## chapter 7 outline

**Section 7.1:**You will identify the relationship between distance, rate, and time and will use it to solve word problems. You will connect your work with percents and scale factors to solve new problems involving part-whole relationships. You will also develop strategies to solve equations with fractional and decimal coefficients. Finally, you will explore percent change and simple interest.

**Section 7.2:**This section reviews and extends the idea of proportional relationships that you studied in Chapter 4. You will learn new strategies for solving proportional situations.

## Big Ideas

- Solve problems involving distance, rate, and time.
- Solve equations that have fractional or decimal coefficients.
- Find the whole amount if you only know a percentage of it, and vice versa.
- Calculate simple interest.
- Set up and solve proportional equations.

## Guiding Questions

- What is the relationship?
- How is it changing?
- What is the connection?
- How can I represent it?
- What strategy should I use?

## vocabulary

box plot

coefficient

constant of proportionality

Fraction Busters

first quartile

Giant One

histogram

interest

interquartile range (IQR)

mean

median

measure of central tendency

outlier

principal

percent change

proportional relationship

rate

scale

similar

stem-and-leaf plot

third quartile

coefficient

constant of proportionality

Fraction Busters

first quartile

Giant One

histogram

interest

interquartile range (IQR)

mean

median

measure of central tendency

outlier

principal

percent change

proportional relationship

rate

scale

similar

stem-and-leaf plot

third quartile

## CCSS Standards in Unit

. 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.**7.EE.2***For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”*. 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.__7.EE.3__*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.*Solve word problems leading to equations of the form__7.EE.4a.__*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 real-world and mathematical problems involving the four operations with rational numbers. (complex fractions included).**7.NS.3**. Represent proportional relationships by equations.**7.RP.2c***For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn*.. Explain what a point**7.RP.2d***(x, y)*on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1,*r)*where*r*is the unit rate.Use proportional relationships to solve multistep ratio and percent problems.**7.RP.3.***Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.*