Difference of Consecutive Numbers

Introduction

In this lesson plan, your learner will embark on a journey to uncover the difference of consecutive numbers. Through fun activities and hands-on practice, they will become adept at spotting differences of one and two, enhancing their math fluency, and making number patterns a breeze to recognize.

Before beginning the lesson, your learner should understand that difference can be represented as subtraction.

Key Concepts

Here is a summary of the main ideas covered in this lesson:

• Difference of Consecutive Numbers: Understanding that consecutive numbers always have a difference of one. For example, "The difference between 4 and 5 is one."
• Difference of Consecutive Odd Numbers: Recognizing that consecutive odd numbers have a difference of two. For example, "The difference between 3 and 5 is two."
• Difference of Consecutive Even Numbers: Recognizing that consecutive even numbers have a difference of two. For example, "The difference between 4 and 6 is two."

Teaching Plan

The following activities will help your learner recognize that consecutive numbers have a difference of one while odd and even numbers have a difference of two.

Examples and visuals to support the lesson:

Difference of Consecutive Numbers

• Begin by using your learner’s understanding of difference to link consecutive numbers, using "one more and one less" and "difference of one." Use a variety of representations to support this concept.
• Use multilink towers lined up from 1 to 10 to form a staircase, plus an additional cube. Your learner can "walk" the extra cube up or down the staircase. At each step, emphasize the difference of one between the consecutive numbers.
• Next, present your learner with a subtraction facts chart (up to ten) and ask them to find or color in facts that show a difference of one (e.g., 4 - 3). Ask, "What patterns do you notice?"
• Work towards the general statement: "Consecutive numbers always have a difference of one."

Skill Check
I know that consective numbers have a difference of one.

Exploring Difference of Two

• After exploring numbers with a difference of one, use the same strategies to explore numbers with a difference of two.
• Start by having your learner can walk two joined multilink cubes up the same "staircase" as before. Encourage them to use the two blocks to identify steps that have a difference of two and describe any patterns that they see.
• Once they recognize that every other step has a difference of two, write equations that represent the difference of every other step. For example, step 1 and step 3 have a difference of two (3 - 1 = 2) just as step 2 and step 4 have a difference of two (4 - 2 = 2).

Skill Check
I can use math tools to find numbers that have a difference of two.

Difference of Odd and Even Numbers

• Move on to walking the two linked cubes up and down an even-numbered staircase. Write equations to represent the difference between the even numbers.
• Then follow the same process for an odd-numbered staircase. Each time, emphasize that there is a difference of two.
• You an also walk the two linked cubes along a number line in steps of two, beginning at either the 0 or the 1 to explore even and odd numbers respectively.
• Ensure that your learner is familiar with the following general statements by the end of this step: "Consecutive odd numbers always have a difference of two. Consecutive even numbers always have a difference of two."
• Finally, present your learner with questions that involve sorting out expressions that do and do not have a difference of two to promote depth of understanding.

Skill Check
I know that consecutive even numbers and consecutive odd numbers have a difference of two.

Summary

This lesson plan will turn your learner into a master of spotting the difference of consecutive numbers, as well as consecutive odd and even numbers. Through engaging activities and visual aids, they will uncover the secrets of number patterns, making math both fun and intuitive.

Teaching Plan adapted from NCETM under OGL license v3.