Learning Goal
Use ratio and rate reasoning to solve real-world and mathematical problems
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
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Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
What you'll learn
- Generate a table of equivalent ratios from a given ratio, find a missing value in such a table, and plot the resulting ordered pairs on the coordinate plane, observing that the points are collinear through the origin.
- Compare two ratios using equivalent-ratio tables or by plotting both on the coordinate plane.
- Solve unit-rate problems involving constant speed and unit pricing -- given a rate, find a total; given a total and one quantity, find the rate.
- Find a percent of a quantity by treating the percent as a rate per 100; find the whole given a part and the percent.
- Convert measurement units within a system (customary or metric) using ratio reasoning, including multi-step conversions of rates (e.g., mi/hr to ft/sec).
Slides
Step through the lesson, or watch it as a narrated video • 2 slide decks
Ratio tables and unit rates
✓ Start herePercent and unit conversion
Practice
Try it on your own
Animated Videos
Short animated explanations of the key idea • 6 animated videos