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 < What happens when you divide both sides of inequality by a positive number? Inequality stays the same! 10 -15 < 30 15 30 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 2 5 2 4 32 16 2 8 Zero Power ÷2 ÷2 3 2 2 2 2 2 0 ÷2 4 1 1 3 ÷2 ÷2 What’s the pattern? 2 0 0 1 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 4 81 ÷3 3 3 27 ÷3 2 3 9 ÷3 1 3 3 3 0 1 ÷3 Ch. 4 Section # 2 2 3 2 2 8 4 1 2 2 2 2 2 2 0 1 2 3 1 1 2 1 4 1 8 Negative Exponents ÷2 ÷2 ÷2 2 1 2 2 2 3 ÷2 ÷2 ÷2 2 4 3 6 1 2 1 4 1 8 1 3 2 1 4 6 7 9 5 2 1 2 1 1 2 2 1 2 3 1 7 5 1 9 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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 1 x n Ch. 4 Section # 2 Multiplying Powers with Same Base 3 4 4 5 4 4 4 4 4 4 4 4 4 8 When multiplying and base is the same, add exponents and keep the base! a 2 6 m 2 a 8 n a 2 m n 68 2 14 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Dividing Powers with Same Base 5 6 5 4 555555 5555 5 2 When dividing and base is the same, subtract exponents and keep the base! a m a n a m n 7 9 7 4 7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5 Raising Power to a Power 2 4 3 2 3 2 3 2 3 2 3 3 3 3 3 3 3 3 3 3 8 When raising a power, multiply the exponents and keep the base! a m n a m n 8 5 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 8 15 Revisit Negative Exponent Simplify expanded form and using power rule 6 3 6 5 6 3 6 5 666 66666 6 35 6 2 Whenever you have a number raised to a negative exponent, move it to the denominator and change the sign of the exponent! 1 6 2 6 2 x n Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 1 6 2 1 x n Revisit Zero Exponent Simplify expanded form and using power rule 7 4 7 4 7 4 7 4 7 7 7 7 7 7 7 7 7 44 7 Any number raised to the zero power is 1! 1 7 0 x 0 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 0 1 1 Squares 1 How many squares are inside perfect squares? 1 1 2 1 2 3 4 2 2 3 1 2 3 4 5 6 7 8 9 11 1 1 3 1 5 49 13 3 4 7 8 11 12 15 16 5 4 2 22 2 4 What are some other perfect squares? 2 6 10 14 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 2 33 3 9 2 4 4 4 16 6²=36, 7²=49, 8²=64, 9²=81, 10²=100… 2 5 5 5 25 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) 4 2 6 10 14 3 4 7 8 4 11 12 15 16 4 64 ? 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