Instructional Strategies MAP2D Quarter 2 Instructional Strategies Grade 7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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

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 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 Ch. 3 Section # 1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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 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

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

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

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

Inequalities When do you flip the inequality? -5 < 10 4 ∙ (-5) 10 ∙ 4 -20 40 What happens when you multiply both sides of inequality by a positive number? Inequality stays the same! < -5 < 10 -3 ∙ (-5) 10 ∙ (-3) 15 -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

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! < -5 10 -15 < 30 What happens when you divide both sides of inequality by a negative number? Inequality flips! < 3 -6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Ch. 3 Section # 7

Chapter 4 Exponents and Roots Grade 7 MAP2D Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Ch. 4 Section # 2

Multiplying Powers with Same Base When multiplying and base is the same, add exponents and keep the base! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Dividing Powers with Same Base 1 1 1 1 When dividing and base is the same, subtract exponents and keep the base! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Raising Power to a Power When raising a power, multiply the exponents and keep the base! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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

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

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

(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

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 + 16 = 25 25 = 25 b 3 1 2 3 4 a 5 6 7 8 4 9 10 11 c 12 b 13 14 15 16 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Congruent (≅) Polygons A 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