Transcript Adding integers

7th Grade Math
Integers
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Contents
Integers
A Adding Integers and Signed Numbers
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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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Homework
• Carnegie – Page 219 - 220
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Adding integers on a number line
Before we begin, you and your group must
complete the following task:
You have 5 minutes to formulate the
process of adding integers using a
number line as your manipulative.
Use the example of -5 + 3 = ?
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Adding 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!!!!
Positive number, move
When adding a ________
to the ________
on the number line.
Right
Negative number, move
When adding a ________
Left
to the ________
on the number line.
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PROCESS for Adding on a Number Line:
Step 1
Zero
•ALWAYS, start at _______!
Direction and ______
Distance
•Move the _________
Addend
Step 2 of the first _________.
•FROM THAT POINT, move the
Distance of
Direction
___________
and _________
Step 3 the second ____________.
Addend
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Adding integers
PROCESS for Adding on a Number Line:
1. Start at zero – Always!
2. Move the direction and distance of the 1st Addend
3. From that point, move the direction and distance of
the 2nd Addend
How close was your group to the
correct steps?
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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 # lines)
= 11
1. 6 + 5 (Do together)
= -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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Practice
• Complete “Adding Integers Number Line”
worksheet
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Let’s Discover/Develop a
Rule…
• Use the “Developing a Rule” Organizer
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Adding Signed Numbers Rule
If both are Positive:
- Add and the sum is positive
(Ex. 8 + 4 = 12)
If both are Negative:
- Add and the sum is negative
(Ex. -6 + -5 = -11)
If they have different signs:
- Subtract the absolute values, and
- the sum will have the sign of the larger absolute
value.
(Ex. -7 + 4 = -3)
Remember counters
and # line
Remember counters
and # line
Do you have more +
or -?
7-4=3
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“Row, Row, Row Your Boat!”
or
“Add, Add, Add Your Integers!”
• 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
and Signed Numbers
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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 would you write an equivalent addition problem?
• 6–5=
– Think of a time when you could experience this subtraction problem.
– How would you write an equivalent addition problem?
• 14 – 8 =
– Think of a time when you could experience this subtraction problem.
– 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
Just remember, …
EVERY SUBTRACTION PROBLEM
CAN BE MADE INTO 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!
This is the Rule!!
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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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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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