grade 6 sample

TEA CHER EDITION

Published by

AnsMar Publishers, Inc.

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TEA CHER EDITION

TEXAS VERSIONTEKS Aligned—STAAR Ready

GRADE 6 SAMPLE

Thanks for requesting a sample of our new Texas Teacher Editions. We welcome the opportunity to partner with you in building successful math students.

This booklet is a sample Texas Teacher Edition for Grade 6 (Table of Contents and first 10 lessons). You can download Kindergarten through Grade 5 Texas Lesson Samples from our website: www.excelmath.com/downloads/state_stdsTX.html

Here are some highlights of our new Texas Teacher Editions:1. The Table of Contents will indicate Lessons that go further than TEKS concepts. There is a star

next to lessons that are “an advanced Excel Math concept that goes beyond TEKS for Grade 6.” With this information, teachers can choose to teach the concept or skip it.

2. For each Lesson Plan (each day) we are changing the “Lesson Objective” to “TEKS Lesson Objective” (see Lesson #1). On days where lessons are not directly related to the TEKS, we will offer instruction for the teacher to alter what they do for the Lesson of the Day so they can still teach a TEKS concept. The Objective on those days will look like this (from Lesson #21):

ObjectiveStudents will recognize patterns.

TEKS AlternativeActivity #2 Ratios and Unit Rates (see page A3 in the back of this Teacher Edition) may be used instead of the lesson part of the Student Lesson Sheet. Have your students complete the Guided Practice and Homework portion of the Student Sheet.--

3. Within Guided Practice when a non TEKS concept is one of the practice problems we will indicate it with the star again.

4. On Test Days (see Test #1) we indicate with a star any non TEKS concepts being assessed.

We are in the very early stages of creating these Texas Teacher Editions. When each one is released, we will have an announcement on our website (focusing on grades K-5 first, and then grade 6). The student sheets are now ready to ship.

In the meantime, you can find updates plus additional downloads on our website (manipulatives, Mental Math, placement tests in English and Spanish, and lots more): www.excelmath.com/tools.html

Please give us a call at 1-866-866-7026 (between 8:30 - 4:00 Monday through Friday West Coast time)if you have questions about these new Excel Math Texas Editions.

Cordially,

The Excel Math Team

www.excelmath.com 1 © 2014 AnsMar Publishers, Inc.

The Common Core State Standards for Mathematical Practice are integrated into

Excel Math lessons. Below are some examples of how to include these Practices into

the tasks and activities your students will complete throughout the year.

Mathematical Practices

1 . Make sense of problems and persevere in solving them . Mathematically proficient students solve real world problems through the application of algebraic and geometric concepts. These problems involve ratio, rate, area and statistics. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “Does this make sense?” “What is the most efficient way to solve this problem?” and “Can I solve the problem a different way?” They check their answers using a different method.2 . Reason abstractly and quantitatively . Mathematically proficient students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.3 . Construct viable arguments and critique the reasoning of others . In Sixth Grade, mathematically proficient students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. dot plots, histograms, etc.). They critically evaluate their own thinking and the thinking of others. Students ask questions such as, “How did you get that?” and ”Why is that true?” They explain their thinking to others and respond to others’ reasoning and strategies.4 . Model with mathematics . In Sixth Grade, students model problems symbolically, tabularly, graphically and contextually. They form expressions, equations or inequalities from real world contexts and connect symbolic and graphical representations. Student use number lines to represent inequalities and use measures of center and variability and data displays (e.g. histograms) to compare data sets. They explain the connections between representations.5 . Use appropriate tools strategically . Mathematically proficient students consider available tools when solving a problem and decide when certain tools might be helpful. For example, they may represent figures on the coordinate plane to calculate area. Students might use physical objects or drawings to construct nets and calculate the surface area of three-dimensional figures.6 . Attend to precision . Mathematically proficient Sixth Grade students use clear and precise language in discussions. They use appropriate terminology when referring to rates, ratios, geometric figures, data displays and components of expressions, equations or inequalities. For example, when calculating the volume of a rectangular prism they use cubic units.7 . Look for and make use of structure . Mathematically proficient students carefully look for patterns and structure. Students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students compose and decompose two- and three-dimensional figures to solve real world problems involving area and volume.8 . Look for and express regularity in repeated reasoning . Mathematically proficient students use repeated reasoning to understand algorithms. They divide multi-digit numbers and perform operations with multi-digit decimals. They make models to show a/b ÷ c/d = ad/bc.

Standards for Mathematical Practice and Excel Math Grade 6

www.excelmath.com i.34 © 2014 AnsMar Publishers, Inc.

LESSON PAGE CONCEPT

1 2 Recognizing numbers less than a million given in words or place value; adding, subtracting and multiplying whole numbers or money amounts with regrouping; recognizing multiples; selecting the correct equation; solving multi-step word problems using addition, subtraction and multiplication with regrouping; calculating change using the least number of coins; recognizing money number words; recognizing addition and subtraction fact families; optional: recognizing ordinal number words up to 100

2 4 Comparing two or more sets of data using bar or line graphs; interpreting information given in a histogram; recognizing the symbols < less than and > greater than; filling in missing numbers in sequences counting by numbers from 1 to 12; arranging 4 four-digit numbers in order from least to greatest and greatest to least; selecting the correct symbol for a number statement 3 6 Recognizing true and not true number statements; using trial and error to solve for unknowns in an

equation; solving algebraic equations with and without parentheses; changing a number statement from ≠ to =; learning the order of operations when solving an equation

4 8 Learning 7 days = 1 week; learning 1 year = 12 months; learning the number of days in each month; optional: computing the date within the month; learning the abbreviations for days and months

5 10 Defining numerator and denominator; determining the fractional part of a group of items when modeled or given in words, sometimes with extraneous information and the word “not”; learning that the whole is the sum of its parts; adding and subtracting fractions and mixed numbers with like denominators 12 Test 1 - Assessment 6 14 Recognizing multiplication and division fact families; learning division facts with dividends up through 81

and dividends that are multiples of 10 (to 90), 11 (to 99) or 12 (to 96); dividing a one-digit divisor into a three-digit dividend using the standard algorithm with a two- or three-digit quotient with no regrouping or remainders; solving multi-step word problems involving division; learning the terminology for multiplication and division

7 16 Adding, subtracting and multiplying with multi-digit decimals using the standard algorithm; solving word problems using deductive reasoning; determining if there is sufficient information to answer the question in a word problem; determining what information is needed to answer the question in a word problem

8 18 Solving word problems by listing possibilities or by making a chart 9 20 Learning division facts with remainders with dividends up through 81; solving word problems involving division with remainders 10 22 Estimating measurements; measuring temperature; learning measurement equivalents for length, weight, volume: feet, inches, yards, centimeters, meters, kilometers, grams, kilograms, liters, milliliters, millimeters, quarts, gallons, ounces, pounds and tons; converting measurements using multiplication or division; making tables of equivalent ratios; determining the measurement that is longer or shorter or heavier or lighter 24 Test 2 24 Create A Problem 2: Decoding Secret Messages 11 26 Measuring line segments to the nearest half inch, quarter inch and half centimeter; comparing U.S. customary and metric units; making tables of equivalent ratios and finding missing values in the tables 12 28 Multiplying by a two-digit multiplier; multiplying multi-digit decimals using the standard algorithm 13 30 Finding the least common multiple of two whole numbers less than or equal to 12; learning 60 minutes

= 1 hour; telling time to the minute; recognizing a quarter past or before the hour and half past the hour; calculating minutes before the hour; optional: calculating elapsed time (hours) involving AM and PM

14 32 Computing the area of the rectangle, doubling it, and comparing the two; learning the terminology of parallel, intersecting and perpendicular lines, plane figure, polygon, quadrilateral, parallelogram, rectangle, square, diagonal, rhombus and trapezoid

15 34 Recognizing three-dimensional figures - sphere, cube, cone, cylinder, rectangular, square and triangular pyramids and rectangular and triangular prisms; learning the terminology of flat and curved faces, bases, edges and vertices 36 Test 3 36 Create A Problem 3: Landscape Design 16 38 Dividing a one-digit divisor into a three-digit dividend with a two-digit quotient with regrouping and remainders 17 40 Determining the lowest common multiple; learning division and multiplication facts with products with 11 (to 121) or 12 (to 144) as a factor 18 42 Understanding ratios; describing a ratio relationship between two quantities; determining equivalent fractions

using models, money, multiplication or division

Lesson Page Reference


LESSON PAGE CONCEPT 19 44 Computing 1/2 to 1/9 of a group of items; optional recognizing odd and even numbers less than 1,000 20 46 Rounding to the nearest ten, hundred or thousand; estimating the answers for addition, subtraction and multiplication word problems using rounding to the nearest ten, hundred or thousand; estimating range for an answer; rounding numbers so there is only one non-zero digit 48 Test 4 48 Create A Problem 4: Designing the Playground 21 50 TEKS Alternate: Activity #2 - Ratios in Word Problems; Opt: learning the terminology of pentagon, hexagon and

octagon; recognizing patterns; determining figures that do or do not belong in a set 22 52 Putting simple fractions in order from least to greatest and greatest to least; determining the fraction with the greatest or least value in a set of fractions 23 54 TEKS Alternate: Activity #3 - Real & Whole Numbers on a Number Line; recognizing lines of symmetry; Opt:

Recognizing similar and congruent figures; recognizing flips, slides and turns; bilateral and rotational symmetry 24 56 Recognizing numbers up through trillions given in words or place value; recognizing numbers given in expanded notation 25 58 Graphing coordinate points in all quadrants of the coordinate grid; learning the sum of the angles of

a rectangle; recognizing right, obtuse and acute angles; measuring and estimating angles; recognizing equilateral, isosceles and scalene triangles; learning the sum of the angles of a triangle

60 Test 5 60 Create A Problem 5: Daily Activities 26 62 Dividing a two-digit divisor into a dividend less than 100 with remainders 27 64 Converting an improper fraction to a mixed or whole number; determining the fraction with the greatest or least value in a set of fractions 28 66 Adding and subtracting fractions with unlike denominators 29 68 Reading maps drawn to scale 30 70 Calculating the area and perimeter of a rectangle; solving word problems involving area and perimeter 72 Test 6 72 Create A Problem 6: The Fruit Juice Stand 31 74 Dividing dollars by dollars 32 76 Determining coordinate points 33 78 Recognizing the pattern in a sequence of figures or pattern of shading; solving for an unknown angle in a triangle 34 80 Understanding ratios; describing a ratio relationship between two quantities; comparing probabilities 35 82 Recognizing tenths and hundredths places; writing mixed numbers as decimal numbers; writing decimal numbers as mixed numbers; recognizing decimal number words; adding and subtracting decimal numbers 84 First Quarterly Test 36 86 Calculating the length of vertical and horizontal lines by subtracting x- and y-coordinates 37 88 Learning the Distributive Property of Multiplication; learning the Associative Property of Multiplication and Addition; learning the Commutative Property of Addition and Multiplication 38 90 Dividing a one-digit divisor into a four-digit dividend with a three-digit quotient; learning the Property of One and the Zero Property 39 92 Adding and subtracting fractions in word problems 40 94 Recognizing multiplication without the “x” symbol; calculating answers to word problems using 2 to 1 and 5 to 1 ratios 96 Test 7 96 Create A Problem 7: A Whole Lotta Shaking Going On 41 98 Learning the equivalent for one year in days and in weeks; learning about leap year; calculating elapsed time crossing months within a week 42 100 Determining the question given the information and the answer; estimating the most reasonable answer 43 102 Calculating elapsed time in minutes across the 12 on a clock 44 104 Converting fractions and decimal numbers to percents by setting up equivalent fractions 45 106 Using Venn Diagrams to understand the union and intersection of sets 108 Test 8


= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6 but may be required by some states. Alternate TEKS Activities are provided in this Teacher Edition.


LESSON PAGE CONCEPT 108 Create A Problem 8: Measuring Vision 46 110 Converting mixed numbers to decimal numbers by setting up equivalent fractions 47 112 Comparing fractions with unlike denominators in less than and greater than problems and in true and not true number statements by setting up equivalent fractions 48 114 Converting improper fractions as part of mixed numbers; recognizing division without the “÷” symbol 49 116 Rounding money amounts and decimal numbers to the nearest dollar or whole number 50 118 Determining factors, prime numbers, composite numbers, prime factors and greatest common factors 120 Test 9 120 Create A Problem 9: Measuring the Heat in Spicy Food 51 122 Multiplying decimal numbers 52 124 Dividing decimal numbers by whole numbers; converting percents to decimal numbers 53 126 Comparing decimal numbers in less than and greater than problems 54 128 TEKS Alternate: Activity #1 - Percent Problems; Opt: recognizing Roman numerals: I, V, X, L, C, D and M 55 130 Calculating averages 132 Test 10 132 Create A Problem 10: Measuring Carats 56 134 Determining the greatest common factor and least common factor 57 136 Simplifying fractions; solving equations involving fractions 58 138 Estimating answers to problems involving numbers with up to nine digits 59 140 Calculating the volume of a rectangular prism with one or more layers of cubes using the formula L x W x H 60 142 Recognizing parts of a circle; calculating diameter and radius; associating the 360 degrees in a circle with one- quarter, one-half, three-quarter and full turns 144 Test 11 144 Create A Problem 11: Diagramming a Class Survey 61 146 Recognizing the thousandths place; rounding decimal numbers to the nearest tenth or hundredth; solving equations involving decimals 62 148 Dividing a two-digit divisor into a three-digit dividend with a two-digit quotient; simplifying fraction answers 63 150 Comparing positive and negative numbers 64 152 Determining numbers that are multiples of one number and factors of another 65 154 Calculating mean, median and mode; using stem and leaf plots 156 Test 12 156 Create A Problem 12: Rainfall Report 66 158 Calculating equivalent ratios 67 160 Determining percent in word problems 68 162 Determining if coordinate points are on a given line 69 164 Using trial and error and charting strategies to solve word problems 70 166 Defining dependent and independent variable, central tendency, statistics and outlier; recognizing factors that

influence data collection; creating a scatter plot and a box plot 168 Second Quarterly Test 71 170 Computing the percent of a whole number, money amount or decimal number 72 172 Calculating cost per unit 73 174 Filling in missing numbers in a sequence of decimal numbers 74 176 Putting decimal numbers in order from least to greatest and greatest to least; evaluating decimal numbers in true and not true number statements 75 178 Calculating the perimeter and area of an irregular figure 180 Test 13 180 Create A Problem 13: Rock Concert 76 182 Calculating area and perimeter given coordinates on a coordinate grid 77 184 Calculating using exponents; calculating square roots 78 186 Selecting an equivalent fraction; simplifying improper fractions as part of a mixed number answer 79 188 Solving word problems involving decimals 80 190 Recognizing complementary, straight and supplementary angles




Lesson Page Reference LESSON PAGE CONCEPT

192 Test 14 192 Create A Problem 14: Road Trip 81 194 Calculating decimal answers in division problems when zeroes need to be added to the right of the dividend 82 196 Dividing using short division 83 198 Converting mixed numbers to improper fractions 84 200 Filling in missing numbers in sequences counting by varying amounts 85 202 Multiplying fractions and whole numbers by fractions 204 Test 15 204 Create A Problem 15: The Last Frontier 86 206 Estimating to the nearest dollar or whole number 87 208 Comparing fractions in word problems 88 210 TEKS Alternate: Activity #8 - Graphing Coordinate & Drawing Polygons on a Plane; Opt: recognizing angles 89 212 Calculating distance, time, rate and speed in word problems 90 214 Selecting the fraction, percent or decimal number that best represents a shaded region 216 Test 16 216 Create A Problem 16: The Great Race 91 218 Solving equations with embedded parentheses 92 220 TEKS Alt: Activity #4 - Area & Perimeter of Triangles; Opt: calculating elapsed time more than one week 93 222 Reducing improper fraction answers to their lowest terms 94 224 Solving problems using data displayed as percent pie graphs 95 226 Recognizing decimal places to the right of the thousandths; multiplying decimals when zeroes need to be added to the product 228 Test 17 228 Create A Problem 17: Gloria’s World Tour 96 230 Solving word problems by working backwards 97 232 Writing probability as a fraction, decimal, percent or proportion (ratio) 98 234 Selecting the most reasonable answer involving percents 99 236 Writing probabilities as lowest-terms fractions 100 238 Calculating the surface area of a rectangular prism; determining the equation that creates a pattern 240 Test 18 240 Create A Problem 18: The Long Jump Competition 101 242 TEKS Alternate Activity #5 - Area & Perimeter of Polygons; Opt: determining reciprocals 102 244 Multiplying and dividing decimal numbers by powers of ten 103 246 Dividing a three-digit divisor into a three-digit dividend with a one-digit quotient 104 248 Multiplying mixed numbers 105 250 Solving word problems involving percent, including the word “not” 252 Third Quarterly Test 106 254 Subtracting fractions with like denominators with regrouping 107 256 Simplifying division problems using powers of ten 108 258 Estimating using rounding to one-digit accuracy; calculating volume in word problems 109 260 Determining negative numbers using coordinate points 110 262 Solving word problems involving sales tax, sale price, interest and profit 264 Test 19 264 Create A Problem 19: Guess the Shape 111 266 Converting decimal numbers to percents and percents to decimal numbers 112 268 Using multiplication and division to simplify fraction multiplication problems; simplifying fractions before

multiplying 113 270 Converting decimal numbers to lowest-terms fractions or mixed numbers 114 272 Determining the equation that represents a problem and the equation that solves it 115 274 Identifying the equation that represents a line on a coordinate graph; learning slope and intercept 276 Test 20 276 Create A Problem 20: Planting Trees




LESSON PAGE CONCEPT

116 278 Determining percent of a whole number 117 280 Solving word problems involving the multiplication of fractions and mixed numbers 118 282 Dividing fractions 119 284 Arranging fractions, decimal numbers and mixed numbers on a number line 120 286 Calculating averages involving decimals and fractions 288 Test 21 288 Create A Problem 21: Planting More Trees 121 290 Calculating the area of a parallelogram 122 292 Multiplying a three-digit number by a three-digit number 123 294 Rounding mixed numbers 124 296 Calculating the area of a triangle 125 298 TEKS Alternate: Activity #6 - Area & Perimeter of Trapezoids; Opt: calculating circumference and area of a circle; π (pi) 300 Test 22 300 Create A Problem 22: Paying Taxes I 126 302 Converting measurements using multiplication or division with fractional or decimal remainders 127 304 Calculating percents in word problems 128 306 Converting fractions to decimal numbers using division; recognizing the symbol for a repeating decimal 129 308 Converting fractions to percents 130 310 Understanding absolute value using number lines; adding positive and negative integers 312 Test 23 312 Create A Problem 23: Paying Taxes II 131 314 TEKS Alt: Activity #9 - Constructing Cubes to Find Volume Using Exponents; Opt: adding positive and negative integers 132 316 Dividing a two-digit divisor into a three-digit dividend with a one-digit quotient 133 318 Calculating expected numbers based on probabilities 134 320 Using rounding to estimate quotients 135 322 Determining percents that are greater than 100% and less than 1% 324 Test 24 324 Create A Problem 24: Climbing Mt. Whitney 136 326 Dividing a three-digit divisor into a four-digit dividend with a two-digit quotient 137 328 Adding and multiplying measurements, then simplifying units 138 330 Dividing a decimal number by a decimal number 139 332 Calculating the volume of a triangular prism or cylinder (optional) 140 334 Reviewing rounding quotients; calculating percents in word problems, rounding to the nearest whole percent 336 Fourth Quarterly Test 141 338 Subtracting measurements by exchanging units 142 340 Dividing mixed numbers 143 342 Subtracting positive and negative integers 144 344 Subtracting positive and negative integers 145 346 Determining the fourth vertex of a parallelogram on a coordinate graph 348 Year-End Test 1 146 350 Subtracting mixed numbers and fractions with unlike denominators with regrouping 147 352 Dividing a three-digit divisor into a four-digit dividend with a one-digit quotient 148 354 TEKS Alternate: Activity #7 - Calculating Surface Area & Ratios; Opt: solving for an unknown with similar polygons 149 356 Determining number patterns 150 358 TEKS Alternate: Activity #17 - Calculating Unit Rate, Speed, Range and Velocity; Opt: calculating the probability of two

separate events as a sum and two consecutive events as a product; calculating using factorials and permutations 360 Year-End Test 2 151 362 Using ration reasoning; comparing the value of products using different currencies 152 364 Calculating and comparing cost per unit 153 366 Solving word problems involving division of fractions and mixed numbers 154 368 Solving unit rate problems; using ratio and rate reasoning; estimating answers to division word problems 155 370 Multiplying and dividing positive and negative integers

= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6. Alternate TEKS Activities are provided in this Teacher Edition.

www.excelmath.com 1 © 2014 AnsMar Publishers, Inc.

Texas Edition6th Grade Lesson Plans #1-10 and Answer Keys

2

Lesson 1

TEKS ObjectiveStudents will add, subtract, multiply and divide integers fluently.

Students will recognize numbers less than a million given in words or place value.

Students will multiply and divide positive rational numbers fluently.

Students will recognize ordinal numbers up to 100.

PreparationFor each student: Ones and Tens Pieces, Hundreds Pieces, Hundreds Exchange Board (masters on M13 – M14 and M16)

Lesson PlanWrite the number 253,874 on the board. Point out that the value of the thousands place is 3 times one thousand (3 x 1,000). The words ten and hundred are repeated in the two places to the left of the thousands place. This pattern will repeat itself in larger numbers. Do #1 and #2 with the students. In each, point out the importance of each zero as a placeholder.

Review the addition, subtraction and multiplication problems in #4 – #9.

Read the definition of multiple with the students. For problems#10 – #11, the students are to select the set that only contains multiples of the given number. The other three choices will contain at least one number that is not a multiple of the given number.

Go over the word problems in #12 – #15. For #12, the students should write their

own equation first and then look for that equation among the choices. Explain that the order for addition and multiplication is not important, but the order is important for subtraction and division. Give your students the following word problem:“Jackson had $5.11. He earned $4.50 and then spent $7.99 on a computer game. How much money does he have now?” ($1.62)

For problems #16 – #18, the students should start with the largest possible coin. If adding another coin takes them over the given amount, they should drop down to the next smaller value coin. As they add coins, they should write an addition problem to verify their choices.

Ordinal Numbers OptionRead through the ordinal numbers section. Explain that ordinal numbers (first, second, third, etc.) indicate position, not value.

StretchStarting with this lesson, there will be a problem of the day or brainteaser called a STRETCH. Write the problem on the board in the morning for bell work. The students will have all day to come up with a solution. Reward those who have the answer by the end of the day when you provide the solution. Sometimes there may be other answers in addition to the ones we provide.

Stretch 1Three consecutive numbers that add to 6 are 1, 2 and 3. (1 + 2 + 3 = 6) What three consecutive numbers add to 345?

Answer: 114, 115 and 116 (114 + 115 + 116 = 345)

= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6.

3

© Copyright 2007-2014 AnsMar Publishers, Inc.www.excelmath.com 6001

2 8 44,3 6 7

9 2+ 6 3

1 2

4 5 6 7 8 9

3

12 13

14 15

5,0 0 0- 1,5 3 5

9,805- 3,452

942x 5

681x 8

469x 7

(6, 12, 18, 24) (12, 24, 36, 48)

(2, 3, 4, 6) (12, 20, 30, 44)

(6, 12, 14, 17) (7, 10, 13, 16)

(9, 12, 15, 18) (3, 11, 14, 18)

1110

16 17 18

2

10¢10¢

+ 3¢23¢

6. 4 + 5 =

7. 5 - 4 =

8. 5 ÷ 4 =

9. 5 x 4 =

NameLesson 1 Date

2 hundred thousands, 7 tens, 8 ones, 9 thousands and 3 hundreds

six hundred fifty-one thousand,eight hundred thirty

Write each number.

Ordinal numbers are used to indicate where an item is located in relation to othersin the same set.

Felipe was waiting in line at the movie theater. He counted the number of people ahead of him in the line. He was the fifty-third person in line. How many people were ahead of him?

A multiple is the result of multiplying two numbers. Some of the multiples of2 are 2, 4, 6, 8 and 10. Some of the multiples of 5 are 5, 10, 15, 20 and 25.

Which set shows multiples of 12? Which set shows multiples of 3?

A picture frame costs 51¢. Amber gave the clerk a dollar. How much was her change?

Eddie has 8 nickels, 6 dimes and 3 quarters. How much moneydoes he have?

Change can be given in several different combinations of coins. For example, 15¢ can be 3 nickels or 1 dime and 1 nickel. If you want to use the fewest coins, it's 1 dime and 1 nickel.

Using the fewest coins,how many dimes arethere in 23¢?

Using the fewest coins,how many nickels arethere in 43¢?

Using the fewest coins,how many quarters arethere in 58¢?

Matilda would like to plant 4 different herbs in each of her 5 gardens. Which equation shows how many herbs shewill need?

Alek threw 26 sticks to his dog on Monday and 13 on Tuesday. Twelve of the sticks got lost in the bushes, sothe dog couldn't bring them back. How many sticks did his dog bring back?

Recognizing numbers less than a million given in words or place value; recognizing ordinal number words up to 100; adding, subtracting and multiplying whole numbers or money amounts with regrouping; recognizing multiples; selecting the correct equation; solving multi-step word problems; calculating change using the least number of coins; recognizing money number words; recognizing addition and subtraction fact families

4,806

651,830209,378

52 people

3,465 6,353 4,710 5,448 3,283

$1.00- .51$ .49

$1.75$ .49

$ .40.60

+ .75$1.75

25¢10¢5¢

+ 3¢43¢

25¢25¢5¢

+ 3¢58¢1 2

20

26+ 13

39

39- 12

27

27 sticks


1. 8 + 4 =2. 4 + 8 =3. 12 - 4 =4. 8 - 4 =

9,850D

G 318,967

E 2,758

C $92.67

F 154

4. (12, 18, 24, 36)

3. (6, 12, 15, 18)

12 x 7 =

6 x 11 =5. (15, 21, 27, 33)

6. (4, 10, 16, 22)

1 23

+ 4 25 7

3 6 8- 4 83 2 0

4 6 0- 6 0

2 4 5+ 1 0 3

57+ 320

377

CheckAnswer CheckAnswer

$3.8 7x 6

$4 0.0 3- 6.0 9

377A 748B

$1.00 = _____ nickels

75¢ = _____ quarters

3 9 73 8

1 0 4+ 2,1 9 2

9,6 5 2- 3,2 4 1

5,7 8 6- 2,3 5 8

NameGuided Practice 1

Which fact does not belong in this set?

two hundred seventeen thousand, eight

thirty dollars and seventy cents

one hundred thousand, fifty-nine

nineteen hundred

Orange soda is sold in packs of six. Which set shows possible numbers of sodas that could be bought?

Marcia did 7 pull-ups on Friday, 8 onSaturday and 3 on Sunday. Vicky did7 fewer pull-ups than Marcia. Howmany pull-ups did Vicky do?

To check your work, add the answers to your problems and compare the result to the CheckAnswer that is provided. If the two numbers are equal, your answers are correct and you may go on to the next problem. If the

sum of your answers does not equal the CheckAnswer, then go back and check your work. If you are unable to find your mistake, ask for help.

Roscoe had $3.74. He spent $2.78 and he earned $3.85. How much money does he have now?

217,008

$30.70

100,059

1,900

84

66

1212

20

38

4

116,411

+ 3,4289,850

42,731

20+ 32,758

$30.704.81

23.22+ 33.94$92.67

484

+ 66154

217,008100,059

+ 1,900318,967

18 - 7 = 11

11 pull-ups

78

+ 318

400+ 348

748400 348

$23.22

$33.94

$4.81

$3.85+ .96$4.81

$3.74- 2.78$ .96

2,731

6,411

3,428

= This is an accelerated Excel Math concept that goes beyond TEKS for Grade 6. The stars are not marked on the Student Lesson Sheets.

4

Lesson 2

TEKS Objective Students will represent numeric data graphically, including histograms, bar graphs and line graphs.

Students will order a set of rational numbers arising from mathematical and real-world contexts and will recognize the symbols “<” less than and “>” greater than.

Students will fill in missing numbers in sequences counting by numbers from 1 to 12.

Students will arrange 4 four-digit numbers in order from least to greatest and greatest to least.

PreparationNo special preparation is required.

Lesson PlanRead through the explanation and do #1 – #4 together. Explain that when multiple sets of data appear on the same graph, a legend is shown below the graph indicating the information each line or bar is representing.

The graph on the bottom right side of the lesson is a histogram. Histograms are used to group data using intervals. (As opposed to bar graphs, which group data according to the amount in each category.) To build a histogram, find the lowest value and the highest value. Divide the values between them into equal groups. Each of the values is then placed into one of the segments.

i The following concept is found on Guided Practice D and E.

Write “2,801” and “2,534” on the board. Ask a student to put notations between

the numbers: two dots next to the larger number and one dot next to the smaller number. Next, connect the one dot to each of the two dots.

You will see a sideways “V”. The bottom point of the “V” points to the smaller (in value) of the numbers. The number statement is “2,801 is greater than 2,534.”

Have the students make “Vs” with their thumbs and pointer fingers. Have them turn their “Vs” sideways. Note that the left “V” shows less than (your fingers look like an “L”). The right “V” shows greater than.

Write on the board a series of numbers that increases or decreases by 12. Ask the class in what direction the sequence is counting (+ or –), by what number the sequence is counting and how they know. (Find the difference between each number.) Then ask them to determine what the missing number in the sequence will be.

Have a student give you 3 four-digit numbers less than 10,000. Write them on the board in random order. Ask a student to come forward and rewrite the numbers in order from least to greatest and have the class explain how to tell if the order is correct. (The values in the thousands place are compared, then the hundreds and so on, down to the ones place.) Have students put more numbers in order, this time from greatest to least.

Stretch 2Kim, Brian and Lee have 42 cats. Lee has twice as many as Kim. Brian has half as many as Kim. How many cats do they each have?

Answer: Kim has 12 cats, Lee has 24 cats and Brian has 6 cats.

5


2120

1 2 3 4 5 6 7

2223242526

2

1

00-5 6-10 11-15 16-20 21-25

3

4

5

6

200020012002

1

2

3

4

25

1520

105

Paul Gail Sean

NameLesson 2 DateComparing two or more sets of data using bar or line graphs; interpreting information given in a histogram; recognizing the symbols < less than and > greater than; fillingin missing numbers in sequences counting by numbers from 1 to 12; arranging 4 four-digit numbers in order from least to greatest and greatest to least

A histogram is a type of graph used when you want to group the data.

Our example shows the amount of time it took students to complete a math test.

We put the information into a tally chart. You will need to know the least amount of time a student took and the greatest amount of time. This is the range of the data. Next, decide how to divide the range into equal parts. We used 5-minute intervals.

Next, transfer the information from the tally chart to the histogram.

Write 3 statements about the information in this graph. How could the information about taking a test help the teacher of this class?

High TemperaturesDuring the First Week in June

Days

Tem

pera

ture

(ºC)

Time Needed to Complete the Math Test

Intervals Number of Students

Minutes

0 - 5 minutes6 - 10 minutes

11 - 15 minutes16 - 20 minutes21 - 25 minutes

Num

ber o

f Stu

dent

s

How much cooler was it on the second day of June in 2000 than in 2001?

How much warmer was it on the third day of June in 2002 than in 2000?

Jan Feb Mar Apr May

Part-time Employees Work DaysHow many more days did Gail work in January than Sean?

How many days did Paul and Sean workin May?

Day

s

Circle or pie graphs are used primarily to organize data. Picture graphsuse symbols and pictures to compare data. Bar graphs also compare

data. Line graphs are used to show change over time.

26- 24

2

26- 22

4

2° cooler

4° warmer

20- 10

10

15+ 520

10 more days

20 days


A 536

(_____ , _____ , 58 , 51 , 44 , 37)

( 413, 405, 397, 389, _____ )

(3,434; 3,343; 3,433; 3,334)

3,343 > ________

CarlyBarryLupe

RuthieGlen

13,354B

759,078D

G 51

E 35

C $160.67

F 17

6. 10 + $5 =7. 10 - $5 =8. 10 x $5 =9. 10 ÷ $5 =

4 1 76 4 9

1,3 0 9+ 1,5 1 8

9,3 6 1- 4,1 9 5

249x 7

638x 4

6.>

7.<

1,611 1,161

2 quarters = ______ dimes

$9.80x 8

$6 7.0 5- 3 6.1 8


Select the number from thegiven set to fill in the blank.

How many took fewer than four photographs?

How many photographs did Carly and Lupe take?

How many more photos does Glen need to take to catch up with Barry?

Taking Photographs

Each represents 2 photos

Rod is nineteenth in line. Thereare _____ ahead of him.

5 ten thousands, 2 tens, 1 thousand, 6 hundred thousands, 9 ones and 4 hundredsone hundred two thousand,

fifteen

twenty-three hundred

Ronnie would like to giveeach of his ten friends a$5.00 gift certificate.Which equation showshow much money he will need?

Dakila feeds her goatssix pounds of grain every day. How many pounds of grain does Dakila feed her goats each week?

Using the fewest coins, how many quarters are there in 33¢?

forty dollars and sixty cents

ten dollars and eighty cents

Brian picked 21 apples on Monday and 15 on Tuesday. Twelve of the apples were bad, so he threw them away. How many apples does he have left?

Draw the correct symbol ( < or > )between the pair of numbers.

3817265

+ 18536

4+ 711

72 65

3,334

381

6 - 2 = 4

2 - Ruthie and Glen

11 photographs

4 more photos

3,8935,1662,552

+1,74313,354

$40.6010.8078.40

+ 30.87$160.67

246

+ 535

842

+ 151

3,3342,300

102,015+651,429759,078

112

+ 417

18

5651,429102,015

2,300

$5042 pounds

6x 742

25¢5¢

+ 3¢33¢

1

$40.60

$10.80

21+ 15

36

24 apples

36- 12

24

3,893 5,166

1,7432,552

>

$78.40 $30.87

6

Lesson 3

TEKS ObjectiveStudents will write one-variable, one-step equations and inequalities to represent constraints or conditions within problems.

Students will model and solve one-variable, one-step equations and inequalities that represent problems.

Students will recognize true and not true number statements.

Students will determine if the given values make one-variable, one-step equations or inequalities true.


Lesson PlanWrite on the board: 4 + 5 = 2 + 7. This is an equation because the value on the left is the same as the value on the right. Ask the class if the above equation is true.

For problems #1 – #3 on the Student Lesson Sheet, the students are to combine any numbers they can before evaluating the statement. If they have trouble, they should cover the comparison symbol and decide which symbol belongs.

Write on the board: N + 2 = N x 3. They already know that N represents a number. Now they will “solve” for N using trial and error. They should start with 0 and work up until they find a value for N that makes a true statement. Do #4 – #6 together.

Write “9” on the board with an equal symbol to the left. Explain that you need

9 on a team. So far you have 3. How many more do you need to complete the team? Write: 3 + __ = 9. Explain that this equation represents the same question you have asked them but in numerical form. Fill in the 6. Do #7 – #9 together.

Replace the letters with the given values and solve problems #10 – #11.

The number statement in #12 is not an equation. Because the right side is greater than the left side, select a number on the right to move to the left and write a new number statement with an “=” symbol.

Explain that we use parentheses to change the order (or sequence) of what is done. Read through the section on the order of operations and do #13 – #15 together.

i Problems #2 – #3 and #7 – #9 do not appear on the Student Lesson Sheets. Please read them aloud from the next page.

Problems in which students choose the correct symbol are not located on the lesson itself but appear on Guided Practice D.

Students should be able to find the value of an unknown by performing the same operation on both sides of an equation.

Stretch 3What number is as much greater than 105 as it is less than 177?

Answer: 141

7


7 8 9

4 5 6

2 + (3 x 2) = N + 5

(3 x 4) - 2 = 10 3 x (4 - 2) = 6

61 5 - Y = 0 x (3 + 4) 2 + (8 - 1) = (2 x 4) + ___

M = 8 N = 2 M ÷ N = K = 3 L = 9 L - K =

8 = N + 5N = 3

3 + 6 + 2 ≠ 6 + 8 + 3

N x 4 = 6 + N

N x 2 = 6 - N

N = 2

012

X x 5 = X + 0

X =

9 + B = B x 4

B =

N = 0 0 x 4 = 6 + 0N = 1 1 x 4 = 6 + 1N = 2 2 x 4 = 6 + 2

7 x 3 ≠ 4 x 531 2

10

12

11

13 14 15

NameLesson 3 Date

For each of these problems, replace the letter or the blank with the number that will make the equation true.

An equation is a number statement with an equal symbol. If a number statement is true,the value on the right side will equal the value on the left side. If both sides are notequal, the number statement is NOT true. It is an inequality. You must replace the equalsign with a not equal, greater than or less than symbol for the statement to be true.

The equal symbol ( = ) means " is equal to ".The not equal symbol ( ≠ ) means " is not equal to ".

but

If you had the equation 3 x 4 - 2 = , would you first multiply the 3 and the 4 or first subtract the 2 from the 4?

Therefore, the proper order for 3 x 4 - 2 is (3 x 4) - 2, which equals 10.

Fortunately, mathematicians have developed rules for solving equations involving multiple operations. These rules help make sure everyone gets the same result. First, combine numbers within parentheses. Second, multiply or divide as you come to them going left to right. Third, add or subtract as you come to them going left to right.

For these problems, letters are used to represent numbers. To find the answers,replace the letters with the numbers they represent.

Determine the number that needs to move so the ≠ can change to =. Circle the number and write the new number sentence.

In this inequality, which number can be moved to change the ≠ to = ?

Put "T" next to each true statement and "NT" next to each one that is not true.

To discover the value of N, start with N = 0 and see if it results in a true equation. Ifit isn't true, try N = 1 and so on until you find a value for N that will make a truestatement.

For each problem, find the value for the unknown (letter) that results in a true statement.

not truenot trueThis statement is true, so N equals 2.

Recognizing true and not true number statements; using trial and error to solve forunknowns in an equation; solving algebraic equations; changing a number statementfrom ≠ to =; learning the order of operations when solving an equation; selecting the correct symbol for a number statement 3 + 4 = __ - 2

7 = 9 - 215 ÷ R = 9 - 6

R = 5

3 6 7__ - 4 = 9 - 310 - 4 = 6

7 7 8

4 6

15 - Y = 0

Y = 15

9 = 8 + 1

1

3 + 3 + 6 + 2 = 6 + 814 1411 174 + 9 > 6 + 6

13 1221 20 10 92 x 5 < 9 x 1T NT T

0

0 0 3 3

30

0123


3 + 6 7 + 3

3. = 4. < 5. >

159.97B

44D 769,021E

A 417

H 150

F 9,377

C 10

G 6,781

15. (3, 8, 13, 18)

16. (2, 5, 15, 30)

17. (10, 20, 30, 40)

6. 9 ÷ 4 =7. 4 x 9 =8. 9 - 4 =9. 4 + 9 =

$ .5 72 8.4 9

6.8 7+ 1 9.3 6

$8 7.0 6- 4 5.3 9

$1.97x 8

$5.25x 9

( 212, _____ , 204, _____ , 196 )

A = 8 B = 42B - A =

8 x 12 =

6,3 2 7- 2,4 4 8

7,3 0 5- 4,4 2 8

876x 7

352x 9

9 + 4 + 2 ≠ 7 + 3 + 1

N x 6 = 15 + N N =


Select the correctsymbol.

Film is sold five rolls to a package. Which set shows possible numbers of rolls that might be purchased?

There are 90 people ahead of Barbara in line. She is ____ in line.

5. ninetieth6. ninety-first7. ninety-second

1 hundred thousand, 4 tens, 3 ones, 3 thousands and 7 hundreds

5 thousands, 2 hundred thousands and 6 tens

four hundred sixty thousand, two hundred eighteen

Frank has four sweatshirts. Al has nine sweatshirts. Which equation could be used to find out howmany more sweatshirts Al has than Frank?

Miguel went to the fair 3 days in a row. He rode the ferris wheel 4 times each day. He needed 4 tickets per ride. How many tickets did Miguel use?

Rachel caught 5 fish on Friday, 6 on Saturday and 3 on Sunday. Emily caught 8 fewer fish than Rachel. How many fish did Emily catch?

Oksana has drum lessons 6 hours and volleyball practice 5 hours a week. How many hours does Oksana play the drums and practice volleyball in seven weeks?

Which number can be moved to changethe ≠ to = ?

Mandi has 3 scarves. She bought 8 new ones. When she got home she discovered that two of her new scarves were torn, so she returned them. How many scarves does she have now?

Ann has 2 dogs, 7 cats and 3 birds. How many more cats than dogs does she have?

<

208200+ 9417

$41.6755.2915.76

+ 47.25$159.97

23

+ 510

3,1686,132+ 779,377

486

+ 96150

64

+ 3444

103,743460,218

+205,060769,021

83,8792,877

+ 176,781

103,743

205,060

460,218

548 tickets

12x 448

3 x 4 = 12

56

+ 314

14 - 8 = 6

6 fish

$55.29$41.67

$15.76 $47.25

200208

34

96

3,879

2,877

6,132

3,168

77 hours

11x 777

6 + 5 = 11

15 11

13 139 + 4 = 7 + 3 + 1 + 2

3

0123

3 + 8 = 11 11 - 2 = 9

9 scarves 7 - 2 = 5 5 more cats

8

Lesson 4

TEKS ObjectiveStudents will compute the date within the month. (This is a review of previous TEKS concepts).

Students will learn 7 days = 1 week and 1 year = 12 months.

Students will learn the number of days in each month.

Students will learn the abbreviations for days and months.


Lesson PlanHave students suggest 5 different activities for which the duration can be measured in minutes, hours, days or weeks. For example:1. It usually takes 1 _______ to do my daily homework.2. I will probably spend 180 _______ in school this year.3. It usually takes about 6 _______ to fly across the United States.4. It might take 1 _______ to paint the inside and the outside of the house.5. If I added up all the hours that I have slept this month, it would probably add up to between 1 and 2 ______.

Next, point to a day on the calendar and ask one of the students to tell you what the date is. Ask what the date will be in 3 days, what day of the week it was 4 days ago, etc.

Ask how they could figure out the answers if they did not have a calendar to look at. Do problems #1 – #2 with the class.

Days/Months Abbreviations OptionReview with the class the abbreviations for days and months.

Read through the next calendar section with the class. One simple rhyme that might help students remember the number of days in each month is:

Thirty days hath September, April, June, and November; All the rest have thirty-one Excepting February alone:

Which has but twenty-eight, it’s fine, ‘Til leap year gives it twenty-nine.

Stretch 4Brian, Peggy and Blaine collect U.S. and foreign stamps.

Brian has 9 U.S. stamps.Blaine has 13 stamps in all.Peggy has 3 times as many U.S. stamps as Blaine has U.S. stamps. Blaine has half as many foreign stamps as Brian.They have a total of 63 stamps, 37 of which are U.S. stamps.

How many stamps of each kind do they have?

Answer:

Brian

U.S. Foreign Totals

12

8

6

26

9

21

7

37Totals

Blaine 13

63

Peggy


9


392A

1 2

8 9 1010 + 14 = 24

NameLesson 4 Date

Dear Parents,

You can help your child by getting involved with homework. You maynot always have time to help, but just showing an interest may reallymotivate your child.

The problems on the back of this Lesson Sheet were done in class.The children check their work by adding the answers of two or moreproblems, then comparing the result to the CheckAnswer that weprovide above and to the right of the problem.

Sometimes we find students will add the answers incorrectly rather thanask for help. If parents and teachers work together, we can help studentslearn the value of asking for help now, rather than being satisfiedwith a wrong answer.

Homework is available four nights a week and will be located on theLesson Sheet where this letter appears starting with Lesson 6. Whenever you have the time, please check to see that the answers on your child's homework are added correctly and the calculations are shown.

With your assistance, I look forward to a successful year in mathematics.Please contact me if you need any clarification of our math program.

Sincerely,

I have read this letter and I will do my best to help at home.

_________________________________________________Parent's signature

Today is Wed, Jul 8. Two weeks from this Friday will be Jul _____ .

Here are the abbreviations for the days and months: Sunday (Sun) Monday (Mon) Tuesday (Tues) Wednesday (Wed) Thursday (Thur) Friday (Fri) Saturday (Sat) January (Jan) February (Feb) March (Mar) April (Apr) May (May) June (Jun) July (Jul) August (Aug) September (Sept) October (Oct) November (Nov) December (Dec)

Today is Tues, May 19.May 10 was on ________ .

W Th F24

The calendar we use is called the Gregorian calender (after Pope Gregory). It was introduced in 1582. You might look up the Julian calendar, which was used before 1582. It was named after Julius Caesar. See how it differs from the Gregorian calendar. Here is one way to determine how many days are in each of the 12 months in a year.

Make a fist with your left hand. With the back of your left hand facing you, list the months of the year starting with January on the knuckle of your little finger. Continue through July using the space between each knuckle and the knuckle itself.Start again with August at the same place you used for January. The months thatland up high on a knuckle have 31 days, while the others down between the knuckleshave 30 days (except February). February has 28 or 29 days, depending on whetherit is a leap year or not. Determining leap year is discussed in Lesson 41.

Jan Mar

Feb

Apr

May

Jun

Jul

Aug

Sept

Oct

Nov

Dec

Fist ofleft hand

Fist ofleft hand

Computing the date within the month; learning the abbreviations for days and months; learning 7 days = 1 week and 1 year = 12 months; learning the number of days in each month

Sunday

19 - 7 = 12 S M T10 11 12


937,756B

7,449D $128.55E

A 38

H 103

F 6,035

C 89

G 1,150

500

300400

200100

Kelly Dawn Tim

7. (2, 4, 6, 8)

8. (12, 20, 24, 28)

9. (14, 18, 22, 26)

6. 60 - 20 = 7. 60 - 15 =8. 20 - 15 =9. 15 + 20 =

4 98 6 7

5,1 3 8+ 1,3 8 6

5,0 0 5- 3,2 2 6

________ ________ ________ ________

(4,814; 4,481; 4,148; 4,841)

7 dimes = ______ nickels

Kelly50.

Dawn100.

Tim150.

10 = ____ - 2

____ + 4 = 17

J = 7 K = 9J x K =

4 x 7 3 x 9

25. = 26. < 27. >

N x 7 = 7 ÷ N

N =

5 + N = 9

N = r =

9 - 2 = r 2 + (3 x 2) = Z + 5

Z =

$9.12x 8

$3.86x 9

9 x 12 =


Picking Berries How many berries were picked on Friday?

How many fewer berriesdid Dawn pick on Tuesdaythan on Wednesday?

Which person picked more berries each day thanthe day before?

Days

Berri

es

M T W T F

If DVDs are sold in sets of four, which set shows possible numbers of DVDs that could be bought?

2 thousands, 1 hundred, 7 hundred thousands, 6 tens, 3 ten thousands and 9 ones

two hundred thousand, nine hundred eighty-seven

forty-six hundred

It is 3:15. Jonah can go out and play after he helps his mother for 20 minutes. Which equation shows how many minutes after 3 it will be when Jonah has finishedhelping his mother?

Sopea takes a weekly 9-mile kayak trip down the river. How far does she kayak in 8 weeks?

three dollars and eighty-seven cents

sixteen dollars and ninety-eight cents

Pamela swims 2 miles and runs 5 miles a day. She also drives 4 miles to work each day. How much farther does she run than swim after 2 days?

Put the numbers in order from least to greatest.

Which number is first? _________

Select the correct symbol.

87,440+ 17,449

277

+ 438

732,169200,987

+ 4,600937,756

723

+ 1489

4,1481,779

+ 1086,035

96

1213

+ 63103

$ 3.8716.9872.96

+ 34.74$128.55

900100

+ 1501,150

250-150100100 berries

350300

+250900900 berries

14

732,169

200,987

4,600

35

72 miles9 x 8 = 72

$3.87 $16.98

5 - 2 = 3

3 + 3 = 6

6 miles farther

7,440

1,779

4,148

4,148

4,481 4,814 4,841

12

13

63

>28 27

1 01

5 + 4 = 947

9 - 2 = 7

6

8 = 3 + 53

$72.96 $34.74 108


10

Lesson 5

TEKS ObjectiveStudents will solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q, and will add and subtract fractions and mixed numbers with like denominators.

Students will determine if the given values make one-variable, one-step equations or inequalities true.

Students will extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0.

Students will define numerator and denominator and will determine the fractional part of a group of items when modeled or given in words.

PreparationFor each student: scissors, Circle Fraction Pieces, Fraction Pieces I and II (masters on M18, M19 and M21)

For the class: a piece of paper cut in half and labeled “One Half”

Lesson PlanFractions describe a portion of a group. The number under the line (denominator) represents the total number of parts in the group. The number above the line (numerator) indicates the part of the total group to which you are referring.

Ask 3 boys and 2 girls to come forward. Ask the class how many total students have come forward. Then ask them how many boys they count. Ask, “What fraction would represent the boy’s portion of the group?” Repeat this with several groups of students.

Group students in threes and have them cut out the fraction pieces. The fraction pieces are labeled in three different ways. The students should understand that they can describe fractions in three ways. Each “whole” is the same size so the fractions can be compared.

Ask the class how your paper labeled “One Half” compares to theirs. (Yours is larger because the whole it came from was larger.)Ask them how both pieces can be labeled “One Half” even though they are different sizes or have perhaps been cut in different ways—horizontally, vertically, diagonally, etc. (Fractional parts are related to the whole of which they are a part.)

Have the students cut out their circle fraction pieces. Ask them if the “one-fourths” bars can be combined with the “one-fourth” pieces of the circle. (No. The “wholes” are not the same, so the parts of the wholes would not be the same.)

Explain that if they add thirds, their answers will be in thirds. Some students will want to add the denominators and write their answers in sixths. Manipulating the pieces should discourage this, however. Keep the pieces available for the students.

Stretch 5Write these three number statements on the board:

AB ÷ C = D, ( A + A ) x C = D and C - (A + A) = A.

The number statements have been written in code. Each letter represents a digit 0 – 9. What are the three number statements in numerical form?

Answer: 18 ÷ 3 = 6, (1 + 1) x 3 = 6 and 3 - (1 + 1) = 1

11


14

+ =310

410 10 - =4

848

0- =56

26 6

14

14

1 2

3

5 6

4

7

9

8

12

13

10 11

14 15

24

46

26

23

25

35

713

35

14

+

131323

3

6

9

2019181716 21

4 fifths- 2 fifths

3 tenths+ 4 tenths

2424-

46

16

+39

79

-

2 8

3 13

13

+

1

7 25

35

-

6

NameLesson 5 DateDefining numerator and denominator; determining the fractional part of a group of items when modeled or given in words; learning that the whole is the sum of its parts; adding and subtracting fractions and mixed numbers with like denominatorsThe bottom portion of a fraction refers to the total number of parts in the group and is called the denominator. The top portion of the fraction is the part of the total group that you are referring to and is called the numerator. For each problem, fill in the numerator and the denominator and then select the correct fraction from the choices.

of the figuresare circles. are shaded.

When writing fractions in words,

is written three fifths. is written seven thirteenths.

Nine children are playing. of them are boys. How many girls are playing?

Corina has 15 apples. Seven fifteenths of them are red. How many of her apples are not red?

You can think of fractional parts as pieces. They can be added or subtracted.

Fill in the missing number.

3 fourths - 2 fourths = 1 fourth 5 sixths - 2 sixths = 3 sixths

4 sevenths+ 2 sevenths

6 sevenths

4 eighths- 3 eighths

1 eighth

How many fourths arethere in 3 wholes?

Four strips of ribbon are cut intohalves. How many pieces will there be?

Draw pictures and use addition or multiplication to compute the answers.

39

Notice that the answer for #15 is not . The denominator (8) is the number of pieces into which the whole has been divided. It does not change.

00

When adding or subtracting mixed numbers, whole numbers can only be added toor subtracted from whole numbers. Fractions can only be added to or subtractedfrom fractions.

A mixed number is a number that is made up of a whole number and a fraction. 3 is a whole number. is a fraction. 3 is a mixed number.1

414

2

5

2

6

8 apples are not red6 girls

15 - 7 = 89 - 3 = 6

7

8

3

12 fourths 8 pieces

3 x 4 = 12

4 + 4 + 4 = 12

4 x 2 = 8

2 + 2 + 2 + 2 = 8

04

56

492 5 2

38 156= 0

2 fifths 7 tenths


34C

A 44

F $107.29

D 32

B 144

E 20

2

1

00-5 6-10 11-15 16-20

3

4

5

6

21-25

6. 3 x 4 =

7. 3 x 1 =

8. 3 + 4 =

9. 2 x 4 =

$9.33x 7

$8.44x 4

32 = Y x 89 x ____ = 90

5 + 1 + 3 ≠ 4 + 2 + 7

6. 8 + 4 ≠ 7 + 6 8. 9 + 2 > 6 + 4

7. 5 + 9 > 3 + 8 9. 4 x 9 ≠ 6 x 6

N x 4 = 9 + N

N =

P =

96 = 12 x P

15 - A = 0 x (3 + 4)

A = 11 x 9 =

Y =


Dana bought 14 cans of paint.

are red, are silver, are gold,

is black and are white.

How many of her paint cans were

not silver? _______ white? ____

gold? _______ not red? ____

514

114

214

314

314

How many fifths arethere in 3 wholes?

Boxes of Cookies Sold How many students sold between 11 and 20 boxes of cookies?

How many students sold at least 16 boxes of cookies?

How many students soldfewer than 6 boxes of cookies?

Boxes

Num

ber o

f Stu

dent

s

Siri waited an hour to get tickets for a concert. Dani stood in line three times as long as Siri. Which equation shows how long Dani stood in line?

Melody paid for dinner with a ten-dollar bill. Her change was two one-dollar bills, three quarters and two dimes. How much was her dinner?

Barney had $1.32. His father gave him a dime and he spent a quarter. How much money does Barney have now?

Which number can be moved to change the ≠ to = ?

Which statements are true? Days in March?

______ days

1 year = _____ months

Today is Sunday, January 25. Three weeks ago last Friday was January _____.6

788

+1544

21231

+ 99144

11329

+ 732

$7.051.17

65.31+ 33.76$107.29

1542

10+ 334

116

+ 320

2 9

11 3

153 x 5 = 15

6 + 5 = 11

5 + 1 = 6

11 students

6 students

3 students

3

$2.00.75

+ .20$2.95

$10.00- 2.95$7.05

$7.05

$1.32+ .10$1.42

$1.17

$1.42- .25$1.17

$65.31

$33.76

410

9 13

1111

5 + 3 + 1 + 2 = 4 + 7

12 13 11 10

14 11 36 36

3 0123

896 = 12 x 8

7

15 - 15 = 015

99

31

12

2

F S S23 24 25

23-21

2

12

Test 1 - AssessmentTest 1This test is an assessment test covering the concepts on Lessons 1 – 30. You can download the TEKS correlations from our website: www.excelmath.com/tools.html

If the class as a whole scores an average of 90% or better, feel free to jump ahead to Lesson 31. If they score below 90%, copy the Score Distribution and Error Analysis charts provided on pages i.20 - i.22 in the front of this Teacher Edition and online:www.excelmath.com/tools.html

Record each student’s identification number on a line, indicating the number of problems he missed. This distribution of test results will help you analyze their work and show parents how their child did in comparison to the rest of the class without revealing names of students who scored higher or lower than their child.Q# Lesson# Concept

1 1 Addition: 4 digits with regrouping

2 1 Subtraction: 4 digits with regrouping

3 12 Multiplication: 3 digits x 2 digits

4 18 Equivalent fractions

5 14 2-D figures: rhombus

6 10 Measurement equivalents

7 25 Sum of the angles in a rectangle

8 1 Number words less than one million

9 48 Simplification of improper fractions

10 21 2-D figures: pentagon

11 1 Number words less than one million

12 10 Measurement equivalents

13 2 Sequences: counting from 1 to 12

14 25 Equilateral triangles

15 6 Multi-step word problems

16 19 1/2 to 1/9 of a group of items

17 9 Multi-step word problems with division

18 7 Deductive reasoning

19 1 Multi-step word problems

20 24 Expanded notation

Use tally marks on the right side of the chart to record how many students missed a particular question. There is no need to review the entire test, but you could go over problems missed by a number of students.

The tables below indicate which questions reflect which objectives, and where that content is taught in this curriculum. Use this guide if you want to have students review one or two specific lessons. If the class is weak in several areas, we recommend you continue through Lessons 6 – 30.

Feel free to skip the starred problem if your students have not learned rotational symmetry.

Q# Lesson# Concept

21 28 Addition of fractions

22 6 1-digit divisor into a 3-digit dividend



25 25 Angle estimation

26 3 Equations with parentheses

27 5 Fractional parts of groups of items

28 20 Rounding to the nearest hundred

29 23 Lines of symmetry

30 20 Rounding to one non-zero digit

31 14 2-D figures: parallelogram

32 11 U.S. customary and metric units

33 17 Lowest common multiples

34 3 True and not true number statements

35 25 Obtuse angles

36 24 Numbers to trillions

37 22 Fractions: greatest and least value

38 23 Rotational symmetry

39 30 Area of a rectangle

40 8 Listing possibilities


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14

Lesson 6

TEKS ObjectiveStudents will multiply and divide positive rational numbers fluently.

Students will recognize multiplication and division fact families.

Students will divide a one-digit divisor into a three-digit dividend with a two- or three-digit quotient with no regrouping or remainders.

Students will solve multi-step word problems involving division.

Students will learn the terminology for multiplication and division.

PreparationFor each student: Number Chart, Ones and Tens Pieces, Hundreds Pieces, Hundreds Exchange Board (masters on M10, M13, M14 and M16), optional calculator

Lesson PlanIn problems #1 – #2, provide one multiplication fact and ask students to fill in the other multiplication fact and the two division facts that are in the same family.

Write the following problem on the board:

As the students go through the following process with the pieces, write on the board what they are representing.

Ask the students if they can divide the one hundred into two equal groups. (Yes. Exchange the one hundred for ten tens.)

On the board, draw a line under the “1” and “2”. Next, ask the students if they

can divide the twelve tens into two equal groups, and if so, how many will be in each group? (yes, six tens)

Are there any tens left over? (no)

Subtract the 12 tens that they have divided and repeat the process with the 4 ones. Ask if the number 124 is now divided into two equal groups. (yes)

Ask the class how they know. Is anything left over? (no)

Explain that when the dividend is a dollar amount, the decimal in the quotient will be directly above where it is in the dividend.

Go through problems #3 – #7 together, checking each answer with multiplication and, if time permits, with repeated subtraction using a calculator.

Do #8 together and review the terminology for multiplication and division problems. Give your students the answers to the starred problems if they have not been taught these concepts (so they can complete the CheckAnswers).

i Problems #1 – #2 do not appear on the Lesson Sheets. Please read them aloud.

Stretch 6Shirley ran 15 km in January.She ran 25 km in February. She ran 35 km in March.

If she continues at this same pace, how many kilometers will she run in July?

Answer: 75 km

2 124

15


x x x x

1

3

8

4 5 6 7

2

x

5 7

x x

4 0 0 5 6 7

xx

$ 1 . 2 62$ 9 . 3 938 8 62

C 9,150

D 5,098

B 14,179

A 620,939

9 1 93 7

8 5 9+ 6,7 0 8

8,1 0 0- 6,2 3 6

474x 8

750x 9

398x 6

4,0 0 1- 2,3 1 8

6,6 0 1- 3,2 5 7

NameLesson 6 Date Homework

For each multiplication fact that is given, write the other multiplication and divisionfacts that are in the same family.

Check each answer with multiplication.

Parts of a division problem

divisor dividend

Parts of a multiplication problem

xmultiplicand

multiplierproduct

(factor)(factor)

quotient + remainder

Erin is fifteenth in line. There are _____ people ahead of her.

4 hundred thousands, 1 ten, 3 thousands, 7 ones and 9 hundreds

two hundred seventeen thousand, eight

Chloe has 2 kites with hearts on them and 4 with birds. Kylie has the same number of kites as Chloe. How many kites do they have in all?

This morning the temperature was 67º F. By lunchtime it had dropped 4º but then the sun came out and it has now gone up 8º. What is the temperature now?

Recognizing multiplication and division fact families; learning division facts withdividends up through 81 and dividends that are multiples of 10 (to 90), 11 (to 99) or12 (to 96); dividing a one-digit divisor into a three-digit dividend with no regrouping or remainders; solving multi-step word problems involving division

Ten chocolate and fiveoatmeal cookies were divided equally among 3 children. How many cookies did each child get?

86

48

68

486

848 8

648

123

36

31236

31236 12

336

15 ÷ 3 = 510 + 5 = 15

5 cookies

4432

886

805

400

817

567

8 0

-4 00 0

8 1

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0

$ .632

$1.26

$3.133

$9.39

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0 9- 9

0

0 3- 3

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4 4 3

0 6- 6

0

0 8- 8

-8

14

403,917 217,008

8,5231,864 3,792

12 kites

2 + 4 = 6 6 + 6 = 12

67- 463

63+ 871

71º F

6,750 2,388

1,683 3,344

8,5231,864

+ 3,79214,179

126,750

+2,3889,150

403,917217,008+ 14620,939

711,683

+3,3445,098


6. 18 - 3 =

B ÷ 6 = 5

7. 18 + 3 =

8. 18 ÷ 3 =

9. 18 x 3 =

72 ÷ 12 =

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5 x 3 = 15

126B

11D 26E

A 26

H 129

C 27

G 394

79

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7. 127

8. 712

88

28 8

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27

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7. 5 + 9 < 8 + 8

8. 7 + 7 > 4 + 9

9. 4 x 6 = 2 x 12

3 + ( 6 x 4 ) 9 x ( 2 + 1)

> = <26. 27. 28.

7 + (5 - 0) = R x 4

R = 8 x 12 =

B =


Miguel has 18 peanuts. He would like to divide them equally among 3 friends. Which equation shows how many peanuts each friend will get?

Which fact doesnot belong?

product ____

numerator = _____

are shaded.

Two pies are cutinto eighths. Howmany pieces arethere?

Deon swims six laps twice a day. How many laps does Deon swimevery week?

Using the fewest coins,how many quarters arethere in 42¢?

Dan organized a 10 km run. He had 348 entries one week before the event. In the last week, 7 canceled and 20 entered late. How many people ran in the race?

Which statements are true?


Today is Friday, May 21. May 15 was on a _________ .

1. Monday2. Sunday3. Saturday

Today is Monday, December 13. December 20 will be on a _______ .

1. Friday2. Monday3. Sunday

Days in September? ______ days

1 week = _____ days 6

6

63126

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273

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6

4

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84 laps

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30

7 x 12 = 84

25¢10¢5¢

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361 people

341+ 20361

14 16

14 13

24 24

=3 + 24 = 27 9 x 3 = 27

12 = 3 x 4

5

3

S S M T W T F

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15 16 17 18 19 20 21

96

Monday

Saturday

30

7

16

Lesson 7


Students will determine if there is sufficient information to answer the question in a word problem.

Students will solve word problems using deductive reasoning and will determine what information is needed to answer the question in a word problem.


Lesson PlanRead through problem #1 on the Student Lesson Sheet with the class. The second sentence states that Eduardo is older than Eric. So draw a vertical line over Eduardo that is longer than the line over Eric.

In the third sentence, we learn that Hugo is younger than Eric. Therefore, the line over Hugo should be shorter than the line over Eric. Hugo’s line is the shortest, so Hugo is the youngest.

Read through #2 with the class. It requires two steps. In order to calculate how late Tia was, we need to calculate how late Will was (sentence #4). From sentence #2 we know that Don was 13 minutes late, and from sentence #3 we know that Will arrived five minutes earlier than Don. Therefore, Will arrived eight minutes late (13 - 5 = 8). From this answer, we calculate that Tia arrived 11 minutes late because we read in sentence #4 that she was three minutes later than Will ( 8 + 3 = 11).

Read problems #3 – #4 with the students and ask them what information they need to answer the questions. Have them select

“not enough information” or “enough information” accordingly. If possible, they should write an equation with the solution if they have enough information.

Read problems #5 – #6 with the students and have them determine whether or not each choice will provide the information that is needed to solve the problem.

After they have chosen the correct answer, show them the equation they would use to solve the problem.

When these problems appear on their Lesson Sheets, the students should try to write the equation that is used to solve the problem. This demonstrates that they understand the concept. You may want to write the equation as a class if some students are having difficulty with the concept.

Then give the class the following word problem: “Jonah bought 3 books at $6.95 each and 4 shirts at $12.35 each. How much did he spend?” (Answer: $70.25)

3 x $6.95 = $20.85 4 x $12.35 = $49.40 $20.85 + $49.40 = $70.25

Remind the class to show their work as they solve the Guided Practice and Homework word problems.

Stretch 7Todd, Chris and Rod have 30 birds.Rod has five times as many as Todd.Todd has one fourth the number that Chris has. How many birds do they each have?

Answer: Todd - 3, Rod - 15, Chris - 12

17


1 2

3 4

5 6

Eric Hugo Eduardo

C 11,931

D 6,721

B 6,974

A $98.37$4 7.2 3- 1 2.7 9

$4.57x 9

$2.85x 8

(151, 162, _____ , 184, 195)

1,9 6 71,5 4 6

8 5 3+ 2,6 9 5

1,3 9 51,1 8 9

6 8 7+ 1,4 9 7

7,0 3 6- 2,1 6 9

8,5 0 0- 6,5 6 2

846x 8


Lawrence has 2 aunts and an uncle. Raquel has aunts and uncles. How many more uncles does Raquel have than Lawrence?

Oliver and Bob were playing basketball. Oliver made five baskets. Bob made four more baskets than Oliver. How many baskets did Bob make?

A. enough informationB. not enough information

A. enough informationB. not enough information

Tristan has two flower gardens in his yard. In one gardenhe has 24 flowers. Whatinformation is needed to find out how many flowers are in the other garden?a. how much he paid for the flowers

b. the total number of flowers

c. how many flowers are roses

a. the amount of paint she used

b. time it took to paint each picture

c. number of pictures Sherry painted

Sherry painted 5 more pictures than her friend did. What information is needed to find out the number of pictures her friend painted?

Solving word problems using deductive reasoning; determining if there is sufficientinformation to answer the question in a word problem; determining what information isneeded to answer the question in a word problem

Tia, Will and Don were late to school. Don arrived 13 minutes late.Will was 5 minutes earlier than Don.Tia was 3 minutes later than Will. How many minutes late was Tia?

Eric, Eduardo and Hugo are brothers. Eduardo is older than Eric. Hugo is younger than Eric. Who is the youngest?

Andrew tried to catch 20 waves when he went surfing. He fell 3 times and missed the wave twice. How many waves did he ride?

Hugo had 16 shells. Leona had 25 shells. They gave 8 shells to Hilda. How many shells do Hugo and Leona have now?

Willie had 15 bags of cement. He used 8 for a patio and 4 for a sidewalk. How many bags of cement does he have left?

(Sherry's pictures) - 5 = number of pictures her friend painted

(Total number of flowers) - 24 = number of flowers in the other garden

11 minutes

13 (Don) - 5 earlier = 8 (Will)8 (Wil l) + 3 later = 11 (Tia)

5 (Oliver) + 4 = 9 (Bob)

$34.44 $41.13 $22.80

173

20- 515

15 waves

2 + 3 = 5

33 shells

16+ 25

41

41- 833

3 bags left

8 + 4 = 1215

- 123 7,061

4,768

4,867

1,938

6,768

33173

+ 6,7686,974

$34.4441.13

+ 22.80$98.37

154,768

+ 1,9386,721

37,061

+ 4,86711,931


6B

76E

A 14,511

H 80

F 123

C 23

G 47

911

2 4

+ 3 - 1

310410

610510

6

- 4

910910

4. 18 ÷ 3 = 5. 3 x 6 = 6. 6 x 6 = 7. 6 x 3 =

7. (12, 18, 21, 27)8. (1, 3, 9, 15)9. (4, 7, 10, 13)

8 ÷ 2 = 4

6. 6 x 3 =

7. 3 + 6 =

8. 6 ÷ 3 =

9. 6 - 3 =

V = 66 W = 11V ÷ W =

a x (18 ÷ 3) = 4 x (3 x 3)

a =

750x 9

338x 6

819x 7

1 8 33 1 4 772 4 665 x 11 =

64 ÷ 8 =

10D 810


denominator = _______

Rob has 5 hats and three fifths are pink. How many of his hats are not pink?

How many halves arethere in 3 wholes?

4 fifths- 3 fifths

2 fourths+ 1 fourth


Richard can buy caps in packages of three. Which set shows the number of caps he could buy?

dividend ____

Christa wrote threeletters a day for sixdays. Which equationshows how many totalletters she wrote?

For each of her six dogs,Mora bought 7 chew toys, two bowls and a leash. How many items did Mora buy?

Today is Friday, December 15. December27 will be on a ___________ .

1. Monday2. Wednesday3. Friday

Days in January? ______ days

Rosalee cooked twenty-nine hamburgers. She ate one and gave two to each of her guests. Therewere none left over. How many guests did she have?

6,7502,028

+ 5,73314,511

23

+ 16

66

+ 1123

6141

+ 21123

6608

+ 680

78

55+ 676

142

+ 3147

112 hats

5 - 3 = 2 6 halves3 x 2 = 6

1 fifth

3 fourths

75 310110 2

6183618

8

18

18

9

3 60 items

10 x 6 = 60

7 + 2 + 1 = 10

14 guests

28 ÷ 2 = 1429- 128

6

a x 6 = 36

6 9

6

F S S M T W22 23 24 25 26 27

Wednesday 15+ 722

6,750 2,028 5,733

6 1 2 1

-1 40 7-70

-1 80 3-30

4 1

-2 40 6-60

55

8

31

5

3

710

2

110

10 810

+

18

Lesson 8

TEKS ObjectiveStudents will give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.

Students will write one-variable, one-step equations and inequalities to represent constraints or conditions within problems.

Students will understand that solving an equation or inequality is a process of answering a question: which values from a specified set, if any, make the equation or inequality true?


Lesson PlanWhen solving a problem, it is sometimes useful to list all the possible solutions. This strategy works best when there is only a small number of possible solutions.

Read the example on the Lesson Sheet. The first sentence identifies the first parameter: the two numbers in the solution must add to 8. Therefore, list all the combinations of two numbers that add to 8. The solution will be one of these choices.

The second parameter is that one of the numbers will be 2 more than the other. The students should look at the choices and pick the one that has a number 2 more than the other. 5 + 3 fits both parameters.

Go through problems #1 – #2 on the Student Lesson Sheets using the above process.

The two rows in the chart in #3 are related. The top row shows the number of rows of plants. The bottom row shows the number

of plants in each row. The students should first determine by what number each row is counting. (The top row is counting by 1, and the bottom row is counting by 6.) They can then fill in the missing number. Do #3 together.

Use the Guided Practice portion of your math lesson to ask students to “explain their thinking.” Texas Knowledge and Skills (TEKS) stress the importance of “students making sense of mathematics by describing their thinking.”

Asking students to explain their work will help you to determine the students’ depth of understanding and will give you a chance to clear up any misconceptions.

Stretch 8Write on the board:

C x C = C

D x A = B

D + A = H

E x E = F

K + G = CD The number statements are written in code. Each letter represents a digit 0 – 9. What are the number statements in numerical form?

Answers: 1 x 1 = 12 x 4 = 82 + 4 = 63 x 3 = 9 5 + 7 = 12

19


30

2 3 4 5

12 18 24

6

3

1 2

C 859,474

B $181.48

A 9,355

(3,773; 3,373; 3,337; 3,737)

________ ________ ________ ________

16.<

17.>

3,883 3,388

$ .4 92 5.6 0

1.8 7+ 1 3.9 8

$7.34x 8

695x 7

6,9 1 1- 2,4 6 8


rows of plants

number of plantsin each row

Solving word problems by listing possibilities or by making a chartMaurice and Donnie have 8 marbles. Maurice has 2 more marbles than Donnie.How many marbles does Donnie have?Make a list of the possible answers: ( 8 + 0 ) , ( 7 + 1 ) , ( 6 + 2 ) , ( 5 + 3 ) and ( 4 + 4 ).

These are possible answers because each pair of numbers adds to 8, which is thetotal number of marbles. The second sentence says that Maurice's number is 2 morethan Donnie's. Which pair of numbers has one number that is 2 more than the other?

Answer: ( 5 + 3 ). Maurice has 5 marbles and Donnie has 3 marbles.

Go through both steps in order to solve each of these problems.

One way to solve the problem is to create a chart and look for patterns.

While visiting a park, Gary noticed that in one area the gardener designed the flowerswith 12 plants in the second row, 18 in the third, 24 in the fourth and 30 in the fifth. Ifthis pattern continues, how many plants will be in the sixth row?

April and Ivy read 9 books over their summer break. April read 1 less book than Ivy. How many books did April read?

Micah and Ruben have 6 belts. Micah has 4 more than Ruben. How many belts does Ruben have?

5 ten thousands, 4 tens, 8 hundreds, 2 ones and 7 hundred thousands

one hundred thousand, fifty-nine

fifty-two hundred

Put the numbers in order from greatest to least.

Which number is third? _________

thirty dollars and six cents

fifty dollars and seventy-six cents

Draw the correct symbol ( < or > )between the pair of numbers.

Days in June? ______ days

36

4 books 1 belt

36 plants

(0+9) (1+8) (2+7)

(3+6) (4+5)

(0+6) (1+5)

(2+4) (3+3)

750,842

100,059

5,200

3,773 3,737 3,373

3,373

3,337

$30.06

$50.76

>

$41.94 $58.72

4,865

30

4,443

$30.0650.7641.94

+ 58.72$181.48

1730

4,443+ 4,865

9,355

3,373750,842100,059+ 5,200859,474


56B

20D 67E

A 24

H 94

C 79

G 80

910

6. 7. 8.17

27

71

48

18

5+ =

67

47

2- =

1

2

+ 18

38

28

-

7868

384

1-

6. 5 x 9 = 7. 45 ÷ 5 = 8. 9 x 5 = 9. 45 ÷ 15 =

7. 8.

12. Andres, Brooke, Derrick13. Derrick, Andres, Brooke14. Andres, Derrick, Brooke

5x 420

6 + 2 + 1 ≠ 7 + 5 + 3

( 3 x 4 ) + 7 6 x ( 2 + 1 )

> < =36. 37. 38.

N x 4 = 12 + NN =

4 x (7 - 4) = (2 x 4) + K

K =

4 2 66

4 2 07

12 x 6 =

36 ÷ 9 =

6F 48


numerator = ____

of the figuresare circles.

Three boards are each cut into ninths. How many pieces are there?


Brooke, Derrick and Andres ran in a race. Brooke finished between Derrick and Andres. Derrick wasn't first. In what order did they finish the race?

Miguel ate 3 carrots and 5 grapes. He also ate some cherries. How many more cherries than carrots did he eat?

enoughinformation

not enoughinformation

Katy, Jess and Elton went to a show. Elton was 13 minutes late. Jess was 5 minutes earlier than Elton. Katy was 3 minutes later than Jess. How many minutes late was Katy?

multiplier ____50¢ = ______ nickels

Brielle bought 89 lb ofice. She used 41 lb for snow cones and dividedthe rest evenly between 6 coolers. How many lbwill be in each cooler?

Vanessa had 52 pennies. She gave 14 of them to a friend and then found 6 more. How many pennies does she have now? Which number can

be moved to changethe ≠ to = ?


Today is Wednesday, January 14. January5 was on a ___________ .

1. Friday2. Wednesday3. Monday

98

+ 724

449

+ 356

472

+ 379

1184

+ 7194

610

+ 420

364

+ 2767

1260

+ 880

9

1

7

27 pieces3 x 9 = 27

8

7

3 338

18

459

453

B DAWe are not told howmany cherries he ate.

11 minutes

E 13 - 5 = 8 J

J 8 + 3 = 11 K

410

8 lb

48 ÷ 6 = 889- 41

48

52- 14

3844 pennies

Monday38+ 644

9 15

12 123 + 6 + 2 + 1 = 7 + 5

>12 + 7 = 19 6 x 3 = 18

401234

12 = 8 + 4

3 8

4

M T W 5 6 7

14- 7

7

7 1

6 0

-4 20 6- 6

0

-4 20 0

72

4

33

38

18

6 48

+

20

Lesson 9


Students will learn division facts with remainders with dividends up through 81.

Students will solve word problems involving division with remainders.

PreparationFor each student: two copies of One to Ten Number Pieces (master on M15)

For the class: items to model the word problems

Lesson PlanWrite, “How many 2s are there in 7?”

Have the students take out a “7” strip and the “2” strips. Ask them to cover up the “7” strip with as many “2” strips as they can without going over the edges of the “7”. If there is any space left over, see how many ones it will take to finish covering the “7”.

Ask how many groups of 2 went into 7. (3) Ask the class if 3 groups of two remind them of anything else they have learned. (6 is a multiple of 2; it is the largest multiple of 2 that goes into 7 without going over 7.)

Remind the students that just as multiplication is a faster way of adding, division is a faster way of subtracting.

For problems #1 – #5 on the Student Lesson Sheets, students should determine the number that when multiplied by the divisor results in the value that comes the closest

to the value of the dividend without going over it. They should then try to mentally subtract to determine the remainder.

Read through the division word problems in #6 – #9 and do them together.

Stretch 9Nine people are in a room.If they each shake hands one time with every other person, how many handshakes will there be?

Answer: 36 handshakes

Write the answer on the board so students can model it:

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36

21


3 r 1

3

2 7

2 7- 6

1

3 r 25 1 7

- 1 52

3 r 68 3 0

- 2 46

1 2 3

6 7

4 5

8 9

2 534 77 3 58 5 06 7 88

C 2,518

D 2,189

B 675,640

A 6,1855,6 5 4

- 3,2 7 9

611x 4

240x 9

5,2 8 5- 1,4 9 6

a =

2 = 14 - a

NameLesson 9 Date HomeworkLearning division facts with remainders with dividends up through 81; solving word problems involving division with remainders

Divide 7 into 2 equal groups.

What multiple of 2 ( 2, 4, 6, 8, ...) comes closest to 7 without going over?

Divide 7 by 2. 3 x 2 is the closest multiple. Put the 3 over the 7. Multiply2 times 3, and subtract 6 from 7. There is 1 left over. When you try to divide7 into 2 equal groups, you get 3 in each group with a remainder of 1.

The "r" stands for remainder.

Erasers are sold 5 to a box. Violet wants to buy erasers for 17 students. How many boxes will she have to buy?

Naomi has 25 flowers. A vase will hold 4 flowers. How many vases does she need?

Sometimes a problem requires two answers.

Hiroko bought 30 pears for her 8 friends. After dividing them equally, how many pears did each friend get? How many pears were left over?

Grace divided 26 toy cars equallyamong 7 boys. How many cars did each boy get? How many cars were left over?

3 pears each 6 left over

4 boxes

For each of these problems try to mentally subtract to find the remainder.

Aaron gives tennis lessonsthree hours per day, four timesa week. How many hours oflessons does he give in sixweeks?

6 hundreds, 3 ten thousands, 1 one and 2 hundred thousands

1 hundred thousand,3 tens, 7 ones and4 thousands

three hundred forty-onethousand, two

Rusty got up to bat 32 times. He struck out 6 times and walked 9 times. The rest of his at-bats were hits. How many hits did he get?

24 months = _____ years

Today is Friday, June 4. Two weeks from this Monday will be June _____ .

6 r 125

-241

4

3 r526

-215

7

7 vases

3 cars each 5 cars left over

8 r16 r5 4 r3 8 r2 9 r6

72 hours

12x 672

3 x 4 = 12

6 + 9 = 15

17 hits

32- 15

17

2,375

2,444

2,160

2

24 ÷ 12 = 2

230,601 104,037 341,002

21

F S S M4 5 6 7

14+ 721

3,789

122 = 14 - 12

230,601104,037

+ 341,002675,640

2,3753,789+ 216,185

172,160+ 122,189

722,444+ 22,518


20B

54E

A 86

H 50

F $2.14

C 29

G 27

1724

+

4818 -

7868-

3838

4. 12 x 6 = 5. 72 ÷ 8 = 6. 6 x 12 = 7. 72 ÷ 6 =

13. 14. 15.Hector Jamal Edgar

10 ÷ 2 = 5

6. 16 - 2 =7. 16 ÷ 2 =8. 2 + 16 =9. 2 ÷ 16 =

1 2 3

5 10 15

4

25. 9 + 9 ≠ 3 x 6

26. 15 ÷ 3 < 9 - 3

27. 8 ÷ 8 > 2 x 0

B =

25 ÷ B = 5

p x (2 x 4) = 2 x (4 x 6)

p =

99 ÷ 11 = 12 x 2 =

$ 3 . 6 09$ 3 . 0 93 $ 4 . 9 77

D 68


denominator = _______

How many thirds arethere in 4 wholes? 7 ninths - 3 ninths = ninths

4 sixths + 1 sixth = sixths

8 tenths - 5 tenths = tenths


Hector, Jamal and Edgar met at the gym after school. Hector arrived last. Jamal didn't arrive first. Who arrived first?

Isabella plays soccer. She usuallyscores two goals in each game she plays. What information do you need to estimate how many goals she scored last season?

6. number of minutes she played7. number of goals the others scored8. number of games she played

Milo and Kari ate 7lollipops. Kari ate 3 more than Milo. How many lollipops did Kari eat?

Alyssa has 12 books. That is 3 fewer books than Hershel. Debra has 5 more than Hershel. How many books does Debra have?

dividend ____

Leigh wants to share her 16 books equally with Joseph. Which equation shows how many books Joseph will get?

Fill in the missing number for the buttons needed for each jacket.

jackets

buttons

Which statements are true?

Days in July? ______ days

26279

+ 2486

512

+ 320

45

+ 2029

$1.03.71

+ .40$2.14

8315

+ 650

2024

+ 1054

157

+ 527

24

12 thirds

3 x 4 = 12

4

5

3

0 58

18

7297212

HE1 2 3

J (number of games) x 2 = total goals

5 lol l ipops

(0+7) (1+6)(2+5) (3+4)

20 books

A 12+ 3

H 15

H 15+ 5

D 20

10

8

20

525 ÷ 5 = 5

6 x 8 = 48

8 24

6

9 24

31

$ .4 0

0 0-3 6

$1.0 3

0 0 9-90

- 3

$ .7 1

0 7- 7

0

-4 90

18

58

68

+

22

Lesson 10

TEKS ObjectiveStudents will give examples of ratios as multiplicative comparisons of two quantities and will make tables of equivalent ratios, relating quantities with whole number measurements and finding missing values.

Students will convert units within a measurement system, including the use of proportions and unit rates.

Students will measure temperature and will determine if a measurement is longer or shorter or heavier or lighter.

PreparationFor the class: Standard and Metric Measurements (master on M12), a ruler and a yardstick, measuring cups, quart and gallon bottles, scales that register in pounds and ounces, thermometers, etc.

Lesson PlanMeasure distances around the classroom in inches, feet, yards, centimeters and meters. Depending on the distance measured, ask the students which unit they would most likely use to measure that distance and why.

Use several items as examples. For each item, give the students three possible choices for that item’s weight or length. Do not give choices that are close. Remember, you are only working on gross estimating.

Explain that a temperature in Fahrenheit can be converted to Celsius by subtracting 32 from the Fahrenheit temperature, multiplying the result by 5, and then dividing that result by 9. A temperature in Celsius can be converted to Fahrenheit by multiplying the Celsius temperature by 9, dividing the result by 5, and then adding 32 to that result.

Use a ruler and a yardstick to demonstrate the equivalents in the lesson.

Using the ruler, measure the length of a table in the room. Write on the board the table’s length in feet and inches. Next, tell the class that you want to lay a piece of tape across the table, but the tape can only be measured in inches. Ask them how they would determine how many inches of tape you would need. (Some of the students will multiply the number of feet times 12 and others will add. Either way is acceptable.)

As a class, make a conversion table for problems #3 – #4 showing the number of inches to feet and feet to yards. Do the first few together. See Lesson 40 if you want to introduce ratios at this time:

Go through problems #1 – #4 on the Student Lesson Sheets together. For problems #5 – #8, the students need to determine how the measurements compare to each other. Do these problems together.

Stretch 10John, Jim, Gino and Bert have 32 baseball cards. Jim has 1 more card than Gino.Jim has one third the number that Bert has.John has twice the number that Gino has. How many cards do Bert, John, Jim and Gino each have?

Answer: Bert-15, Jim-5, Gino-4, John-8

Inches Feet

12 1

18 1.5

24

Feet Yards

3 1

4.5 1.5

6

23

5045403530252015105


1 2x 22 4

2 4+ 32 7

3

1 2

4

6 75 8

12

34

56

78 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

12

34

56

78

7075

65

NameLesson 10 DateEstimating measurements; measuring temperature; learning measurement equivalentsfor length, weight and volume; converting measurements using multiplication or division;determining the measurement that is longer or shorter or heavier or lighter

2 feet 3 inches = _____ inches

Sometimes converting a measurement requires 2 or 3 steps.

shorter? longer?a. 22 inchesb. 2 feet = 24 inches

a. 3 milesb. 56 feet

For each problem, draw a circle around the letter representing the correctanswer. Sometimes you will need to convert one of the choices.

heavier?a. 46 ouncesb. 4 pounds

lighter?a. 3 kilogramsb. 26 grams

27 3 yards 2 feet = ____ feet

Inches, feet, yards, miles, centimeters, meters and kilometers are all units of length or distance.

A door might be measured in centimeters or inches, the width of a room in feet, yards or meters, and the length of a road in miles or kilometers.

Cups, pints, quarts, gallons, milliliters and liters are units of volume.A thimble filled with water might be measured in milliliters. If you fill

the gas tank of a car, it might be measured in gallons or liters. Milk is sold by the pint, quart or gallon.

The temperature is _____° F.In Celsius, it is _____° C.

Temperature is measured using a thermometer. Degrees Fahrenheit (F) or Celsius (C) are the terms used to describe how hot or cold it is. The symbol ° represents the word "degrees".

6. grams.7. gallons.8. kilometers.

The weight of a sparrow might be measured in

1. miles.2. kilometers.3. inches.

The height of a small childmight be measured in

The prefix "kilo" means a thousand.

The prefix "milli" means "one-thousandth of".1000 grams (g) = 1 kilogram (kg) 1000 meters = 1 kilometer (km)

1000 milliliters (ml) = 1 liter (l) 1000 millimeters (mm) = 1 meter (m)Other standard measurement equivalents are:

1 yard (yd) = 3 feet (ft) 1 foot (ft) = 12 inches (in)100 centimeters (cm) = 1 meter (m)

12 items = 1 dozen 1 gallon (gal) = 4 quarts (qt)1 pound (lb) = 16 ounces (oz) 1 ton = 2,000 pounds (lb)

Grams, kilograms, ounces,pounds and tons are all

measures used for weight.

A pencil might be measuredin grams, a bird in ounces, a

person in pounds or kilogramsand an elephant in tons.

11

7222

3x 3

9

9+ 211


268C

A 25 r14

F 24

B 46

E 2,000

6. 123

7. 126

8. 612

500

300400

200100

Trout Bass Carp

- =78

68

+ =38

28

- =58

487

3

2

1

9 4

7. (6, 12, 15, 18)

8. (3, 9, 15, 21)

9. (12, 24, 30, 36)

5. 6. 7.Ricky Fran Abby

3 x (4 - 1) = (2 x 2) + B

B =

96 ÷ 12 =

12 x 4 =

8 5 4

9 5 3

2 4 88 5 4 06 6 3 77

22D 78


are shaded.

LakeRoam

LakeSoar

LakeWindy

LakeMudd

Fish in 4 Lakes How many trout are in allfour lakes?

How many more troutthan bass are there inLake Windy?

What is the total number of fish in Lake Mudd?

Fish

Celia can buy stickerssix to a page. Which setshows the number ofstickers she could buy?

Ricky is older thanFran but youngerthan Abby. Who isthe youngest?

Brock and Buzz have been to 10 concerts. Buzz attended 2 fewer than Brock. How many concerts did Brock see?

Kyla visited 29 states onher 3-month trip. She visited12 states in April and another7 in May. How many states did she visit in June?

Boyd wants to put his 18 books into boxes.Each box will hold fivebooks. How many boxes will he need?

Reilly collected 348 rocksover 6 days. 276 were granite and the rest were quartz. If he collected the same number of quartz rocks every day, howmany did he collect each day?

Today is Monday, January 7. January22 will be on a ___________ .

1. Monday2. Tuesday3. Wednesday

Days in November? ______ days

1065

+ 425

259

+ 3046

612

+ 624

8483190

+ 91268

1,050350

+ 6002,000

6

12

400200400

+ 501,050

50300

+ 250600

1,050 trout

600 fish

400- 50350350 more trout

18

58

18

5

4

5

A R Foldest youngest

6 concerts

(1 + 9) (2 + 8)(3 + 7) (4 + 6)

(5 + 5)

10 states

12 + 7 = 19

29 - 19 = 10

4 boxes

3 r31 8

- 1 53

5

12 quartz rocks72 ÷ 6 = 12

348- 276

72

43

9 = 4 + 55

Tuesday

M T21 22

7+1421

8

48

30

6 r6

- 4 86

5 r8

- 4 58

3 1

-2 40 8-80

9 0

-5 40 0

9 1

-6 30 7- 7

0

r6r8

r14

85

4

18

5 18

58

22 78

+

M1

ManipulativesTable of Contents

Coins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M2

One and Two Dollar Bills . . . . . . . . . . . . . . . . . . M3

Five, Ten and Twenty Dollar Bills . . . . . . . . . . . . M4

Random Pictures I . . . . . . . . . . . . . . . . . . . . . . . M5

Random Pictures II . . . . . . . . . . . . . . . . . . . . . . . M6

Analog Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . M7

Rulers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M8

Percent Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . M9

Number Chart . . . . . . . . . . . . . . . . . . . . . . . . . M10

Positive and Negative Cubes . . . . . . . . . . . . . . M11

Standard and Metric Measurements . . . . . . . . M12

Ones and Tens Pieces . . . . . . . . . . . . . . . . . . . . M13

Hundreds Pieces . . . . . . . . . . . . . . . . . . . . . . . . M14

One to Ten Number Pieces . . . . . . . . . . . . . . . M15

Hundreds Exchange Board . . . . . . . . . . . . . . . M16

One Whole, Tenths and Hundredths . . . . . . . . M17

Fraction Pieces I . . . . . . . . . . . . . . . . . . . . . . . . M18

Fraction Pieces II . . . . . . . . . . . . . . . . . . . . . . . M19

Fraction Pieces III . . . . . . . . . . . . . . . . . . . . . . . M20

Circle Fraction Pieces . . . . . . . . . . . . . . . . . . . . M21

Area of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . M22

Area of a Parallelogram . . . . . . . . . . . . . . . . . . M23

Area of a Triangle . . . . . . . . . . . . . . . . . . . . . . . M24

Area of an Irregular Figure . . . . . . . . . . . . . . . M25

Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M26

Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M27

Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M28

Rectangular Prism . . . . . . . . . . . . . . . . . . . . . . M29

Rectangular Pyramid . . . . . . . . . . . . . . . . . . . . M30

Triangular Prism . . . . . . . . . . . . . . . . . . . . . . . . M31

Triangular Pyramid . . . . . . . . . . . . . . . . . . . . . M32

IntroductionThe manipulatives below are used in lessons throughout the year but are not necessarily included in this book . Each lesson plan will specify the required manipulative for that day’s lesson .

In place of items we suggest, you may want to substitute items you already have in your classroom .

Many of the manipulatives are used repeatedly, so it might be helpful to store them in small plastic bags, one for each student . 1 . Numeration blocks for ones, tens, hundreds 2 . Play money: pennies, nickels, dimes,

quarters, half dollars and one-dollar bills 3 . Analog clock with moveable hands 4 . Balance scale 5 . Inch ruler 6 . Centimeter ruler 7 . Yardstick 8 . Meter stick/wheel 9 . Scale that measures ounces and grams 10 . Scale that measures pounds and kilograms 11 . Containers for cup, pint, liter, quart, half

gallon and gallon 12 . Fractional pieces 13 . Advertisements or labels from products

that show length, weight, volume and area (carpet sizes, food quantities, etc .)

14 . Three-dimensional figures: spheres, cones, cylinders, cubes, rectangular prisms, rectangular pyramids, square pyramids, triangular prisms and triangular pyramids

15 . Number line chart that includes positive and negative numbers 16 . Coordinate grid with four quadrants

For additional manipulatives, visit us online:www .excelmath .com/downloads/manipulatives .html

www.excelmath.com M13 Permission granted to copy this page

Ones and Tens Pieces

Do not cut up the other eight bars. Use them for tens pieces.

Cut these two bars into ones pieces.

Permission granted to copy this page M14 www.excelmath.com

Hundreds Pieces

grade 6 sample

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