Name ______________
Date _______________
Equivalent Expressions in Context
1. Which expression is not equivalent to the other three? Justify your reasoning.
−8 − 7𝑛 + 16𝑛
9(𝑛 − 8)
𝑛 − 8 + 8𝑛
9𝑛 − 8
2. Why are the expressions 3(𝑛 − 2) + 2(𝑛 − 2) and 5(𝑛 − 2) equivalent? Justify
your answer.
3. Patricia, Hugo and Sun work at a music store. Each week, Patricia works three
more than twice the number of hours that Hugo works. Sun works 2 less than Hugo.
(a) Let x represent the number of hours that Hugo works each week. The number of
hours that Hugo, Patricia, and Sun work can be modeled is shown below. Write an
expression that represents each person’s number of hours.
Hugo ___________
Patricia ___________
Sun ___________
(b) Model the total number of hours that Patricia and Sun work together. Draw the
result below. Then write an expression for the drawing.
(c) Like tiles are tiles that have the same shape. Using your model, group like tiles
together and remove the zero pairs. Draw the result below. Then write an
expression for your drawing.
4. Which expression is not equivalent to the other three?
2(1 + 2𝑛 + 3𝑛)
2(1 + 2𝑛) + 2(𝑛 + 2𝑛)
6𝑛 + 2 + 4𝑛
2(3𝑛 + 1) + 4𝑛 + 1
5. Write a real world problem for the expression 5.75𝑛 + 25.
6.
How many squares will be in the 5th and 6th LOGO? How many squares will be in
the 100th LOGO? How many squares will be in the nth LOGO? Please explain how
your pattern works.