Finding the Difference of Two Quantities

Introduction

This lesson plan will teach your learner how to find the difference of two quantities. This involves understanding and describing comparisons between quantities both qualitatively and quantitatively. By practicing these skills, your learner will build a solid foundation for understanding mathematical differences.

Before beginning the lesson, your learner should be able to subtract within 10 and use the subtraction sign in equations.

Key Concepts for Finding the Difference of Two Quantities

Here are a few concepts that are helpful to know for the lesson. While your learner does not need to know the terms qualitative and quantitative, understanding these concepts will come in handy as you are working through various examples during the lesson.

• Qualitative Difference: Qualititative difference involves describing relationships between quantities using terms like bigger, smaller, older, younger, more, less, fewer, heavier, and lighter. For example, "The blue ribbon is shorter than the yellow ribbon."
• Quantitative Difference: On the other hand, quantitative difference involves using numbers to describe the difference of two quantities. For example, "There are two more red cars than blue cars."
• Modeling Differences: Many types of visual aids can be used to help learners recognize qualitative and quantitative differences including bar models and number lines.

Teaching Plan

The following activities will help your learner become confident in finding the difference of two quantities.

Examples and visuals to support the lesson:

1. Practicing Qualitative Differences

• Present a range of practical contexts for comparison, including both discrete objects (e.g., cars, sweets) and continuous measures (e.g., length, age). Discrete objects can be separated and counted individually while continuous measures cannot.
• Begin with qualitative differences (e.g., one ribbon is longer/shorter than the other) before moving to quantitative differences.
• Ask your learner to describe the relationship between two values in sentences. For example: "There are more red cars than blue cars." "The blue ribbon is shorter than the yellow ribbon."
• Use a variety of examples to draw out a range of vocabulary: "bigger", "smaller", "older", "younger", "more", "less", "fewer", "heavier", "lighter."

Skill Check
I can use words to describe the sizes and amounts of things.

2. Moving to Quantitative Differences

• Begin to put a "value" on the gap between two quantities by representing it with a number.
• Continue to encourage your learner to describe the contexts in two ways using full sentences. For example: "There are two more red cars than blue cars. There are two fewer blue cars than red cars."
• Support this comparison by using bars to represent the two values. For example, a bar whose value is 5 with a bar whose value is 3 aligned below it. You can also use concrete manipulatives like multilink blocks alongside pictorial representations.

Skill Check
I can use numbers to compare the sizes and amounts of things.

3. Introducing the Term "Difference"

• Once your learner can confidently compare values quantitatively, introduce the term "difference" to describe the numerical gap between two values.
• For example: "The difference between the number of cars and the number of motorbikes, is three." "The difference between the number of tractors and the number of cars, is four."
• Make sure that your learner understands the difference both ways: "There are more cars than motorbikes; the difference between the number of cars and the number of motorbikes is three." "There are fewer motorbikes than cars; the difference between the number of cars and the number of motorbikes is three."

Skill Check
I know that finding the difference can mean using numbers to compare the sizes and amounts of things.

4. Finding the Difference Between Numbers

• Once your learner is comfortable with the concept of difference in real-world contexts, move to abstract comparisons.
• Focus on the "gap" between numbers: "The difference between four and seven is three. The difference between seven and four is three."
• Use the bar model and number line for visual representation. Encourage your learner to use these tools to show the difference between two numbers themselves.

Skill Check
I can use bar models and number lines to find the difference between numbers.

Summary

In this lesson plan, your learner practiced comparing quantities both qualitatively and quantitatively, and learned how to find the difference of two quantities using pictures and other visual aids. The also learned that in math the term difference can be used to compare the numerical gap between two numbers.

Teaching Plan adapted from NCETM under OGL license v3.