Sums Equal to Multiples of 10

Introduction

In this lesson plan, your learner will connect known number bonds to ten with new calculations with one-digit and two-digit numbers that have sums equal to multiples of 10. We'll also explore their related subtraction equations. Through visual aids, patterns, and varied practice, they will develop a deeper understanding of how these sums and differences work and their applications in math.

Before beginning the lesson, your learner should know pairs that make 10.

Key Concepts for Sums Equal to Multiples of 10

• Using Knowledge of Numbers Which Sum to Ten: Learners can use their knowledge of pairs of numbers that sum to ten to add a single-digit number and a two-digit number that sum to a multiple of ten. For example, knowing that 6 + 4 = 10 helps in understanding that 16 + 4 = 20 and 26 + 4 = 30.
• Subtraction from a Multiple of Ten: Learners can also use this knowledge to subtract a single-digit number from a multiple of ten. For example, knowing that 10 - 4 = 6 helps in understanding that 20 - 4 = 16 and 30 - 4 = 26.
• Visual Aids: In this lesson, visual aids such as ten-frames, bead strings, number lines, and number bonds will be used to help reinforce these concepts. These tools provide a clear visual representation of the relationships between numbers and help learners see patterns and make connections.

Teaching Plan

The following activities will help your learner develop confidence in calculating sums that equal multiples of ten. Be sure to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Relating Sums of Ten to Multiples of Ten

• Begin with visual aids such as tens frames and bead bars to help your learner relate sums of ten to sums that are multiples of ten. For example: Fill tens frames with 6 and 4 to show 10, then apply this to 16 + 4 = 20, 26 + 4 = 30, etc.
• Use the stem sentence: "I know that __ plus __ is equal to ten, so I know that ___ plus ___ is equal to ___."
• Transition to a blank number line to represent sums. Mark only the numbers involved in the calculations to draw your learner's attention to the pattern.
• Begin to draw out the pattern by asking questions such as: "What is the same each time?" "What is different?" "Is it true that if a number ends in a seven and we add three, do we always get a multiple of ten? Why or why not?" Your learner should explain that this is true because seven and three sum to ten.
• Present part of a pattern, then ask your learner to give the answer to a related calculation, for example: "Can you use this pattern to calculate 87 + 3?"
• Ask a challenging question such as: "If one addend has two ones, how many ones must the other addend have for the sum to be a multiple of ten?"

Skill Check
When adding with two-digit numbers, I know that if the ones digits have a sum of 10, the total sum will be a multiple of 10.

2. Addition Practice

• Provide a range of calculations based on number bonds to ten in the form of missing number problems.
• Initially, your learner can use concrete and pictorial representations, such as those described in the previous examples, for support.
• They can then progress to just being supported with part-part-whole diagrams and should finally be able to complete equations without support.
• The use of the part-part-whole diagrams will also help prepare your learner for the next step (subtraction of a single-digit number from a multiple of ten).
• Continue to ask questions and discuss the patterns to avoid the exercises becoming procedural.
• Note that calculations related to 9 + 7 have been included in the examples, bringing together all calculations related to bonds to ten.

Skill Check
I can solve missing number problems where the sum is a multiple of 10.

3. Linking to Subtraction

• Connect addition to subtraction using part-part-whole diagrams and the same visual aids. Focus on equations where the single-digit number is the subtrahend: 20 - 3 = 17.
• Use the stem sentence: "I know that ten minus ___ is equal to ____, so I know that ___ minus ___ is equal to ___."
• You can use a blank number line to highlight subtraction patterns. Ask questions to draw attention to the patterns: “What pattern can you see? Why is this pattern created?”
• For example: "What do you notice about the tens digits in the minuend (the number from which we are subtracting) and the difference?" "What do you notice about the ones digits in the subtrahend and the difference?"

Skill Check
I can use what I know about subtracting from 10 to help me subtract from multiples of 10.

4. Subtraction Practice

• Present missing number problems to highlight mathematical structure and reinforce your learner's understanding of the lesson.
• Use concrete and pictorial representations initially, then progress to part-part-whole diagrams and abstract equations.

Encourage explanation of patterns with questions like:

• "If I subtract four from a multiple of ten, the ones digit of the difference will always be six. True or false?"
• "I subtract six from a multiple of ten, what can you tell me about the difference?"
• "My minuend was a multiple of ten and my difference had three ones. What can you tell me about the subtrahend?"

Skill Check
I can solve missing numbers that involve subtracting from a multiple of 10.

Summary

By using visual aids and exploring patterns, your learner will gain a comprehensive understanding of sums that are multiples of ten. This foundation will support their future math skills and help them confidently tackle more complex calculations. Through varied practice and in-depth exploration of patterns, your learner will develop a strong grasp of these essential math concepts, preparing them for more advanced studies.

Teaching Plan adapted from NCETM under OGL license v3.