Math CC 7: ACCENTUATE THE NEGATIVE INV. 2 Investigation 2 ... · 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that

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Math CC 7: ACCENTUATE THE NEGATIVE INV. 2 Name: _______________________________ Per: ______

Investigation 2: Adding and Subtracting Integers

Student Signature: ________________________________ Due: _____________________________

Parent/Guardian Signature: ________________________________ Due: _____________________________

Date Learning Target/s Classwork

Homework

Self-Assess Your Learning

Day 1 Tuesday 9/20

Students move from concrete representations to addition algorithms.

Pg. 2-3: ATN 2.1a Pg. 6: ATN 2.1a Top ½ of page. Watch ED Puzzle Take notes.

Day 2 Wednesday 9/21

Students move from concrete representations to addition algorithms.

Pg. 4-5: ATN 2.1b Pg. 6: ATN 2.1b Bottom ½ of page. Watch Ed Puzzle, Take notes.

Day 3 Thursday 9/22

Students use chip boards and number lines to explore and gain experience in finding and representing differences of rational numbers. Students will explore the Commutative Property and Absolute Value.

Pg. 7-8: ATN 2.2a Pg. 11: ATN 2.2a Top ½ of page. Watch ED Puzzle

Take notes.

Day 4 Friday 9/23

Students use chip boards and number lines to explore and gain experience in finding and representing differences of rational numbers. Students will explore the Commutative Property and Absolute Value.

Pg. 9-10ATN 2.2b Pg. 11 ATN 2.2b Bottom ½ of page. Watch Ed Puzzle, Take notes.

Day 5 Monday 9/26

Students use chip models to understand the "take away" interpretation of subtraction.

Pg. 12 and 13-ATN 2.3

Pg. 14 Complete “What is the title of this picture?”

Complete (except pg 15-16) and sign packet

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

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Problem 2.1a: Extending Addition to Rational Numbers

A. 1. Find the sums of each group:

2. What do the examples in Group 1 have in common?

1)

2)

3)

What do the examples in Group 2 have in common?

1)

2)

3)

Using a chip model, diagram the equation from Group 1: ⁺2 + ⁺8 = ____

Using a chip model, diagram the equation from Group 2: ⁺2 + ‾8 = ____

Show the same number sentence on the number line:

Show the same number sentence on the number line:

When Adding numbers with DIFFERENT SIGNS:

1. Ignore the ______________ and __________________ the _________ ________________.

2. Give the answer the __________ of the _______________ A__________________ V_____________. Complete the examples:

‾2 + ⁺7 │‾2│ + │⁺7│ │ 2│ ― │ 7│= Which number is larger? _______

The answer will be + or - ? _______

‾2 + ⁺7 = ________

‾6 + ⁺5 │‾6│ + │⁺5│ │ 6│ ― │ 5│= Which number is larger? _______

The answer will be + or - ? _______

‾6 + ⁺7 = ________

Your example:

=

=

=

=

=

=

=

=

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3. Describe an ____________________________ for adding the ________________ in each group.

_______________ + _______________ = Positive

Example: 250 + 325 = ____________________

Your example:

_______________ + _______________ = Negative

Example: ‾45 + ‾15 = ____________________

Your example:

Positive + Negative = 1. Find the ____________________________

2. Take the sign with the ______________ ____________ _____________.

Example: 90 + ‾20 = ____________________

Your example:

Negative + Positive = 1. Find the ____________________________

2. Take the sign with the ______________ ____________ _____________.

Example: ‾400 + 25 = ____________________

Your example:

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Problem 2.1b: Extending Addition to Rational Numbers B. You know that ‾5 + ‾3 = ‾8. Use this information to solve these problems. Each is shown vertical and horizontal.

Show on the number line: 1.) ‾5 ¼

+ ‾3 or ‾5 ¼ + ‾3 = __________________

2.) ‾5 ⅕

+ ‾3 ⅗ or ‾5 ⅕ + ‾3 ⅗ = ___________________

3.) ‾5 ⅓ + ‾3 ⅔ or ‾5 ⅓ + ‾3 ⅔ =

__________________

C. You know that ‾8 + ⁺5 = ‾3. Use this information to solve these problems. (Remember the rule for adding a positive and a negative: Take the Absolute Value of each and find the Difference. Then use the sign of the larger #.)

1. ‾8.75 + ⁺5 =

2. ‾8.35 + ⁺5 =

3. ‾8.55 + ⁺5.3 =

4. ‾8.65 + ⁺5.25 =

5. ‾5.75 + ⁺8 =

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D.

Decide whether or not the expressions are equal or not equal.

Prove your answer with a chip model or a number line:

1.) ‾4 + ⁺6 and ⁺6 + ‾4 Equal or Not equal?

2.) ⁺2 ⅔ + ‾5 ⅞ and ‾5⅞ + ⁺2 ⅔ Equal or Not equal?

3.) ‾7 ⅔ + ‾ 1 ⅙ and ‾1⅙ + ‾7 ⅔ Equal or Not equal?

A Math rule that states the order addition or multiplication of two numbers does not change the result is called the

____________________________ Property.

Why is addition commutative? _____________________________________________________________________

_______________________________________________________________________________________________

_______________________________________________________________________________________________

E.

1. Find the sums in Group 3:

2. Name at least two things the examples in Group 3 have in common.

1.)

2.)

=

=

=

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+ + + +

+

+ +

+ +

+

2.1 Day 1 Homework: Solve using the algorithm below and correct with EDPuzzle

Positive + Negative or Negative + Positive: 1) Keep the sign of the number with a higher absolute value. 2) Subtract the numbers (largest number –smallest number)

Negative + Negative or positive +positive: 1) Keep the sign 2) add the numbers

Example 1: -150 + 30 Example 2: -45 + -15

12 + 4 =

12 + −4 =

−12 + 4 =

−7 + −8

4.5 + −3.8

−4.5 + 3.8




−250 + −750

−6,200 + 1,200 0.75 + −0.25

2

3+ −

1

6

−8

5+ −

3

5

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Problem 2.2a: Extending Subtraction to Rational Numbers Otis earned $5 raking leaves. He wants to buy a used bike that costs $7. 1.) Write a number sentence to represent this: 2.) Explain Otis’ situation using these chips boards.

Otis starts with $5

Change + / -

Otis ends with

Explain: Explain: Explain:

Show Otis’ situation using this number line:

The Arroyo family just passed mile 25 on the highway. They need to get to the exit at mile 80.

1.) Use this number line to show in how many more miles they need to travel (the change):

2.) Write the number sentence: start + change (+ / -) = end

Suppose the Arroyos drive back from mile 80 to mile 25. The would travel the same distance; however, they would travel in the opposite direction.

3.) Use this number line to show how many miles back they need to travel:

4.) Write the number sentence: start + change (+ / -) = end

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Find the Arroyos’ overall total distance by taking the A________________ V____________ of the difference between the two points on the number line. Write out the two _______________ _______________ expressions to represent the total distance traveled:

│ - │ and │ - │

What is the total distance driven? (Show your work)

A. Benjamin takes $75 from his savings. He goes shopping for school supplies and has $35 left when he is done. Use this number line to show how much he has spent:

1.) How much money has he spent?

2.) How should Benjamin label what he spent to show that this is money that he no longer has?

B. During a game of Math Fever the Super Brains have a score of ‾500 points. Earlier in the game, they incorrectly answered a questions for ‾150 points. However, the moderator later determined that the question was unfair. So ‾150 points are taken away from their score.

Use this number line to show how ‾150 points are taken away.

1.) Is subtracting ‾150 points going to increase or decrease the Super Brains’ score? Explain.

2.) What is the Super Brains’ score after ‾150 points are removed?

3.) Write a number sentence in two ways (addition and subtraction) to represent the Super Brains’ change in score. 1) 2)

This situation helps to us see that subtracting (―) a negative (―) is the same as adding a positive.

So remember, Don’t ______________________, ___________ the Opposite. Then follow the Addition Rules!

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Problem 2.2b: Extending Subtraction to Rational Numbers C. Use chip models or number line models to help solve the following:

1.) Find the differences in each group given below.

REMEMBER: Don’t ___________________, ADD the ___________________.

3.) Write a new number sentence that would fit in Grp 1:

Write a new number sentence that would fit in Grp 2:

4.) Describe the algorithm (what you did to solve the problems) in Grp 1:

Describe the algorithm (what you did to solve the problems) in Grp 2:

D. Apply the algorithm you developed on these rational number problems.

Change to + Solve Change to + Solve

1.) ‾1 ― ⁺3 =

2.) ‾1 ― ⁺¾ =

3.) ‾1½ ― ‾2 =

4. ) ‾1½ ― ‾¾ =

5.) ‾3 ― ⁺1¾ =

6.) ‾2 ― ‾¼ =

7.) ‾11 ―‾2½ =

8.) ‾25 ―‾222 =

E. 1. Consider the points ‾10 and 5 on a number line. a. Write two absolute value expressions, one moving in a positive direction and one moving in a negative direction, to represent the distance between these two points.

1.) │ │ 2.) │ │

b. What is the distance between the points ‾10 and 5 on a number line?

=

=

=

=

change to +

=

=

=

=

change to +

=

=

=

=

=

=

=

=

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2. a. Write two absolute value expressions, one moving in a positive direction and one moving in a negative direction, to represent the distance between these two points.

1.) │ │ 2.) │ │

b. What is the distance between the points on a number line?

F. Decide whether or not the expressions are equal or not equal.

Prove your answer with number sentences and a chip model or number line:

1.) ‾2 ― ⁺3 and ⁺3 ― ‾2 Equal or Not equal?

2.) ⁺12 ― ‾4 and ‾4 ― ⁺12 Equal or Not equal?

3.) ‾15 ― ‾20 and ‾20 ― ‾15 Equal or Not equal?

4.) ⁺45 ― ⁺21 and ⁺21 ― ⁺45 Equal or Not equal?

Is there a Cummutative Property of Subtraction? ______ How do you know that?

Write a word problem about temperature that can be represented by the this number sentence: ⁺7 ― ‾4 = ⁺11

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-

−

− −

− −

−




Subracting a negative number: 1) Rewrite the subtraction sign and negative sign to make a + 2) Follow algorithm that applies Example 1: −7 − (−4) =

−15 + 23

15 + 23

−15 + 23

−15 − 23

2.1 Day 4 Homework: Solve using the algorithms above and correct with EDPuzzle

−0.8 + 0.5

0.8 + 0.5

−0.8 − .05

0.8 + − 0.5

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Problem 2.3: The “ + / ― ” Connection and Practice A. The chip board shows a value of ⁺5: 1. There are two possible moves, one addition and one subtraction, that would change the value of the board to +2

a. Complete the number sentences to represent each move and show it on the chip boards:

⁺ 5 + ____ = ⁺ 2 and ⁺ 5 ― ___ = ⁺ 2

b. Describe how these moves are different from each other on the chip boards.

2a. How would you complete the number sentences below to change the value on the board to ⁺8?

⁺5 + ____ = ⁺8 and ⁺5 ― ___ = ⁺2 b. Describe how these moves are different from each other on the chip boards.

B. 1. Complete each number sentence.

a. ⁺5 + ‾4 = ⁺5 ― _____ b. ⁺5 + ⁺4 = ⁺5 ― ________

c. ‾ 7 + ‾2 = ‾7 ― ______ d. ‾7 + ⁺2 = ‾7 ― _______

2. What patterns do you see that can help you restate any addition problem as an equivalent subtraction problem?

C. 1. Thinking about restating a subtraction problem as an addition problem. How can you complete these numbers sentences so that each subtraction problem is restated as an addition problem?

a. ⁺8 ― ⁺5 = ______ + ______ b. ⁺8 ― ‾5 = ________ + _________ c. ‾4 ― ⁺6 = ______________ d. ‾4 ― ‾6 = ____________________

2. What patterns do you see that can help you restate any subtraction problem as an equivalent addition problem?

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+ ADDING Integers Rules +

― SUBTRACTING Integers Rules ―

D. Solve the following using the Rules for Addition and the Rules for Subtraction. SHOW ALL YOUR WORK!

1.

2.

Subtracting an integer is the same as: Adding its _____________

Therefore,

Subtracting a positive is the same as: Adding a ______________

Subtracting a negative is the same as: Adding a ______________

Then, just use the _____________ RULES to solve!

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Page 15 and 16 is not required to be completed for packet credit. It is designed for extra

practice if classwork is finished early.

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Documents

Math CC 7: ACCENTUATE THE NEGATIVE INV. 2 Investigation 2 ... · 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that