Unit 1: Understanding and Representing Ratios
Lesson 1 of 18
Define ratio and use ratio language to describe associations between two or more quantities.
The core standards covered in this lesson
— Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
The foundational standards covered in this lesson
— Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.
For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
— Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
You have the following collection of shapes:
These shapes can be sorted into different groups. For example, you can make a group of squares and a group of circles. We can use ratios to describe how these groups are related; for example, the ratio of squares to circles is 4 to 10, or 4:10.
Sort the shapes into as many different groups as you can think of. For each one, describe the association between the groups using a ratio.
Some teachers and students are playing games during recess.
After recess, Mr. Hill shares this information with his class. He asks his students to compare the students and teachers playing different games.
Mika said: “Eight more students played basketball than jumped rope.”
Chaska said: “For every student who jumped rope, two students played basketball.”
Mr. Hill said, “Mika compared the students by looking at the difference, and Chaska compared the students using a ratio."
a. Compare the number of teachers who played basketball and jumped rope using the difference. Write your answer as a sentence as Mika did.
b. Compare the number of teachers who played basketball and jumped rope using a ratio. Write your answer as a sentence as Chaska did.
c. Compare the number of students who played basketball to the number of teachers who played basketball using a ratio. Write your answer in two different ways.
Games at Recess, accessed on July 18, 2017, 1:23 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Abigail mixed 2 cups of white paint with 6 tablespoons (T) of blue paint.
Write at least four ratio statements to describe the situation. Can you write more than four?
Many Ways to Say It, accessed on July 18, 2017, 1:55 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
An example response to the Target Task at the level of detail expected of the students.
A set of suggested resources or problem types that teachers can turn into a problem set
The following resources include problems and activities aligned to the objective of
the lesson that can be used to create your own problem set.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Different types of sports balls are shown below.
Write 4 ratio statements to compare the different types of sports balls in the collection.
Topic A: Understanding & Describing Ratios
Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Equivalent Ratios
Define and find equivalent ratios.
Reason with equivalent ratios and determine if two ratios are equivalent.
Represent ratios using double number lines and identify equivalent ratios.
Solve ratio problems using strategies including double number lines.
Find equivalent ratios using ratios with “per 1” unit.
Compare situations using equivalent ratios and double number lines.
Use ratio reasoning to solve a three-act task.
Topic C: Representing Ratios in Tables
Represent ratios in tables.
Understand the structure of tables of equivalent ratios. Solve ratio problems using tables.
Solve ratio problems using tables, including those involving total amounts.
Compare ratios using tables.
Solve ratio problems using different strategies.
Topic D: Solving Part:Part:Whole Ratio Problems
Solve part:part ratio problems using tape diagrams.
Solve part:whole ratio problems using tape diagrams.
Solve more complex ratio problems using tape diagrams.
Solve ratio problems using a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.