Subtracting Consecutive Numbers

Introduction

Welcome to today's lesson plan on subtracting consecutive numbers! By the end of this lesson, your learner will be able to confidently identify consecutive numbers and demonstrate how subtracting them always yields a difference of one. We will use story problems, equations, and visual aids like ten frames to deepen our understanding of this arithmetic principle.

Before beginning the lesson, your learner should be able to write subtraction expressions and be familiar with first-then-now subtraction stories.

Key Concepts for Subtracting Consecutive Numbers

Here are a few concepts that are helpful to know for this lesson.

• Consecutive Numbers: Consecutive numbers are numbers that follow each other in the counting sequence. For example, 3 and 4, 9 and 10, or 15 and 16 are consecutive numbers. Visually, we can see consecutive numbers on a number line as being one unit apart.
• Difference of One: Subtracting consecutive numbers always results in a difference of one. For instance, when we subtract the smaller number from the larger number in a pair of consecutive numbers, such as 10 - 9, the result is always 1.
• Developing Fluency in Subtraction: Recognizing consecutive numbers in subtraction equations helps learners develop fluency in arithmetic. By identifying consecutive numbers, learners can quickly anticipate the solution without having to rely on counting methods.
• Parts of Subtraction Equations: The minuend is the number from which another number is subtracted. The subtrahend is the number that is subtracted from the minuend. The difference is the result obtained by subtracting the subtrahend from the minuend. In the equation 4 − 3 = 1, the minuend is 4, the subtrahend is 3, and the difference is 1.

Teaching Plan

The following activities will help your learner develop fluency in recognizing and subtracting consecutive numbers. Be sure to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. First-Then-Now Consecutive Number Stories

In this activity, your learner will explore first-then-now stories that have consecutive numbers.

• Start by presenting a first-then-now subtraction story. For example: "First there were six children playing. Then five children went home. How many children are playing now?"
• Use counters and ten frames to act out each step of the story. As you tell the story, write out the equation and the solution. Discuss the numbers and draw attention to "all except one" object leaving.
• Explore a variety of "difference of 1" contexts. Point out the link between "all except one" object leaving and the subtrahend being one less than the minuend.
• Work towards the generalized statement: "Consecutive numbers have a difference of 1."

Skill Check
I can recognize and solve first-then-now stories that have a difference of 1.

2. Part-Part-Whole with Consecutive Numbers

Now, we'll explore consecutive numbers in the context of part-part-whole relationships.

• Present a part-part-whole story where the parts are consecutive numbers. For example: "There are nine children. Eight of them are reading. How many of them are not reading?"
• Draw a part-part-whole model (cherry or bar model) to represent the story along with an equation and the solution.
• Continue to draw attention to the minuend and subtrahend being consecutive numbers and the difference being one.

Skill Check
I can recognize and solve part-part-whole stories that have a difference of 1.

3. Expressions with a Difference of 1

In this activity, your learner will progress to working with expressions that do not have a story context.

• Once your learner has recognized the pattern, provide them with a series of expressions where the minuend and subtrahend are consecutive numbers.
• Encourage your learner to find the difference by applying what they learned about consecutive numbers rather than resorting to counting strategies (e.g. solving 5 - 4 by starting at 5 and counting back by 4).
• Next, provide your learner with practice in identifying expressions with a difference of one from a range of expressions. Encourage them to justify why each expression does or does not have a difference of one. For example: "They are consecutive numbers, so they have a difference of 1." Or, "They are not consecutive numbers, so they do not have a difference of 1."

Skill Check
I can recognize expressions that have a difference of 1. I know that subtracting consecutive numbers always makes a difference of 1.

5. Varied Practice

Provide varied practice with solving problems that involve both subtracting one (such as 5 - 1) and subtracting consecutive numbers (such as 8 - 7). Present various missing number problems in the form of equations, number lines, part-part-whole diagrams, and story problems.

Summary

Through this lesson plan, your learner has gained insight into subtracting consecutive numbers. With the use of story problems, equations, and visual representations like ten frames, your learner has discovered that when subtracting consecutive numbers, the difference is always one. Moving forward, they will be able to apply this knowledge to solve a variety of arithmetic problems and further strengthen their mathematical skills.

Teaching Plan adapted from NCETM under OGL license v3.