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MAP2D
Quarter 2
Instructional Strategies
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
MAP2D
Chapter 3
Properties and Inequalities
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
It’s like
what you
learned in
All About
the Facts!
Properties
Commutative Properties
Think of “commuting” from home to school…
Addition
4+5=5+4
a + b = b + a
Addends trade places
3 + (7 + 6) = (7 + 6) + 3
Multiplication 3 ∙ 6 = 6 ∙ 3
ab = ba
Factors trade places
5(4 ∙ 8) = (4 ∙ 8)5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1
Associative Properties
Groups change, Numbers stay in same order
Addition
(7 + 5) + 6 = 7 + (5 + 6)
a + (b + c) = (a + b) + c
You are just regrouping the numbers so “friends” can be together.
Multiplication
4(3 ∙ 7) = (4 ∙ 3)7
(a ∙ b)c = a(b ∙ c)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1
Identify the Property
Compare left and right sides of equal sign
Ask, “What has Changed?”
Order – Commutative
Grouping - Associative
1. 16 + ½ = ½ + 16
1.Order Commutative of Add
2. 6(5a)=(6 ∙ 5)a
2.Grouping  Associative of Mult.
3. 4 ∙ (f ∙ 9) = (f ∙ 9) ∙ 4
3.Order  Commutative of Mult.
4. (g + h) + k = g + (h + k)
4.Grouping  Associative of Add
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1
Distributive Property
a (b  c )  a  b  a c
and
a (b  c )  a  b  a c
Think of a teacher distributing something
to every student in the class.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1
The Distributive Property
PROBLEM: 4(x + 3)
Four is multiplying the quantity “x + 3”
That means four will multiply both the x
and the 3!
 Multiply 4 times x
 Copy the operation sign
 Multiply 4 times 3
4 times x
4 times 3
4(x + 3)
4x + 12
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1
Inequalities
When is it an operation and when is it an inequality?
x—9
1. 9 less than x
Subtraction and switch the order When an “is”
is in front of
2. 9 is less than a
an operation
9 < a
phase like
Inequality 
“less than”
3. 10 greater than y y + 10
“greater than”
“more than”
Addition and switch the order
and “fewer
4. 10 is greater than b
than”, it is
10 > b
an inequality.
Inequality 
<
>
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 5
Inequalities
When do you flip the inequality?
-5 < 10
4 ∙ (-5)
-20
<
10 ∙ 4
What happens when you multiply
both sides of inequality by a positive
number?
Inequality stays the same!
40
-5 < 10
-3 ∙ (-5)
<
15
10 ∙ (-3)
-30
What happens when you multiply
both sides of inequality by a
negative number?
Inequality flips!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 7
Inequalities
When do you flip the inequality?
-15 < 30
 15
30
3
3
-5
10
What happens when you divide both
sides of inequality by a positive
number?
<
Inequality stays the same!
-15 < 30
30
 15
5
5
3
-6
What happens when you divide both
sides of inequality by a negative
number?
Inequality flips!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 7
<
MAP2D
Chapter 4
Exponents and Roots
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5
2  32
Zero Power
÷2
4
2  16
3
2 8
÷2
÷2
2
2 4
1
2 2
0
2 1
÷2
÷2
What’s the
pattern?
0
2 1
0
3 1
Any number raised
to the zero power
is 1!
x
0
1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
34  81
÷3
3
3  27
÷3
2
3 9
1
3 3
÷3
÷3
0
3 1
Ch. 4 Section # 2
3
2 8
2
2 4
1
2 2
0
2 1
1
2
1

2
1
2 
4
1
23  8
2
Negative Exponents
÷2
1
1
2

1
÷2
2
÷2
1
1
22  4  2
2
1
1
23  8  3
2
÷2
÷2
÷2
2
3

4 6 
1
23
1
4
6
7
5
1
2

9 2 
1
75
1
Whenever you
have a number
raised to a
negative
exponent, move it
to the
denominator and
change the sign
of the exponent!
x
n
2
9
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

1
x
n
Ch. 4 Section # 2
Multiplying Powers with Same Base
4  4  4  4  4  4  4  4  4  4
3
5
4
8
When multiplying and base is the same,
add exponents and keep the base!
a a a
m n
2 2  2
6
8
m n
68
2
14
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Dividing Powers with Same Base
555555
5

4
5555
5
2
6
5
When dividing and base is the same,
subtract exponents and keep the base!
a
m n

a
n
a
m
7
5

7
4
7
9
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Raising Power to a Power
3 
2 4
3 3 3 3 
2
2
2
2
 3  33  33  33  3
3
8
When raising a power, multiply the
exponents and keep the base!
m n
m n
5 3
15
a 
a
8 
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
8
Revisit Negative Exponent
Simplify  expanded form and  using power rule
1
6

6

6
6
 2

5
66666 6
6
3
1

2
6
6  2
35
2

6
6
5
6
6
3
Whenever you have a number
raised to a negative exponent,
move it to the denominator and
change the sign of the exponent!
x
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
n

1
x
n
Revisit Zero Exponent
Simplify  expanded form and  using power rule
7
7
7
7
4
4
4
4
7 7 7 7


7 7 7 7
 7
4 4

7
Any number raised
to the zero power
is 1!
1
0
0
7 1
x
0
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
1
Squares
1
How many squares are inside perfect squares?
1
1
2
1 2
3 4
2
3
1 2 3
4 5 6
7 8 9
3
1
5
49
13
2
6
10
14
3 4
7 8
11 12
15 16
1 1  1  1
4
2
22  2  4
What are
some other 3  3  32  9
perfect
squares?
2
5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 18 20
21 22 23 24 25
5
4 to the second
power Or
4 squared
4

4

4

16
6²=36, 7²=49,
2
8²=64, 9²=81, 10²=100… 5  5  5  25
2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Radical
√ Square Roots √
16  ?
1
5
“Square root of 16 is ?” 4
What’s the side of a square that 9
13
has 16 square units?
(4•4=16)
64  ?
4
2
6
10
14
3 4
7 8
4
11 12
15 16
4
Square root of 64 is ?
What’s the side of a square that has 64
square units?
Or ask what times itself is 64?
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
8•8=64
Pythagorean Theorem
a
Right Triangles Only
b
c
2
3
4
5
5
1
6
6
2
leg²+ leg²= hypontuse²
7
3
8
(longest side)
9
a² + b²= c²
9
4
7
1 2 3
13 10 11 8
5
14
4 5 6 3 5 15 12
16
7 8 9
3²
4
1
3
1 2 3 4
5 6 7 8
4 9 10 11 12
13 14 15 16
+ 4² = 5²
9 + 16 = 25
25
= 25
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
c
a
b
a
b
c
Congruent (≅) Polygons
A
B
D
C
M
N
O
L
Trapezoid ABCD ≅ Trapezoid LMNO
Which means:
∠A ≅ ∠L
∠B ≅ ∠M
∠C ≅ ∠N
∠D ≅ ∠O
AB ≅ LM
BC ≅ MN
CD ≅ NO
DA ≅ OL
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7