1. Instructional Strategies
MAP2D
Quarter 2
Instructional Strategies
Grade 7
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2. Properties and Inequalities
MAP2D
Chapter 3
Properties and Inequalities
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

3. Properties Commutative Properties Addition 4 + 5 = 5 + 4 a + b = b + a
It’s like what you learned in All About the Facts!
Properties
Commutative Properties
Think of “commuting” from home to school…
Addition = 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
Ch. 3 Section # 1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

4. 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

5. Identify the Property 16 + ½ = ½ + 16 6(5a)=(6 ∙ 5)a
Compare left and right sides of equal sign
Ask, “What has Changed?”
Order – Commutative Grouping - Associative
16 + ½ = ½ + 16
6(5a)=(6 ∙ 5)a
4 ∙ (f ∙ 9) = (f ∙ 9) ∙ 4
(g + h) + k = g + (h + k)
Order Commutative of Add
Grouping  Associative of Mult.
Order  Commutative of Mult.
Grouping  Associative of Add
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1

6. Distributive Property
and + 5 5 = +
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

7. 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!
4 times x
4 times 3
 Multiply 4 times x
4(x + 3)
 Copy the operation sign 4x + 12
 Multiply 4 times 3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 1

8. Inequalities When is it an operation and when is it an inequality?
9 less than x
9 is less than a
10 greater than y
10 is greater than b
x — 9
When an “is”
is in front of
an operation
phase like
“less than”
“greater than”
“more than”
and “fewer
than”, it is
an inequality.
Subtraction and switch the order
9 < a
Inequality  <
y + 10
Addition and switch the order
10 > b
Inequality  >
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 3 Section # 5

9. Inequalities When do you flip the inequality?
-5 < 10
4 ∙ (-5) ∙ 4
What happens when you multiply both sides of inequality by a positive number?
Inequality stays the same!
<
-5 < 10
-3 ∙ (-5) ∙ (-3)
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

10. Inequality stays the same!
Inequalities When do you flip the inequality?
-15 < 30
What happens when you divide both sides of inequality by a positive number?
Inequality stays the same!
<
-15 < 30
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

11. Chapter 4 Exponents and Roots Grade 7 MAP2D
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12. Any number raised to the zero power is 1!32 81 ÷2 ÷3
What’s the pattern? 16 27 ÷2 ÷3 8 1 ÷2 9 1 4
Any number raised to the zero power is 1! ÷3 ÷2 3 2 ÷3 ÷2 1 1
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Ch. 4 Section # 2

13. Negative Exponents 8 ÷2 4 ÷2 2 ÷2 1 ÷2 ÷2 ÷2
Whenever you have a number raised to a negative exponent, move it to the denominator and change the sign of the exponent! 4 ÷2 2 ÷2 1 ÷2 ÷2 ÷2
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Ch. 4 Section # 2

14. Multiplying Powers with Same Base
When multiplying and base is the same,
add exponents and keep the base!
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15. Dividing Powers with Same Base1 1 1 1
When dividing and base is the same, subtract exponents and keep the base!
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16. Raising Power to a Power
When raising a power, multiply the exponents and keep the base!
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17. Revisit Negative Exponent
Simplify  expanded form and  using power rule 1 1 1
Whenever you have a number raised to a negative exponent, move it to the denominator and change the sign of the exponent!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

18. Any number raised to the zero power is 1!
Revisit Zero Exponent
Simplify  expanded form and  using power rule 1 1 1 1
Any number raised to the zero power is 1!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

19. Squares How many squares are inside perfect squares?1 4 3 2 1 7 8 9 4 5 6 1 2 3 15 14 12 10 8 7 6 13 9 5 4 1 3 2 16 11 13 18 17 14 12 9 8 7 16 11 6 4 1 3 2 24 10 15 20 5 23 22 21 25
4 to the second power Or
4 squared
What are some other perfect squares?
6²=36, 7²=49,
8²=64, 9²=81, 10²=100…
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

20. (4•4=16) √ Square Roots √ 4 “Square root of 16 is ?” 4 4 4 8•8=64
Radical 4 15 14 12 10 8 7 6 13 9 5 4 1 3 2 16 11
“Square root of 16 is ?”
What’s the side of a square that has 16 square units?
(4•4=16) 4 4 4
Square root of 64 is ?
What’s the side of a square that has 64 square units?
8•8=64
Or ask what times itself is 64?
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

21. Pythagorean Theorem a² + b²= c² c a b 3² + 4² = 5² + 16 = 25 25 = 25
Right Triangles Only
leg²+ leg²= hypontuse²
(longest side)
a² + b²= c² b 5 6 4 c 7 1 3 8 2 5 2 9 3 6 9 1 4 7 10 1 2 3 4 3 5 13 8 c 11 5 a 14 4 5 6 12 15 16 7 8 9
3² + 4² = 5²
= 25
= 25 b 3 1 2 3 4 a 5 6 7 8 4 9 10 11 c 12 b 13 14 15 16
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22. Congruent (≅) PolygonsA B
Trapezoid ABCD ≅ Trapezoid LMNO
Which means:
∠A ≅ ∠L
∠B ≅ ∠M
∠C ≅ ∠N
∠D ≅ ∠O
AB ≅ LM
BC ≅ MN
CD ≅ NO
DA ≅ OL D C M N O L
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7