Add and Subtract Across Multiples of 10

Introduction

In this lesson plan, your learner will explore how to add and subtract across multiples of 10. This lesson builds on the make-ten strategy for addition and the subtracting through ten strategy for subtraction. Visual aids such as tens frames, number lines, and equations will be used alongside one another to demonstrate these concepts.

Before beginning this lesson, your learner should know pairs that make ten. They should also be familiar with sums that add to multiples of ten.

Key Concepts to Add and Subtract Across Multiples of 10

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

• Adding Across Multiples of 10: This involves using the make-ten strategy to simplify addition problems where the sum crosses a multiple of ten. By partitioning one of the addends, learners can create a multiple of ten first and then add the remaining part. For example, to solve 16 + 7, partition 7 into 4 and 3. First, add 16 and 4 to make 20, then add the remaining 3 to get 23.
• Subtracting Across Multiples of 10: This strategy involves partitioning the subtrahend to reach the nearest multiple of ten before subtracting the remainder. For example, to solve 23 - 5, partition 5 into 3 and 2. First, subtract 3 from 23 to get 20, then subtract the remaining 2 from 20 to get 18. This method helps learners handle crossing the ten boundary efficiently.

Teaching Plan

The following activities will help your learner confidently add and subtract across multiples of 10. Be sure to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Making Ten and Multiples of Ten

• Begin by using ten-frames, number lines, and equations to review crossing the ten boundary. For example, show 8 + 3 on a number line by starting at 8, jumping two units to 10, then one more unit to 11. Writing the equation can show 3 being partitioned into 2 and 1, where 8 and 2 make 10, then adding the 1 gives a total of 11.
• Encourage your learner to describe calculations in full sentences: "First, I partition the three into two plus one. Then eight plus two is equal to ten. And ten plus one is equal to eleven."
• Next, extend the make-ten strategy to "make a multiple of ten." Partition the single-digit addend so a multiple of ten can be made. For example, to add 16 + 7, partition 7 into 4 and 3. Add 16 and 4 to make 20 (a multiple of ten). Then combine 20 and 3 for a total of 23. (16 + 7 = 16 + 4 + 3 = 20 + 3 = 23)
• Provide ample practice with concrete representations, focusing on reasoning rather than counting to find the sums.

Skill Check
I can add across multiples of 10 using number lines and by making ten.

2. Comparing Related Calculations

• Use base-ten blocks and equations to show related examples alongside one another, helping your learner make connections between the different representations.
• Next, show the related calculations on a number line and write equations one above the other to highlight links between calculations. For example, show 6 + 7 on one number line and 16 + 7 on a number line directly below it.

Ask questions to deepen understanding of the related calculations:

• "What's the same?" (The ones digits are the same for both the addends and the sum)
• "What's different?" (The tens digits are different in each calculation)
• "What do you notice about the tens digit in the sum each time?" (The tens digit of the sum is one more than the tens digit of the larger addend)
• "Why?" (Because the ones digits sum to ten or more, making another ten)

Skill Check
I can notice and describe patterns with adding across multiples of 10.

3. Addition Practice

• Provide varied practice with missing number problems. Start with scaffolding strategies, such as number lines and writing out each step, then progress to solving equations without scaffolding.
• Present a challenge question such as: "Look at these two pairs of equations. What's the same within each pair and what’s different? 57 + 8 = 65 and 58 + 7 = 65; 45 + 6 = 51 and 46 + 5 = 51. Can you write some similar examples?"

To help your learner practice identifying related number facts ask questions such as:

• "Which number fact can I use to help me add eight to fifty-four?"
• "Is it true that if I add three to a number ending in eight, the sum will always end in one? Explain why/why not."
• "What can you tell me about the tens number in the sum when we add three to a number ending in eight?"
• "Can you give me an example of some additions that require bridging a multiple of ten? And some which don't?"

Skill Check
I can use number facts to help me add across multiples of 10.

4. Subtracting Through Multiples of Ten

• Next, extend the subtracting through ten strategy to subtraction through multiples of ten. Demonstrate partitioning the single-digit subtrahend to reach the previous multiple of ten, then subtracting the remainder.
• For example, to subtract 23 - 5: Partition 5 into 3 and 2. First subtract 3, then subtract 2. (23 - 3 = 20 then 20 - 2 = 18)
• Use base-ten cubes to physically exchange one ten for ten ones, emphasizing the bridging-ten aspect. Focus on reasoning how this strategy works, rather than counting manipulatives.
• Encourage your learner to describe the calculations in full sentences: "First, I partition the five into three and two. Twenty-three minus three is twenty. And twenty minus two is eighteen."

Just as with the addition examples, show the calculations on a number line and write the equations one above the other to draw attention to the link between the calculations. Ask your learner questions such as:

• "What's the same?" (The ones digits are the same in all calculations, for the minuend, the subtrahend, and the difference)
• "What's different?" (The tens digits are different in each calculation)
• "What do you notice about the tens digit in the difference each time?" (The tens digit of the difference is one less than the tens digit of the minuend)
• "Why?" (Because the difference between the ones digits is greater than or equal to ten; we exchanged one of the tens for ten ones so we could subtract the ones)

Skill Check
I can use different strategies to help me subtract through multiples of 10.

5. Varied Practice

Provide a range of real-world problems, including measures contexts:

• "Megan and Hamza are going on holiday. Megan's suitcase has a mass of eight kilograms and Hamza’s has a mass of seventeen kilograms. What is the total mass of their suitcases?" (aggregation/part-whole)
• "David is using a measuring cylinder to measure rainfall. At first, it contains forty-seven milliliters, and then eight milliliters more rain falls. How much water is in the measuring cylinder now?" (augmentation/joining)
• "Jane’s summer holidays were forty-three days long. It rained on seven of the days. How many days did it not rain?" (partitioning)
• "Ella has collected seventy-four stickers. If she gives eight stickers to her friend, how many stickers will she have left?" (reduction/take away)

Provide additional challenge and depth with questions such as:

• "A plant is nineteen centimeters tall and grows eight centimeters each week. How tall is it in three weeks?"
• "The teachers have eighty biscuits in the staff room. They eat eight each day. How many days until they have forty-eight left?"

Also use questions to assess depth of understanding:

• "Is it true that if I subtract three from a number ending in one, the difference will always end in eight? Explain why/why not."
• "What can you tell me about the tens number in the difference when we subtract three from a number ending in one?"
• "Can you give me an example of some subtractions which require bridging a multiple of ten? And some which don’t?"

Skill Check
I can solve different types of word problems that involve adding and subtracting across multiples of 10.

Summary

By the end of this lesson plan, your learner will confidently add and subtract across multiples of 10 using their experience with the make-ten strategy and subtracting through ten. They will be able to use visual aids and partitioning techniques to simplify addition and subtraction problems, making math both engaging and intuitive. These skills will help them develop a solid foundation for more advanced math concepts.

Teaching Plan adapted from NCETM under OGL license v3.