Ratios and Proportional Relationships
20 short narrated lessons in 4 chapters, each with pictures, a quiz with a hint and a second try, and an explanation for every answer.
Standards: 7.RP.A.1 7.RP.A.2 7.RP.A.3
What your child will learn
Unit rates with fractions
- Rates and Unit RatesFind a unit rate, like miles per hour, as the amount for one unit of the second quantity.
- Complex FractionsSimplify a complex fraction like one half divided by one fourth by dividing the fractions.
- Unit Rates with FractionsFind unit rates like walking one half mile in one fourth hour equals two miles per hour.
- Comparing Unit RatesCompare unit rates to decide which deal or speed is better.
- Unit Rates with Fractions Review ReviewReview finding unit rates, including rates with fractions, and comparing them.
Proportional relationships
- Testing Tables for ProportionalityDecide whether a table shows a proportional relationship by checking for equivalent ratios.
- Graphs of Proportional RelationshipsTell whether a graph shows a proportional relationship by checking for a straight line through the origin.
- The Constant of ProportionalityFind the constant of proportionality from a table, graph, equation or description.
- Writing Equations Like y equals k xWrite an equation like y equals k x for a proportional relationship and explain what the point one comma k means on its graph.
- Proportional Relationships Review ReviewReview recognizing proportional relationships in tables and graphs and writing y equals k x equations.
Percent problems
- Solving Percent Problems with ProportionsFind a part, whole or percent using a proportion or an equation.
- Percent Increase and DecreaseFind the percent a quantity went up or down compared with the original amount.
- Percent ErrorFind percent error by comparing an estimate or measurement with the actual value.
- Simple InterestFind simple interest by multiplying the principal, the rate and the time.
- Percent Problems Review ReviewReview percent proportions, percent change, percent error and simple interest.
Percents in everyday life
- Sales Tax and TipsFind the sales tax, tip and total cost of a purchase or meal.
- Markups and DiscountsFind sale prices after a discount and store prices after a markup.
- Commissions and FeesFind how much a salesperson earns from commission or how much a fee adds to a cost.
- Percents in Everyday Life Review ReviewReview sales tax, tips, markups, discounts, commissions and fees.
- Unit 3 Test: Ratios and Proportional RelationshipsShow what you learned in the whole unit (Unit rates with fractions, Proportional relationships, Percent problems, Percents in everyday life) by answering mixed questions.
Try a question from this unit
From the lesson “Rates and Unit Rates”
A garden hose fills a 150-gallon water trough in 6 minutes. What is the unit rate in gallons per minute?
Show the answer
25 gallons per minute. Gallons per minute means gallons divided by minutes: 150 ÷ 6 = 25 gallons each minute. The choice 1/25 comes from dividing in the reverse order, and 900 comes from multiplying instead of dividing.
Hint kids see after a wrong try: “Per minute means the amount for one minute. Decide which quantity belongs on the bottom before you divide.”
Key words
- rate
- unit rate
- complex fraction
- better buy
- proportional
- equivalent ratios
- origin
- straight line
- constant of proportionality
- equation
- percent
- proportion
- percent increase
- percent decrease
- percent error
- simple interest
- principal
- interest rate
- sales tax
- markup
- discount
- markdown
- commission
- fee
Try these lessons in Kids Shelf
Narrated lessons, pictures and quizzes for every grade from K to 8. Works offline.
