Introducing Doubles and Halves

Introduction

This lesson plan focuses on introducing doubles and halves through engaging activities and visual aids. We'll start by reviewing even numbers and using pictures of seesaws to create and understand equations. By introducing the idea of "doubling," we'll learn that adding the same number to itself always results in an even number. We'll use ten frames, part-part-whole diagrams, and interactive games to solidify our understanding. Once we're confident with doubling, we'll transition to the concept of halving, learning how it is the inverse operation of doubling.

Key Concepts for Introducing Doubles and Halves

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

• Doubling Numbers: Doubling a number means adding the same number to itself. For example, doubling 3 is the same as calculating 3 + 3. When you double any whole number, the result is always an even number.
• Halving Numbers: Halving a number means dividing it into two equal parts. For example, halving 8 means dividing 8 by 2, which gives 4. Halving is the opposite operation of doubling. If you know that double 4 is 8, you can also determine that half of 8 is 4.

Using Doubles and Halves in Calculations

Understanding doubles and halves can help perform calculations with addition and subtraction. In future lessons, it will also help with multiplication and division.

• Addition with Equal Addends: Doubling is a useful strategy when adding two equal addends. For example, if you have 6 + 6, you can quickly recognize that it’s double 6, which is 12.
• Using Halves in Subtraction: Since doubling helps with addition, the inverse of doubling (halving) can be useful in subtraction (the inverse of addition). For instance, if you start with 8 and subtract 4, you get 4, which is half of 8.
• Near-Doubles: Sometimes, when adding numbers that are close to each other, you can use the doubles strategy to make the calculation easier. For example, if you need to add 3 + 4, you can recognize that 4 is just one more than 3, so you double 3 (which is 6) and then add 1, resulting in 7.
• Near-Halves: Similarly, you can use the concept of halving for numbers that are close to being halves. For example, if you need to subtract 9 - 4, you can recognize that 9 is near 8. Half of 8 is 4. Then add one more (since 9 is one more than 8) which gives 5 as the solution.

Keep in mind that while doubles and halves are powerful tools, it’s important for learners to use strategies that feel most natural and intuitive to them. Expose your learner to a variety of strategies for them to explore and choose their preferred methods. This will help them develop a deeper understanding and confidence in their arithmetic skills.

Teaching Plan

The following activities will help your learner become confident in their understanding of doubles and halves.

Examples and visuals to support the lesson:

1. Review of Even Numbers

• Begin by reviewing counting even numbers to ten, both forward and backward.
• Next, introduce pictures of seesaws or other balancing models where the quantity on each side is the same.
• Have your learner write equations for each picture. For example, a picture that has two children on each side of a seesaw can be represented by 2 + 2 = 4.
• Encourage your learner to discuss the pictures and equations by describing what they have in common and what the numbers represent. Point out that the sums are all even numbers.

Skill Check
I can name the even numbers up to 10.

2. Understanding Doubles

• Next, introduce the word "double." Explain that when both addends are the same, we are doubling. If we have three plus three, we can say that we are doubling three.
• Use ten frames that are oriented vertically (as two vertical columns) to demonstrate the doubling pattern.
• Emphasize that doubling always results in an even number because each item (counter, object, etc.) always has another to pair up with.
• You can also draw part-part-whole diagrams and draw attention to the fact that the two parts are the same and the whole is always an even number.
• Work towards the generalized statement: "Double a whole number always gives an even number."

Skill Check
I can find the double of a number by adding it to itself. I know that doubling a number always gives an even number.

3. Developing Fluency with Doubling Numbers

• Use this activity to provide your learner with opportunities to develop fluency in doubles. You can create a poster of part-part-whole diagrams for doubles that your learner can refer to as they practice.
• Have your learner play games such as "Snap" for doubles. Provide them with cards that have a variety of numbers and addition expressions. When a card comes up that represents a double, have your learner say "snap" and explain how the card shows a double. For a card that shows 10 or 5 + 5, they can say "five plus five is equal to ten" and "double five is ten."

Skill Check
I can find and recognize doubles of numbers.

4. Exploring Halves of Numbers

• Once your learner is confident in doubling numbers 0 to 5, introduce the concept of halving numbers.
• Provide a picture such as a seesaw image with two children on each side but cover up one side. Ask your learner, "How many children are on the other side of the seesaw?"
• Write an addition and subtraction equation to represent the problem. For this example, the equations are 2 + ? = 4 and 4 - 2 = ?.
• Point out that in the subtraction equation, the subtrahend is half of the minuend.
• Continue to practice with story problems, part-part-whole models, and equations. Work towards the generalized statement: "Halving is the inverse of doubling."

Skill Check
I know that halving numbers is the opposite of doubling numbers. I can use what I know about halves to solve different problems.

Summary

By the end of this lesson plan, your learner have a strong grasp of doubling and halving. They will understand that doubling a number always results in an even number and be able to apply this concept using various visual aids and activities. They'll also learn that halving is the inverse of doubling, allowing them to solve problems by breaking down numbers into equal parts. With these foundational skills, your learner be well-prepared to tackle more complex arithmetic operations confidently.

Teaching Plan adapted from NCETM under OGL license v3.