standard_description: 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.
problem_activity: Activity
The purpose of this activity is for students to practice rewriting expressions representing percent change so that they only use multiplication.
Launch
Allow students to work with a partner or individually.
Student Facing
Write an equivalent expression using the distributive property:
\(65 - 0.45 \boldcdot 65\)
\(65 + 0.45 \boldcdot 65\)
\(91 \boldcdot (1.2)\)
\(x + 0.04x\)
Evaluate by multiplying just two numbers in your calculator. Write down the expression you calculated.
130 increased by 10%
25 decreased by 30%
50% more than 38
6% less than 200
Write an equivalent expression that only uses multiplication:
\(p - 0.35p\)
\(z - 0.85z\)
\(q + 0.06q\)
\(r + 0.64r\)
Student Response
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Activity Synthesis
Either display the correct solutions or invite students to share their solutions. Here are sample questions to promote discussion:
“Why is it okay to rewrite an expression like
\(z - 0.85z\)
so that it looks like
\(0.15z\)
?” (Use the distributive property, or think about how an amount decreased by 85% is the same as 15% of the amount.)
“Have you heard some examples of percent increase or decrease used in the real world? What were they?” (Sample response: The news might talk about crime decreasing by 10% compared to last year, or home prices in an area increasing by 25%.)
“How is an expression representing percent increase (like
\(1.05x\)
) different from an expression representing percent decrease (like
\(0.95x\)
)?” (The coefficient is greater than 1 versus less than 1. This is a result of adding or subtracting a percentage of the original amount.)


aligns: no