© boardworks ltd 2004 1 of 42 7 th grade math integers
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© Boardworks Ltd 2004 1 of 42
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
5 minuteChalleng
e
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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
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