Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
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The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.
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A student solved the problem below as part of her homework. Review her work and check for any mistakes. For each line in her work, explain what she did to get her next step.
Homework Problem:
$${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$$
Student’s Work:
$${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$$
$${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$$
$${\left ( -\frac{5}{3}-1 \right )x+0}$$
$${-\frac{8}{3}x}$$
Find the perimeter of the parallelogram.
An expression is given.
$${-2y+\frac{3}{2}x+\frac{7}{4}}$$
Which are equivalent to the given expression? Select each correct answer.
a. $${-\frac{1}{2}xy+\frac{7}{4}}$$
b. $${\frac{3}{2}x-2\left ( y+\frac{7}{2} \right )}$$
c. $${-\frac{1}{4}y+\frac{3}{2}(y+x)}$$
d. $${-2y+\frac{1}{2}\left ( 3x+\frac{7}{2} \right )}$$
e. $${\frac{1}{4}(-8y+6x+7)}$$
Math Spring Operational 2016 Grade 7 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 10:59 a.m..
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Which expressions are equivalent to the expression $${\frac{5}{8}(x-y)-\frac{1}{4}x+y}$$?
Select three correct answers.
a. $${\frac{3}{8}x+\frac{3}{8}y}$$
b. $${\frac{3}{8}x+1\frac{5}{8}y}$$
c. $${\frac{5}{8}x-y-\frac{1}{4}x+y}$$
d. $${\frac{5}{8}x-\frac{5}{8}y-\frac{1}{4}x+y}$$
e. $${\frac{5}{8}x-\frac{1}{4}x+y-\frac{5}{8}y}$$
Math Spring Operational 2015 Grade 7 Performance Based Assessment Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 11:08 a.m..
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