Introducing Ratio Vocabulary

Introduction

Understanding ratios is a fundamental concept in math that allows us to compare quantities and understand relationships between them. This lesson plan introduces learners to the world of ratios, starting with simple drawings and observations to grasp the concept. We'll then define ratio vocabulary and distinguish between different types of ratios.

Key Concepts

Here are a few concepts that are important to understand about ratios and introducing ratio vocabulary:

• Ratio: A ratio is a comparison between two quantities, typically expressed in the form of a fraction or with a colon (:). It represents the relationship between the sizes or amounts of two different elements or parts within a whole. For example, if there are 3 red balls and 5 blue balls in a bag, the ratio of red balls to blue balls is 3:5.
• Ratio Vocabulary: Ratio vocabulary includes terms such as "per," "each," "for every," and others, which are used to describe the relationship between the quantities being compared in a ratio. These words provide context and clarify the meaning of the ratio, indicating how many units of one quantity are associated with each unit of another quantity.
• Equivalent Ratio: Equivalent ratios represent the same comparison between quantities but are expressed in different numerical values. This means that although the numerical values may differ, the relationship between the quantities remains the same. For instance, the ratios 6:8 and 3:4 are equivalent because they both represent the same relationship of 3 parts to 4 parts.
• Part-Part Ratios: Part-part ratios compare the relationship between two parts or components within a whole, without considering the total quantity. For example, if there are 4 red marbles and 6 blue marbles in a bag, the part-part ratio of red marbles to blue marbles is 4:6.
• Part-Total Ratios: Part-total ratios compare one part to the total quantity of all parts combined. Using the same example, the part-total ratio of red marbles to the total marbles would be 4:10, representing the 4 red marbles out of the total of 10 marbles. Understanding these concepts helps learners comprehend the relative sizes and proportions within a given set of quantities or data.

Teaching Plan

The following activities will help your learner become confident with using ratio vocabulary. Remember to go at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Comparing Quantities

This activity will give you a chance to see what vocabulary your learner uses to describe the relationships between quantities. You can then build on their knowledge to introduce them to ratio vocabulary.

• Show your learner an image with groups of items in different quantities, such as the image of the camping gear. Give them a moment to study the image and describe what they see.
• Ask them to compare the quantities of the items in one group to the quantity in another group. As they make comparisons, take note of any ratio vocabulary that they use such as "each", "per", and "for every."
• Some of the comparisons that lead to fractions may be more difficult for them to identify. For example: There are six bottles of water per day for four people; therefore, each person gets 1 1/2 bottles of water per day.
• Encourage your learner to list as many comparisons as they can. But at this stage, they don't have to find every comparison. The important thing is to get a sense of what they intuitively notice about ratio relationships.
• Extend your learner's thinking by asking what other gear should be brought on the camping trip. Have them list how many of each item there should be and relate it to the other gear. For example, bringing 8 granola bars for 4 people means that each person can have 2 granola bars.

Skill Check
I can compare quantities using words like "each", "per", and "for every."

2. Drawing Pictures of Ratios

This activity will have your learner draw pictures that represent ratios and encourage them to think about equivalent ratios.

• Provide your learner with prompts that involve drawing ratios of items. For example, ask them to draw a jar of marbles where there are 3 blue marbles for every 5 red marbles.
• Notice that the task does not tell them how many to draw in total. They may draw exactly 3 blue and 5 red, 6 blue and 10 red, etc. Even though they are different quantities, the ratios are still the same which makes them equivalent ratios.

Skill Check
I can draw pictures to represent relationships of quantities.

3. Using Ratio Vocabulary

In this activity, your learner will describe their drawings using ratio vocabulary. As they analyze their descriptions, they will distinguish part-to-part ratios from part-to-total ratios.

• Ask your learner to describe the quantities of the marbles using ratio vocabulary (per, each, for every). Write the statements down and help them analyze each one in more detail. Have them identify whether the numbers represent the total or part of the total.
• Next, determine whether each statement represents the parts (a part-to-part ratio) or a part and the total (a part-to-total) ratio. For the marble example, 3 to 5 can represent the number of blue marbles to red marbles (part-to-part). Another ratio is 3 to 8, which is the ratio of blue marbles to the total (part-to-total).
• If you haven't already, provide your learner with a formal definition of ratio. A ratio expresses a relationship between two or more quantities. Have them add "ratio" to their vocabulary list or word wall.

Skill Check
I can write statements with ratio vocabulary. I can recognize part-to-part and part-to-total ratios.

Summary

In this lesson, we began by introducing learners to ratios through drawings and observations, laying the foundation for their understanding. We then explored ratio vocabulary, equipping learners with the language necessary to express and interpret ratios. Finally, we learned how to distinguish between part-part and part-total ratios. With this newfound knowledge, learners are well-equipped to navigate the world of ratios and apply them in various mathematical contexts.

Teaching Plan adapted from Utah Middle School Math Project under CC BY 4.0.