do to find any of the missing addends they covered with

their fingers.- Listen to students responses and acknowledge anyone who shows the correct steps.- Model out for children the correct steps to solve these problems.- Allow students to practice and to assess their understanding of it.- Next, present a subtraction problem for students on the white board.- Ask them to cover the subtrahend with their fingers and describe what would they do to find that

missing number.- Listen to students how they would go about solving this problem. Then elaborate of provide correct

steps for children to solve this type of problem.- Now have students do likewise with the minuend and repeat the last three steps with them.- Provide enough examples for students and practice to assess their understanding of this problem.

- Have children work on the mixed practice section of their Saxon Math books to reinforce previous concepts covered and the present ones.

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Day two:

- Students perform warm-up activities – Addition Facts, Mental Math, and Problem Solving.- Present a multiplication fact to students. Ask them to cover any of the factors with their fingers.- Have them come up with a way of describing how they can use the two uncovered numbers to find the

covered number.- Listen to children’s responses and carry out from suggestions they have offered.- Instruct them how to go about working this type of problem.- Provide them with different examples and allow the class to participate in completing the steps of each

example given.- Have students practice some problems and assess their understanding of these problems.- Do likewise with a division problem. Have students covered all the three numbers in division problem

and offer ideas how we could find the covered number.- Follow on from suggestion given by students and show them step by step how to go about solving these

problems. - Have students work problems of the practice section of this lesson.- Check work and go over problems where children had difficulty.- To reinforce past concepts covered and these ones, have children work on the mixed practice of the

lesson.

Day three:

- Students perform warm-up activities – Addition Facts, Mental Math, and Problem Solving.- Write the following problems for students on the white board: 9 – 4 + 3 = 4- Ask students try to work out this problem.- Invite anyone who thinks has the correct answer to come to the board and write it.- Acknowledge the students if he got it correct, if not, congratulate him/her for trying.- Next, instruct students the steps taken to work out such problem.- Provide them with problems where parentheses are used. Show clearly to students how to solve this type

of problem. Involve the class in finding the solution to the problem.- Provide students with other examples to achieve understanding of the problems.- Then have them work on the practice section of the lesson to assess their understanding of this lesson.

Day Four:

- Students will be tested on the last five lessons by doing the mixed practice of lesson 5.

Assessment Strategies:

- Oral participation- Lesson practices- Tests

Reference/Materials:

- Saxon Math 7/6 Teacher Resource Book – page 12 – 22- Saxon Math 7/6 - Students Book – Lesson 3 - 5.- Markers- White board

Evaluation:

Week Three


Lesson Topic: Fractional Parts; Lines, Segments, Rays; Linear Measurement.

Class: Standard V

Previous Knowledge:

Students are able to identify numerator and denominators.

Objectives:

Through use of direct instruction, Class discussion and practice, students will be able to:Lesson 061. Use a fraction to name part of a whole.2. Use a fraction to use part of a group.3. Divide a number into equal parts to find a fractional part of that number.Lesson 071. Identify line, segments, and rays.2. Use an inch rule to measure line segments to nearest quarter of an inch.3. Use a centimetre ruler to measure line segments in centimetres and millimetres.

Reference / Materials:

- Saxon Math 7/6 Teacher Resource Book – page 23 - 30- Saxon Math 7/6 - Students Book – Lesson 6 - 7- Markers- Bristol board- ruler- strips of paper

Concepts:

- Fractions – is written with two numbers and a fraction bar.- Denominator – is the bottom number, shows the numbers of equal parts in the whole.- Numerator – the top number shows the number of the parts being represented.- A mathematical line has no endpoints. We use arrowheads to indicate a lines unending quality.- A segment is part of a line and has two endpoints.- A ray has one endpoint. We represent it with one arrowhead.

Skills:

- Defining skills as they define mathematical vocabulary.- Identifying skills as students identify numerator, denominator, lines, rays, etc ...

Attitudes:

- Awareness that math is used in our daily life.- Appreciation for numbers. - Respect for others and their ideas.

Teaching / Learning Strategies:

Day One:

- Students perform warm-up activities – Addition Facts, Mental Math, and Problem Solving.- Write the following terms on the board fraction, denominator and numerator. - Elicit from students what each term means. - Next, use a picture fraction and number fraction to explain each one to students.- Show students examples of fractions of a whole and of fractions of a group. Make sure students know

the different between the two of them.- As a class study and workout the examples found in the book.- Have students work on practice set a – h.- Check work and go over problems where children had difficulty.

Day two:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Draw on the white board an illustration of a line, line segment, rays and endpoints.- Have students examine the illustrations and state what differences they observe in the illustrations.- As a class read the information on the book, and discuss. Have students write notes in their exercise

book. - Discuss the difference between each illustration shown.- Distribute strips of paper to students. With the use of their rulers students will draw inch marks on the

paper.- Next, have students draw half inch marks on their paper. Tell them to estimate the distance and draw the

half inch mark slightly shorter than the inch marks. - Tell them to show quarter marks by estimating the have the distance between each half inch.

- Have students turn their attention to the centimetre ruler now and explain the different measurements, that is, centimetre and millimetres.

- Have students compare the inch ruler and the centimetre ruler and discuss what differences are observed.

- Work the examples on the book to practice measuring with an inch ruler and a centimetre ruler. - Students work on practice set while teacher walks around checking students work.- Have children work on the mixed practice section of their Saxon Math books to reinforce present and

past concepts covered.

Wednesday: Fence decoration

Thursday: Children’s rally

Friday: Independence Day Holiday

Assessment Strategies:- Drills- Practice sets- Oral participation- Illustrations of inch ruler and centimetre ruler

Evaluation:

Week four


Lesson Topic: Lines, Segments, and Rays; Linear Measure; Perimeter, the number line, ordering and comparing; Sequence and Scale

Class: Standard V

Previous Knowledge:

Students have used a ruler before and can identify the symbols used to compare numbers.

Objectives:

Through the use of rulers, diagrams, teacher direct instruction and class discussion, students will be able to:Lesson 71. Identify lines, segments, and rays. 2. Use an inch ruler to measure line segments to the nearest quarter inch.

3. Use a centimetre ruler to measure line segments in centimetres and millimetres. Lesson 8

4. Recognize that the total distance around the classroom is perimeter of the classroom. 5. Find the perimeter of a shape by adding the lengths of the shape’s sides. 6. Find the length of a side of a square when the perimeter of the square is known.

Lesson 97. Use number line to order numbers from least to greatest.8. Use symbols >,<, and = to compare two numbers.9. Find the value of two expressions and compare them using the symbols.

Lesson 1010. Identify addition and multiplication sequence.11. Identify even and odd numbers.12. Find the value of marks on a scale.13. Read the number indicated on a scale.

Concepts:

- Endpoints points at which segments end.- Line – a straight collection of points extending in opposite direction without end. - Ray – a part of a line that begins at a point and continues without end in one direction.- Segment – a part of a line with two distinct endpoints.- Perimeter - the distance around a closed flat shape.- Counting numbers - The numbers used to count: the members of the set (1, 2, 3, 4, 5, …). Also

called natural numbers. - Negative numbers – numbers less than zero. - Number line - a linfor representing and graphing numbers. Each point on the line corresponds to a

number. - Whole numbers: The members of the set (0, 1, 2, 3, 4, …)- Celsius scale - a scale used on some thermometers to measure temperature. - Even numbers can be divided by 2 without a remainder. - Odd numbers have a remainder of 1 when divided by 2. - Fahrenheit scale is used on some thermometers to measure temperature. - A scale displays numbers with an indicator to show the value of a certain measure.

Skills:

- Comparing skills as they compare numbers. - Add and division skills as they find perimeter, length or width. - Identifying skills as they identify the rule for an addition or multiplication sequence. - Reading and finding skills as they find the value of the marks on a scale.

Attitudes:

- Awareness that math is used in our daily life.- Appreciation for numbers. - Respect for others and their ideas

Teaching Strategies/ Students Activities:

Monday:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Draw on the white board an illustration of a line, line segment, rays and endpoints.- Have students examine the illustrations and state what differences they observe in the illustrations.- As a class read the information on the book, and discuss. Have students write notes in their exercise

book. - Discuss the difference between each illustration shown.- Distribute strips of paper to students. With the use of their rulers students will draw inch marks on the

paper.- Next, have students draw half inch marks on their paper. Tell them to estimate the distance and draw

the half inch mark slightly shorter than the inch marks. - Tell them to show quarter marks by estimating the have the distance between each half inch. - Have students turn their attention to the centimetre ruler now and explain the different measurements,

that is, centimetre and millimetres.- Have students compare the inch ruler and the centimetre ruler and discuss what differences are

observed. - Work the examples on the book to practice measuring with an inch ruler and a centimetre ruler. - Students work on practice set while teacher walks around checking students work.- Have children work on the mixed practice section of their Saxon Math books to reinforce present and

past concepts covered.

Tuesday:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Elicit from students the definition of perimeter. Together discuss the definition and use examples to

clarify the concept.- Have students draw a rectangle and go out and walk the perimeter of the volleyball court and count their

steps. Tell them to write the amount of steps for each side and write on the rectangle drawn in their exercise books.

- Once students are finished they will go back to the class and answer the questions on page 35 of their books.

- Have students use rulers and measure their exercise books and their Saxon Math books and then find the perimeter of each.

- Discuss answers and steps taken to arrive at them.- Discuss examples in the book and ask students to explain how we know that the lengths of the unlabeled

sides of the rectangle are 2 cm and 3 cm. Listen to students’ responses and discuss. - Students will work on practice set a-f. Once they are done we will review as a class. - Students will start to work on the thirty questions found in Mixed Practice Set. They will complete this

exercise for homework.

Wednesday:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Present a number line to students. Ask them if they know how we call this diagram. If they don’t know,

tell them how we call it.- Have students observe it and tell you (the teacher) what it has (a line, marks, and numbers).- Tell them that a number line may be numbered with different types of numbers that is, counting

numbers (whole numbers including zero), negative numbers, etc.- Have students observe that this line is made up of whole numbers and negative numbers. Discuss with

them how numbers increase in value when we move to the right side of the number line and decrease in value when we move to the left.

- Use example 1 from the book to show students how to arrange numbers from least to greatest using a number line.

- Explain to students that we can use a number line to compare the value of numbers.- Talk about the symbols used to compare the value of numbers.- Discuss the examples given on the book along with students. Probe students through questioning to

assess their understanding of the examples being discussed.- Explain to them step by step what we do when comparing two numbers of different values:

Check if the numbers have the same amount of digits. Compare its place value one by one until you arrive at the number with the greatest

value. Once found, decide what symbol should be used (> greater, < less than). If the number is

the same, then you use an equal sign. - Students will work on practice set from A – F. Teacher will walk around checking students work and

aiding those who need help. - Once students are done with practice set they will then start working on mixed practice 1 - 30.

Thursday:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Write the following two sequences on the board:

a. 5, 10, 15, 20, 25, …b. 5, 10, 20, 40, 80, …

- Ask students if they know how we call these sets of numbers – sequences.- Tell students that a sequence is an ordered list of numbers, called terms.- Discuss the two types of sequences presented.- Students analyze the sequences and find out what rule was used to form both sequences presented.- Guide students to arrive to a conclusion.- Explain to students that sequences follow a rule. Sometimes it may be by adding the same number to the

term. In this case we did that in the first sequence; hence, we have an addition sequence. In the second sequence we multiplied by two each term, therefore, we have a multiplication sequence. Tell students that whenever we look for a missing number in a sequence, we inspect the numbers to discover the rule for the sequence. Then we use the rule to find other numbers in the sequence.

- Work examples given in the book to reinforce these concepts. Tell students that sequences can be formed out of even and odd numbers. Show examples.

- Next, present a scale of a thermometer on the board.- Explain to students that numerical data or information many times is presented to us in the form of a

scale. Discuss what a scale is.- With the diagram of the thermometer presented in class discuss how to find the measures being

presented here.- Talk about the two scales (Fahrenheit scale and Celsius scale) and what is the “trick” to read the values

of each.- Use examples given in the book to reinforce concept.- Students work on practice set to assess their understanding of these two topics.- Walk around to assess students work. Offer your assistance to students who might have trouble working

with the problems.- Students exchange exercises to check work just done.

Friday: - Students will receive Mixed Practice found on page 45 – 47 as a Test.

Reference / Materials:- Saxon Math book 7/6 pp. 30 - 47

- Rulers- Thermometer scale- Number line

Evaluation:

OCTUBER

Week five


Lesson Topic: Frequency Tables, Histograms, Surveys; Problems about combining and separating; place value through trillions, multistep problems.

Class: Standard V

Previous Knowledge:

Students have worked with charts before.

Objectives:

Through class reading and discussion, and individual work, students will be able to :

Investigation 114. Interpret a frequency table. 15. Count and write tally marks.16. Make a frequency table. 17. Interpret a histogram18. Make a histogram19. Interpret survey results. 20. Distinguish between a closed-option survey and an open-option survey.

Lesson 1121. Identify the addition pattern in story problems about combining and separating. 22. Follow the four-step method to solve story problems about combining and separating. 23. Write an equation to solve a story problem about combining and separating.

Lesson 1224. Identify the place value through trillions of a digit in a whole number. 25. Use words and digits to write numbers through trillions. 26. Use addition, subtraction, multiplication, and division to solve problems with several steps.

Concepts:

- Histogram - a method of displaying a range of data. A histogram is a special type of bar graph that displays data in intervals of equal size with no space between bars.

- Survey - a method of controlling data about a particular population. - Like stories in reading books, many of the stories we analyze in mathematics have plots. We can use

the plot of a math story to write an equation for the story. Stories with the same plot are represented by the same equation. That is why we say there are pattern for certain plots.

- Addition pattern – some + some more = total- Operation of arithmetic – the four basic mathematical operations: addition, subtraction,

multiplication and division. - Place value is the value of a digit based on its position within a number. - We use a hyphen to connect two words. Example: twenty-one, forty- five

Skills:

- Counting and marking tally marks

- Interpreting charts. - Interpreting and making histograms and surveys. - Follow four steps when solving story problems about combing and separating.

Attitudes:

- Awareness that math is used in our daily life.- Appreciation for numbers. - Respect for others and their ideas

Teaching Strategies/ Students Activities:

Day one & two:

- Have students open their books to page 48 of their books. Study the table in their books. - Explain how we use the marks and together as a class study and interpret the information presented in

the table. - Have students answer questions that follow in the table. - Have a picture of a histogram on the board. - Explain all the elements of the charts: bars, names, frequency etc…- Relate the information that was first studied in the frequency table to the histogram. - Have students answer the questions on page 49. - As instructed in the book, students will be placed in groups and make a frequency table and a histogram

for the data provided. - Have volunteers read the information on the survey and discuss. - Study the examples provided on page 50. - Students will answer the questions on page 51. - Students will make a histogram based on the frequency table provided in their books. - They will then conduct a class survey of favourite foods in the class.

Day three:

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving- Have a volunteer read the information in new concepts page 52. - Analyze the problem about combining found in the book. - Go over the steps that students need to follow to solve the problems. - Go over each step to solve the problems provided in the book. - Tell students to show all the steps and to write neatly. Let them know that step 4 is important because it

reminds them to reread the original problem to be sure their solution answers the question asked. - Challenge students to write their own story problems. Have each student write one story problem about

combining or about separation. - Ask volunteers to read the problems, and have all students write an equation for each problem. - Students will work on practice set. Teacher will walk around checking students work and aiding those

who need help. - Once students are done with the practice set, they will then start working on mixed practice 1 - 30.

Day four:

- Students perform warm-up activities – Multiplication facts.- Present place value chart through trillions.- Discuss how the place value chart works.- Present examples of numbers through trillions and let students using the place valued chart identify the

value of different numbers.- Remind students that commas are used after every three digits, that is after thousands, millions, billions

and trillions. - Present different examples of numbers without the comma and let students insert commas in the

appropriate places. - Use an example and discuss with class the correct way of writing this numbers using words.- Have children practice writing numbers using digits as well as words.- Provide students with multi-step problems and discuss how to go about working them.- Present chart with terms and let students use them appropriately when solving out word problems.- Have students work on the practice section and the problem set to assess learning.

Friday: - Students will receive Mixed Practice found on page 61 – 62 as a quiz.

Reference / Materials:- Saxon Math 7/6 Teacher Resource Book – page 48 - 61- Saxon Math 7/6 - Students Book – Investigation 1 and Lesson 11 - 12- Markers- News print- ruler- charts - histogram, frequency table, place value

Evaluation:

Week 6


Topics: Place Value through Trillions, Multistep Problems; Problems about Comparing, Elapsed-Time Problems; The Number Line, Negative Numbers.

Previous Knowledge:

Students are able to read and write numbers up to million, and have been introduced to a number line in lesson 9.

Objectives:

Through research, viewing pictures, project and class discussion students will be able to:

Lesson 1214. Identify the place value through trillions of a digit in a whole number. 15. Use words and digits to write numbers through trillions. 16. Use addition, subtraction, multiplication, and division to solve problems with several steps. Lesson 1317. Identify the subtraction pattern in a story problem about comparing. 18. Write and equation to solve a story problem about comparing. 19. Identify the subtraction pattern in a elapsed-time problem. Lesson 1420. Use a number line to order and compare integers21. Identify numbers that are opposites. 22. Use a number line to subtract a larger number from a smaller number. Lesson 15

23. Identify the pattern in a story problem about equal groups. 24. Write an equation to solve a story problem about equal groups.

Concepts:

- In our number system the value of a digit depends upon its position. The value of each position is called its place value.

- The operations of arithmetic are addition, subtraction, multiplication, and division. In this table we list the terms for the answers we get when we perform these operations.

Sum – addition, difference – subtraction, product – multiplication, quotient – division. - Story problems about comparing have a subtraction pattern.

Large – smaller = difference ( L – S = D)- Story problems about elapsed time contain a subtraction pattern.

Later – earlier = difference ( L – E = D)- In a number line the points to the right of the zero represent positive numbers. The points to the left of

the zero represent negative numbers. - Zero is neither positive nor negative. - Negative numbers are used in various ways. A temperature of five degrees below zero Fahrenheit may

be written as -50.

Skills:

- Reading skills as students read numbers up to the trillion place value. - Writing skills as students write numbers in digits and words- Comparing skills as students compare numbers. - Analyzing skills as students analyze number line. - Comprehension skills as students understand problem solving stories.

Attitudes:

- Awareness that math is used in our daily life.- Appreciation for numbers. - Respect for others and their ideas. - Cooperation as students work in groups.

Teaching/Learning Strategies:

Day One

- Students perform warm-up activities – Multiplication facts.- Present place value chart through trillions.- Discuss how the place value chart works.- Present examples of numbers through trillions and let students using the place valued chart identify the

value of different numbers.- Remind students that commas are used after every three digits, that is after thousands, millions, billions

and trillions. - Present different examples of numbers without the comma and let students insert commas in the

appropriate places. - Use an example and discuss with class the correct way of writing this numbers using words.- Have children practice writing numbers using digits as well as words.- Provide students with multi-step problems and discuss how to go about working them.- Present chart with terms and let students use them appropriately when solving out word problems.- Have students work on the practice section and the problem set to assess learning.

Day two:

- Students perform warm up activities – Mental Math- Review the four-step process to solve a word problem.- Elicit from students what comparing is and discuss how it applies to word problems.- Provide students with problems about comparing and discuss the subtraction pattern they follow.- Talk about the common equation we get when working with these problems which will facilitate our

answers.- Use an example to outline the steps to follow when working these types of problems.- Explain how to go about when working with elapsed-time problems. - Together as a class write an equation to work out this type of problems.- Use illustrations to explain how the equation for these types of problems works.- Have students practice several examples outlining steps for every problem correctly.- Let students work individually on the practice section, check around the classroom and help struggling

students.

Day three:

- Students perform warm up activities – Multiplication facts- Present a number line on a strip of paper on the blackboard.- Elicit from students the many uses of a number line. Listen to their responses and write them on board.- Have them look at both negative and positive numbers. Explain that numbers on opposite sides of the

zero are known as opposite pairs. - Talk about integers and use several examples to compare them using less or more than. - Use the number line to show how to go about subtracting different integers.- Have students practice using different examples.- Allow students to work on several problems of real life where you need to apply these concepts.- Students work on problem set for home work.

Day four:

- Have students work on multiplication facts drill. - Grant students five minutes for them to work-out these problems- When finished, go over answers for them to check how they did.

- Provide students with example problem about equal groups.- As a class read the problem and have students state how they would solve the problem. - Next, explain the procedure how we go about solving problems of equal groups.- Have students read information in their text book as you explain each step of the problem. - Go over each example of the text book and allow students to work out the lesson practice problems. - Check students work for misunderstanding. Allow fast learners to help with struggling students. - Students who finish quickly start working on the mixed practice section which will be completed as part

of their homework.

Day five:

- Students will seat a test on the last five lessons covered.

Assessment Strategies:

- Use of worksheets- Oral participation- Test/quizzes- Construction of number lines

Reference/Materials:

- Saxon Math 7/6 Teacher Resource Book – page 58 – 71- Saxon Math 7/6 - Students Book – Lesson 12 – 15.- Type sheets- Markers- Shop paper

Evaluation:

Week seven


Lesson Topics: Problems about Equal Groups, Rounding Whole numbers, estimating, fractions and mixed numbers, line graphs.

Previous Knowledge:

Students are familiar with fraction and number lines; they have also worked with rounding numbers in Standard IV.

Objectives:

Through use of charts, objects, rulers, working in groups and individually, students will be able to:

1. Identify the pattern in a story problem about equal groups. 2. Write an equation to solve a story problem about equal groups. 3. Round numbers to the nearest ten, hundred, and thousand. 4. Use rounding to help estimate the answer to a problem. 5. Use estimation skills when reading graphs. 6. Determine which fraction or mixed number is represented by a point on a number line. 7. Measure length of segments to the nearest sixteenth of an inch. 8. Make equal groups to find and average. 9. Identify a number that is halfway between two numbers by finding the average of the two

numbers.

Concepts:

- Rounding off:

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.

Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0.

There are points on the number line between the integers that can be named with fractions or mixed numbers.

A mixed number is a whole number plus a fraction. Halfway between 0 and 1 is ½. The distance between consecutive integers on a number line may be divided into halves, thirds, fourths,

fifths, or any other number of equal divisions. Average – the number found when the sum of two or more numbers is divided by the number of

addends in the sum, also called mean.

Skills:

- Comprehension skills as students understand concepts.- Manipulative skills as students work with objects to solve problems. - Multiplication skills as students solve problems. - Rounding off skills as students round off numbers.

Attitudes:

- Awareness that we use mathematics in our daily lives. - Respect for others and their ideas. - Ability to work with others in harmony.

Teaching Strategies / Learning Activities:

Day one: no classes

Day two: Assessment (test)

Day three:- Have students work on multiplication facts drill. - Grant students five minutes for them to work-out these problems- When finished, go over the answers to check how they performed this time.- Through questioning elicit from students the rules for rounding numbers. - Discuss the rules and as a class go over different examples - Have students practice rounding whole numbers. - Have them select tow cards from a set of index cards labelled 1 – 9. Place them side by side, face

up, have the child read the number formed by the cards, and ask him/her to round the number to the nearest ten. Check for correct answer and repeat the procedure with other students. After students are comfortable rounding to the nearest ten, draw three cards and ask them to round the numbers to the nearest hundred. Then ask them to draw four cards and round to the nearest thousand.

- Discuss with students what is estimating and what background information we need to have in order work with problems dealing with this concept.

- Present an example and together as a class, go over the procedure for solving it.- Provide practice for students by working on lesson practice letters a – o.

Day four:- Have students work on multiplication facts drill. - Grant students five minutes for them to work-out these problems- When finished, go over the answers to check how they performed this time.- Begin this lesson by having students create a number line from -5 to 5 and marking and labelling

fractions and mixed numbers from -41/2 to 4 1/2. - Explain how to find fraction points using this number line.- Next, have student create a ruler showing marks up to sixteenths. - Provide each students with a paper in which they will form a ruler. Have them divide it in half,

then in fourths, and so on up to sixteenths. - Explain how we use the ruler to measure objects to one sixteenth of an inch. - Have students examine their own ruler and identify all the marks in it. - Allow students to work on some exercises to practice measuring with a ruler to one sixteenth of

an inch. - Finally, students will start working on mixed practice in class and complete it for homework.

Day five:- Have students work on multiplication facts drill. - Grant students five minutes for them to work-out these problems- When finished, go over the answers to check how they performed this time Procedure:- Preview the lesson by posing the introductory story as a problem to act out. Collect 18 books

from students and make three stacks of 8, 7, and 3 books, respectively. Ask volunteers to find the average number of books in the three stacks by reconfiguring the stacks to make three stacks with an equal number of books in each.

- Discuss what students do in order to solve the problem. - Go over the information on the book by reading the information as a class.

- Emphasize to students that finding an average is a two-step process that involves ‘combining’ and finding ‘equal groups.’

- Have students use colour tiles from paper cut outs to illustrate example 2. Give each student piles of 3, 7, and 8 items, and have students use the objects to illustrate each step in the example. Have them combine the three piles into one large pile and then count each item in the large pile. Next, ask students to divide the items into three equal groups and count the number in each group to find the average.

- Review with students how to read a line graph before solving example 4. Place an example of the graph on the board. Ask students how to find the value of a point on the graph. Then ask them how to estimate values that are between intervals.

- Students will start working on the lesson practice in their books. If students are unable to complete work they will do so for homework.

Assessment strategies:

- Class participation- Measuring objects with ruler- Completion of written exercises- Quiz/tests

Reference:

- Saxon math 7/6 Teachers book lesson 16 – 18- Saxon Math 7/8 Students Book lesson 16 - 18

Materials:- Flash cards 1 – 9- Tape- Rounding off chart. - Strips of papers for number lines- rulers

Evaluation:

Week eight


Lesson Topics: Average, Line Graph; Factors, Prime Numbers; Greatest Common Factor (GCF)

Objectives:

through class discussion, students participation, and individual work students will be able to:

- Name all the factors of a given number.

- Identify prime numbers.- Find the greatest common factor of two or more numbers. - Determine which fraction or mixed number is represented by a point on a number

line. - Measure length of segments to the nearest sixteenth of an inch. - Make equal groups to find an average. - Identify a number that is halfway between two numbers by finding the average of

the two numbers. - Create fraction manipulative to solve problems involving fractions.

Concepts:

- Average – the number found when the sum of two or more numbers is divided by the number of addends in the sum, also called mean.

- A factor is a whole number that divides another whole number without a remainder. - A prime number is a counting number greater than 1 whose only two factors are the number 1 and itself. - Greatest Common Factor (GCF) – the largest whole number that is a factor of two or more given

numbers.

Skills:

- Identifying factors of numbers. - Naming the prime numbers. - Critical thinking skills as students analyze concepts.

Attitudes:

- Appreciate mathematics in our lives as it makes daily life easier. - Respect towards others ideas and opinions. - Leadership as they work with a partner in order to solve the mathematical problems.


Day One:

- Have students work on multiplication facts drill.

- Grant students five minutes for them to work-out these problems

- When finished, go over the answers to check how they performed this time Procedure:

- Preview the lesson by posing the introductory story as a problem to act out. Collect 18 books

from students and make three stacks of 8, 7, and 3 books, respectively. Ask volunteers to find

the average number of books in the three stacks by reconfiguring the stacks to make three stacks

with an equal number of books in each.

- Discuss what students do in order to solve the problem.

- Go over the information on the book by reading the information as a class.

- Emphasize to students that finding an average is a two-step process that involves ‘combining’

and finding ‘equal groups.’

- Have students use colour tiles from paper cut outs to illustrate example 2. Give each student

piles of 3, 7, and 8 items, and have students use the objects to illustrate each step in the example.

Have them combine the three piles into one large pile and then count each item in the large pile.

Next, ask students to divide the items into three equal groups and count the number in each

group to find the average.

- Review with students how to read a line graph before solving example 4. Place an example of

the graph on the board. Ask students how to find the value of a point on the graph. Then ask

them how to estimate values that are between intervals.

- Students will start working on the lesson practice in their books. If students are unable to

complete work they will do so for homework.

Day two:

- Write the word factor on the board. Ask students if they know what factor means or if they have

ever heard the word before.

- Give and explain the definition of factors.

- After hearing the definition of a factor have students try to give examples. Teacher will then provide

examples to students.

- With the use of construction paper cut into tiles, teacher will illustrate factors of 6, 10 and 12.

- Have students read the information on their Saxon Math book on page 95.

- Explain prime numbers to students.

- Go over a few examples on how to find prime numbers with students.

- .Students will then work on practice set, page 97.

- Teacher will go around checking students work.

- Students will then start working on mixed practice on page 98, they will complete this for

homework

Day three:

- Through questioning elicit from students the definition of greatest common factor. Explain to

student what it means.

- On the board find the GCF of 12 and 18, by using a Venn diagram with two overlapping circles. The

common factors will be placed in the overlapping section.

- Go over a few examples with students without using the Venn diagram.

- Students will work on lesson practice on page 101. Teacher will walk around checking students

work.

- Time will then be taken to go over the work as a class.

- Students will then proceed and start working on Mixed Practice which will be completed for

homework.

Day four:

- Provide students with a set of fraction manipulative, they will need scissors to cut the fractional

circles.

- Have students color code the fraction manipulative to make sorting easier.

- Have students separate the fraction manipulative by cutting out the circles and cutting apart the

fraction slices along the lines.

- Students will then open their Saxon Math book to page 104. Together as a class answer the first five

questions using the manipulative.

- Students work with a partner to aanswer questions 6 – 30.

- Teacher will go around checking and aiding students with the work.

Day five: Assessment (test)


- Class participation- Using manipulatives to learn about fractions- Completion of written exercises- Quiz/tests

Reference:


Materials:- markers- Tape- Strips of papers for number lines- Rulers- Construction paper cut into small tiles

Evaluation:

Week 9


Lesson Topics: Working with Fractions using manipulative; Divisibility, and equal groups ‘Stories with fractions’

Previous Knowledge:

Students have previously worked with fractions, and have used ratio in daily life while sharing things in groups but do not know the proper name.

Objectives:

Through class discussion, students participation, use of manipulatives, and individual work; students will be able to:

1. Create and use a set of fraction circle manipulatives. 2. Use fraction circles to solve problems.3. Use divisibility test to determine whether a number is divisible by 2,3,5,9, or 10.4. Use divisibility tests to determine if 2,3,5,9 and 10 are factors of a number.5. Use two steps to solve equal group problems with fractions. 6. Divide objects into equal groups and count to find a fractional part of number. 7. Divide a given number into equal groups and then multiply to find a fractional part of the number.

Concepts:

- There are ways of discovering whether some numbers are factors of other numbers wihtout actually dividing. For instance, even numbers can be divided by 2. Therefore, 2 is a factor of every even counting number.

- Tests of divisibility can help us find the factors of a number.

- In collection of objects, the collection is divided into equal groups. - Example: What number is 2/3 of 66?

66 / 3 = 222 x 22 = 442/3 of 66 is 44

Skills:

- Identifying skills as students identify numbers that are divisible by a given number. - Naming skills as students name the parts of fractions. - Critical thinking skills as students analyze concepts. - Dividing numbers into equal groups to find fractional parts of numbers. - Identifying skills as they identify rations and write them in fraction form.

Attitudes:

- Appreciate mathematics in our lives as it makes daily life easier. - Respect towards others ideas and opinions. - Sportsmanship as they work with a partner in order to solve the mathematical problems.- Appreciation for numbers and knowledge for mathematical concepts


Day One:

- Have students work on multiplication facts to 49, set A. Students will be allowed 7 minutes to work

on the 100 problems. Check work as a class to find results.

Begin Lesson:

- Provide students with a set of fraction manipulative, they will need scissors to cut the fractional

circles.

- Have students color code the fraction manipulative to make sorting easier.

- Have students separate the fraction manipulative by cutting out the circles and cutting apart the

fraction slices along the lines.

- Students will then open their Saxon Math book to page 104. Together as a class answer the first five

questions using the manipulative.

- Students work with a partner to answer questions 6 – 18.

- Teacher will go around checking and aiding students with the work.

Day two:- Have students work on multiplication facts to 49, set B. Students will be allowed 7 minutes to work

on the 100 problems. Check work as a class to find results.- Students will then complete questions found in their Saxon Math page 104 – 107. They will work

with the partner that they had on the previous class. - As class, go over the work and explaining difficulties that children had while working this set.

Day three:

- Have students work on multiplication facts to 49, set C. Students will be allowed 7 minutes to work


Begin the lesson:

- Tell students to complete the mental math in page 108, on their Saxon Math.

- Once students have completed the mental math, go over the questions and answers with them

solving it together mentally.

- Go over the divisibility box with students which they have from previous class. Point out to student

that any counting number that ends with 0 is divisible by 2, 5, and 10. Give students a simple

number, such as 40 to illustrate this.

- Have volunteers read the information on “New Concepts” section from their book.

- Have different students go over to the board and solve examples.

- Analyze the examples as a class.

- Have students complete the Practice Set. Teacher will go around checking students work.

Day four:

- Have students work on multiplication facts to 49, set D. Students will be allowed 7 minutes to

work on the 100 problems. Check work as a class to find results.

Begin the lesson:

- Have students complete the mental math.

- Allow them exchange their books with one another.

- Go over the each question and work out the answer as a class.

- Use big tiles taped on the board as manipulative kits. Model example 1 for students. Use 12 tiles

to represent the 12 musicians in the problem. Divide the tiles into three equal groups, and count

the number of tiles in two of the three groups.

- Use the same procedure to solve example two with the use of the tiles.

- Once students understand the concept, go over example 3, 4, and 5 using the multiplication

symbol.

- Students will work on thirty questions found on the mixed practice.

- They will be allowed to work with a partner.

- Teacher will walk around checking students work.

- Students will finish for homework whatever they did not finish in class.

Day five:

- Have students work on multiplication facts to 49, set E. Students will be allowed 7 minutes to work on the 100 problems. Check work as a class to find results.

- Students will receive quiz on what they have covered throughout the week. Quiz will consist of 30 problems.


- Class participation- Using manipulatives to learn about fractions- Completion of written exercises- Quiz/tests

Reference:


Materials:

- Activity Master 3-7, one copy of each master per two students

- Scissors

- Plastic bags

Evaluation:

Untis of November

Week 10



Previous Knowledge:

Students have previously worked with fractions, and have used ratio in daily life while sharing things in groups but do not know the proper name. Students have also generated a manipulative fraction kit on previous classes.

Objectives:


1. Use ratios to describe relationships between numbers. 2. Identify ratios and write them in fraction forms. 3. Use fractions manipulatives to model addition and subtraction of fraction that have common

denominators. 4. Add and subtract fractions that have common denominators. 5. Write the answers to division problems as mixed numbers. 6. Write improper fractions as mixed numbers. 7. Use manipulatives to reduce fractions. 8. Add and subtract mixed numbers by first subtracting the fraction parts and then the whole-number parts.

Concepts:

- Ratio is a comparison of two numbers by division. - When writing ratios in fraction form, we keep the following points in mind:

o We write the terms of the ratio in the order we are asked to give them. o We reduce ratios in the same manner as we reduce fractions. o We leave ratios in fraction form. We do not write ratios as mixed numbers.

- When fractions that have common denominators are added or subtracted, only the numerators are added or subtracted.

- The remainder in a division problem can be written as a fraction with the remainder as the numerator of the fraction and the divisor as the denominator.

- Circle is a closed, curved shape in which all points on the shape are the same distance from its center.

Skills:

- Manipulative skills as students work with fraction manipulatives. - Comprehension skills as students understand concepts. - Critical thinking skills as students solve the problems. - Dividing numbers into equal groups to find fractional parts of numbers. - Identifying skills as they identify rations and write them in fraction form.

Attitudes:

- Appreciate mathematics in our lives as it makes daily life easier. - Respect towards others ideas and opinions. - Sportsmanship as they work with a partner in order to solve the mathematical problems.- Appreciation for numbers and knowledge for mathematical concepts


Day One: Lesson 23

- Have students work on multiplication facts to 64, set E. Students will be allowed 5 minutes to work


Begin Lesson:

- Students will complete the mental math section.

- Allow them to exchange their books with one another.

- Go over the each question and work out the answer as a class.

- Have students look at the New Concept on page 119. Have volunteers read the information.

- Ask students to share their understanding of the concept.

- Clarify students’ understanding if there is any need or further explain the concept.

- Go over example one with students.

- Emphasize to students that ratios are not expressed as mixed numbers.

- Have students read example two and have them think of how to solve the problem. Allow them a

few minutes to try to solve the problem.

- Ask students to explain how to find the number of girls in the class.

- Ask students to find the girl-boy ratio for their class.

- For further practice, ask students to write the ratio of vowels to consonants in their first name.

- Write students’ names on the board and have students tell you their ratios. If a name has an equal

number of vowels and consonants, express the ratio as 1/1.

- Students will work on thirty questions found on mixed practice.

- They will be allowed to work with a partner.

- Walk around to observe students at their work.

- Have students work on the mixed practice section.

- Students will complete for homework whatever they don’t finish in class.

Day two: (lesson 24 & 25)- Have students work on multiplication facts to 64, set F. Students will be allowed 5 minutes to work


- Students take a few minutes to do the “Warm-up” exercises. Remind them that they are to do all

working out mentally.

- Students exchange their exercise books and go over each mental math problem as a class.

- Tell students that they will use their manipulative fraction kit for this lesson.

- Write two fractional problems on the board, guide students into modeling these two problems

individually.

- Work out the problems as a class.

- Write an example on the board and have students model the problem on their own. Once they have

done so go over the working out.

- Same process will be done with four other problems.

- Write examples of division problems on the board and demonstrate to students on how to write their

answers as mixed numbers.

- Provide students with work for them to do on their own. (Practice set and Mixed Practice)


Day three:

- Have students work on multiplication facts to 64, set G. Students will be allowed 5 minutes to work


Begin the lesson:

- Students do the “warm-up” exercise and exchange their books to go over each math problem as a

class.

- Have students use their fraction kit.

- Show students how to simplify and express fractions in lowest terms using the fraction kit.

- As a class work on the different examples given in the book.

- Emphasize the different steps that students need to take to solve different problems.

- Finally students work on the practice set.

Day four:

- Have students work on multiplication facts to 64, set I. Students will be allowed 5 minutes to


Begin the lesson:

- Today students will work on different word problems that they have been having difficulties

over the past days. Teacher will show steps and remind them of key words which they need to

identify when working with these problems.

- Students will follow steps along with teacher. Then they will be allowed to worm on similar

problems and the teacher will float around to check on students and also to offer assistant to

those having difficulties.

Day five:

- Have students work on multiplication facts to 64, set H. Students will be allowed 5 minutes to work on the 100 problems. Check work as a class to find results.



- Class participation- Using manipulatives to learn about fractions- Completion of several practice sets- Quiz/tests

Reference:


Materials:- Fraction kit

Evaluation:

Week 11



Previous Knowledge:

Students have previously worked with fractions, and have used ratio in daily life while sharing things in groups but do not know the proper name. Students have also generated a manipulative fraction kit on previous classes.

Objectives:


- Identify the circumference, diameter and radius of a circle. - Find the diameter of a circle when the radius is known and vice-versa. - Identify parallel lines, perpendicular lines, and oblique lines. - Name angles using one letter, three letters, or one number. - Identify right angles, acute angles and obtuse angles. - Identify common multiples of two numbers. - Multiply fractions.- Reduce fractions by common factors- Find the least common multiple (LCM) OF TWO NUMBERS. - Identify reciprocals as numbers that have a product of 1 when multiplied.

Concepts:

- A circle is a closed, curved shape in which all points on the shape are the same distance from its center.

- Circumference is the perimeter of a circle. - Compass is a tool used to draw circles and arcs. - Diameter is the distance across a circle through its center. - Radius is the distance from the center of a circle to a point on the circle. - Acute angle – an angle that is less than 90°- Right angle – an angle that is 90° exactly- Obtuse angle – an angle that is greater than 90° but less than 180°- Straight angle – and angle that is 180° exactly.- Reflex angle – an angle that is greater than 180°- When we multiply fractions, we multiply the numerators to find the numerator of the product, and

we multiply the denominators to find the denominator of the product.- To reduce a fraction we find a common factor that divides both the numerator and denominator

evenly. Such number is found by finding the GCF of both the numerator and denominator.- When the multiples of two or more numbers are listed in order from least to greatest, the first

number that is a common multiple is always the least common multiple (LCM).- Least common multiple (LCM) – The smallest whole number that is a multiple of two or more given

numbers. - Reciprocal – two numbers whose product is 1.

Skills:

- Identifying skills as students identify the parts of a circle and different angles. - Manipulative skills as students work with fraction manipulatives. - Comprehension skills as students understand concepts. - Critical thinking skills as students solve the problems.

Attitudes:

- Awareness that angels are found all around us. - Respect for others as they work in groups. - Cooperation as they work with peers.


Day One: Lesson 27

- Have students work on multiplication facts to 81, set A. Students will be allowed 5 minutes to work


Begin Lesson:

- Students do “Warm-up” exercises. Remind them that they are to do all working out mentally.

- Together as a class check results for the “warm-up” exercise.

- Demonstrate for the class how to use a compass by drawing a circle with a radius of 3 inches.

- Model for students how to draw a dot for the center before drawing the circle in case the

compass slips.

- Have students carry out activity a, b, and c on page 139.

- Elicit from students the concept of radius and diameter.

- Have them use a ruler to draw a radius and a diameter on the circles they have constructed in

parts a, b, and c of the activity.

- To reinforce the relationship between radius and diameter, ask students to find, without

measuring, the lengths of the diameters of the circles in problems a, b, and c of the activity.

- Work on the examples as a class.

- Have students work on practice set, individually.

Day two: Lesson 28- Have students work on multiplication facts to 81, set B. Students will be allowed 5 minutes to work


- Allow students a few minutes to do the “Warm-up” exercise. Remind them that they are to do all

working out mentally.

- Once the time is up have students exchange their exercise books and go over each mental math

problem as a class.

- Have students look around the classroom and identify different types of lines.

- Explain parallel lines, perpendicular lines and oblique lines.

- Instruct students to find examples of these lines in the class or outside.

- Have volunteers read information on the book.

- Discuss information as a class, and then allow students to give more examples.

- Work on examples provided in the book with students.

- Have students work on practice set individually.


- As part of children homework, explain to them to look for pictures where these angles occur. Let

students obtain at least five pictures of different objects around the environment and identify these

angles. Children will paste these pictures on a typing sheet and will be collected for grading.

Day three: Lesson 29

- Have students work on multiplication facts to 81, set C. Students will be allowed 5 minutes to work


Begin the lesson:

- Students do the “warm-up” exercise and exchange their books to go over each math problem as a

class.

- Present students with a picture of ½ of ½ of a circle.

- Have students look at it and then instruct them that when we are looking to the answer of such a

problem we are actually multiplying.

- Tell them that the word “of” in “1/2 of ½” means to multiply. Therefore the problems becomes:

½ x ½ = ¼. This is portrayed on the graphic representation of fraction when we draw it.

- Provide other examples for students to help them reinforce and grasp this concept.

- Next, tell them that such fractions can be reduced by dividing the numerator and denominator by

common factors.

- Show them the two ways how to reduce a fraction such as 6/12.

- Tell them that there is the long way and then there is the method where we look for the GCF of

both numbers and reduce by that factor.

- Work on another example and then let students work on the practice section.

- Walk around and check to see if students are following the right steps, if not, indicate to them

where they are going wrong.

- Use fast learners to help others understand the concepts.

- Students will work on problem set of this lesson for homework.

Day four: Lesson 30



Begin the lesson:

- Students begin the lesson by doing the “warm up” exercises.

- Remind them to work these problems mentally.

- Together as a class check answers on this section.

- Explain to students that they are going to be working on a new math skill this morning and they

already know the first steps.

- Tell that we are going to be looking for the Least common multiple (LCM)

- Provide them with the numbers 2 and 3 and ask them to look for the multiples of these two

numbers.

- Elicit answers from students and write them on the board.

- Next, ask students to circle all the common multiples found in the two numbers.

- Now have students write all the common multiples.

- Tell them to select the least multiple.

- Inform students that they have just found the LCM of 2 and 3 which is 6.

- Allow students to work on another examples and then work on the next part of the lesson.

- Present students with the term “reciprocals” and explain what it means.

- Show students the different examples of the lesson and explain how to work these examples.

- Children work the examples along with the teacher so that they can also practice as the teacher

explains.

- Work on examples with whole numbers and fractions.

- Children will then be allowed to work on the practice set of the lesson.

Day five:

- Have students work on multiplication facts to 81, set E. Students will be allowed 5 minutes to work on the 100 problems. Check work as a class to find results.



- Class participation- Completion of several practice sets- Quiz/tests

Reference:


Materials:- Fraction kit- Compass- Typing sheets- Bristol board

- markers

Evaluation:

Week 12 – Children’s week

Week 13 – Review Week

December

Week 14 – Exam Week

Week 15 – Exam discussion – Christmas Program – class party – closure

January

Week 16


Lesson Topics: Least Common Multiple, Reciprocals; Measuring and Drawing Angles with a Protractor; Areas of Rectangle; Expanded Notation, More on Elapsed Time; Writing Percent as Fractions, part 1

Previous Knowledge:

Students have worked with multiples, and have studies angles

Objectives:

Through investigation, cooperative learning, individual work and use of manipulatives, students will be able to:

1. Identify common multiples of two numbers. 2. Find the least common multiple (LCM) OF TWO NUMBERS. 3. Identify reciprocals as numbers that have a product of 1 when multiplied4. Use a protractor to find the measure of an angle and to draw an angle with the given

measurement. 5. Identify square units as the units used to measure area. 6. Multiply length by width to find the area of a rectangle. 7. Find the side length and the perimeter of a square when the area of the square is known. 8. Write a number in expanded notation, 9. Rename hours and minutes as minutes to solve an elapsed-time problem. 10. Write percent as a reduced fraction.

Concepts:

- When the multiples of two or more numbers are listed in order from least to greatest, the first number that is a common multiple is always the least common multiple (LCM).

- Least common multiple (LCM) – The smallest whole number that is a multiple of two or more given numbers.

- Reciprocal – two numbers whose product is 1. - Protractor – is a tool used to measure and draw angles. - To ensure that the correct scale on the protractor is used, it helps to decide whether an angle is acute,

obtuse, or right before measuring. - Area is the number of square units needed to cover a surface. - Formula for finding area of a rectangle = Length x Width- To write a number in expanded notation, each nonzero digit is written times its place value.

Example: (3 x 1000) + (9 x 100) + (4 x 10)- The hours of the day are divided into two parts: a.m. and p.m. We can use the later-earlier difference

pattern to solve elapsed-time problems about hours and minutes. - A percent is actually a fraction with a denominator of 100. The word percent and its symbol %,

mean “per hundred.” To write a percent, we remove the percent sign and write the number as the numerator and 100 as the denominator.

Skills:

- Identifying skills as students identify common multiples of two numbers.

- Use of a protractor to measure and draw angles. - Calculating area of a rectangle in square units by multiplying length multiplied by width. - Reducing fractions.

Attitudes:

- Cooperation as they participate in class and pair activity. - Respect for others and their ideas. - Awareness of new concepts learnt in lessons. - Confidence in math.


Day 1: Lesson 30

- Have students work on multiplication facts to 121, set A. Students will be allowed 5 minutes to


Begin the lesson:




- Explain to students that they are going to be working on a new math skill this morning and they

already know the first steps.

- Tell that we are going to be looking for the Least common multiple (LCM)

- Provide them with the numbers 2 and 3 and ask them to look for the multiples of these two

numbers.

- Elicit answers from students and write them on the board.

- Next, ask students to circle all the common multiples found in the two numbers.

- Now have students write all the common multiples.

- Tell them to select the least multiple.

- Inform students that they have just found the LCM of 2 and 3 which is 6.

- Allow students to work on another examples and then work on the next part of the lesson.

- Present students with the term “reciprocals” and explain what it means.

- Show students the different examples of the lesson and explain how to work these examples.

- Children work the examples along with the teacher so that they can also practice as the teacher

explains.

- Work on examples with whole numbers and fractions.

- Children will then be allowed to work on the practice set of the lesson.

Day 2 :( Investigation 3)

- Have students work on multiplication facts to 121, set B. Students will be allowed 5 minutes to


- Begin lesson by showing students a protractor.

- Elicit from students the use of this instrument.

- Read information about it found in their math books and discuss it with them.

- Use an enlarge version of a protractor to draw several types of angles on the board to

demonstrate how to use it.

- Have students carry out the activity on their books and guide them how to successfully complete

it.

- Draw some more examples for them, clearly showing how to use the protractor to draw angles.

- Tell students to work on the practice section.

- Move around checking students work and the proper use of the protractor.

Day 3 (lesson 31)

- Have students work on multiplication facts to 121, set C. Students will be allowed 5 minutes to





- Have students use their math books and measure the length and width of their books.

- Have them add up the measurements.

- Elicit from students what measurements they have calculated – perimeter.

- Have students multiply these two measures.

- Inform them that they have calculated area.

- Together as a class read concepts in the book and discuss each one.

- Go over and explain the different examples in the book.

- Then have students work on the practice section for this lesson.

- Go around identifying possible problems and helping those children that are having difficulties.

- Students begin the mixed practice in class and finish it for homework.

Day 4: Lesson 32



Expanded Notation




- Allow volunteers from the class to read information on New Concepts found in their books.- Provide examples on expanded notation to students and show them how to go about do it. - Go over examples given in the book.

Elapsed Time:

- Review the concepts of a.m. and p.m. with the class.

- Discuss what elapsed time means.

- Work on different examples from the books to teach this concept.

- Make sure students follow step by step each example given as this type of problems usually creates

confusion.

- At the end have students work on the practice section of both parts of the lesson taught today.

- Go over any misconceptions that students might have.

Day 5 (lesson 33)

- Have students work on multiplication facts to 121, set E. Students will be allowed 5 minutes to


- Students perform the “Warm Up” exercises.

- Remind them to work on each problem mentally.

- Have them exchange exercises and check the work as a class.

- Have volunteer read the information on New Concept in their books

- Explain examples found in the book.

- Have students work on some to assess understanding.

- Then let them work on the practice section individually.

- Students who finish first will help the teacher check and help other struggling students.

- Once students are finished they will begin working on the mixed practice which will be finished

as part of their homework.


- Class participation- Written exercises- Completion of several practice sets- Test/quizzes

Reference:

- Saxon Math 7/6 Teachers Resource Book. Lessons 30 to 33- Saxon Math 7/6 Students Book. Lessons 30 to 33

Materials:- Protractor- Place value chart- Compass- Rulers

Evaluation:

Week 17


Lesson Topics: Writing Percent as Fractions, part 1; Decimal Place Value; Writing decimal numbers as fractions; Reading and writing decimal numbers; Subtracting Fractions and Mixed Numbers from Whole Numbers

Previous Knowledge:

Students know that percentage is out of a 100, they also have a good knowledge of whole number place values, as well of fractions and mixed numbers.

Objectives:

Through discussion, cooperative learning, individual work and use of illustrations, students will be able to:

11. Write percent as a reduced fraction. 12. Identify the value of the decimal places through millionths. 13. Write a decimal number as a fraction.14. Read and write a decimal number.15. Subtract a mixed number from a whole number.16. Convert a whole number into a fraction name for one.

Concepts:

- A percent is actually a fraction with a denominator of 100. The word percent and its symbol %, mean “per hundred.” To write a percent, we remove the percent sign and write the number as the numerator and 100 as the denominator.

- Each place to the right of the ones place has a value that is one tenth of the value of the place to its left.

- Decimal numbers are actually fractions of denominators 10, 100, 1000 and so on. The denominator of decimal is not written. Instead, the denominator is indicated by the number of decimal place values.

- To subtract a mixed number from a whole number we first change the whole number into a whole number plus a fraction name for one (e.g. 5 is change into 4 plus 3/3). It depends on the denominator of the fraction of the mixed number.

Skills:

- Writing and reading decimals- Subtracting mixed numbers from whole numbers- Reducing fractions.

Attitudes:



Day 1 (lesson 33)

- Have students work on multiplication facts to 121, set E. Students will be allowed 5 minutes to





- Have volunteer read the information on New Concept in their books

- Explain examples found in the book.

- Have students work on some to assess understanding.

- Then let them work on the practice section individually.

- Students who finish first will help the teacher check and help other struggling students.

- Once students are finished they will begin working on the mixed practice which will be finished

as part of their homework.

Day 2 :( Lesson 34)

- Have students work on multiplication facts to 121, set F. Students will be allowed 5 minutes to


- Students work on the “Warm Up” exercises.

- As a class go over the work.

- Use illustrations and discuss the new concept with students.

- Place a decimal chart on the board and go over the examples given on the book with students.

- Involve students while explaining examples to come to the board and help solve the examples

given.

- As practice and assessment, have students work on practice set a – d.

Day 3 (lesson 35)

- Have students work on multiplication facts to 121, set G. Students will be allowed 5 minutes to


- Students work on the “Warm Up” exercises.

- As a class go over the work.

- Have students go to page 183. Discuss with students how to write fractions from decimal

numbers.

- Explain to students that one decimal place value after the decimal place has a denominator of 10,

then 100, 1000 and so on.

- Have students notice that the number of zeros in the denominator equals the number of decimal

places in the decimal number. Example: 0.003 = 3/1000

- Tell students that the digits to the right of the decimal point are written as the numerator of the

fraction. Explain that when one or more zeros come directly after the decimal point but before a

nonzero digit, the zeros are not written in the numerator.

- Write different decimal numbers on the board. Have students practice reading decimal numbers

aloud.

- Go over the examples provided on the book.

- Have students work on lesson practice from lesson 35

- Go around checking students work and helping those who might have any misunderstanding.

Day 4: assessment

- Students will do the mixed practice of lesson 35 as part of their weekly evaluation (test)- Note that one of the groups will do it the next day (day 5)

Day 5: lesson 36

- Have students work on multiplication facts to 121, set H. Students will be allowed 5 minutes to


- Students work on the “Warm Up” section.

- Go over the work once there are finished.

- Present topic to students and tell that today they will learn how to subtract mixed numbers from

whole numbers.

- Read a “separating” story problem about pies.

- Show illustrations of this story to students for better understanding.

- Discuss with class the step taken to solve this type of problems.

- Have students clearly understand how to change whole number into fraction name for one as this

skill is important to subtract mixed numbers form whole numbers.

- Work several examples along with the class by eliciting the various steps from students.

- Have students work on the practice set.

- Provide extra practice for students who are struggling.

- Give them one to one instructions and involve their classmates to help them understand how to

solve these problems.



Reference:


Materials:- Bristol Board- Place value chart- Ruler

Evaluation:

Week 18


Lesson Topics: Adding and Subtracting Decimal numbers; Adding and Subtracting Decimal Numbers and Whole Numbers; Squares and Square Roots; Multiplying Decimal Numbers; Using Zero as a Placeholder; Circle Graphs

Previous Knowledge:

Students are aware of decimal numbers and can read and write them.

Objectives:

Through discussion, cooperative learning, individual work and use of illustrations, students will be able to:

17. Add and subtract decimal numbers.18. Write a whole number with a decimal point.19. Add decimal numbers and whole number.20. Subtract decimal numbers from a decimal numbers. 21. Square a number.22. Use the exponent 2 to indicate squaring or square units.23. Simplify and expression by applying exponents and then adding, subtracting, multiplying, or

dividing.24. Find the square root of a number25. Multiply a decimal number by a decimal number.26. Multiply a decimal number by a whole number.27. Use zeros to fill in each empty decimal place when subtracting, multiplying, and dividing

decimal numbers.28. Use zeros as placeholders as needed when writing in digits the word form of a decimal number.29. Interpret information displayed in a circle graph.

Concepts:

- We line up decimal numbers for addition and subtraction by lining up decimal points.- To find the sum of a decimal number and a whole number, write the whole number with a decimal

point and line up the decimal points before adding.- Squares and square roots – from the model of a square comes the expression “squaring number.” We

square a number by multiplying the number by itself. “Five squared” is 5 x 5, which is 25. To indicate squaring, we use the exponent 2. 52 = 25. “Five squared equals 25.” Notice that the exponent is elevated and written to the right of the 5. An exponent shows how many times the other number, the base, is to be used as a factor. In this case, 5 is to be used as a factor twice.

- A number is a perfect square if it has a square root that is a whole number. Starting with 1, the first four perfect squares are 1, 4, 9, and 16.

- The number of decimal places in the product is determined by counting the total number of decimal places in the factors.

- When subtracting, multiplying, and dividing decimal numbers, we often encounter empty decimal places. When this occurs, we will fill each empty decimal place with a zero. In order to subtract, it is sometimes necessary to attach zeros to the top of the number.

- Circles graphs, which are sometimes called pie graphs or pie charts, display quantitative information in fractions of a circle.

Skills:

- Adding whole and decimal numbers- Multiplying decimal numbers

- Finding the square roots of numbersAttitudes:



Day 1 (lesson 37)

- Have students work on multiplication facts to 144, set A. Students will be allowed 5 minutes to


- Students work on the “warm up” section.

- Go over the work together as a class once they are finished.

- Present two problems of addition and subtraction of decimal numbers to students.

- Have students try to find a solution to solve the problems.

- Invite a student who has come up with the solution to the problems to come to the board and

show the class.

- If nobody can come up with a solution, show students how to work out this type of problems.

- Remind students of the important rule to follow when adding and subtracting decimal numbers.

- Go over the examples given in the books with students.

- Finally have them work on the practice section and check their work to assess for understanding

of the concepts.

Day 2 (lesson 38)

- Have students work on multiplication facts to 144, set B. Students will be allowed 5 minutes to





- Show students how to write dollars in two ways.

- Write any number and show students how to write in four different ways, with decimal and

without decimal numbers

- Provide examples of different addition and subtraction problems and show students how to add

and subtract these. Remind students that empty places are treated as zeros when adding or

subtraction whole and decimal numbers

- Square and square roots: Hold a class discussion from where the expression “squaring comes”.

- Discuss with students the new vocabulary words; namely, exponent and base.

- Provide examples for students and together as a class look at the necessary steps to square a

number.

- Talk about how to simplify numbers elevated to the second power and how to simply problems

dealing with squares.

- Guide students to find the square roots of different given numbers as wells as to realize that

certain numbers have perfect squares. Discuss this concept and have students look of the squares

of different given numbers.

- Provide students with practice to reinforce concepts given above.

Day 3 (lesson 39)

- Have students work on multiplication facts to 144, set C. Students will be allowed 5 minutes to


- Students work on the “Warm Up” section.

- Go over the work once there are finished.

- Present topic to students and tell that today they will learn how to multiply decimal numbers.

- Provide students with a problem about finding the area of a given rectangle. Include decimals

and ask students to calculate the answer to this problem.

- Invite a student to write the answer on the board and teacher and class evaluate if the working

was done correctly.

- Take the opportunity to correct any mistake and show students the proper procedure to multiply

decimal numbers. Remind them of the important concept to follow when multiplying decimal

numbers: The number of decimal places in the product is determined by counting the total number

of decimal places in the factors.

- Work on other examples and show students how to proceed with each one.

- Have students work on the practice section and observe that they are following the proper steps if

not offer them individual help.

Day 4 (Lesson 40):

- Have students work on multiplication facts to 144, set D. Students will be allowed 5 minutes to work on the 100 problems. Check work as a class to find results.

- Students work on the “warm up” section.

- Go over the work together as a class once they are finished.

- Tell students that many times it is necessary to use the zero as a placeholder. Such is the case

when we are subtracting, multiplying, and dividing decimal numbers. Show examples of this to

students.

- Show students examples of subtraction and multiplication and show when it is necessary to place

a zero.

- Circle Graphs: Discuss circle graphs and how this is important because it shows quantitative

information in the form of fractions.

- Use the example given on the book on page 210 and analyze and synthesize information given

on it.

- Show students the different steps that are needed to analyze and synthesize the information on

this pie chart.

- Finally, have students work on the practice set given on the book.

Day 5: Chapel



Reference:


Materials:- Bristol Board- markers- Place value chart- Ruler

Evaluation:

Week 19


Lesson Topics: Data Collection and Survey; Finding a percent of a number; renaming fraction by multiplying by 1; Equivalent division problems; simplifying and comparing decimal numbers

Previous Knowledge:

Students have been working with decimals and fractions.

Objectives:

Through class discussions, collecting data, and individual work, students will be able to:

30. Describe whether data is quantitative or qualitative in nature. 31. Explain why a sample is not representative of a population.32. Conduct surveys and collect data. 33. Write a percent as a decimal. 34. Find the percent of a number by changing the percent to either a fraction or a decimal and

multiplying. 35. Rename fractions by multiplying them by fractions equal to 1. 36. Find division answers by forming equivalent division problems.37. Find the missing number in a fraction or decimal problem. 38. Attach extra zeros to the ends of decimal numbers to help compare them. 39. Order decimal number from least to greatest

Concepts:

- Statistics is the science of gathering and organizing data in such a way that we can draw conclusions from the data.

- Data can be either quantitative or qualitative in nature. Quantitative data comes in numbers, and qualitative data comes in categories.

- To describe part of a group, we often use a fraction or a percent. We also use percents to describe financial situations.

- To check the solution to a missing-number problem that involves fractions or decimal numbers, replace the letter problem with the solution and test the result.

- Attaching zeros to the end of a decimal number does not change the value of the number. When comparing decimal numbers, attaching zeros so that the numbers have the same number of decimal places can make the numbers easier to compare.

Skills:

- Identifying skills as students work with data- Finding percent of a number- Rename a fraction by multiplying it by a fraction equal to 1 - Compare and order decimal numbers

Attitudes:

- Awareness on how data and survey help us in our life. - Cooperation when working with others.- Respect for others and their ideas.


Day 1(Investigation 4)

- Play Hang the Man and have students come up with the words data collection and survey. - Elicit meaning of these from students. If they cannot come up with meaning, have them search in

their dictionaries and give definition of each term. - Elaborate on this concept so that students gain a better understanding of it. - Have students state why it is important or how we use these in our daily life. - Have them read the information on their book on page 213. - Together discuss definition of quantitative and qualitative. Have children answer questions from

1 – 5 in their book. Have them exchange their book and check each other’s work. - Then have two different volunteers read information after the questions. After reading the

information, answer question 6 as a class.- As a class read the information that follows. Have students answer questions 7 – 10.- Give instruction and explain to students a survey that they will carry out. - Have a couple of students explain their understanding of what they are supposed to do.

Day 2 (Lesson 41 and 42:

- Have students perform warm up exercises done the beginning of every lesson.- Time students for this activity and have them exchange exercises to check work. - Read and discuss information on new concepts. - Have students read aloud different percents as fractions and as decimals. - Illustrate for students that percent is out of a 100%.- Discuss thoroughly the three examples provided in the book.- Have students complete the practice section and evaluate if they understood the concept, if not

elaborate more on some examples. - Next, have students look and different illustrated fractions on page 222 on their books and go

over information on new concepts as a class. - Use several examples to explain how to write a fraction name for one to obtain equivalent

fractions.- Go over each example provided in the book making sure students understand the procedures.- Have students work on practice set for this lesson. - Teacher will go around checking students work.

Day 3 (lesson 43)

- Students perform warm up exercises. Time students while they work on this metal math exercises.

- Once they are finished, have them exchange their work with a classmate and go over it as a class.

- Write the examples from the book on the board. Explain the procedure of how to solve each problem in order for students to understand, since teacher believes that this concept will be challenging for students.

- Ask students if they have any questions or concerns as you explain. - Tell student that the steps they follow to find missing decimal numbers and fractions are the

same steps they follow to find missing whole numbers.- Point out that that the equation is a subtraction problem in which the first number is missing and

the other two numbers are given. - Have students work on lesson practice.

- Once they are done lesson practice and it has been checked they will work on mixed practice.

Day 4 (Lesson 44 to 45):

- Students perform warm up exercises. Time students while they work on this metal math exercises.

- Once they are finished, have them exchange their work with a classmate and go over it as a class.

- Write a math problem on the board. Have a volunteer go to the front of the class and solve the problem with a calculator while the others do the working out in their exercise.

- Once everyone is done. Have the person who solved it with the calculator write the answer on the board. Have students compare the calculator answer with the one in their book.

- Work on example 1 as a class. Have a volunteer read the concepts that follow in their book. - Go to example 2. Help students to compare the two decimal numbers. On the board write an

example. Have student compare digit, starting with the ones place. - When students discover that the digit are equal, have them move on to the next place to the right.

When they reach the thousandth place, point out that 0 is less than 3, o 0.300 i le than 0.303. - Review with students dividing dollars and cents by a whole number. - Write three examples on the board and have students go and work it out. - Go over students work. - Have students work on lesson practice for lesson 44 and 45. - Go around checking children’s work.

Day 5:

- Students will do the mixed practice of lesson 45 as part of their weekly evaluation (test).



Reference:

- Saxon Math 7/6 – teacher resource book. Investigation 4 and Lesson 41 – 45- Saxon Math 7/6 – student book. Investigation 4 and Lesson 41 – 45

Materials:- Fractional manipulative- Calculator

Evaluation:

February

Week 21


Lesson Topics: Writing Decimal Numbers in Expanded Notation, Mentally Multiplying Decimal Numbers

Previous Knowledge:


Objectives:


40. Write decimal numbers in expanded notation. 41. Write a number written in expanded notation in decimal form. 42. Mentally multiply whole and decimal numbers by 10 or by 100. 43. Use the formula C = πd, C or C =2 πr, to find the circumference of a circle

Concepts:

To multiply a decimal number by 10, shift the decimal point one place to the right. To multiply a decimal number by 100, shift the decimal point two places to the right.

Example: Write 3.706 in expanded notationo (3 x 1) + (7 x 1/10) + (6 x 1/1000)

The actual number of diameters in the circumference of a circle is equal to pi (π) In the formula C=πd, C stands for circumference and d stands for the diameter of a circle. In the formula C=2πr, C stands for circumference and r stands for the radius of a circle 3.14 or 22/7 = π

Skills:

- Mentally multiplication of decimal numbers. - Write numbers in expanded notation.

Attitudes:

- Cooperation when working with others.- Respect for others and their ideas.


Day 1 (Lesson 46:

- Have students perform metal math activities.- Time students while they work these exercise.- . Once children are finished, have them exchange their book with a classmate and go over the

work. - Go over with students on how to expand whole numbers in expanded notation form.

- Inform students that during this lesson they will learn on how to expand decimal numbers in expanded notation form.

- Have a volunteer read the information on new concept. - As a class go over the examples provided in the book. Write the example on the board one by

one and explain in own words on how to work out the problem. - Then have a volunteer read the solution provided in the book. - Help students to remember how to shift the decimal point when multiplying by 10 or 100. Say:

“When we multiply by 10 or by 100, we shift the decimal point the same number of places to the right as the number of zeros in 10 or s100. The number 10, for example, has one zero, so we shift the decimal point one place to the right when multiplying by 10. When we multiply by 100, which have two zeros, we shift the decimal point two places to the right. ”

- Have students work on lesson practice. - Once they are done lesson practice and it has been checked they will work on mixed practice.

Day 2 (Lesson 47):

- Have students perform metal math activities.- Time students while they work these exercise.- Once children are finished, have them exchange their book with a classmate and go over - Students will be asked to take circular objects to class such as plastic plates, cups, toilette paper

roll, etc…- Divide students into groups of three’s. - As a class go over the instructions given in the book, explain in own words in order for students

to understand what they are suppose to do. - Have students carry out activity. - Write the formulas for finding circumference on the board. - Explain that the d for diameter can be replaced by 2r in the second formula. - Have students work on lesson practice for lesson 47. Go around checking children’s work.



Reference:

- Saxon Math 7/6 – teacher resource book. Lesson 46 – 47- Saxon Math 7/6 – student book. Lesson 46 – 47

Materials:- Ruler- String, scissors, circular objects.

Evaluation:

Week 22


Lesson Topics: Circumference, Subtracting Mixed Numbers with Regrouping, Dividing by a Decimal Number

Previous Knowledge:


Objectives:


44. Use the formula C = πd, C or C =2 πr, to find the circumference of a circle.45. Subtract mixed numbers with regrouping.46. Divide numbers using decimals.47. Locate decimal numbers (tenths) on a number line.48. Divide numbers by a fraction.

Concepts:

- The actual number of diameters in the circumference of a circle is equal to pi (π)- In the formula C=πd, C stands for circumference and d stands for the diameter of a circle. - In the formula C=2πr, C stands for circumference and r stands for the radius of a circle- 3.14 or 22/7 = π- When the divisor of a division problem is a decimal number, we change the problem so that the divisor

is a whole number. - One way to change a division problem is to multiply the divisor and the dividend by 10. - We can locate different kinds of numbers on a number line. - It is often necessary or helpful to round decimal numbers. For instance, money amounts are usually

rounded to two places after the decimal point because we do not have a coin smaller than one hundredth of a dollar.

Skills:

- Finding the circumference of circle - Dividing numbers by a decimal and a fraction- Locating a decimal on a numberline

Attitudes:



Day 2 (Lesson 47):

- Have students perform metal math activities.- Time students while they work these exercise.

- Once children are finished, have them exchange their book with a classmate and go over - Students will be asked to take circular objects to class such as plastic plates, cups, toilette paper

roll, etc…- Divide students into groups of three’s. - As a class go over the instructions given in the book, explain in own words in order for students

to understand what they are suppose to do. - Have students carry out activity. - Write the formulas for finding circumference on the board. - Explain that the d for diameter can be replaced by 2r in the second formula. - Have students work on lesson practice for lesson 47. Go around checking children’s work.

Day 3 (Lesson 48 & 49):

- Students perform metal math activities.- Time students while they do this work.- Go over the work with students. They should exchange their exercises and evaluate how they did

in the activity. - Call students to the information on new concept. - Go over it and use the illustrations presented in the book to clarify the information presented. - Write examples from the book and work out on the board along with the class.- Go over the procedure several times and elicit from students part of the procedure as you work

the problems on the board. Clarify any misunderstanding students may have. - Provide students with some more examples and invite some of them to come and work out on

the board, meanwhile the rest work them on their exercise books. - As a class go over the examples that students have work on the board and instruct students to fix

their mistakes if any. - Have students work on mixed practice of each lesson.

Day 4 (Lesson 50):


in the activity. - Provide each student with a number line. Place an enlarge version of this number line on the

board.- Use this number line to demonstrate to students how to read decimal numbers (tenths).- Provide several examples for students and then ask them to find different examples provided on

the board. - Have students use the number lines illustrated in their books to go over each example given in it. - As a class work on example one. - Have a volunteer read the information on dividing by a fraction. After reading the information

have various students explain their understanding of what they just read. - Go over the example provided on the book. - Write two examples on the board. Have students work it out in their exercise books. Then

randomly call on two students to go and work it out on the board. - Go over the procedure to working out the problem. - Have students work on practice set of lesson fifty and fifty-one. - Teacher will go around checking students work.

Day 5:

- Assessment - Students will receive a quiz covering the different topics that we learnt this week.



Reference:


Materials:- Ruler- String, scissors, circular objects.

Evaluation:

Week 23


Lesson Topics: Displaying Data, Mentally Dividing Decimal Numbers by 10 and by 100, Decimal Chart, Simplifying Fractions, Reducing by Grouping Factors Equal to 1, Dividing Fractions, Common Denominators, Part 1

Previous Knowledge:


Objectives:


49. Display qualitative data on graphs.50. Define mean, median, mode and range.51. Display quantitative data in a stem-and-leaf plot.52. Mentally divide decimal numbers by 10 and by 100.

53. Use decimal arithmetic reminders when working with decimals.54. Simplify fractions to its lowest terms.55. Reduce factors equal to one.56. Divide fractions.57. Find common denominators for fractions.58. Rename a fraction.

Concepts:

- In a pictograph, pictured objects represent the data being counted. Each object represents one or more units of data.

- The name for a circle graph is a pie chart. - In a circle graph each category corresponds to a sector of the circle. We use circle graphs when we are

interested in the fraction of the group represented by each category and not so interested in the particular number of units in each category.

- We use compass and protractor to help us use a circle graph. - When we divide a decimal by 10 or by 100, the quotient has the same digits as the dividend; however

the position of the digits is shifted.- When the denominators of two or more fractions are equal, we say that the fractions have common

denominators.

Skills:

- Mentally multiplication of decimal numbers. - Write numbers in expanded notation.

Attitudes:



Day 1 & 2 (Investigation 5):

- Refresh students mind about the activity they did in investigation four. Let them know that they looked at collecting data and inform them that in this investigation they will look at various ways to display data.

- Review with students quantitative and qualitative data. Inform students that they will use bar graphs to display qualitative data.

- Have a volunteer read the information in the book on page 269. Study the chart provided for the information.

- Explain the properties of a bar graph to students. - Read the information on pictographs. Have students write the definition in their notebooks. - Explain and discuss the properties of a pictograph with students. - Have a volunteer keep on reading information on pie chart. - Explain and demonstrate to students on how to change a given amount to degrees. - Provide extra examples for students to practice.

- Have students read information on quantitative data on their own. Have various students explain what they understood.

- Explain mean, median, mode and range. - Practice along with students on how to look for those terms using a number of data. - Explain stem-and-leaf plot to students. Have them practice on examples. - Have students work on extension work on page 273, allow students to work with a partner. - Teacher will go around checking students work.

Day 3 (Lesson 52 & 53):

- Students will do the mental math activities.- Have them take five minutes and then exchange their work and then check it together as a class. - Have a volunteer read the information on new concept. - Go over the examples provided in the book with students. - Write the example on the board and work it out as a class. Once we have gone over the

procedure as a class, go over the procedure once again with students in order to clarify any misunderstanding.

- Have students examine the chart provided on page 283 and have them copy it in their exercise books.

- As a class work on example provided in the book. - Write a couple of examples on the board and have volunteers go to the board to work it out

while the rest do it in their exercise. - Go over the working out as a class, instruct students to check their own work and fix mistakes if

any. - Have students work on mixed practice of Lesson 52 and 53.

Day 4 (Lesson 54 & 55):


in the activity. - Display a problem on the board. Ask students how they would reduce factors that equal to one.

Listen to students response. - Explain to students on how to reduce by grouping factors equal to one. - Go over the example provided in the book. - Have a volunteer read the information on how to divide fractions. - Write examples on the board. Have students guide the teacher on how to go about solving the

problem. Teacher will then explain procedure and provide examples for students to work on their own.

- Have students work on practice set of lesson 54 and 55. - Teacher will go around checking students work.

Day 5:

- Assessment - Students will receive a quiz covering the different topics that we learnt this week.



Reference:


Materials:- Ruler- Compass- Protractor- Typing sheets

Evaluation:

MARCH

Week 24 & 25


Lesson Topic: Common Denominators, part 2; Adding and Subtracting Fractions: Three Steps; Probability and chance, adding mixed numbers, polygons ,attribution of geometry solids.

Previous Knowledge: Students have been working with mixed numbers for the past weeks.

Objectives:Through class discussion, individual work, and peer help, students will be able to:

1. Rename two fractions so that they have common denominators.2. Add or subtract two fractions that do not have common denominators by remaning both

fractions.3. Compare two fractions that do not have common denominators by renaming one or both

fractions.4. Follow three steps – shape, operate, simplify – to add or subtract fractions.5. Express the probability that an event will occur as a reduced fraction, a decimal, or percent.6. Express the probability that an event will not occur as a reduced fraction, a decimal, or a percent.7. Find the probability of an event by dividing the number of outcomes in the event by the number

of possible outcomes.8. Use three steps – shape, operate, and simplify – to add mixed numbers with fractions that do not

have common denominators.9. Identify common polygons by the number of sides they have.10. Use the term congruent to describe geometric figures.11. Find the length of a side of a regular polygon when the perimeter of the polygon is known.12. Recognize, name and draw common geometric solids.13. Identify the number of faces, edges, and vertices in various geometric solids.14. Find the surface area of a polyhedron.15. Identify patterns that can be folded into a specified three-dimensional figure.

Reference:

- Saxon math 7/6 Teachers book lesson 56 – Investigation 6- Saxon Math 7/8 Students Book lesson 56 – Investigation 6

Concepts:- The three steps for adding and subtracting fractions are:

Step 1: Shape. If the fractions do not have common denominators, rewrite them with common denominators.Step 2: Operate. Perform the operation indicated (addition or subtraction).Step 3: Simplify: Reduce the answer, if possible, or write an improper fraction as a mixed number.

- The study of probability helps us assign numbers to uncertain events and compare the likelihood that various events will occur.

- Polygons are closed shapes with straight sides. They are named by the number of sides they have. - The polygons are: triangle, quadrilateral, pentagon, hexagon, octagon, etc…- Geometry solids have length, width, and height. In other words they take up space.- Geometry solids are: triangular prism, rectangular prism, cube, pyramid, cylinder, cone, sphere.- To add three or more fractions, we find a common denominator for all fractions being added.

Skills:- Observing skills ass teacher explains example.- Solving skills as students solve problems

Attitudes:- Awareness of the importance of math in our daily life.- Appreciation for numbers and math.


Day one:- Students work on drill “30 Fractions to Reduce” (Test G). - Students will be given 5 minutes to work on these fractions and the exchange exercises correct as a

class.- Students perform warm up exercises. Give students 5 minutes to work on this metal math exercises.- Once they are finished, have them exchange their work with a classmate and go over it as a class.- Present examples of fractions with uncommon denominator and invite students to think of ways to

solve these types of fractions.- Listen to students suggestions. Acknowledge any one who comes up with the correct answer and

follow up from there.- Explain students that the steps to follow will be first looking for the LCM of the two denominators

and then renaming the fractions and then add.- Present other examples to students and show them a step by step process to solve for these types of

fractions.- Involve students during the process and have them work every step up to the end with you.- Use manipulative to show students how to compare different fractions with unlike denominators.- Let use the picture fractions to visualize it and then use then follow the proper steps to solve it.- Have students work on the practice set of their Saxon Math books.

Day two:- Students work on drill “72 Multiplication and Division Facts” (Test H). - Students will be given 5 minutes to work on these fractions and the exchange exercises correct as a

class.- Students perform warm up exercises. Give students 5 minutes to work on this metal math exercises.- Once they are finished, have them exchange their work with a classmate and go over it as a class.- Present students with the three steps to solve fraction problems: shape, operation, and simplify.- Explain one of them and provide students with different examples of each.- Help students remember these steps by teaching them the mnemonic SOS (Shape, Operation, and

Simplify).- Have students work on the practice set of the lesson and use the three steps to solve these problems.

Day three:

- Have children open their math book to page 307, and ask them to start work on warm up exercise (mental math).

- Time students while they work. Once children are finished, have them exchange their book with a classmate and go over the work.

- Use a die to introduce probability to students.- Have a volunteer read the information on the book, then proceed to explain the information using

the die. - Roll the die various times to bring out the information.- Go over examples provided in the book. - To bring out example 3, use marbles in order for students to understand concept. - Provide an example for students to work.- Have students work on practice set, in pairs.- Teacher will go around checking students work.

Day four:- Have children open their math book to page 314, and ask them to start work on warm up exercise

(mental math). - Time students while they work. Once children are finished, have them exchange their book with a

classmate and go over the work. - Place examples which are in the book on the board.- Go over three examples then have students perform some on their own. - Give students information on polygons then read notes from the book in for students further - Have students work on mixed practice individually. - Teacher will go around checking students work.- Investigation 6 which is from pages 322 - 326 is only practice work for students, comprise of 25

questions.- They will carry out the work and teacher will go around helping them and checking their work.

Day five:- Have children open their math book to page 327, and ask them to start work on warm up exercise


classmate and go over the work. - Have a volunteer read the information in the book. - Have students explain the information in their own words.- Draw illustrations to further explain concepts to students.- Go over examples given in the book. Have volunteers go to the board and work on other examples.- Students will complete lesson practice from their book.- They will then exchange their work, and students will be called to go to the board and explain the

procedure to solve the problems.

Week 26


Lesson Topics: Adding Three or More Fractions; Writing Mixed Numbers as Improper Fractions; Subtracting Mixed Numbers with Regrouping, Part 1; Classifying Quadrilaterals; and Prime Factorization – Division by Primes – Factor Tress

Previous Knowledge:

Students have worked with mixed numbers as well as fractions on previous lessons. They also have a good knowledge of factors, squares, and rectangles.

Objectives:

Students will be able to:

1. Add three or more fractions or mixed numbers.

2. Change a mixed number to an improper fraction.

3. Find the product of two mixed numbers by changing each number to an improper fraction and then multiplying.

4. Rename fractions so that they have common denominators and then regroup to subtract numbers.

5. Identify, classify, and draw quadrilaterals according to the characteristics of their sides and angles.

6. Identify a composite number as a number with more than two factors.

7. Write the prime factorization of a given composite number.

8. Use division by primes to find the prime factorization of a given number.

9. Make a factor tree to find the prime factorization of a given number.

Concepts:

- To add three or more fractions, we find a common denominator for all the fractions being added.

- A mixed number may be changed to an improper fraction either by changing the whole number part to an improper fraction and adding it to the fraction part or by multiplying the denominator by the whole number and adding the numerator.

-

- Rename the fractions with common denominators before subtracting.

- A trapezium has no parallel sides; a parallelogram has two pairs of parallel sides.

- Parallelogram – A quadrilateral that has two pairs of parallel sides.

- Rectangle – A quadrilateral that has four right angles.

- Rhombus – A parallelogram with all four sides of equal length.

- Square – A rectangle with all four sides of equal length.

- Trapezium – A quadrilateral with no parallel sides.

- Trapezoid – A quadrilateral with exactly one pair of parallel sides.

- Every whole number greater than 1 is either a prime number or a composite number.

- A prime number has only two factors (1 and itself).

- A composite number has more than two factors.

- When we write a composite number as a product of its prime factors, we have written the prime factorization of the number.

- We can factor a composite number by division by primes and factor trees.

Skills:

- Adding up to three fractions

- Using the division method or factor trees to factorize a composite number

- Renaming a fraction before subtracting or adding

Attitudes:

- Cooperate in class.

- Respect and acceptance of classmates’ opinions


Day One: Lesson 61

- Have students work on 72 Multiplication and Division Facts (Test H)

- Together as a class check work and have students look at their results.



- Present students with problems of addition of fractions (two or three).

- Give students the opportunity to suggest ways how to add these fractions.

- Listen to students suggestions and the proceed to show them the proper ways of adding fractions:

1. Find LCM of all denominators2. Rename all fractions3. Add and simplify (reduce) if possible.

- Work another example with students and then have them practice on their own by working on the lesson practice.

- Take the time offer one to one instructions to struggling students.

Day two: Lesson 62

- Have students work on 30 Fractions to Reduce (Test G)




- Some students may have good background knowledge of changing mixed numbers to improper fractions.

- Explain to students that today we will learn two methods how to convert a mixed number to an improper fraction.

- Use illustrations so that students who struggle can have a visual representation of how to convert mixed numbers to improper fractions.

- Show students each step and have them follow you each step of the way.

- Have students ask questions if they have any, if not, have them work on the practice section of the lesson.

- Check and help students who are struggling or are confused at some point of the lesson.


- Have students work on 64 Multiplication Facts (Test D)




- Present topic on the white board and present objectives for this lesson.

- Show students the different steps to subtract mixed numbers with regrouping.

- Review what was done in lesson 48 with respect to regrouping.

- Children will need this previous knowledge to be able to work this lesson.

- Children work on lesson practice and teacher circulates to check work and guide students who are having trouble.

Day four: Lesson 64

- Have students work on 24 Mixed Numbers to Write as Improper Fractions (Test J)




- Present students with vocabulary for this lesson.

- Next present them with chart on classification of Quadrilaterals

- Discuss the chart.

- Students create models of these and include characteristics on each.

- Students work on the lesson practice.

Day five: Lesson 65





- Present vocabulary for this lesson.

- Explain the concepts prime factorization, division by primes and factor trees through the examples given on the lesson.

- Have students choose the preferred method they like to factorize a composite number.

- Students work out the lesson practice.

- Move around to check students’ work and help those who are struggling. Fast learners can help students who do not understand certain steps.


- Class participation

- Completion of several practice sets

- Make models of quadrilaterals

Reference:

- Saxon math 7/6 Teachers book lesson 60 – 65

- Saxon Math 7/8 Students Book lesson 60 - 65

Materials:

- Newsprint

- Markers

- Charts

- Models of quadrilateral

Evaluation:

Month of April

Week 27


Lesson Topics: Multiplying Mixed Numbers; Using Prime Factorization to Reduce Fractions; Dividing Mixed Numbers; and Lengths of Segments – Complementary and Supplementary Angles

Previous Knowledge:


Objectives:


1. Multiply a mixed number by a whole number.

2. Multiply a mixed number by a mixed number.

3. Divide a mixed number by a whole number.

4. Divide a mixed number by a mixed number.

5. Write an equation showing that the length of a segment is equal to the sum of the lengths of its parts and solve the equation for the missing length.

6. Identify complementary and supplementary angles.

7. Name and find the measure of the complement of an angle.

8. Name and find the measure of the supplement of an angle.

Concepts:

- To multiply mixed numbers, write mixed numbers and whole numbers as improper fractions.

- When dividing a mixed number, the first step (shape) will always be writing the dividend and the divisor as improper fractions.

- We use letters to designate points. We can use two points to identify a line, a ray, or a segement.

- Complementary angles are two angles whose sum is 90 degrees. Supplementary angles are two angles whose sum is 180 degrees.

Skills:

- Finding the product of two mixed numbers.

- Using prime factorization to reduce fractions.

- Dividing a mixed number by a whole number and mixed number by a mixed number

Attitudes:

- Work harmoniously with others.

- Offer their unconditional help to others


Day One: Assessment (Test)

- Students will receive a cumulative test on the lessons already covered.

Day two: Lesson 66





- Begin the lesson by having students recall a previous lesson where the three steps to solving arithmetic problems with fractions was taught.

- Elicit from students the three steps: Shape – Operation – Simplify.

- Introduce today’s concepts by explaining to students that when we multiply mixed numbers we have to write the fractions in fraction forms.

- Take an example and explain what is meant by writing fractions in fraction forms.

- Show students how to write mixed numbers and whole numbers as improper fractions.

- Work a second example and have them follow you through each step.

- Invite students to try one on their own.

- Quickly browse the class to see if they are working it correctly.

- Take time to work this example with them and allow time for them to identify their mistakes if they made any.

- Direct students to the practice lesson and work on each problem given.

- Take this opportunity to circulate around the class and help those students who are struggling. At the same time correct problems from students who have done one or two already so that they know that they are working the correctly.

- Students who finish may start the mixed practice set.






- Explain students the procedure of prime factorization to reduce fractions through examples:

a. Find the prime factorization of each number.b. Reduce or cancel pairs of numbers.c. Multiply the remaining factors.d. Write your reduced fraction

- Work several examples with students and answer any question they might have about any of the steps.

- Have children work on the lesson practice.- Take this time to walk around and offer individual help to students.

Day four: Lesson 68

- Have students work on 28 Improper Fractions to Simplify (Test I)




- Have students recall the three steps to solving arithmetic problems with fractions – shape, operation, and simplify if possible.

- Now present examples to class and have them work up to the first step.

- Students should change mixed numbers to improper fractions when dividing fractions.

- Next, explain to them that when dividing we find the reciprocal of the divisor (in other words we invert the number).

- Then we multiply the result.

- Go over other examples with students following the same steps.

- Then have students work on the lesson practice.

- Take time to help struggling students.

Day five: Lesson 69





- Discuss with students lengths of segments.

- Take time to explain to students how to read, label and measure lengths of segments using illustrations.

- Present vocabulary of complementary and supplementary angles.

- Use different illustrations to show students these types of angles.

- Present them with various examples in which these types of angles could be found.

- Let students use the newly learnt skills and solve problems found in the lesson practice.

- Take this opportunity to help students who are confused.

- Students work on the mixed practice set of 30 problems and take the remaining to finish for homework.





Reference:



Materials:

- Newsprint

- Markers

- Charts


Evaluation:

Week 28 & 29


Lesson Topic: Parallelograms, Fraction Chart (multiplying three fractions), Exponents (writing decimal numbers as Fractions), Writing factions as decimal numbers, Writing fractions as decimal percents.

Previous Knowledge: Students have been working with fractions and quadrilaterals during the past week.


1. Identify opposite and adjacent angles in a parallelogram.2. Find the area of a parallelogram. 3. Find the measure of an angle in a parallelogram when the measure of its opposite angle or

adjacent angle is unknown.4. Recognize the rules for adding, subtracting, multiplying, and dividing fractions. 5. Read expressions with exponents.6. Find the value of expressions with exponents.7. Write prime factorization of a number using exponents. 8. Convert fractions and mixed numbers to decimal numbers.9. Write a fraction as a percent and vice versa.

Reference:- Saxon math teachers resource book, lessons 71 - 76- Saxon math students book, lessons 71 - 76

Concepts:- Parallelogram: in every parallelogram, opposite angles are equal and adjacent angles are

supplementary. The area of a parallelogram changes as the angles change size,, but the perimeter remains the same.

- Multiplying fractions: A fraction chart using the S.O.S. (shape, operate, simplify) steps summarizes the rules for adding, subtracting, and dividing fractions and mixed numbers.

- students will follow the three step rule to multiply three or fractions or mixed numbers. Steps to solve an arithmetic problem with fractions

o Put the problem into shape.o Perform the operation indicatedo Simplify the answer if possible

- Exponents: Exponents indicate repeated multiplication. We read numbers with exponents as power. When the exponent is 2, we usually say “squared,” and when the exponent is 3, we usually say “cubed.”

Example: 52 “ five to the second power” or “five squared” 103 “ ten to the third power” or “ten cubed” 34 “three to the fourth power”

- Writing fractions as decimal numbers: To convert a fraction to a decimal number we, we divide the numerator by the denominator. When a fractions is written, the fraction bar indicates division. When we write out a fraction to divide, we can attach a decimal point and zero, after the numbers have been divided. We can then perform the division and write out the quotient as a decimal number.

- Writing fractions and decimals as percents: A percent is actually a fraction with a denominator of 100. Instead of writing the denominator 100, we can use percent sign (%). So 25/ 100 equals 25%. E.g. 0.08 is the same as 8/100. Eight hundredths is equivalent to 8%.

Skills:- Observing skills ass teacher explains example.- Solving skills as students solve problems

Attitudes:- Awareness of the importance of math in our daily life.- Appreciation for numbers and math.


Day one and two Lesson 71 and 72: - Have children open their math book to page 379, and ask them to start work on warm up

exercise (mental math). - Time students while they work. Once children are finished, have them exchange their book with- Review with students what quadrilaterals are. Have them name the different quadrilaterals.

Explain to students that we will be focusing on parallelograms. Elicit from students what they know about parallelograms.

In pairs, provide students with a picture of a parallelogram. Have students measure the angles. Elicit from students which angles are the same, and which are different. Introduce adjacent angles to students.

Have students turn to page 381 and discuss, have then draw out a parallelogram and find the area.

Place on chalkboard three strips of paper that contain two fractions being multiplied. Have volunteers go to the board to work them out.

Teacher will then place a problem with three fractions being multiplied. Elicit from students how they can solve the problem.

Have students turn to 387 and have them discuss information. Place on chalkboard different problems, have volunteers work them out.

As a class go over examples provided on the book. Have students copy examples in their note books.

Have students work on practice set on both lessons. Teacher will go around checking students work.

Day three Lesson 73 and 74: - Have children open their math book to page 392, and ask them to start work on warm up

exercise (mental math). - Time students while they work. Once children are finished, have them exchange their book with

a classmate and go over the work. Cards with numbers that contain exponents will be placed under some students’ tables. Students

will be asked to look under their tables. Students will be asked what the smaller number on the

card is called. Teacher will introduce exponents. Have students with cards read out their numbers.

Class will review how to read different numbers with exponents. Teacher will place decimal numbers on the chalkboard. ( E.g. 1.25) Students will be asked what

they can do to convert decimals to a mixed number. Have students recall that the one (1) in the decimal number is a whole number and the (.25) is a fraction.

As a class have students work on several problems. Explain to students that fractions can also be converted to decimals numbers. Explain to students

procedure, have students practice converting fractions to decimal numbers. Have students write notes on concepts. Have students work on practice set individually. Teacher will go around checking students work.

Day four: lessons 75 and 76: - Have children open their math book to page 401, and ask them to start work on warm up

exercise (mental math). Time students while they work. Once children are finished, have them exchange their book with a classmate and go over the work. - Have a volunteer read the information in the book ( percents) - Have students explain the information in their own words.- Go over the two examples provided in the book, explaining step by step on how to solve the

problems. - Have four volunteers go to the board to solve a problem each. Meanwhile the rest of students

are solving the problems in their note books. - Have students review what they learnt the previous day. Converting fractions to decimal

form. - Have students turn to page 406. Explain to students that they will be converting fractions in

order to compare them. Have students practice converting and comparing. - Go over each working out as a class. - Students will complete lesson practice from their book.- They will then exchange their work, and students will be called to go to the board and

explain the procedure to solve the problems.Day five:

- Students will receive quiz based on what was covered this week.

Evaluation:

Month of May

Week 30 & 31


Lesson Topic: Finding Unstated Information in Fraction Problems; Capacity; Area of a Triangle; Using Scale Factor to Solve Ratio Problems; Geometric Construction of Bisectors; Arithmetic with Units of Measure; Volume of a Rectangular Prism; and Proportions

Class: Standard V

Previous Knowledge: Students have worked with fractions, units and finding volume.


1. Find unstated information in Fraction Problems. 2. State the units for liquid measure.3. Explain what capacity is. 4. State what area is.5. Find the area of triangle.6. Find information in a ratio problem to create a ratio box.7. Use scale factors to solve ratio problems.8. Use a compass to create different bisectors.9. Recognize the rules for adding, subtracting, multiplying, and dividing using units of measure.10. Solve problems that contain units of measure.11. Explain what volume is.12. Find the volume of a rectangular prism. 13. State what proportion is. 14. Find equivalent ratios to form a proportion.

Reference:- Saxon math teachers resource book, lessons 77 - 83- Saxon math students book, lessons 77 - 83

Content:- Unstated information in Fraction Problems: Often fractional-parts statements contain more

information than what is directly stated. Example: Three fourths of the 28 students in the class are

boys. The sentence directly states information about the number of boys in the class. It also indirectly states information about the number of girls in the class.

- Capacity: To measure quantities of liquid we use the units gallons (gal), quarts (qt), pints (pt), and ounces (oz). In the metric system we use liters (L) and milliliters (mL). The amount of liquid a container can contain is called capacity. We can use a table to show the relationship between units within each system.

Equivalence table for Units of Liquid MeasureCustomary System Metric System

1 gallon = 4 quarts1 quart = 2 pints1 pint = 2 cups

1 cup = 8 ounces

1 liter = 1000 milliliters

- Finding the Area of a Triangle: The area of a triangle is half the area of a parallelogram with the same height and base. The area of a parallelogram can be found by multiplying its base by its height (A = b*h). So the area of a triangle can be determined by finding half of the product of its base and height. Either of the following formulas can be used to find the area of a triangle:

Area of a triangle = ½ b*h Or A = b*h/ 2

- Using Scale Factor to Solve Ratio Problems: We see two used for numbers in ratio problems. One use is to express ratio. The other use is to express actual count. A ratio box can help us sort the two uses by placing the ratio numbers in one column and the actual counts in another column. We write the items being compared along the left side of the rows.Example: The ratio of little boys to little girls in the nursery was 3 to 2. If there were 6 little girls, how many little boys were there? Ratio numbers and actual counts are related by a Scale Factor. If we multiply the terms of a ratio by the correct scale factor by which the actual count. Ratio is a reduced form of an actual count. If we can determine the factor by which the actual count was reduced to form the ratio, then we can recreate the actual count. Step 1 Step 2

Boys Girls

Step 3 Boys

Girls

- Geometric Construction of Bisectors: Bisect means “to cut into two equal parts.” We bisect a line when we draw a line (or segment) through the midpoint of the line segment.

Ratio Actual Count3 2 6

Ratio Actual Count3 x scale factor ?2 x scale factor 6

Ratio Actual Count3 x (3) 9 2 x (3) 6

- Arithmetic with Units of Measure: The operations of arithmetic are addition, subtraction, multiplication, and division.

- We may add or subtract measurements that have the same units. If the units are not the same, we first convert one or more measurements so that the units are the same. Then we add or subtract.

- The units do not change when we add or subtract measurements. However, units do change when we multiply or divide measurements. When multiplying, we multiply the units as well.

- Volume of a Rectangular Prism: The volume of a shape is the amount of space that the shape occupies. We measure volume by using units that take up space, such as cubic centimeters or cubic inches. The number of cubic units of space that the shape occupies is the volume measurement of that shape. We use the following formula to find the volume of a rectangular prism.

Volume = Length * Width * Height or V=(l)(w)(h) Proportions: A proportion is a true statement that two ratios are equal.

Example: ¾ = 6/8

- We read this proportion as “three is to four as six is to eight.” Two ratios that are not equivalent are not proportional.

Skills:- Solving skills as students solve problems- Critical thinking skills as students come up with definitions and formulas- Observation skills as students do hands on activities to observe and form concepts.

Attitudes:- Awareness of the importance of math in our daily life.- Appreciation for numbers and math.- Cooperation and participation in class activities.


Day One: lesson 77 and 78:- Have children open their math book to page 410, and ask them to start work on warm up exercise


classmate and go over the work. - Place on the chalkboard the following fraction problem: Three eighths of the 40 little engines could

climb the hill. - Elicit from students what information they can gather from the problem posted on the chalkboard.

Probe and prompt students to come up with the unstated information as well.- Explain to students that fractional-part statements sometimes contain information than what is

stated. That sometimes these statements give us indirect information. - Have students practice finding direct and indirect information from fraction problems using the

examples given in the lesson 77. - After students have completed this task have them turn to page 415 to lesson 78. Have students read

and discuss information. - Elicit from students how using units of measurement and capacity help us in our daily lives. - As a class go over examples provided in the book. Have students copy examples in their note

books. - Have students work on practice set on both lessons.- Teacher will go around checking students work.

Day two: Lesson 79 and 80: - Have children open their math book to page 419, and ask them to start work on warm up exercise

(mental math).

- Time students while they work. Once children are finished, have them exchange their book with a classmate and go over the work.

- Review with students what area is and how to find area in a parallelogram. - Explain to students that today they will be finding the area of a triangle. - Have students complete the following activity:- Have students fold a folder sheet in half, and draw a triangle on the folded paper. - While the paper is folded, have students cut out the triangle so that they will have two congruent

triangles. - Have students arrange the two triangles to form a parallelogram.- Have students chose measurements their parallelogram (having the two triangles forming the

parallelogram). Have students find the area of the parallelogram. - Have students then discuss how to find the area of a triangle. - Explain to students that the area of a triangle is half of a parallelogram. That if they were to take

their parallelogram apart, they would have two equal triangles. With this information have students come up with an equation to find the area of a triangle.

- Place examples on the chalkboard and have students find the area. Ask volunteers to work them out on the chalkboard. As a class review the problems.

- Have students turn to page 424 and discuss as a class how to use scale factor to solve ratio problems.

- Place on the chalkboard a problem. Have students state how to create a ratio box. Have volunteers come to the board to label and plug in the information in the ratio box.

- Have students then solve the problem as a class. - Place on the chalkboard three more problems. Have students work them out in their exercise books.

After a few minutes have volunteers work them out on the board.- Have students work on practice set on both lessons.- Teacher will go around checking students work.

Day three: Investigation 8 and lesson 81:- Have children open their math book to page 434, and ask them to start work on warm up exercise

(mental math). Time students while they work. Once children are finished, have them exchange their book with a classmate and go over the work.

- Have students review what are segments, lines, rays and angles. - Explain to students that today they will be constructing perpendicular bisectors and angle bisectors.

Explain to students what the word bisector is. - Have students take out their materials they were asked to bring beforehand. (pencil, eraser, ruler,

compass, folder sheet).- As a class, have students read and follow instructions on how to construct the different types of

bisectors. - After students have completed the task have them turn to page 438 to lesson 81. - Have students recall the S.O.S. (Solve, Operate, and Simplify) steps of solving arithmetic. - Explain to students that they will be solving the operations of arithmetic while including units of

measure. - Have students look at example provided in the lesson for each type of arithmetic operation, have

them discuss.- Place on the chalkboard a problem for each operation, have students work it out as a class. - Have students write notes on concepts. - Have students work on practice set individually. Teacher will go around checking students work.

Day 4: lessons 82 and 83:

- Have children open their math book to page 440, and ask them to start work on warm up exercise (mental math). Time students while they work. Once children are finished, have them exchange their book with a classmate and go over the work.

- Present to students a box. Explain to students that we want to find out how many 1 inch building blocks we can place inside for storage.

- Elicit from students what they will be looking for. Explain to students that today they will be learning how to look for volume. Have students come up with a definition of volume.

- Add measurements to the box and have students solve how many building blocks would fit in the box. Provide students with additional problems for them to practice on. Have volunteers come to the board to work them out and to explain how they worked out the problem.

- Have students turn to page 445 to lesson 83. - Have a volunteer read the information in the book ( on proportions) - Have students explain the information in their own words.- Go over the two examples provided in the book, explaining step by step on how to solve the

problems. Have four volunteers go to the board to solve a problem each. Meanwhile the rest of students are solving the problems in their note books.

- Go over each working out as a class. - Students will complete the lesson practice from both lessons in their note books.- They will then exchange their work, and students will be called to go to the board and explain the

procedure to solve the problems.Day five:

- Students will receive quiz based on what was covered this week.

Evaluation:

Week 32: Education week

Week 33


Lesson Topics: Order of Operations, Part 2; Using Cross Products to Solve Proportions; Area of a Circle; Finding Missing Factors

Previous Knowledge:

- Students have worked with problems involving order of operations before.

- Children know what a product is as well as factors.

- Students can identify the different parts of a circle, that is, circumference, diameter, and radius.

Objectives:


1) Follow the order of operations when simplifying an expression.

2) Use cross products to determine whether two fractions are equal or weather two ratios form a proportion.

3) Use cross products to find a missing term in a proportion.

4) Estimate the area of a circle drawn on a grid.

5) Use the formula A = πr2 to determine the area of a circle.

6) Solve a missing factor problem in which the unknown factor is a mixed number.

7) Solve a missing factor problem in which the unknown factor is a decimal number.

Concepts:

- When more than one operation occurs in an expression, the operations are performed in this order:

1. Perform operations within parentheses2. Multiply and divide from left to right3. Add and subtract from left to right

- Equal fractions have equal cross products. - Two ratios form a proportion if their cross products are equal- Cross Products: The product of the numerator of one fraction and the denominator of another.- The area of a circle drawn on a grid can be estimated by counting the square units that lie

completely or mostly within the circle and adding ½ times the number of squares units that have about half their area inside the circle.

- The formula to find the area of a circle is πr2; where π has a value of 3.14, and r being the radius of the circle.

- To find an unknown factor, divide the product by the known factor.

Skills:

- Solving a missing factor problem in which the unknown factor is a mixed number or a decimal number.

- Estimating the area of a circle drawn on a grid.

- Using the formula A = πr2 to determine the area of a circle.

- Use cross products to determine whether two fractions are equal or whether two ratios form a proportion.

- Use cross products to find a missing term in a proportion.

Attitudes:

- Work quietly in class

- Develop a positive attitude towards the use of mathematics


Day one: Lesson 84

- Have students work on Linear Measurement (Test K)




- Have students recall the four operations of arithmetic – addition, subtraction, multiplication, and division.

- Explain to students that when morethan one type of operation occurs in the same expression, we perform the operations in the following order:

1. Perform operations within parentheses.

2. Multiply and divide from left to right.

3. Add and subtract from left to right.

- Place examples on the board and explain to students how to work those following the steps

described above.

- Have students follow every step of the process.

- Children are then instructed to work on the lesson practice.

- Teacher walks around to make sure students are following the steps and also to check problems

that students have finished already.

- If students are having difficulties, have them work on more examples found in the supplemental

section of the book.

- Use the remedial periods to go over the problems with students.

- Students who finish all their work with few errors can work on the mixed practice, which should

be finished for homework.

Day two: Lesson 85

- Have students work on Liquid Measurement (Test L)




- Presents pair of fractions on the board.

- Show students how to look for cross products.

- Students should realize that equal fractions have equal cross products – explain this.

- Work on rations and show students how to look for cross products to see if the rations are equal.

- Introduce the concept of missing terms.

- Tell students that since equivalent ratios have equal cross products, we can use cross products to find a missing term in a proportion or fraction.

- Show students the steps to find a missing term in a given set of proportions.

- Work another example with students and allow them time to work it out with you.

- Give time for students to ask questions and clarify them.

- Have students work on the lesson practice and assess their understanding by checking and going around to see that they are following the steps and are doing it correctly.

Day three: Assessment (Test)

- Students will receive a cumulative test on previous lessons

Day four: Lesson 86

- Have students work on 30 Fractions to Reduce (Test G)




- Show students how estimate the area of a circle.

- Work out the area of circle using the formula A = πr2.

- Explain students each step, making sure they understand how to include each part of the formula to calculate area of a circle.

- Students work on lesson practice.

- Teacher checks work and provides individual help to students during this time.

- Students who finish quickly should start the mixed practice set of 30 problems which should be finished at home.

Day five: Lesson 87





- Give students some times to go over the lesson and then invite anyone who wants to solve the first problem and explain it.

- If the student gets lost in the process jump in and offer you help.

- Next, take the next problem and show students step by step how to solve for missing factors.

- Students should not struggle for this lesson, since they have been working for missing terms since lesson 4.

- Students work on the lesson practice and teacher circulates around to assess students understanding of this lesson.

- Teacher checks work and helps students who are stuck at some point of the problem.





Reference:



Materials:

- Newsprint

- Markers

- Charts


Evaluation:

Week 34


Lesson Topics: Using Proportions to Solve Ratio Problems, Estimating Square Roots, Measuring Turns, and Investigation: Experimental Probability

Previous Knowledge:


Objectives:


1. Use proportions to solve ratio problems.

2. Find the square root of a perfect square greater than 100.

3. Use guess and check to estimate the square roots of numbers that are not perfect squares.

4. Identify and describe turns measured in degrees.

5. Solve problems involving turns.

6. Estimate the probability of an event from data gathered by performing a probability experiment.

7. Present data in a relative frequency table.

8. Conduct probability experiments.

Concepts:

- Ratio boxes can help organize information needed to set up proportions correctly.

- Perfect squares are numbers squared whose squares are a whole number.

- A full turn is a 360 degrees turn, a half turn is 180 degrees, and a quarter turn is a 90 degrees turn. The direction of a turn is to the right (clockwise) or to the left (counter clockwise).

- Relative frequency is the frequency of an outcome divided by the total number of outcomes in an experiment. The sum of all the relative frequencies for an experiment is 1.

- The more times an experiment is repeated, the closer the experimental probabilities will be to the theoretical probabilities.

- Experimental probability: The probability of an event occurring as determined by experimentation.

- Theoretical probability: The probability that an event will occur, as determined by analysis rather than by experimentation.

- Representative: Typical

- Residents: People who live in a particular place.

- Opaque: Can’t be seen through.

Skills:

- Using proportion to solve ratio problems.

- Finding the square root of a perfect square greater than 100.

- Using guess and check to estimate the square roots of numbers that are not perfect squares.

- Identifying and describing turns measured in degrees.

- Solving problems involving turns.

Attitudes:

- Work quietly in class

- Develop a positive attitude towards the use of mathematics


Day one: Lesson 88

- Have students work on Liquid Measurement (Test L)




- Present students with a proportion problem to review how we solve proportion problems using cross products.

- Explain to students that in today’s lesson we will be using proportions to solve ratio problems.

- Present the first problem to students and work out the solution giving them active participation.

- Tell that a visual representation is very important to solve this type of problem.

- The ratio box is the visual representation which should be used to solve this problem.

- Explain how to use the ratio box using the problem just given.

- Once the problem has been set up in the ratio box, explain the steps to find the solution to the ratio problem – show students the two methods to solve the problem.

- Use other examples for students to get a better picture of how to solve these problems.

- Write problems that deal with their daily lives and give time for them to try to work them out and then together as a class, work the problems.

- To reinforce concepts and assess students’ understanding of the concept, have them work on the lesson practice.

- Move around to check students work and to help any student who is having trouble at a certain step.

Day two: Lesson 89

- Have students work on Measurement (Test K)




- Review with students perfect squares from 1 to a 100.

- Explain that in today’s lesson we will be looking for squares greater than a hundred.

- Tell students we need to know this information in order for us to solve squares greater than a hundred.

- Present examples to students and show them how to use the guess and check method to solve for squares greater than 100.

- Tell students that we need to logic and find hints in each problem to make the best guess.

- Take time to explain that there is no exact square root for 20 and we only write an approximate value because the square root of 20 is an irrational number.

- Explain to students what an irrational number is and give examples.

- Have students use a calculator to see why the square root of 20 is an irrational number and we only a write an approximate value.

- The practice section of this lesson will be worked together as a class to further reinforce the concepts.

- Children will be given the opportunity to explain how they arrive at their answers.

- The will continue practicing by working out the supplemental practice of this lesson for homework.

Day Three: Lesson 90

- Have students work on 24 Mixed Numbers to Write as Improper Fractions (Test J).




- Begin this lesson by paste a poster with a compass on a North wall of the class room.

- Tell students that in today’s lesson will be working with turns – explain what a turn is.

- Tell students that turns are measured in degrees.

- Point out to the compass you have pasted on a North wall of the classroom.

- Tell students that we will use the compass to know the direction in which our turn is made – right or left or clockwise or counter clockwise.

- Explain the following to students and practice making the turns using the compass:

1. A complete turns measures 360 degrees.

2. Half a turn is 180 degrees.

3. One fourth of a turn is 90 degrees.

- Present problems dealing with this concept and together as a class workout each problem.

- Tell students they can draw diagrams to help understand the problem.

- Tell to read each problem carefully and understand what it is asking us to solve.

- Model out for students how to solve the problems following the guidelines of the book.

- Have children work on the lesson practice and discuss answers together as a class.

- Students complete the mixed practice for homework.

Day Four: Assessment (Test)

- Students will receive a cumulative test on previous lessons

Day five: Investigation 9

- Write the topic on the white board, “Experimental Probability”

- Ask students to share what they know about probability – students should have some knowledge based on what was covered in lesson 58 about theoretical probability.

- Listen to students responses and elaborate on them.

- Present the vocabulary for this lesson and go over it.

- Choose students at random to read information from the book about experimental probability.

- Pause at each important point and discuss it with students.

- Discuss how to carry out and experimental probability experiment. Talk about how to find results.

- Next, allow students to apply their knowledge and work out the one given on the book.

- Then together discuss the results.

- Students should actively participate and explain how they arrive at their answers.

- Carry out the activity of the probability experiment.

- Students should have all materials ready in their groups before they begin each step.

- The teacher will circulate around making sure students are following the steps.

- Students should create a tally and a relative frequency table when they are finished with the activity, then they are two answers questions given in this lesson about probability.

- Teacher will walk around and discuss with each group their findings.

- Get back together as a class and share some of the results.

- Finally students will work on the “extensions” section of this lesson. Here they will farther reinforce what was covered in this lesson.




- Carrying experiments to determine the probability of an outcome

Reference:

- Saxon math 7/6 Teachers book lesson 88 – 90, Investigation 9

- Saxon Math 7/8 Students Book lesson 88 – 90, Investigation 9

Materials:

- Newsprint

- Markers

- Charts

Evaluation: