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Common Core Learning Standards GRADE 7 Mathematics EXPRESSIONS & EQUATIONS Common Core Learning Standards Use properties of operations to generate equivalent expressions. Concepts operations with linear expressions 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Embedded Skills Add linear expressions with rational coefficients. Subtract linear expressions with rational coefficients. Factor (GCF) linear expressions with rational coefficients. Expand(Distributive property) linear expressions with rational coefficients. Apply properties of operations to all operations with rational coefficients. Translate word situations to algebraic expressions. Identify the GCF of rational coefficients in linear expressions. Identify like terms. Rigorous Sample Tasks Vocabulary Rational Coefficients Add Subtract Factor GCF properties of operations expand (distribute) Constant Like Terms Monomial Binomial Variable Scaffolded Sample Tasks Sue earns $15.95 per hour (h) plus a $100 bonus. Steve earns $8.50 per hour (h) plus a $300 bonus. If they combine their incomes, how much does the household make? Simplify the following: 15a + 3a (5x – 4y) – (3x + 7y) Simplify the expression: 3m + 4w + 6m + 5w Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. John has 6 boxes of b baseball cards and 17 additional cards. Mark has 4 boxes of b baseball cards and 200 additional cards. What’s the difference between them? Frank earned $10.80 per hour (h) plus $200.00 sales bonus for each of eight consecutive weeks. Write two different expressions to represent his income during this timeframe. The area of a rectangular cornfield is represented by 24x + 54. The length of the field is represented by (4x + 9). What is the width of the field? An architect is designing a rectangular fountain for the city park. Its area is represented by 16x – 40. Factor this binomial to determine the greatest whole number the length of the fountain could be. 3 8 Evaluate: 12 x 1 1 4 7x 2 8 Evaluate: 9x – 6.2(7.4x – 12) Will was told to fully factor the expression 8x – 4y + 12. His answer was 2(4x – 2y + 6). Explain why Will’s answer is not fully factored. Find the difference between 18.5 and 9.03 What is the GCF of (16m + 40)? What is the GCF of (12w – 9wx)? Factor the expression (8a + 6b – 10) Simplify the expression 7(4y + 11) Simplify 6(9a – 4) – 123a Simplify -7(3b – 12) + 15b Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Use properties of operations to generate equivalent expressions. Concepts rewriting algebraic expressions 7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” Embedded Skills Translate situation problems to algebraic expressions. Simplify expressions. Expressions Rewrite expressions to help analyze problems. Explain how an equivalent expression relates to the original situation problem. Rigorous Sample Tasks In finding the circumference of a circle, Mary said that she used the formula Cindy said that she used the formula C=2πr. Their teacher said that they both were correct. Explain how can this be? The cost of a Sabres jersey is represented as j. The jersey is on sale for 20% off the retail price. Write two equivalent expressions that represent the sale price. At a restaurant, Theresa estimated the 15% tip by multiplying the total bill by 1.15. Explain why this method can be used. Simplify 4.5c + ¾ c + 20% Vocabulary Scaffolded Sample Tasks 20% x – 11 – 15%x + 16 Change each percent to a decimal and then simplify the expression Combine like terms: 7 x – 2 + 0.5x 4 Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Concepts Embedded Skills multi-step equations Solve multi-step real-world problems involving all types of rational numbers. Justify the reasonableness of solutions using mental computation and estimation. Apply properties of operations to solve multi-step real-world problems with all rational numbers. Convert fluently between forms for common decimals, fractions, and percents. 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Rigorous Sample Tasks John says 2/3 is 2.3. Ida says John is incorrect. Who do you agree with and why? Erin bought 2 pairs of jeans for $29.99 each and 3 shirts for $17.99 each. Vocabulary Rational numbers Estimation mental Computation Integers Fractions Decimals Equivalent Explain the significance between different forms of equivalent rational numbers. Scaffolded Sample Tasks Write 25% as fraction and a decimal Write 1/5 as a percent and decimal Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. a.) If she has a $25 off coupon, how much will she pay before tax? b.) What percent of the original price did she save (round to the nearest whole number)? Mrs. Aumer will be hanging a 3 foot poster in her classroom. From corner to corner the length of the wall is 62 Explain how to convert 0.6 to a percent 1 inches long. After the 4 poster is hung, what is the distance, in inches, from the edge of the poster to the corner? Emerson had a vegetable garden last year with dimensions of 15 feet by 20 feet. This year, he wants to increase each dimension by 5-1/2 feet, what is the new area of the garden? Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Concepts Solve real-life and mathematical problems using numerical and algebraic expressions and equations. fluency with two step equations Embedded Skills Construct and solve two step linear equations from real-world problems. Translate verbal situations to two step linear equations. Vocabulary Solve two step linear equations. Explain the steps used in solving the equation. 7.EE.4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve two step linear equations fluently. Identify the sequence of operations used to solve a problem. Compare algebraic solutions to arithmetic solutions. Rigorous Sample Tasks Wendy is buying hand knitted hats for d dollars for her four daughters and herself. She also wants to purchase a cute $3.00 flower for each hat. Her total order (without tax) is $75.00. What is the cost of each hat? Explain how the distributive property can be used to help solve this problem. The length of a rectangle is three times its width. The perimeter is 40 cm. Write and solve an equation to determine the dimensions of the rectangle? You may use a picture to help you. Mike saves ¾ of his paycheck and his parents contribute $15 to his savings. If the total amount saved was $75, how much is his paycheck? Algebraic solution Arithmetic solution Two-step linear equations Property of Equality Inverse Operations Linear equations Distributive Property Scaffolded Sample Tasks Solve the equation 7.5(3x – 2) = 120. Explain each step you used to solve for x. Henry earns $8.50 per hour (h) that he works. He received a $100 sales bonus and his gross pay was $308.25. Write and solve an equation to determine how many hours he worked. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Concepts Solve real-life and mathematical problems using numerical and algebraic expressions and equations. fluency with two step inequalities 7.EE.4b.Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Rigorous Sample Tasks Embedded Skills Construct and solve two step linear inequalities from real-world problems. Graph the solution set of two step linear inequalities from real-world problems. Interpret and describe the solution in the context of the problem. Explain when and why it is necessary to change an inequality symbol. Explain when/why an open or closed dot is used on a number line. Write a linear inequality from a given graph. Vocabulary Two-step linear Inequalities At least At most ≤, <,>,≥ Inequalities Number line Closed dot Open dot Solution set Graph the solution set Explain how the solution set relates to the problem. Scaffolded Sample Tasks Thomas received a $5.00 i-tunes gift card from his friend for his birthday. He already has $15.52 saved in an account. He wants to purchase songs for his iPod. How many $ 0.95 songs (s) can Thomas purchase? Find your solution by writing an inequality. Solve and graph the solution on a number line. 2x – 3 < 12 If the perimeter of a rectangle is at most 72 feet, find the largest dimension for the width if the length is 19 feet. Solve and graph the solution on a number line. 5 – 7x ≥ 54 The new sign regarding height requirements at the entrance of the Viper Roller Coaster ride at Darien Lake is shown below. Your friend meets the sign’s requirements. Write an algebraic inequality to show his height (h) and write a replacement sign in word form that could Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only. be used at the Viper’s Entrance. 47 48 49 50 51 52 inches Explain the steps involved in solving this inequality: -8a + 1.7 < 0.1 When solving which of the following inequalities would result in a solution of x > 9: a) -5 x +8 < -37 b) 6x – 3 < 51 Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.