Doubles and Halves within Teen Numbers

Introduction

Welcome to today’s lesson plan on doubles and halves within teen numbers! We'll explore how numbers 11 to 19 can be doubled and halved. By the end of this lesson, your learner will confidently work with these numbers, using visual tools, language, and patterns to understand and solve problems involving doubling and halving.

Before beginning the lesson, your learner should be familiar with doubles and halves up to 10.

Key Concepts Doubles and Halves within Teen Numbers

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 6 is the same as calculating 6 + 6 which is 12. 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 12 means dividing it into two equal groups, which in this case makes two groups of 6. Halving is the opposite operation of doubling. If you know that double 6 is 12, you can also determine that half of 12 is 6.

Teaching Plan

The following activities will help your learner become confident with doubles and halves within numbers 11 to 19. Remember to go at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Review of Doubles and Halves within 10

Start by reviewing doubles and halves within 10. Use seesaw images and part-part-whole diagrams to illustrate:

• "When both addends are the same, we are doubling."
• "If we have three plus three, we can say we are doubling three."
• "Doubling a whole number always gives an even number."
• "Halving is the inverse of doubling."

Encourage the use of both addition/subtraction and doubling/halving language to describe calculations:

• "Three plus three is equal to six; double three is six."
• "Six minus three is equal to three; half of six is equal to three."

Skill Check
I can find doubles and halves of numbers up to 10.

2. Doubling and Halving within Teen Numbers

• Present a scenario like "Yassin has a magic doubling bag. He put six beans into his bag. When he emptied the bag, the number of beans had doubled. How many beans does he have now?"
• Represent six on two tens frames and ask your learner to double the beans on the frames, showing double six as composed of double five and double one.
• Record the calculation in a table, showing the number of beans before (six) and after (twelve).
• Repeat the process for doubling seven, eight, and nine, each time showing the starting number as "five and a bit." Complete the table with the results.
• Emphasize that doubling a whole number always gives an even number because every 'one' is doubled. Remind your learner of this generalized statement and use base-ten number boards to reinforce the relationship.

Ask your learner questions to check their understanding. For example:

• "Yassin put seven beans in the bag at the start; then the bag doubled the beans; how many beans are in the bag now?"
• "Yassin takes eighteen beans out of the bag; how many beans must he have put in the bag at the start?"
• Reinforce answers with: "Yes, that’s right; double seven is fourteen." and "Yes, that's right; half of eighteen is nine."

Skill Check
I can find doubles of numbers 6, 7, 8, and 9. I can find halves of numbers 12, 14, 16, and 18.

3. Visual Representations and Language

• Have your learner represent doubles using base-ten number boards and describe using both addition and doubling language.
• For example: "Show me double seven." "Double seven is fourteen." "Seven plus seven is equal to fourteen."
• Link with halving by asking: "Double seven is fourteen, so what is half of fourteen?"
• Summarize the pattern of doubles and halves and highlight the difference of two between consecutive doubles. For example, double seven (14) is two more than double six (12).
• Provide missing number problems and practice moving between doubling and halving.

Skill Check
I can use number patterns to remember doubles and halves.

4. Practice and Review

Ensure your learner practices these doubles facts regularly, incorporating them into routines and games.

• Use flashcards or display the facts on a poster for reference. Provide practice with real-life contexts and missing number problems with numbers 11 to 19.
• Examples of real-life contexts: "I am making twelve cupcakes. I have put out six cupcake cases. How many more cases do I need?" "A movie download costs eight dollars. I buy two of them. How much do I spend altogether?"

Use strategies to help your learner memorize doubles facts, such as:

• Linking the position of 6 and 12 on the clock face.
• Learning double eight as two more than 14.
• Learning double nine as two less than 20.
• Discuss the meaning of the word "fortnight" (two weeks = 14 days) to link seven and fourteen.

Skill Check
I can use what I know about doubles and halves to solve problems with numbers 11 to 19..

Summary

Through this lesson plan, your learner will gain a strong understanding of doubles and halves within teen numbers. By using visual aids, patterns, and language, they will confidently solve problems involving numbers 11 to 19 and be prepared for more advanced topics including multiplication, division, and fractions.

Teaching Plan adapted from NCETM under OGL license v3.