Hannah RuebeckLehigh Valley SummerbridgeSummer 20137th Grade Six-Week Unit PlanCore Team 1

Week 1: June 17-21

The first week will focus on students getting to know each other and myself while also learning the basics of integers and integer properties. We will go over the expectations and rules of the Summerbridge program as well as my expectations in the classroom, as well as doing some icebreaker activities. I will introduce the individual whiteboards that students will be using for all in-class work – the whiteboards allow me to see who is struggling or very comfortable with specific topics but they also make the work more exciting for students. I will explain my expectations regarding the whiteboards and proper use of the tools. Students will discuss their own feelings about math as well as how they think they learn math best. I will share my own journey to loving math. The rest of the week will be spent reviewing integers - students will work with identifying and ordering integers on a number line. Problems will progress in difficulty by introducing integer operations (addition and subtraction) to the problems, and students will be introduced to the absolute value sign and what it means. The students will focus on the number line and it’s uses, as well as learning about the Cartesian Plane as a system of two intersecting number lines. We will discuss fractions and they will pop up in other activities. Students will also learn about large-integer addition and subtraction while review the place values of larger integers. Activities will include a human number line as well as reading excerpts from the first and second chapters of the book “The Number Devil,” a child-oriented creative discussion of mathematical concepts. Excerpts will focus on integers and some fractions, negative numbers, and the importance of the numbers 1 and 0. The reading will hopefully wrap up the concepts of the first week as well as get students excited about the topics of the coming week. Students will be encouraged to read the rest of the book if they are interested.

Week 2: June 24-28

The second week will expand on the concepts that the students became comfortable with during the first week. After review of integer addition and subtraction, we will move on to integer multiplication and division. We will go over how multiplication is related to addition and then how division is related to multiplication. I will explain how fractions fit into these problems and we will work on incorporating fraction addition and subtraction into problems. Activities will include figuring out how to divide a special small “prize” amongst the class and discussing patterns that we see in everyday life, with a presentation of pictures of nature in which mathematical patterns are present. Students will also be expected to demonstrate their

understanding of integers by writing a creative word problem. The next day, groups of students will work on solving each other’s word problems.

Week 3: July 1-3. (3-day week due to 4th of July Holiday and Olympics Day)

During the third week, students will cement their understanding of solving word problems with integers and all integer operations. Students will learn to recognize key words in word problems and to infer what they mean in a mathematical sense. I will introduce the order of operations and the importance of pneumonic devices in math before explaining PEMDAS and “Please Excuse My Dear Aunt Sally.” Then we will practice integer operations under the order of operations. Activities will include students creating their own pneumonic devices for the order of operations, which they will decorate and hang in the classroom. Week 4: July 8-12

I will begin week four by introducing the importance of algebra and its uses in problem solving. Students will suggest situations they have experienced in their lives where they could have used algebra to solve a problem, or when they think they will use algebra in their futures. We will build on the importance of key words in word problems and I will introduce the key words that indicate algebraic expressions. We will write a math story on the board – each student will add a sentence until we have complete story, and then we will translate the story into a system of mathematical expressions. I will remind students of “The Number Devil” and we will discuss the importance of writing and inference in math. Students will then work on evaluating algebraic expressions using what they know about integer operations and the order of operations. Expressions will get gradually more difficult.

Week 5: July 15-19

Week five will begin with a review of algebraic expressions and methods of evaluating them. I will then introduce algebraic equations by changing an integer to a variable, and discussing what a variable represents. I will introduce inequalities and we will graph inequalities on a number line. We will then go over the methods of solving algebraic equations. We will start with solving 1-step equations and then move on the 2-step equations. These skills require a lot of practice, and so the focus of this week will be on repeated problem-solving. By the end of the week, students will present a problem to the class and explain to their classmates how to solve the particular problem.

Week 6: July 22-26

The sixth week will be a time in which students continue to work on solving missing-variable equations. We will discuss and practice applying the skills we have learned over the past 5 weeks to specific problem-solving situations. While doing so, we will return to our conversations during the first week about the importance of math and the reasons why math is important in real life. Students will each give an

example of a way in which they used something they learned this summer outside of class (or homework). We will finish up the week by reviewing concepts for the Skills Test, focusing on topics that the students have questions about or had the most trouble with during the summer. We will end with a game of Jeopardy that encompasses all of the topics we covered in this class.

Hannah RuebeckLehigh Valley SummerbridgeSummer 20137th Grade Week 1 Lesson PlansCore Team 1

DAY 1: June 17 th Topic: Welcome to Summerbridge

Objectives: o Students will feel comfortable with each other and myself and be able

to name everyone in the class.o Students will be familiar with my classroom rules and expectations.o Students will start to get excited about the possibilities that math

puts in front of them and will understand that I am here to help them be as excited as I am about math.

Materials Usedo Chalk and chalkboardo Individual whiteboards and markers o Classroom rules (handout)o Week 1 Syllabus (handout)o Homework (handout)

Methodology:o Introduction: [5 min]

I will introduce myself (name, school, where I live) I will bring out the whiteboards and explain that they are going

to be a big part of our class. Students will be responsible for picking one up on their way into class, and markers will be passed out when we are going to use the whiteboards. I will explain that students will use the whiteboards to do their math problems in class, and that there will always be accompanying worksheets with copies of the problems that they are doing.

o Activity 1: [18 min] I will pass out the whiteboards and ask students to write their

name, age, and favorite number. We will go around the circle and each student will introduce him or herself and explain why they picked their favorite number. Then they will turn their whiteboards around, and the next person will have to remember the name and favorite number of all of the people before them.

Next, each student will have to write their favorite number’s worth of interesting facts about him or herself. For example, if my favorite number is 5 I have to write 5 things about myself on the whiteboard. If a student’s favorite number is larger than their age, then they can choose to do one fact for each year of

their age. We will then go around the circle again, sharing these facts.

o Activity 2: [10 min] Each student will write 3 classroom rules that they expect to

see on the handout, and we will again go around the circle talking about classroom rules and expectations. At the end of the activity, I will add any rules that they did not cover and hand out the worksheet that explains my classroom expectations.

I will hand out the syllabus and explain that students can know what to expect each day by following the syllabus.

o Activity 3: [10 min] We will go around the circle once more, and each student will

share one thing that he or she likes or dislikes about math, as well as how he or she thinks they learn math best.

I will explain that I used to be really frustrated by math, and how I came to love it. Nobody loves something all the time, but I hope to impart my enthusiasm while still staying realistic about my students’ feelings about math.

o I will then distribute and explain the homework sheet. [2min] Homework:

o Math Survey Worksheet

Classroom Rules and Expectations Summer 2013 Core Team 1 Hannah Ruebeck

Welcome to your Summerbridge Math Class! Congratulations on finishing your first day – hopefully you had some fun and are excited about the rest of the summer (I know I am!)

Please keep this sheet in an easily accessible place, as it is going to be your guide to success in this math class.

Rules:1. Respect yourself, your classmates, your classroom, and your teacher.2. Be prepared by bringing everything you need to class, paying

attention to lessons, and completing all assignments.3. Participate by joining in class discussions and actively completing

problems, but do not speak while someone else is speaking. Raise your hand if you have a question or comment.

4. Work together with your classmates when appropriate to insure that all students get the most possible out of this experience.

5. Be honest by only handing in your own work. Working with a classmate is encouraged but the work you hand in should all be your own.

6. Be positive by avoiding the word “can’t.” You can do anything you set your mind to and there are many ways for you to seek help with a topic or problem that you are struggling with.

7. No distractions like cell phones, iPods, or toys are allowed. The individual whiteboards are only to be used for the tasks I assign you.

8. Always try your hardest to do your best – I can’t ask for anything else!

Expectations:1. Homework: You will receive homework every day except Friday and

it will be due the next day. The homework will be listed on your weekly syllabus along with each day’s lesson topic and take-home sheets.

2. Take-home sheets: If we did work as a class or on the whiteboards, these sheets will include any problems that we did along with solutions. You will get them at the end of class and they are to be used as review sheets or memory-joggers.

3. Missing Class: If you know you will be missing class in advance, see me before you leave the day before. If you are sick, see me the day after you get back. You will be responsible for any work that you miss.

7 th Grade Syllabus: Week 1 Summer 2013 Core Team 1 Hannah Ruebeck

DAY LESSON TOPIC TAKE-HOME SHEET

TONIGHTS’ HOMEWORK

Monday Welcome to Summerbridge

Math Survey Worksheet

Tuesday Introduction to Integers

Chalkboard number line,whiteboard

number line,definitions.

Integer

Worksheet 1

Wednesday The Cartesian Plane

Comparing numbers,

Cartesian Plane definitions

Graph your initials

ThursdayInteger

OperationsInteger

operation rules, example

problems.

Integer Worksheet 2

FridayInteger

Operations with Large Numbers

Addition and subtraction

rules,Large integer

practice problems.

Name: _________________________________ Grade: ________________ Date: _________

MATH SURVEY

Answer the following questions to the best of your abilities:

1. What is your favorite thing about math? Please explain.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

2. What is your least favorite thing about math? Please explain.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

3. What is one way you can use math outside the classroom?

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

4. How comfortable are you doing math? Please circle one.

5. How do you learn math best? Circle up to three.

--Reading from a textbook --Listening to a teacher’s lesson

--Working on problems --Talking with other students about a topic

--Doing homework --Teaching someone else how do to a problem

DAY 2: June 18 th Topic: Introduction to Integers

Objectives: o Students will be able to identify positive and negative integers and

fractions and order them on a number line. o Students will understand the meaning of absolute value and how it

affects integers. Materials Used

o Chalk and chalkboardo Note cards and tapeo SMARTboardo Individual Whiteboards and markerso The Number Devil excerpts (handout)o Take-home sheet (handout)o Homework (handout)

Methodology:o Warm-Up: [12 min]

I will collect last night’s homework. Each student will go around the room and try to name each of his or her classmates. Any student from EAMS who missed the first day will also share two facts about themselves. Then, I will ask students what they know about integers, fractions, and number lines. I will then show them The Number Devil and explain that it is a book written for children that explains different mathematical phenomena in a creative and simple way. I will read the first few excerpts of the book, which explain integers, fractions, and the importance of zero. After I make sure that the students understand the definitions of each of these topics, they will each supply an example of a fraction, a positive integer, and a negative integer. I will explain that the “opposite” of a positive number is the same number but negative and vice versa.

o Activity 1: [15min] I will draw a line across the board and ask the students what

they think this is going to be. Once we have established that we want to make a number line, I will ask the students what should go in the middle, where we find positive numbers, and were we find negative numbers. I will explain that every number that exists has a place on the number line and that it goes on forever in both directions. I will ask students “what is so special about the number zero?” We will make a list on the board above the number zero. After students have offered their opinions, I will add any of the following properties if they are missing: 1) zero is known as the origin

2) Multiplicative property: zero times any number equals zero 3)Additive property: zero plus or minus any number equals the original number 4) zero is neither positive nor negative.

I will pass out a notecard to each student that has either a positive or negative integer or fraction on it. Students will go up to the board one at a time and tape their cards where they belong on the number line. Once everyone has gone, I will ask the class if they think the finished number line is correct. I will call on volunteers to change any values they think are incorrect until the class agrees that the number line is correct. The correct number line will be included on today’s take-home sheet.

o Activity 2: [15 min] I will draw absolute value signs on the board and ask students

what they mean. We will discuss that it means the distance from a number to the origin, regardless of its positivity or negativity. I will relate this to the real world by projecting an image of a mountain next to a deep lake. I will explain that the origin here is ground level, and ask the students how they think we would find the distance between the top of the mountain and the bottom of the lake. I will explain that this is the same as taking the absolute value of the distances and adding them together. I will draw several more math examples on the number line and ask students the absolute value of several numbers and the distances between different numbers on the number line. Then, I will project a list of positive and negative integers and fractions, including some with absolute value signs, on the SMARTboard and pass out the whiteboard markers. Students will create a number line on their boards and will order the projected numbers on the number line. I will check each board and then project the correct number line, which will also be included on today’s take-home sheet.

When everyone is done, I will ask for volunteers to answer the following questions.

What is an integer?What is a fraction?Why is zero important?What is absolute value? What do number lines tell us?

o I will then explain the worksheet that they will be filling out for homework, and pass out tonight’s homework and take-home sheet. I will also distribute the first week syllabus and classroom rules to any student from EAMS and ask them to read both tonight. [3min]

Homework:

o Integers Worksheet 1Name: _________________________________ Grade: ________________ Date: _________

INTEGERS WORKSHEET 1

Are these numbers integers? Mark each by writing “yes” or “no.”

21 _______−316 _______ -13 _______

45 _______ 0_______ 1002 _______

Write the opposite of each number.

4 : _______ -101: _______ 12 : _______ 0: _______

Write if the number is positive, negative, or neither.

20: ___________________ -11: ___________________ 38 : ___________________

0: ___________________ 180: ___________________ -2: ___________________

Compute the absolute value.

|7| _____ |-13| _____ |−23 | ______ |-1| _____

Put the following numbers on the number line:

0, 3, -2, −13 , 5, |-6|, 1 ,

12

INTRODUCTION TO INTEGERS TAKE-HOME SHEET

Definitions:

A Number Line is a line on which numbers are marked to illustrate their relation to each other.

Positive Numbers are numbers that are greater than zero

Negative Numbers are numbers that are less than zero

The Absolute Value of a number is the distance between a number and the origin.

The Multiplicative Property says that zero times another number equals zero.

The Additive Property says that adding or subtracting zero doesn’t change a number.

Chalkboard Number Line:

Whiteboard Number Line:

-21 -13 -5 -2 -1 0 1 3 10 15

-17 -5 -1 0 1 |4| |-13| 20

DAY 3: June 19 th Topic: The Cartesian Plane and Point Plotting

Objectives: o Students will review the importance of the number line. o Students will understand how to use a number line to compare

numbers.o Students will be introduced to the Cartesian Plane as two number

lines and will be comfortable plotting points. Materials Used

o Chalk and chalkboardo SMARTboardo Individual Whiteboards and markerso Take-home sheet (handout)o Homework (handout)

Methodology:o Warm-Up: [5 min]

I will collect last night’s homework. For the last time, each student will go around the room and try to name each of his or her classmates. I will have a line on the board with dashes for each of the numbers between -15 and 15. I will ask each student to go to the board and fill in a few nonconsecutive integers until we have a complete number line.

o Activity 1: [10 min] I will ask students how they know whether a number is bigger

or smaller than another number. After they have responded, I will explain that we can always use a number line to figure it out. The number further to the right is always bigger. I will ask the class if they know the math symbol that means “equal,” and then explain that there are also math symbols that mean “greater than” or “less than.” I will ask the students if they know those symbols, and then demonstrate the symbols on the board if they don’t know them. I will also introduce the pneumonic device of the alligator’s mouth always eating the bigger number.

With the number line still on the board, I will put two numbers up on the SMARTboard and ask students to come up one at a time and draw a correct math symbol between the two numbers. Each student will get a different set of numbers, and the pairs will sometimes include absolute values. Each of the pairs that we do in class will appear on today’s take-home sheet.

o Activity 2: [15 min] I will ask the students what intersecting lines are, and call on

volunteers to draw intersecting lines on the chalkboard. I will suggest to the students that we could think of two number

lines as intersecting, and ask each student to draw what they think that would look like on his or her whiteboard. I will then project an image of a Cartesian Plane on the SMARTboard and ask the students if they have ever seen this image before. If they have, I will ask them what it is used for. I will explain that we can think about this image, called a “Cartesian Plane” as two intersecting number lines. We will label the origin, and recognize that the number lines intersect at the point where both are zero. I will explain that the horizontal axis is the “x axis” and the vertical axis is the “y axis.” So as x increases, we move to the right, and as x decreases we move to the left. As y increases we move up, and as y decreases we move down.

I will draw a point on the Cartesian Plane with dotted lines leading to each axis. Pausing for a minute, I will ask the students how we identify each other. We have a first and a last name, right? I will show them that we can label points on a graph in the same way. The “x-value” tells us where on the x-axis (or number line) the point falls, and the “y-value tells us where on the y-axis (or number line) the point falls. When we write these pairs of numbers down, we call them “coordinate pairs” and they are written in the form (x, y). The x-coordinate is like the point’s first name, and the y-coordinate is like the point’s last name.

I will ask each student to come up to the board to plot a point from the coordinate pair that I give them. Then I will ask what quadrant the point is found in.

o Activity 3: [12 min] I will pull up the following website on the SMARTboard.

(http://www.mathsisfun.com/data/click-coordinate.html). Each student will have a minute to get as many points as they can on the “beginner” level, but if they are stuck on one point the class will work together to plot the point so that the student can continue.

o I will then explain the project that they will be making for homework, and hand out graphing paper, homework instructions, and today’s take-home sheet. [3min]

Homework: o Plotting your initials:

Each student will be given a piece of graphing paper on which there is a copy of the Cartesian plane that we worked with in class today. They will plot and label at least 10 points, with at least one point in each quadrant, which can be connected to illustrate their initials. Students are welcome to decorate their plots, as they will be hung around the classroom. I will show

them my hand-made example as well as the digitally made one on their homework sheet.

Name: _________________________________ Grade: ________________ Date: _________

GRAPH YOUR INITIALS PROJECT

The goal:

Your finished project should illustrate your first and last initials.

The procedure:

1. Using pencil, plot 10 points that can be connected to form the first letters of your first and last name. There should be at least 1 point in each quadrant.

2. Still using pencil, connect the points and make sure that you are happy with your product. You are welcome to change any points.

3. Using a marker or dark pen, go over the points that you plotted. Using pen or pencil, label each point with its coordinate pair in the form (x, y).

4. Get creative! You are welcome to add any colors or other decorations that you want – the finished products will be hung in our classroom!

Here is an example:

COMPARING NUMBERS AND TAKE-HOME SHEETTHE CARTESIAN PLANE

Comparing Numbers:A number to the right on a number line is always bigger. A number to the left on a number line is always smaller.

Problems:

10 > 4 -3 < 1 7 < |-9|

-4 > -11 -14 < 3 |3| < 5

12 > |-7| 2 = |-2| 6 > -1

The Cartesian plane, or the Coordinate Plane:

4

3

2

1

0

-1

-2

-3

-4

-4 -3 -2 -1 0 1 2 3 4

First quadrantSecond quadrant

DAY 4: June 20 th Topic: Integer Operations

Objectives: o Students will review the importance of the number line. o Students will be comfortable adding and subtracting positive and

negative integers Materials Used

o Chalk and chalkboardo SMARTboardo Individual Whiteboards and markerso Take-home sheet (handout)o Homework (handout)

Methodology:o Warm-Up: [6 min]

I will collect last night’s homework to be checked and then displayed in the classroom. Then, I will ask students to each write down two things that we have used a number line for on their whiteboards and to show them to the class. We will discuss all of the responses. Then, I will explain to them that we are going to be going back to working with one number line today and ask them to write down two new things that they think we can do with number lines. I will explain that we will be learning how to do integer addition and subtraction today and ask for advice in how to use the number line to do so.

o Activity 1: [26 min] Now that we have reviewed the number line and many of its

properties, we will use it to understand integer addition and subtraction. I will ask the students how they think we can use the number line to add or subtract integers. I will suggest that we try to add 6+4. I will demonstrate (on our number line) that if we start at the number 6 and move 4 spaces to the right, we get 10. If we start at 6 and move 4 spaces to the left, we get 2. This will lead students to understand that adding positive numbers moves to the right and subtracting positive numbers moves to the left, which I will write on the board as the beginning of a little chart. We can think about this in terms of ‘getting more or less positive.’ I will ask the class what happens when we add a positive number plus a positive number, and prompt them that it is always positive. I will write “Positive + Positive = Positive” on the SMARTboard. This makes sense because we know that numbers to the right are always bigger, and adding two positive numbers together always gives us another positive number, etc. I

Fourth quadrantThird quadrant

I will ask the students what they think will happen if we add two negative numbers together. How would we solve -3+( -2)? This equals -5, and so we move to the left when adding negative numbers (add to chart). What if we had moved to the right? This equals -1, which is what we get if we do -3-(-2). So we move to the right when subtracting negative numbers (add to chart). I will ask the students what seems to be true when we add two negative numbers together. If they are unsure, I will provide several examples until they see the pattern that “Negative + Negative = Negative,” which I will write on the SMARTboard as well.

What if we are adding a negative and a positive? I will write several examples on the board and the students will conclude that the answer can be either positive or negative. I will ask them if they see a pattern between the numbers that we are adding and whether the answer is positive or negative. I will show them that the answer always takes the sign of the number that has the larger absolute value. I will have a new addition rule chart, which I will hang in the classroom after the lesson. It will say:

1. Find the absolute value of each integer2. Subtract the smaller value from the larger value3. This is your answer, and it takes whatever sign the

larger value had originally. I will explain this method to the class and I will wrap up by repeating several earlier examples with this method.

Next, I will have the students examine the chart that we made about moving to the left or right on a number line when we are adding or subtracting positive or negative numbers and ask them if they notice anything about the conclusions we have drawn. I will elaborate by explaining that adding a negative number is the same as subtracting the opposite of that number and that subtracting a negative number is the same as adding the opposite of that number. I will demonstrate with several examples.

I will explain to the class that it is their choice whether to use the method that is on the poster to add two numbers of different signs or that they could change adding a negative to subtracting a positive, etc. I will put up a problem on the board and ask for one volunteer to solve the problem each way.

o Activity 2: [10 min] I will pass out the whiteboard markers and will read out

problems for the students to copy down and complete. They will hold up the problems, to check that they wrote them down correctly, and then again after they have done the problem. They can work up by the board to use the number line if they

would like or choose to work at their desks. The problems and their solutions will be found on today’s take-home sheet.

o I will then explain the worksheet that they will be filling out for homework, and pass out tonight’s homework and take-home sheet. [3min]

Homework: o Integers Worksheet 2

Name: _________________________________ Grade: ________________ Date: _________

INTEGERS WORKSHEET 2

Fill in each blank with a “<” “>” or “=”

6 ______ 9 -5 ______ -7 3 ______ -2

|-4| ______ 8 15 ______ 9 |-14| ______9

5 ______ |-5|34 ______ 2 -12 ______ -1

Solve the following equations:

1. -8+4= 4. 9--4=

2. 12+-3= 5. -5-3=

3. -6+6= 6. 7-11=

INTEGER OPERATIONS TAKE-HOME SHEET

Addition and Subtraction Rules:

Positive + Positive = PositiveNegative + Negative = Negative

Positive + Negative = ??? 1. Find the absolute value of each integer2. Subtract the smaller value from the larger value3. This is your answer, and it takes whatever sign the larger value had

originally.

Adding a negative number is the same as subtracting the opposite of that number. Subtracting a negative number is the same as adding the opposite of that number.

Examples: 4- (-2) is the same as 4 + 23+(-5) is the same as 3 – 5

Integer Addition and Subtraction Problems:

Five minus two: 5 - 2 = 3

Negative seven minus three: -7 - 3 = -10

Four plus negative eight: 4 + -8 = -4

Eleven plus the absolute value of negative three: 11+ |-3| = 14

Negative five plus eight: -5 + 8 = 3

The absolute value of 2 minus six: |-2| - 6 = -4

Nine minus negative four: 9 - -4 = 13

Negative eleven minus negative two: -11 - -2 = -9

Twelve minus the absolute value of four: 12 - |4| = 8

Negative one plus eleven: -1 + 11 = 10

DAY 5: June 21 st Topic: Integer Operations in Larger Numbers

Objectives: o Students will know the place values of large integers. o Students will be comfortable adding large integers and carrying

values.o Students will be comfortable using the borrowing method to subtract

large numbers. Materials Used

o Chalk and chalkboardo SMARTboardo Individual Whiteboards and markerso Take-home sheet (handout)o Homework (handout)

Methodology:o Warm-Up: [8 min]

We will go over last night’s homework and then I will collect it. We will discuss any problems that the students had with the homework and talk about how they think they can use the things they have learned so far outside of the classroom. I will go first and give an example. We will talk about how many of the real-world applications of math deal with much larger integers than the ones we have been working with.

o Activity 1: [12 min] I will project a word problem on the SMARTboard.

I will ask for a volunteer who thinks they can read the numbers in the problem to read the problem to the class. First, I will ask the students what they think the problem is asking us to do. Then I will copy the problem (78,230,000+86,440,000=?) on to the board and ask students if they know what the place values. I will go through and have each student come up to label one of the places in the first number. When everything is labeled, I will ask if the class is in agreement that the numbers are

labeled correctly, and then have them guide me through labeling the second number.

I will ask the students if they know what the place values have to do with adding large numbers. We will come to the conclusion that you line up the numbers so that the place values are lined up on top of each other, and then add each column. We go from right to left, and so this problem starts with four 0+0 columns. Then we will add 3+4 and 2+4, which the students know how to do. I will ask them what to do next, and we will add 8+6. This equals 14, and I will ask for a student volunteer to come up and write the answer in the correct column. We will talk about carrying over the one to the next place value. Then we will move over to the final column, add 7+8=15, and talk about how you could carry the 1 of the 15 but that then you would just have one more column of 1+0. So in the last column it’s okay to just write the answer. I will ask a student to read the number that we have as our solution, and then ask for another volunteer to explain what that number represents in terms of our problem.

o Activity 2: [12 min] Now that we have reviewed place values, we will follow the

same procedure for discussing subtracting large integers using the borrowing method. I will write the numbers 113 and 261 on the board and ask how we find the difference between these two numbers. We will talk about how we had been using number lines and how now we don’t have a number line that goes out that far, so we need a new method. I will ask students whether they think we will be using addition or subtraction and what word I used that made them think that (“difference”). I will write the problem vertically, and then I will go over the basics of subtracting large numbers while demonstrating on the problem at hand:

The larger number always goes on top Match up the place values so that they are in the same

columns. When the digit on top is less than the digit on the

bottom, you have to “borrow.” To “borrow” you cross out the number that is too small

and rewrite the number that you just crossed out with a one in front of it. To compensate for that, you cross out the next number to the left and subtract one from it, and write that new number above the same column.

o Activity 3: [10 min] We will review the rules about addition and subtraction that

we learned yesterday about positive and negative numbers.

I will pass out the whiteboard markers and will project several problems with larger integers that include positive and negative numbers and absolute values. Students will complete the problems and I will check their work. I will take note of who is struggling and who is working quickly and make sure that all students are appropriately challenged in Monday’s review activities. These problems will appear on today’s take-home sheet.

When they have finished the problems, we will return to our conversation about large numbers in the real world. I will ask each student for an example of something that deals in very large numbers, after giving the example that there are trillions of cells in the human body.

o Activity 4: Friday Wrap-Up: [3 minutes] I will pass out notecards to the students and ask them each to

write one activity or lesson that they liked this week, one activity or lesson that they didn’t like this week, and their favorite thing at Summerbridge so far.

o I will pass out today’s take home sheet. Homework:

o None

LARGE INTEGER OPERATIONS TAKE-HOME SHEET

Place Values:

We carry over when a column in an addition problem adds to be more than 10. We put the number in the tens place over the number in the column to the left of the column we are working in, and add it to those numbers.

We borrow when the top number in a subtraction problem is smaller than the bottom number. We cross out the number that is two small and write that number with a one in front of it instead. We cross out the number to the left of the original number and write that number minus one in its place.

Whiteboard Problems:

77 +(-38) = - 3,113 – |-13| = -74 + (-82) ==77-38 = 39 =-3,113+ -13 = -3126 =-156

|- 27| + -218= -1,614 + 89= |-548| - |-349|==27-218= -191 =-1525 =548-349= 199

Hannah RuebeckLehigh Valley SummerbridgeSummer 20138th Grade Six-Week Unit PlanCore Team 1

Week 1: June 17-21

The first week will focus on students getting to know each other and myself while also reviewing the basics of integers and integer operations. We will go over the expectations and rules of the Summerbridge program as well as my expectations in the classroom, as well as doing some icebreaker activities. I will introduce the individual whiteboards that students will be using for all in-class work – the whiteboards allow me to see who is struggling or very comfortable with specific topics but they also make the work more exciting for students. I will explain my expectations regarding the whiteboards and proper use of the tools. Students will discuss their own feelings about math as well as how they think they learn math best. I will share my own journey to loving math. The rest of the week will be spent reviewing integer operations - students will work with absolute values and integer addition, subtraction, multiplication, and division in problems progressing in difficulty throughout the week. I will introduce fractions and their relation to integers, and will explain how to simplify expressions that include fractions – fraction addition, subtraction, multiplication, and division. A cumulative activity will be a human number line that incorporates integers, fractions, and numerical expressions. We will discuss solving word problems that incorporate all of the integer operations as well as some fractions. We will also be reading excerpts from the first and second chapters of the book “The Number Devil,” a child-oriented creative discussion of mathematical concepts. Excerpts will focus on integers and fractions, negative numbers, and the importance of the numbers 1 and 0. The reading will hopefully wrap up the concepts of the first week as well as get students excited about the topics of the coming week. Students will be encouraged to read the rest of the book if they are interested.

Week 2: June 24-28

The second week will expand on the concepts that the students became comfortable with during the first week. After a quick review of integer operations, we will discuss the order of operations and the acronym PEMDAS. After a discussion of the importance of pneumonic devices, students will create their own pneumonic device for the order of operations and display it creatively on a small poster to be displayed in the classroom. We will review the mathematical equation and discuss one-step equations. Students will complete practice problems and work on identifying the correct method of solving equations. I will then introduce two-step equations in relation to one-step equations and students will again work to solve practice problems and identify the correct method to solving equations. We will discuss the

importance of equations due to their real-world applications, and students will offer examples of problems that can be explained, simplified, or solved by using an algebraic equation. After some practice word problems, students will write their own based on an event or problem they have experienced first-hand.

Week 3: July 1-3. (3-day week due to 4th of July Holiday and Olympics Day)

The third week will focus on simplifying equations. Now that students have a firm grasp of solving two-step equations, they will be expanding that knowledge to simplify more complicated equations in order to solve them. I will introduce how to combine like terms and the importance of the distributive property as well as how to apply it. Students will understand why they have been learning about the order of operations and how to apply it now to these simplification techniques. Students will then translate all of this knowledge into solving more complicated word problems with unknown variables.

Week 4: July 8-12

The fourth week will center on the coordinate plane, plotting points, and graphing equations using t-tables. I will introduce the coordinate plane, and ask students for help in identifying the many key aspects of the plane – we will identify the origin, the 4 quadrants, and the x- and y- axes. I will introduce how to plot points on the coordinate plane and students will practice identifying quadrants, identifying coordinates, and plotting points. Students will get extra practice by creatively plotting their initials to be hung around the classroom. Now that students are comfortable maneuvering the coordinate plane, I will segue from plotting points to plotting simple linear functions. I will introduce t-tables as a way to plot lines of equations in the form y=mx+b.

Week 5: July 15-19

After reviewing the importance of equations in the form y=mx+b, we will look at the possibility of changing equations so that they take this linear form. Students will practice manipulating equations in this way and then graphing them with t-tables. I will then introduce slope as “rise over run,” its visual meaning, and students will compare slopes they have calculated to the original equations in y=mx+b form. Students will discover the meaning of the “m” and in the equation and that it indicates the slope of the line. We will discuss slope as a fraction. I will then introduce intercepts in their visual sense as where linear plots cross the x- and y-axes. Students will identify the y-intercepts of given graphs and compare them to the original equation in the form y=mx+b. Students will discover that the “b” in the equation represents the y-intercept. I will explain how students can use these facts to plot graphs or to check their work with t-tables. Students will practice finding the slope and intercepts for given equations and we will talk about what their graphs would look like. Students will then work on applying their new knowledge to problem-solving situations.

Week 6: July 22-26

The sixth week will see a continuation of applying the concepts students learned this summer to specific problem-solving situations. While doing so, we will return to our conversations during the first week about the importance of math and the reasons why math is important in real life. Students will each give an example of a way in which they used something they learned this summer outside of class (or homework). We will finish up the week by reviewing concepts for the Skills Test, focusing on topics that the students have questions about or had the most trouble with during the summer. We will end with a game of Jeopardy that encompasses all of the topics we covered in this class.

Hannah RuebeckLehigh Valley SummerbridgeSummer 20138th Grade Week 1 Lesson PlansCore Team 1

DAY 1: June 17 th Topic: Welcome to Summerbridge

Objectives: o Students will feel comfortable with each other and myself and be able

to name everyone in the class.o Students will be familiar with my classroom rules and expectations.o Students will start to get excited about the possibilities that math

puts in front of them and will understand that I am here to help them be as excited as I am about math.

Materials Usedo Chalk and chalkboardo Individual whiteboards and markers o Classroom rules (handout)o Week 1 Syllabus (handout)o Homework (handout)

Methodology:o Introduction: [5 min]

I will introduce myself (name, school, where I live) I will bring out the whiteboards and explain that they are going

to be a big part of our class. Students will be responsible for picking one up on their way into class, and markers will be passed out when we are going to use the whiteboards. I will explain that students will use the whiteboards to do their math problems in class, and that there will always be accompanying worksheets with copies of the problems that they are doing.

o Activity 1: [18 min] I will pass out the whiteboards and ask students to write their

name, age, and favorite number. We will go around the circle and each student will introduce him or herself and explain why they picked their favorite number. Then they will turn their whiteboards around, and the next person will have to remember the name and favorite number of all of the people before them.

Next, each student will have to write their favorite number’s worth of interesting facts about him or herself. For example, if my favorite number is 5 I have to write 5 things about myself on the whiteboard. If a student’s favorite number is larger than their age, then they can choose to do one fact for each year of

their age. We will then go around the circle again, sharing these facts.

o Activity 2: [10 min] Each student will write 3 classroom rules that they expect to

see on the handout, and we will again go around the circle talking about classroom rules and expectations. At the end of the activity, I will add any rules that they did not cover and hand out the worksheet that explains my classroom expectations.

I will hand out the syllabus and explain that students can know what to expect each day by following the syllabus.

o Activity 3: [10 min] We will go around the circle once more, and each student will

share one thing that he or she likes or dislikes about math, as well as how he or she thinks they learn math best.

I will explain that I used to be really frustrated by math, and how I came to love it. Nobody loves something all the time, but I hope to impart my enthusiasm while still staying realistic about my students’ feelings about math.

o I will then distribute and explain the homework sheet. [2min] Homework:

o Math Survey Worksheet

Classroom Rules and ExpectationsSummer 2013 Core Team 1 Hannah Ruebeck

Welcome to your Summerbridge Math Class! Congratulations on finishing your first day – hopefully you had some fun and are excited about the rest of the summer (I know I am!)

Please keep this sheet in an easily accessible place, as it is going to be your guide to success in this math class.

Rules:9. Respect yourself, your classmates, your classroom, and your teacher.10.Be prepared by bringing everything you need to class, paying

attention to lessons, and completing all assignments.11.Participate by joining in class discussions and actively completing

problems, but do not speak while someone else is speaking. Raise your hand if you have a question or comment.

12.Work together with your classmates when appropriate to insure that all students get the most possible out of this experience.

13.Be honest by only handing in your own work. Working with a classmate is encouraged but the work you hand in should all be your own.

14.Be positive by avoiding the word “can’t.” You can do anything you set your mind to and there are many ways for you to seek help with a topic or problem that you are struggling with.

15.No distractions like cell phones, iPods, or toys are allowed. The individual whiteboards are only to be used for the tasks I assign you.

16.Always try your hardest to do your best – I can’t ask for anything else!

Expectations:4. Homework: You will receive homework every day except Friday and

it will be due the next day. The homework will be listed on your weekly syllabus along with each day’s lesson topic and take-home sheets.

5. Take-home sheets: If we did work as a class or on the whiteboards, these sheets will include any problems that we did along with solutions. You will get them at the end of class and they are to be used as review sheets or memory-joggers.

6. Missing Class: If you know you will be missing class in advance, see me before you leave the day before. If you are sick, see me the day after you get back. You will be responsible for any work that you miss.

7 th Grade Syllabus: Week 1 Summer 2013 Core Team 1 Hannah Ruebeck

DAY LESSON TOPIC TAKE-HOME SHEET

TONIGHTS’ HOMEWORK

Monday Welcome to Summerbridge

Math Survey Worksheet

Tuesday Integer Addition and Subtraction

Chalkboard number line, Addition and subtraction

rules, whiteboard problems.

Integer

Worksheet 1

WednesdayInteger

Multiplication and Division

Multiplication and division

rules, whiteboard problems.

Integer Worksheet 2

ThursdayInteger

Operations and Word Problems

Word problem strategy

Integer Worksheet 3

FridayInteger

Operation Review

List of links for integer

operation practice

Name: _________________________________ Grade: ________________ Date: _________

MATH SURVEY

Answer the following questions to the best of your abilities:

6. What is your favorite thing about math? Please explain.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

7. What is your least favorite thing about math? Please explain.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

8. What is one way you can use math outside the classroom?

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

9. How comfortable are you doing math? Please circle one.

10.How do you learn math best? Circle up to three.

--Reading from a textbook --Listening to a teacher’s lesson

--Working on problems --Talking with other students about a topic

--Doing homework --Teaching someone else how do to a problem

DAY 2: June 18 th Topic: Integer Addition and Subtraction

Objectives: o Students will review integers, number lines, and absolute value. o Students will be comfortable adding and subtracting integers.

Materials Usedo Chalk and chalkboardo Individual whiteboards and markers o SMARTboardo The Number Devil excerpts (handout)o Take-home sheet (handout) o Homework (handout)

Methodology:o Warm-Up: [8 min]

I will collect last night’s homework. Each student will go around the room and try to name each of his or her classmates. Any student from EAMS who missed the first day will also share two facts about themselves. Then, I will ask students what they know about integers, fractions, and number lines. I will then show them The Number Devil and explain that it is a book written for children that explains different mathematical phenomena in a creative and simple way. I will read the first few excerpts of the book, which explain integers, fractions, and the importance of zero. After I make sure that the students understand the definitions of each of these topics, they will each supply an example of a fraction, a positive integer, and a negative integer. I will ask students what the “opposite” of a number is: the opposite of a positive number is the same number but negative and vice versa.

o Activity 1: [10 min] I will draw a line across the board and ask the students what

they think we are going to make. I will ask several students to come up to the board and each fill in where zero goes, where positive numbers go, and where negative numbers go.

I will draw absolute value signs around a number on the board and ask students if they know what this means. I will elaborate by explaining that these are absolute value signs and that they indicate the distance between the number and zero, regardless of sign. I will demonstrate on the number line, and students will answer several examples as a class.

I will pass out a notecard to each student that has either a positive or negative integer, absolute value, or fraction on it. Students will go up to the board one at a time and tape their cards where they belong on the number line. Once everyone

has gone, I will ask the class if they think the finished number line is correct. I will call on volunteers to change any values they think are incorrect until the class agrees that the number line is correct. The correct number line will be included on today’s take-home sheet.

o Activity 2: [15 min] Now that we have reviewed integers, absolute value, and the

properties of a number line, we will use it to understand integer addition and subtraction. I will ask the students how they think we can use the number line to add or subtract integers. I will suggest that we try to add 6+4. I will demonstrate (on our number line) that if we start at the number 6 and move 4 spaces to the right, we get 10. If we start at 6 and move 4 spaces to the left, we get 2. This will lead students to understand that adding positive numbers moves to the right and subtracting positive numbers moves to the left, which I will write on the board as the beginning of a little chart. We can think about this in terms of ‘getting more or less positive.’ I will ask the class what happens when we add a positive number plus a positive number, and prompt them that it is always positive. I will write “Positive + Positive = Positive” on the SMARTboard. This makes sense because we know that numbers to the right are always bigger, and adding two positive numbers together always gives us another positive number, etc. I

I will ask the students what they think will happen if we add two negative numbers together. How would we solve -3+( -2)? This equals -5, and so we move to the left when adding negative numbers (add to chart). What if we had moved to the right? This equals -1, which is what we get if we do -3-(-2). So we move to the right when subtracting negative numbers (add to chart). I will ask the students what seems to be true when we add two negative numbers together. If they are unsure, I will provide several examples until they see the pattern that “Negative + Negative = Negative,” which I will write on the SMARTboard as well.

What if we are adding a negative and a positive? I will write several examples on the board and the students will conclude that the answer can be either positive or negative. I will ask them if they see a pattern between the numbers that we are adding and whether the answer is positive or negative. I will show them that the answer always takes the sign of the number that has the larger absolute value. I will have a new addition rule chart, which I will hang in the classroom after the lesson. It will say:

4. Find the absolute value of each integer

5. Subtract the smaller value from the larger value6. This is your answer, and it takes whatever sign the

larger value had originally. I will explain this method to the class and I will wrap up by repeating several earlier examples with this method.

Next, I will have the students examine the chart that we made about moving to the left or right on a number line when we are adding or subtracting positive or negative numbers and ask them if they notice anything about the conclusions we have drawn. I will elaborate by explaining that adding a negative number is the same as subtracting the opposite of that number and that subtracting a negative number is the same as adding the opposite of that number. I will demonstrate with several examples.

I will explain to the class that it is their choice whether to use the method that is on the poster to add two numbers of different signs or that they could change adding a negative to subtracting a positive, etc. I will put up a problem on the board and ask for one volunteer to solve the problem each way.

o Activity 3: [10 min] I will pass out the whiteboard markers and will read out

problems for the students to copy down and complete. They will hold up the problems, to check that they wrote them down correctly, and then again after they have done the problem. They can work up by the board to use the number line if they would like or choose to work at their desks. The problems and their solutions will be found on today’s take-home sheet.

o I will then explain the worksheet that they will be filling out for homework, and pass out tonight’s homework and take-home sheet. I will also distribute the first week syllabus and classroom rules to any student from EAMS and ask them to read both tonight. [3min]

Homework: o Integers Worksheet 1

Name: _________________________________ Grade: ________________ Date: _________

INTEGERS WORKSHEET 1 – Addition and Subtraction

Solve the following equations:

4. |-11| + 4 = 6. 9 - -4=

5. 12 + -7 = 7. -5 - |3| =

6. -6 + 6 = 8. 7 - 11 =

7. -8 + |-13| = 9. -12 - -9 =

8. 221-61= 10. 733 + 89 =

INTEGER ADDITION AND SUBTRACTION TAKE-HOME SHEET

Chalkboard Number Line:

Addition and Subtraction Rules:

Positive + Positive = PositiveNegative + Negative = NegativePositive + Negative = ???

4. Find the absolute value of each integer5. Subtract the smaller value from the larger value6. This is your answer, and it takes whatever sign the larger value had

originally.

Adding a negative number is the same as subtracting the opposite of that number. Subtracting a negative number is the same as adding the opposite of that number.

Examples: 4- (-2) is the same as 4 + 23+(-5) is the same as 3 – 5

Integer Addition and Subtraction Problems:

Five minus two: 5 - 2 = 3

Negative seven minus three: -7 - 3 = -10

Four plus negative eight: 4 + -8 = -4

Eleven plus the absolute value of negative three: 11+ |-3| = 14

Negative five plus eight: -5 + 8 = 3

The absolute value of 2 minus six: |-2| - 6 = -4

Nine minus negative four: 9 - -4 = 13

Negative eleven minus negative two: -11 - -2 = -9

Twelve minus the absolute value of four: 12 - |4| = 8

Negative one plus eleven: -1 + 11 = 10

-17 -5 -1 0 1 |4| |-13| 20

DAY 3: June 19 th Topic: Integer Multiplication and Division

Objectives: o Students will be familiar with the rules of integer multiplication and

division.o Students will be able to evaluate products and quotients.

Materials Usedo Chalk and chalkboardo Individual whiteboards and markers o SMARTboardo Review problems (cards)o BattleMath cardso Take-home sheet (handout) o Homework (handout)

Methodology:o Warm-Up: [8 min]

For the last time, each student will go around the room and try to name each of his or her classmates. I will ask for any questions about the homework, and after any/all have been answered I will collect last night’s homework. I will ask the students to pair off, and each pair will get a card with an addition or subtraction problem on it. I will walk around the class to check their progress and will ask a pair that has mastered their problem to explain their method to the class.

o Activity 1: [14 min] I will ask the students what they know about multiplication.

We will talk about how multiplication is like adding over and over again, and I will have the class say the 3,4, and 5 times tables as I write them on the board for a quick review.

Then I will introduce the first rule of integer multiplication. I will ask the students what they think happens if we multiply a negative number times a positive number. I will pull up today’s take-home sheet and reveal Rule #1: The product of mixed signs (a positive and a negative number) is always negative. I will ask the students if they can think of a real-world example of this. If they are stuck, I will explain that this is how we would think about owing money to multiple people. If I owe $5 to 4 people, and owing means that the $5 is negative, then I owe (-5)(4) = -20 dollars.

Next I will introduce the second rule of integer multiplication. I will ask the students what they think happens if we multiply two positive numbers together, and after they have answered, I will ask the students what they think will happen if we multiply two negative numbers together. Since we decided already that the product of two positive numbers is positive,

they may expect the product of two negative numbers to be negative. I will explain that the two negative signs cancel each other out and will display the next line of today’s take-home sheet: Rule #2: The product of two integers of the same sign (two positive numbers or two negative numbers) is always positive.

I will write several problems on the board that are using the information we have covered so far, and students will do them on their whiteboards. These problems will appear on today’s take-home sheet. The last problem will have three integers being multiplied together.

I will ask the students what they think we should do when we have more than two integers. What order do we multiply them in? After the students’ responses, I will reveal the third rule of multiplication from the take-home sheet. Rule #3: Multiplication is associative. This means that it doesn’t matter what order you multiply the integers in. I will ask the students what 2*3 is, and what 3*2 is. I will show them the procedure for multiplying more than one integer. Ex: (4)(5)(-8)=(20)(-8)=(4)(-40)= -160. Once the students are convinced that this rule is true, we will do several more whiteboard problems with more than two integers.

o Activity 2: [10 min] Next we will cover integer division. I will ask if students know

the relationship between multiplication and division. Once we have determined that division is just multiplying by a fraction 1

number , I will ask the students if they think the division rules

will be similar to the multiplication rules (the answer should be yes).

I will reveal Division Rule #1 from the take home sheet: The quotient of mixed signs (a positive number and a negative number) is always a negative integer. I will demonstrate with an example on the board : 9/(-3) = -3

I will reveal Division Rule #2: The quotient of same signs (two positive numbers or two negative numbers) is always a positive integer. I will demonstrate with two examples: (12)/(4)= 3 and (-16)/(-8)=2.

o Activity 3: [10 min] I will pass out the “BattleMath” cards: notecards that each have

a positive or negative integer on them. Students will pair up. To play, each student pulls out the top card and the first student to multiply them together correctly gets to keep both cards (like the card game ‘war’). After five minutes, we will switch to division.

o I will then explain the worksheet that they will be filling out for homework, and pass out tonight’s homework and take-home sheet. [3min]

Homework: o Integers Worksheet 2

Name: _________________________________ Grade: ________________ Date: _________

INTEGERS WORKSHEET 2 – Multiplication and Division

Solve the following equations:

1. |-11| 2 = 6. (9)(-6) =

2. (-30) / (-5) = 7. (-5)(3)(-2)=

3. |-6| / (2) = 8. |(-4)3| =

4. (4)(6)(-3) = 9. (-18) / (9) =

5. (32) / (-4)= 10. |7| (-7) 3

INTEGER MULTIPLICATION AND DIVISION TAKE-HOME SHEET

Multiplication Rules:1. The product of mixed signs (a positive and a negative number) is

always negative.2. The product of two integers of the same sign (two positive

numbers or two negative numbers) is always positive.3. Multiplication is associative. This means that it doesn’t matter

what order you multiply the integers in.

Division Rules:1. The quotient of mixed signs (a positive and a negative number) is

always negative.2. The quotient of two integers of the same sign (two positive

numbers or two negative numbers) is always positive.

Whiteboard Problems:

|-3| 6 = (5)(-8) =3 6= 18 = -40

(-7) (-4) = (2) (-4)== 28 = -8

6 2 = |(-4)3| == 12 = |-12|= 12

(6)(2)(-2) = (-1)49 ==(12)(-2)= -24 = (-4)9= -36=(6)(-4)= -24 = (-1)36=-36

(-3)(5)(-2)= 2 (-5) 3=(-15)(-2)= 30 = -10 3= -30=(-3)(-10)=30 = 2 (-15)= -30

DAY 4: June 20 th Topic: Integer Operations Review and Word Problems

Objectives: o Students will be comfortable evaluating all four integer operations. o Students will be comfortable applying integer operations to word

problems to turn them into math expressions and solving them. Materials Used

o Chalk and chalkboardo Individual whiteboards and markers o SMARTboardo Integer Rules Postero Take-home sheet (handout) o Homework (handout)

Methodology:o Warm-Up: [8 min]

I will ask for any questions about the homework, and after any/all have been answered I will collect last night’s homework. I will ask the students to pair off, and each pair will get a card with a multiplication or division problem on it. I will walk around the class to check their progress and will ask a pair that has mastered their problem to explain their method to the class.

o Activity 1: [10 min] This activity will be a review of the information that we

learned over the last two days. We will review the rules for absolute value, how to use a number line, and all four integer operations. I will present a poster that will hang in the classroom that describes all of the rules for addition, subtraction, multiplication, and division.

o Activity 2: [15 min] Next I will introduce the students to word problems . I will

project a word problem on the SMARTboard – “A man is at the top of a mountain that is 950 feet tall. If he climbs down 300 feet, what is his new elevation?” We will draw and label a picture on the SMARTboard. We will translate the word problem into math. I will ask the students how we knew what math signs to use, and explain that we inferred certain information from the words. We turned words into math! I will ask the students what other words they can think of that mean something in math. We will make a list on the board.

I will ask the students to help me come up with a strategy for attacking word problems. I will ask what we did first – we read the problem. What did we do second? – we drew and labeled a picture. What did we do third? – we decided what information from the problem was important to our question, and looked

for key words that translated into math. What did we do fourth? – we created an expression, and then fifthly we solved the expression. This strategy will appear on tonight’s take-home sheet.

o Activity 3: [10 min] Students will work on a handout with word problems. I will

circulate, answer questions, and make note of any students having trouble. With five minutes left, students will form groups of two or three and share their answers.

o I will then explain the worksheet that they will be filling out for homework, and pass out tonight’s homework and take-home sheet. [3min]

Homework: o Integers Worksheet 3

Name: _________________________________ Grade: ________________ Date: _________

INTEGERS WORKSHEET 3 – Word Problems

1. Zoe bought 12 apples for $36 dollars. How much was each apple?

2. Nemo the clownfish lives 21 kilometers below the surface of the ocean. If he swims up 7 kilometers, what is his new location?

3. At his lemonade stand, Josh made 72 dollars. If he charged 3 dollars for each glass, how many glasses of lemonade did Josh sell?

4. At the top of Mt. Everest, it is -5 degrees Fahrenheit and at the bottom of Mt. Everest it is 20 degrees Fahrenheit. What is the difference between the two?

5. Rebecca bought 3 pairs of jeans for 25 dollars each. She bought 2 shirts for 10 dollars each. How much money did Rebecca spend?

6. The Western Roman Empire began in 27 B.C. and ended in 476 A.D. The Incan Empire began in 1438 A.D. and ended in 1533 A.D. How long did each empire last? How much longer did the Roman Empire last than the Incan Empire?

WORD PROBLEMS WITH INTEGERS TAKE-HOME SHEET

Word Problem Strategy:

1. Read the problem.

2. If possible, draw and label a picture

3. Identify important information and find key words

4. Create an expression

5. Solve the expression

Name: _________________________

In-Class Worksheet: Practice with Word Problems

1. Laura owes the bookstore 20 dollars. Each of her 4 friends will help her pay her debt. How much will each friend pay?

2. A submarine 1,100 feet below sea level rises 450 feet. What is the submarine’s new position?

3. The empire state building is 1,454 feet tall. The Eiffel Tower is 1,063 feet tall. Which building is taller? How much taller is it?

4. Joe is selling 5 baby kittens. If he charges 12 dollars for each kitten, how much money will he make?

5. It takes 3 hours for Sarah to chop down a tree. How long will it take her to chop down 7 trees? (Whenever we chop down a tree, we should plant another one in its place. How many seeds does Sarah need to plant?)

DAY 5: June 21 st Topic: Integer Operations Review

Objectives: o Students will understand the rules for using computers in class.o Students will be comfortable using the computers.o Students will review all four integer operations.

Materials Usedo Chalk and chalkboardo Individual whiteboards and markers o SMARTboardo Integer Rules Postero Take-home sheet (handout) o Homework (handout)

Methodology:o Warm-Up: [7 min]

I will ask for any questions about the homework, and after any/all have been answered I will collect last night’s homework. I will ask each student for one example of a word that indicates a mathematical function. We will talk about ‘talking to the text’ in terms of its math applications.

o Activity 1: [15 min] We will review the integer operations and their rules. I will ask

the students to explain to me the rules of each operation [this part of the activity will take 5 minutes].

I will read out problems for the students to copy onto their whiteboards. They will include large and small positive and negative integers, absolute value, and all four integer operations. The problems and their solutions will appear on today’s take-home sheet. Students will hold up their whiteboards when they have copied the problem and then again when they have completed it. I will make note of the level that each student is at, and direct him or her towards the appropriate level game in our next activity. [This part of the activity will take 10 minutes].

o Activity 2: [20 min] I will introduce the students to the rules of using the

computers in class. They will be written on the board for reference throughout this activity. Rules:

Class time is for math activities only. (Pay attention to the math and ignore any distractions that the computer offers).

Do not click on any advertisements or pop-up windows. If you have any problems or questions, raise your hand

to ask for help or guidance.

I will hand out today’s take-home sheet early, as it has a list of all of the links to the websites we are going to be using today.

Students that were struggling with the review whiteboard problems will be directed towards sites that offer practice with explicit explanation of the topics.

Integer Addition: http://www.aaamath.com/add65_x3.htm

Integer Subtraction: http://www.aaamath.com/subint1.htm

Integer Multiplication: http://www.aaamath.com/mul65_x2.htm

Integer Division: http://www.aaamath.com/div65_x2.htm

Students that are comfortable with the integer operations will be directed towards any one of these sites to practice integer operations with games.

The Football Game: reviews number lines, addition and subtraction, and key indication words in word problems. http://www.mathgoodies.com/games/integer_game/football.html

The Calculator Game: reviews integer multiplication and addition. http://www.mathplayground.com/calculator_chaos.html

CyberOlympics: reviews comparing numbers, and integer addition. http://pbskids.org/cyberchase/math-games/cyber-olympics/

Stop that Creature: reviews integer addition, subtraction, multiplication, and division along with pattern recognition. http://pbskids.org/cyberchase/math-games/stop-creature/

Space Race: reviews integer addition: http://www.arcademicskillbuilders.com/games/orbit-integers/orbit-integers.html

Space race: reviews integer multiplication: http://www.arcademicskillbuilders.com/games/integer-warp/integer-warp.html

The Spider Game: reviews integer addition. http://www.arcademicskillbuilders.com/games/spider-match/spider-match.html

Mathman: reviews integer division. http://www.sheppardsoftware.com/mathgames/mathman/mathman_division.htm

Mathman: reviews integer subtraction. http://www.sheppardsoftware.com/mathgames/mathman/mathman_subtraction.htm

Who wants to be a millionaire? : reviews absolute value, integer addition, subtraction, multiplication and division. http://www.quia.com/rr/41496.html

I will walk around the classroom as students are playing games in order to check their progress and make sure everyone is working on math games only.

o Activity 4: Friday Wrap-Up: [3 minutes] I will pass out notecards to the students and ask them each to

write one activity or lesson that they liked this week, one activity or lesson that they didn’t like this week, and their favorite thing at Summerbridge so far.

Homework: o None

INTEGER OPERATION REVIEW TAKE-HOME SHEET

Did you enjoy the games we played in class today? Do you want to do some fun review over the weekend? Here is the list of links to the games we played this weekend. These websites have many more fun and interesting games, so don’t be afraid to go exploring!

Here are some links to explanations of integer operations, and a practice section if you scroll down the webpage.

Integer Addition: http://www.aaamath.com/add65_x3.htm Integer Subtraction: http://www.aaamath.com/subint1.htm Integer Multiplication: http://www.aaamath.com/mul65_x2.htm Integer Division: http://www.aaamath.com/div65_x2.htm

Here are some links to some games that review integer operations, absolute value, and number lines.

The Football Game: reviews number lines, addition and subtraction, and key indication words in word problems. http://www.mathgoodies.com/games/integer_game/football.html

The Calculator Game: reviews integer multiplication and addition. http://www.mathplayground.com/calculator_chaos.html

CyberOlympics: reviews comparing numbers, and integer addition. http://pbskids.org/cyberchase/math-games/cyber-olympics/

Stop that Creature: reviews integer addition, subtraction, multiplication, and division along with pattern recognition. http://pbskids.org/cyberchase/math-games/stop-creature/

Space Race: reviews integer addition: http://www.arcademicskillbuilders.com/games/orbit-integers/orbit-integers.html

Space race: reviews integer multiplication: http://www.arcademicskillbuilders.com/games/integer-warp/integer-warp.html

The Spider Game: reviews integer addition. http://www.arcademicskillbuilders.com/games/spider-match/spider-match.html

Mathman: reviews integer division. http://www.sheppardsoftware.com/mathgames/mathman/mathman_division.htm

Mathman: reviews integer subtraction. http://www.sheppardsoftware.com/mathgames/mathman/mathman_subtraction.htm

Who wants to be a millionaire? : reviews absolute value, integer addition, subtraction, multiplication and division. http://www.quia.com/rr/41496.html