Name____________________________________________________________

Operations with Rational Numbers Pre-assessmentAnswer each question with the best of your ability. Show your work. This is NOT a test. You

are NOT expected to know how to do every problem.

Evaluate each expression.

1. 5 + (-6) =

2. -11 - 15 =

3. -12 + 14 =

4. + =

5. .09 + .206 =

6. (-5)(6)=

7. (-1)(-3)=

8. (-7) (-6) =

9. 8

10. 36/(-6) =

11. (-72)/(-6) =

Read the following problems and solve them.

12. Your mom gave you $20 to spend at the movies. Your ticket costs $7.50. At the

concession stand, you want to buy a drink and popcorn combo that costs $12.45. Will

you have enough money for the combo after purchasing your ticket?

13. The distance between your house and Grandma’s house is 16 miles. Today is her

birthday and you want to visit her. You travel 5 miles towards her house and realize you

forgot her gift. You go back to your house to get her gift and start traveling to her house

again. What are the total number of miles you traveled to get to your Grandma’s house?

14. There are 10 pieces of Starburst per package. If you bought 5 packages of Starburst,

how many pieces do you have?

C2 Operations with Rational Numbers 10/23/2014

Classifying Numbers

Time: 90 minutes

Standard:7.NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Objectives:SWBAT:-know the properties of counting numbers, whole numbers, integers, and rational numbers.-apply the properties of numbers to classify them into their appropriate category.

Materials:- Notebooks- 5 Copies of Matching Game

Procedure:1. Collect Construction Packets/Create a House

2. Take Preassessment (15-25 minutes)

3. Start lesson on Classifying Number

Lesson:

1. Ask students to get out notebooks. 2. Ask students what they consider to be counting numbers.

2.1. Counting numbers: Another name is natural numbers. Numbers we have learnedsince we are babies. Start at 1, 2, 3, and so on.

2.2. Give me an example of a counting number.

3. Ask what a whole number is.3.1. Whole numbers: Counting numbers including 0.

4. So we have whole numbers, but what about negative numbers? What name classifies them in the number system?4.1. Integers : Whole numbers and their opposites. Opposites meaning opposite of

each other on the number line. Such as 1 and -1. 2 and -2….4.2. Draw a number line. The further you go left, the numbers get smaller. The further

right you go, the larger the numbers get. 4.2.1. Which is larger? -2 or -3? Compare using < or >.

5. What about fractions? Decimals? Would they be considered integers?5.1. These numbers are Rational Numbers5.2. Rational numbers: Numbers that be written as fractions or ratios. A fraction made

up of an integer as a numerator and the denominator.5.2.1. ex. -½ is a rational number. -1 and 2 are integers. 2.5/3.5 is not a rational

number. 2.5 and 3.5 are not integers.5.3. Terminating decimals, repeating

6. Rationals numbers is one big category. It includes integers, which then includes whole numbers, which includes counting numbers.

6. Matching Game (10 minutes)With their group, students will match numbers to their proper name.Directions: Each group with get a set of cards. In your group, work together to put

numbers into their proper classification. I also want arrange your matches in such a way to showthat each category can be included into rational numbers, but yet negative numbers are not included into whole numbers.

Each group must turn in a diagram of their matching.

HWCh. 2 (20-26, 39, 45-47)Matching Numbers worksheet

Rational Number Integer

Whole Number Counting Number

0 -7

2.98 0.0

26 -0.67

0.

10.1 + 4.5

7.909359034 7

Name___________________________________________________________

What’s that Number? Directions: Match the letter with its corresponding word to a number based on its properties. A letter may be used more than once, and a number may have multiple names (i.e. -7 is an integer as well as a rational number)

A. Rational Number B. Integer C. Whole Number D. Counting

__________ 1. 67

__________ 2. -0.963

__________ 3.

__________ 4. -84

__________ 5. 0.

__________ 6.

__________ 7. 5.2392389

__________ 8. 0

C2 Operations with Rational Numbers

Time: 45 minutes

Standards: 7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Objectives:SWBAT:

● use a number line to add integers

Procedure:- Correct homework from last night- Pass out graded Create a House- Ask the students to get out their notebooks, title page “Adding Integers with a Number

line”- Go over these examples

Show examples using three different learning styles:Auditory: “So we have -3 + (-6), so thats means we go 3 to the left from zero and

then 6 units to the leftVisual: Draw an arrow pointing the left, then arrow pointing to left againKinestic: Have students move their fingers along the number line from 0 to -3,

then from -3 to -6.

HW: 2-2 (13-20)

C2 Unit 2 Operations with Integers

Adding/subtracting Integers Using Chips and Problem Solving

Time: 90 minutes

Standards:7.NS.A.1:Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.1b:Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts

7. NS.A.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p+ (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

Objectives:SWBAT:

● use red/yellow counter chip manipulatives to add and subtract integers● know the definition of additive inverse● apply properties of operations of adding and subtracting integers to real-life problems

Materials:- 2-2 Problem Solving- 2-3 Problem Solving- Red/Yellow Integer Chips- Notesheet (problems from

http://www.mathgoodies.com/lessons/vol5/challenge_vol5.html) cut in half

Procedure1. Have students clear off their desk of everything.2. Pass out the integer chips to each table.3. Do Lab 2-2 pg.804. Do Lab pg. 865. Have the students put the chips in a pile on their desks and Lauren/Cindy/I will collect

them.6. Pass out Notesheet to students

7. Them them cut out and paste the two problems in their notebook.7.1. Lauren/Cindy will pass out scissors, tape and glue.

8. Go over problem #1.9. Go over problem #2.

10. Introduce new topic of additive inverse. 10.1. What does inverse mean?10.2. What does additive mean?10.3. Based on the definition of these words, what do you think it means?10.4. Additive inverse: Sum of two numbers is 0.

10.4.1. Give me two numbers when added together give me 0.

HW2-2 PS odds2-3 PS odds

1.

In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

13. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?

1.

In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

14. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?

C2 Unit 2 Operations with Integers

Subtraction and Absolute Values

Time: 90 minutes

Standards:7. NSA .1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7. NSA .1 c : Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

6. NS . C .5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Objectives:SWBAT:

● Use a number line to subtract integers● formulate an addition and subtraction rule for integers● recognize an absolute value sign● show that the distance between two rational numbers is the absolute value of their

difference● know examples of the use of positive and negative numbers in real-life and the meaning

of 0 in each situation

Materials:NotebookAbsolutely! Worksheet

Procedure:- Correct homework (15 minutes)- Have the student take out their notebooks.- Let’s think about a rule for adding integers. However, do that we need to learn about

absolute values. - Draw a number line.

- What is the distance between 0 and 2? Distance btw 0 and -2?- What is the absolute value?

- Distance between 0 and a number on the number line. Denoted by |n|, n is any number

- Examples |-2|, |6|.

- So when we add integers, we use a rule that involves the absolute value.- To add two integers using the same sign, meaning they are both negative or both

positive, find the sum of their absolute values. Use the same sign as the numbers.

- example -5 + (-7) = |-5| + |-7| = 5 + 7 = 12, answer is -12- Do a number line to show its true.

- To add two integers with a different sign, find the difference of their absolute values. Use the sign of the number with the greatest absolute value.

- example: 6 + (-7) |6| = 6, |-7| = 7, 7-6= 1. 7 has greatest abs. valeu, so use sign of -7, so answer is -1.

- Do a number to show it true.- Go over subtraction with a number line

- Have student think about makinga rule for subtracting integers

- What if I said 2 + 3? Or -4 + (-2)?

3.3 Subtraction Rule: When subtractingintegers, add the opposite.

11. Using absolute value to find distancebetween two rational numbers.

11.1. Find the distance between -5and -6.

11.1.1. What does differencemean?

11.1.2. Remember rule forsubtracting integers.

11.1.3. Use the absolute value tofind their distance.

11.2. Find the distance between -17 and -9 on your own using the method we discussed. Be prepared to explain your answer.

12. Lastly, let’s think of some examples we see in real-life that use negative numbers.12.1. Students will brainstorm examples. Have them explain what the negative means.

HW2-3 #13-19 odd, 35, 37-43 odd

Name ________________________________________________

Absolutely!Find the absolute value.

14. |5| 2. |-9| 3. |1|

15. |-7| 5. |8-9| 6. |6+5|

Find the distance between the two given rational numbers using the absolute value of your difference. Use a number line to confirm your answer.

15. -8, 12

16. 7, -5

17. -4, -9

18. -1, 5

C2 Operations with Integers

Multiplication with Integers

Time: 90 minutes

Standards:

7.NS.2a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Objectives:SWBAT:

● know the rules for multiplying integers● recognize the various representations of multiplication (*, ()(), x, ab)● apply the distributive property to solve multi-digit multiplication problems

Materials:- Integer chips- Multiplying Integers

Procedure:13. Check homework and answer questions14. Have students get out their notebooks

Multiplying Integers

15. Give rules for multiplying signs Same signs (+ + = +, - - = - )

16. Ask why two negatives equal a positive.17. Give analogy (Tell you to eat, is a positive. Tell you to not eat is negative. But if I tell you

to no not eat, it turns back into a positive statement.Different signs (+ - = - )

Check for understanding:

19. Hand out integer chips.19.1. Students will use integer chips to determine whether the answer will be positive

or negative. Red = negative, Yellow = positive.19.2. Students hold up the correct color when prompted. 19.3. Then call on student to tell me the numerical answer.19.4. Problems

6 times 8 -2 times -3 -3 times 75 times -8 7 times 8 -1 times 4 -2 times -10Students will write these problems and answers down in their notebooks.

- Representations of multiplication- 5*6?- 5(6)?- 5 dot 6- These are representations of multiplication, and they will give the same product.

!!! x, *, ()(), and dot all mean multiplication !!!!Distributive property

2. Ask 5 students to come up the front of the room. 2.1. Here we have 5 people. 2.2. I’m going to ask you to arrange yourselves into a group of 2 and a group of 3.

2.2.1. Do we still have 5 people?1.3 Arrange into group of 1 and group of 4.

Do we still have 5 people?1.4 What’s another way they can represent 5?

5 groups of 1 1.5 rearrange back into 2 and 3.

Give each student 2 chips.Ask the group of 2 how many chips they have.Ask the group of 3 how many chips they have.How many chips do we have in total?

Students may go sit down4. Ask what the word distribute means.

4.1. It means to spread evenly.5. Let’s do the problem 6*36.

5.1. Find the answer, 216.5.2. We can find the answer a different way.5.3. What are ways we can represent 36, like we did with the 5 people?

Ex) 6 and 30, 18 and 18, 12 and 24, etc.Rewrite as 6*(12 + 24)Let’s say I gave 12 people 6 chips, and 24 6 chips. How can I represent that?

6*12 6*24. (use arrows to connect)How can I find the total number of chips I gave out?

3. This is called distributive property. We are distributing the 6 evenly to each number.Check for understanding:

4. By yourselves, I want you to multiply 5(10) using the distributive property.

HW Multiplying Integers

Name_____________________________________________________

Multiplying Integers

Find the product.

5. 2. 3.

6. 5. 6.

Use the distributive property to find the product. Confirm your answer using a calculator.

7. 3(12)

7. 2(56)

B. 10(54)

10. 7(13)

C2 Unit 2 Operations with Integers

Dividing Integers and Application Problems

Time: 90 minutes

Standards:7.NS.2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts

Objectives:SWBAT:

● know the rules for dividing negative and positive numbers● recognize the different representations for dividing● apply multiplication and division of integers to solve real-life problems

Materials:- Application problems (https :// app . activateinstruction . org / playlist / resource -

sview / id /50 f 1 adbfefea 659 c 39000007/ rid /523 debd 807121 c 88435 cbd 12/ bc 0/ search / bc 1/ user / bc 2/ playlist / bc 1_ id /51 c 363 fe 07121 c 8742240425, http://www.glencoe.com/sites/common_assets/workbooks/math/pdf_workbook/m3pwp.pdf) cut in half

- 2-4 Exercises- 2-4 Problem Solving- I Can Statements

Procedure:1. Check homework and answer any questions2. Have students get their notebooks out.

Division16. Since division is the inverse of multiplication, it uses the same rules as multiplying for

integers.16.1. Same signs = positive16.2. Different signs = negative

17. Division can be represented two different ways17.1. As a fraction17.2. /, ÷

3. Example problems(-9)/(-3)8/2

-6/3

Application18. Pass out the application sheets, scissors and glue.

18.1. Students will put the problems in their notebooks19. Think-Pair-Share

19.1. For 5 minutes, I want to look at the two problems by yourselves. Then after 5 minutes, talk about the problems with the person next to you. Then we will come back as a whole group and discuss our answers.

19.2. I want you to write an expression first. What is an expression?19.3. Then, evaluate and interpret. What does evaluate mean?

Go over I Can Statements for Test

HW 2-4 25-41 odds, 2-4 Problem Solving Odds, Test Thursday

A person has a debt of $200. Five friends offer to pay off all of the debt. How much does each person need to pay in order to pay off the debt?

At an office supply store, pens are $1.69 per dozen and note pads are $4.59 per dozen. Can Shirley buy 108 pens and 108 note pads for $50? Explain your reasoning.

A person has a debt of $200. Five friends offer to pay off all of the debt. How much does each person need to pay in order to pay off the debt?

At an office supply store, pens are $1.69 per dozen and note pads are $4.59 per dozen. Can Shirley buy 108 pens and 108 note pads for $50? Explain your reasoning.

I can... I can do it! Made Notecard

I can classify numbers based on their properties.

I can add and subtract integers with a number line.

I can evaluate expressions with adding and subtracting integers.

I can find the absolute value of a number.

I can determine the distance between two integers using the absolute value of their difference.

I can evaluate expressions with multiplying and dividing integers.

I can use the distributive property as a strategy to multiply multi-digit integers.

I can apply addition, subtraction, multiplication, and subtraction to solve real-life problems.