Transcript Adding and Subtracting integers on number line

7th Grade Math
Integers
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Contents
Integers
A Adding 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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+
─
+
+
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Adding Integers using Counters
• Let’s Try:
-4
+ -1 = ?
4 Negatives + 1 Negative
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─
─
─
─
+
─
─
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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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+
─
─
─
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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 Addend
3. Move the direction and distance of the 2nd Addend
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Adding integers
–2 + 5 = 3
-2
3
1. Start at zero
2. Go to first addend
3. Move in the direction and distance of the second
addend
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Adding integers
–3 + –4 = –7
-7
-3
1. Start at zero
2. Go to first addend
3. Move in the direction and distance of the second
addend
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Examples: (Show process on provided # line)
1. 6 + 5
= 11
= -9
2. -7 + -2
3. 5 + (-3)
=2
= -1
4. -3 + 2
5. 6 + (-7)
6. -9 + 4
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= -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.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25
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3+2
-5 + 5
-10 + 5
5+3
-5 + -4
-6 + 13
-35 + 10
-5 + 9
-8 + -7
-50 + 30
-7 + 17
-6 + 3
-30 + 10
5 minute
Challenge
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
-1 + 3
-9 + 3
-15 + 32
-4 + 7
-3 + 9
-30 + -15
6+7
-3 + 2
-10 + 4
0+7
-7 + 13
-12 + -1
-34 + 16
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Contents
Integers
A Subtracting Integers
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Use Sticky Notes:
• 3 – 1=
(Questions for following problems)
– 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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Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
5 – 8 = –3
5 + (-8) = –3
-3
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5
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Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
3 – –6 = 9
3+6=9
3
3 – –6
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is the same as
9
3+6
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Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
–4 – –7 == 3
–4 + 7 = 3
-4
–4 – –7
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3
is the same as
–4 + 7
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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 THREE
WORDS…
LITTLE, BITTY, TINY
ADD THE OPPOSITE!
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Examples:
1. 8 – 13
2. 6 – 14
3. - 10 – 1
4. 1 – (-2)
5. 4 – (-8)
= -5
= -8
= -11
=3
= 12
6. -3 – (-5)
7. -7 – (-4)
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=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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Exercise
Work out the following
1) 4 – 6
9) 3 – 6
2) +5 – 6
10)– 2 – 3
3) 4 – 10
11) – 3 – 3
4) 2 – 6
12) 0 – 5
5) 3 – 3
13)5 – 11 – 2
5 minute
Challenge
6) 4 – (-2)
7) 5 - -4
8) -9 – (-5)
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Extra Practice Below
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Exercise B
1) – 8 + 9
9) 5 – 9
16) 4 + – 2
2) – 6 + 10
10) – 8 + 8
17) 2 + – 3
3) – 2 + 8
11)6 – 12 – 4
18) 4 – (–2)
4) 0 – 8
12)7 – 10 + 3
19) 5 – (– 4)
5) 3 – 10
13)– 3 + 10 – 7
20) 15 – (– 3)
6) 8 – 10
14) 6 – 12 + 6
21) 4 – (– 6)
7) 7 – 9
15)8 – 16 – 3
22) – 9 – (– 5)
8) 4 – 10
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23) – 10 + – 7
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Exercise C
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
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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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