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7th Grade Math

Integers

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Contents

Integers

AAdding Integers

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Adding Integers using Counters• Red Chips are Negative (─)

• White Chips are Positive (+)

• What is Additive Inverse?

• What is the value of the red chip + the white chip? Red + White = ?

─ +

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Adding Integers using Counters• This is called a “Zero Pair” because added

together they make zero!

• We can use these to add integers.

─ +

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Adding Integers using Counters• Let’s Try:

5 + 2 = ?

5 Positives + 2 Positives ─

+

++

+++

++

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Adding Integers using Counters• Let’s Try:

-4 + -1 = ?

4 Negatives + 1 Negative ─

+

─

──

──

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Adding Integers using Counters• Let’s Try:

-5 + 3 = ?

5 Negatives + 3 Positives ─

+

─

──

──+

++

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Adding Integers using Counters• Let’s Try:

6 + -2 = ?

6 Positives + 2 Negatives ─

+

─

─+++

+++

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Adding Integers

• Let’s practice a few with your counters.

-5 + 6

7 + -2

8 + 3

-7 + -1

10 + -3

-4 + -2

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Adding integers

We can use a number line to help us add positive and negative integers.

What directions can you move on a number line?How do you determine distance on a number line?

Direction: The way you are moving on a number line

(positive direction or negative direction)

Distance: How far you are moving on a number line

(ex. 5 places, 7 places, etc.)

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Adding integers

KEY POINTS!!!!

Label the number line in your notes (use coloring pencils, ink pens, highlighters, etc.)

1.When adding a positive integer, move to the right on the number line.2.When adding a negative integer, move to the left on the number line.

1. Start at zero – Always!2. Move the direction and distance of the 1st Addend3.Move the direction and distance of the 2nd Addend

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Adding integers

–2 + 5 =

-2 3

= 3

1. Start at zero2. Go to first addend3. Move in the direction and distance of the second

addend

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–3 + –4 == –7

-3-7

Adding integers

1. Start at zero2. Go to first addend3. Move in the direction and distance of the second

addend

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Examples: (Show process on provided # line)

1.6 + 5

2.-7 + -2

3.5 + (-3)

4.-3 + 2

5.6 + (-7)

6.-9 + 4

= 11

= -9

= 2

= -1

= -1

= -5

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Let’s Discover/Develop a Rule…

• Use the “Developing a Rule” Organizer

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What’s the rule?If both addends are Positive:

- Add together and the sum is positive(Ex. 8 + 4 = 12)

If both addends are Negative:- Add together and the sum is negative

(Ex. -6 + -5 = -11)If addends have different signs:- Subtract the absolute values, and - the sum will have the sign of the larger

absolute value. (Ex. -7 + 4 = -3)

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“Row, Row, Row Your Boat!”

• Operations with Integers song

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Independent Practice

• Glencoe Textbook – – Page 98 - #1 – 8– Page 98 - #10 – 27– Page 98 - #28 – 36

1.Write the actual problem on your paper

2.Use the rule to solve it.

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1. 3 + 2 2. -1 + 3

3. -5 + 5 4. -9 + 3

5. -10 + 5 6. -15 + 32

7. 5 + 3 8. -4 + 7

9. -5 + -4 10. -3 + 9

11. -6 + 13 12. -30 + -15

13. -35 + 10 14. 6 + 7

15. -5 + 9 16. -3 + 2

17. -8 + -7 18. -10 + 4

19. -50 + 30 20. 0 + 7

21. -7 + 17 22. -7 + 13

23. -6 + 3 24. -12 + -1

25 -30 + 10 26. -34 + 16

5 minuteChalleng

e

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Contents

Integers

ASubtracting Integers

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Use Sticky Notes: (Questions for following problems)

• 3 – 1=– Think of a time when you could experience this subtraction problem.

– How do you represent this situation with integers?

– How would you write an equivalent addition problem?

• 6 – 5 = – Think of a time when you could experience this subtraction problem.

– How do you represent this situation with integers?

– How would you write an equivalent addition problem?

• 14 – 8 =– Think of a time when you could experience this subtraction problem.

– How do you represent this situation with integers?

– How would you write an equivalent addition problem?

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Let’s Discover/Develop a Rule…

• Use the “Developing a Rule” Organizer

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Contents

Make each of these subtraction problems an

equivalent addition problem:1.5 - 3 =

2.6 - 4 =

3.10 – (-1) =

4.-5 – 4 =

5.-2 – (-7) =

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5-3

Subtracting integers

We can use a number line to help us subtract positive and negative integers.

5 – 8 == –3 5 + (-8) == –3

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3 – –6 =

3 9

= 9

We can use a number line to help us subtract positive and negative integers.

3 – –6 is the same as 3 + 6

Subtracting integers

3 + 6 == 9

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We can use a number line to help us subtract positive and negative integers.

–4 – –7 =

-4 3

= 3

–4 – –7 is the same as –4 + 7

Subtracting integers

–4 + 7 == 3

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Contents

Just remember, …

EVERY SUBTRACTION PROBLEM CAN BE MADE AN ADDITION

PROBLEM!!!

(The inverse of subtraction is addition.Also helps with commutative and

associative properties!)

For standard subtraction, just do it!!

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Contents

JUST REMEMBER THREELITTLE, BITTY, TINY WORDS…

ADD THE OPPOSITE!

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Examples:1.8 – 13

2.6 – 14

3.- 10 – 1

4.1 – (-2)

5.4 – (-8)

6.-3 – (-5)

7.-7 – (-4)

= -5

= -8

= -11

= 3

= 12

= 2

= -3

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Independent Practice

• Glencoe Textbook – – Page 105 - #1-11– Page 105 - #13-28

– Challenge - #37-40

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Subtraction Card Game

• Either “Subtract One” or “Partner Play”

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Dazzling Line Designs

• “Paper Folding” – Integer Subtraction

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Signed Rational Numbers

• “Fraction, Decimal and Integer Practice” Worksheet

• Buckle Down – page 23

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Work out the following

1) 4 – 6

2) +5 – 6

3) 4 – 10

4) 2 – 6

5) 3 – 3

6) 4 – (-2)

7) 5 - -4

8) -9 – (-5)

9) 3 – 6

10)– 2 – 3

11) – 3 – 3

12) 0 – 5

13)5 – 11 – 2

Exercise

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Extra Practice Below

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1) – 8 + 9

2) – 6 + 10

3) – 2 + 8

4) 0 – 8

5) 3 – 10

6) 8 – 10

7) 7 – 9

8) 4 – 10

9) 5 – 9

10) – 8 + 8

11)6 – 12 – 4

12)7 – 10 + 3

13)– 3 + 10 – 7

14) 6 – 12 + 6

15)8 – 16 – 3

Exercise B

16) 4 + – 2

17) 2 + – 3

18) 4 – (–2)

19) 5 – (– 4)

20) 15 – (– 3)

21) 4 – (– 6)

22) – 9 – (– 5)

23) – 10 + – 7

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Work out the following

1) 4 + – 2

2) 2 + – 3

3) 4 – –2

4) 5 – – 4

5) 15 – – 3

6) 4 – – 6

7) – 9 – – 5

8) – 10 + – 7

Exercise C

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Exercise E

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Ordered addition square

Copy the grid and work out the numbers in the empty squares

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Ordered subtraction square

Copy the grid and work out the numbers in the empty squares

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Mixed subtraction square

Copy the grid and work out the numbers in the empty squares

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Integer cards - addition and subtraction

Complete the sums