Search form

Here is a 15-minute lesson for the Math-Aids Ratios Worksheets that includes several worksheet types: simple ratios, equivalent ratios, ratio tables, ratios from word phrases, unit rates, and ratio word problems.

> View all 15-Minute Lessons

15-Minute Math Lesson Plan: Understanding Ratios

15 minute math lesson

Grade Level: Grades 5–7
Time: 15 minutes
Topic: Writing, Simplifying, and Understanding Ratios

Learning Objective

Students will understand ratios, write ratios in different forms, simplify ratios, and recognize equivalent ratios.

Materials

1. Warm-Up (3 minutes)

Explain that a ratio compares two quantities.

Write this example on the board:

There are 6 red pencils and 9 blue pencils.

Ask students:

  • How many red pencils are there?

  • How many blue pencils are there?

  • What is the ratio of red pencils to blue pencils?

Write:

6 to 9

Explain that ratios can be written in three ways:

  • 6 to 9

  • 6:9

  • 6/9

Tell students that the order matters. Red to blue is different from blue to red.

2. Teacher Modeling (4 minutes)

Model how to write and simplify a ratio.

Example 1: Simplifying a Ratio

A classroom has 8 boys and 12 girls. What is the ratio of boys to girls in simplest form?

Step 1: Write the ratio.

8:12

Step 2: Find the greatest number that divides evenly into both numbers.

Both 8 and 12 can be divided by 4.

Step 3: Divide both numbers by 4.

8 ÷ 4 = 2

12 ÷ 4 = 3

Answer: 2:3

Explain that a ratio is simplified by dividing both numbers by the same number.

Example 2: Finding an Equivalent Ratio

If the ratio of boys to girls is 2:3, what is an equivalent ratio with a first number of 4?

Step 1: Multiply the first number by 2.

2 × 2 = 4

Step 2: Multiply the second number by 2 as well.

3 × 2 = 6

Answer: 4:6

Explain that equivalent ratios are made by multiplying or dividing both parts by the same number.

3. Guided Practice (3 minutes)

Work through these problems together.

Problem 1: Write a Ratio

A basket contains 5 apples and 10 oranges. What is the ratio of apples to oranges in simplest form?

5:10

Divide both numbers by 5.

Answer: 1:2

Problem 2: Find an Equivalent Ratio

Complete the missing number:

3:4 = 6:___

Ask students what happened to the first number.

3 × 2 = 6

Multiply the second number by 2.

4 × 2 = 8

Answer: 8

Ask students why both numbers must be multiplied by the same amount.

4. Independent Worksheet Practice (3 minutes)

Have students complete a few problems from one of the Math-Aids ratio worksheets.

Choose a worksheet that matches the skill being taught:

  • Simple Ratios: Identify and write ratios from groups of pictures or symbols.

  • Equivalent Ratios: Complete ratios and solve for missing numbers.

  • Tables with Equivalent Ratios: Identify which ratios in a table are equivalent.

  • Rows of Equivalent Ratios: Fill in missing numbers in a series of ratios.

  • Ratios from Word Phrases: Write ratios from descriptions.

  • Rates and Unit Rates: Calculate rates and find the amount for one unit.

  • Ratio and Rate Word Problems: Apply ratios and rates to real-world situations.

Remind students to show their work and check that they are comparing quantities in the correct order.

5. Exit Ticket (2 minutes)

Ask students to solve:

A recipe uses 4 cups of flour and 6 cups of sugar.

  1. What is the ratio of flour to sugar?

  2. Write the ratio in simplest form.

  3. Give one equivalent ratio.

Answers:

  1. 4:6

  2. 2:3

  3. 6:9 (or another equivalent ratio)

Differentiation

Support: Use pictures, counters, or colored objects to help students visualize the quantities being compared. Begin with simple ratios that have small numbers.

Extension: Introduce unit rates. For example, if 12 apples cost $6, divide $6 by 12 to find the cost per apple: $0.50.

Common Misconceptions

  • Reversing the order: Remind students that the order in a ratio must match the order in the question.

  • Dividing only one number: Both parts of a ratio must be divided by the same number when simplifying.

  • Confusing equivalent ratios: Multiplying or dividing only one part does not create an equivalent ratio.

  • Confusing ratios and rates: A rate compares quantities with different units, such as miles and hours.

Assessment

Review student responses during guided practice and check their independent worksheet problems and exit tickets.

Success Criteria: Students can write a ratio, simplify it, identify equivalent ratios, and explain how ratios compare two quantities.

Teacher tip: The Math-Aids page has several different ratio skills. For a first lesson, I recommend starting with Simple Ratios or Equivalent Ratios before moving on to unit rates and word problems.

-----------

Posted 11/14/26

Education World®