In this lesson, your learner will explore how to subtract two-digit numbers by partitioning the number being subtracted (the subtrahend) into tens and ones. This strategy helps your learner understand subtraction step by step and build confidence before moving on to more complex problems, like subtracting across tens boundaries.
Key Concepts for Subtracting Two-Digit Numbers by Partitioning
Here are a few helpful ideas to keep in mind:
Partitioning the Subtrahend: This means breaking apart the number you are subtracting into tens and ones to make the subtraction simpler. For example, in 87 – 15, the 15 is partitioned into 10 and 5.
Subtracting Without Bridging a Tens Boundary: These are problems where subtracting the ones part doesn’t cross into a different group of tens. For example, 62 – 31.
Subtracting with Bridging a Tens Boundary: In these problems, subtracting the ones does cross a tens boundary, requiring more careful steps. For example, 73 – 35.
Different Structures of Subtraction: Subtraction can mean taking away, finding the difference, or working out what is left in a set.
Avoiding Common Mistakes: Learners may be tempted to subtract the tens from tens and ones from ones separately, which can lead to mistakes when bridging tens.
Teaching Plan
These activities will help your learner gain confidence in subtracting two-digit numbers by partitioning. Feel free to adapt or skip any steps depending on what works best for your learner.
Examples and visuals to support the lesson:
1. Exploring Subtraction Stories
Begin by connecting subtraction to a story context to make it meaningful.
Revisit a story problem your learner is already familiar with (such as taking away 23 from 45).
Compare doing the subtraction in two steps (subtracting 20, then subtracting 3) and doing it all at once.
Discuss together:
What’s the same? (Both problems start with 45 and remove 23, leaving 22.)
What’s different? (One removes 20 and then 3, the other removes 23 at once.)
Use objects like base-ten blocks (Dienes) to show visually that subtracting all at once or step by step gives the same result.
Summarize the process by showing a clear equation and describing the steps.
Skill Check
I can describe different ways to subtract two-digit numbers.
2. Partitioning the Subtrahend Without Crossing Tens
Now focus on problems where subtracting the ones does not cross into a new group of tens.
Model partitioning the subtrahend using base-ten blocks and number lines.
Use examples such as:
59 – 27
40 – 23
62 – 30
Encourage your learner to describe each calculation using a sentence stem:
To subtract __, we can subtract __ and then subtract __.
Provide incomplete equations for your learner to complete, showing both “subtract tens first” and “subtract ones first.”
Skill Check
I can split the number I am subtracting into tens and ones.
3. Calculating Answers Without Crossing Tens
Practice solving subtraction problems while still avoiding crossing tens boundaries.
Use real-life examples such as: "I saved up sixty-five pounds. Then I spent thirty-one pounds. How much money do I have left?" "There are seventy-eight children at a party. Twenty-five have taken their party bags. How many haven’t?"
Model the subtraction on a number line, emphasizing that the number line is for showing steps—not counting back in ones.
Encourage mental subtraction of the tens and the ones.
Skill Check
I can subtract tens and ones separately to find the answer.
4. Subtracting with Coins
Use coins to make subtraction concrete.
Give your learner a total amount (e.g., 87p in coins).
Ask them to remove a smaller amount (e.g., 15p) by selecting coins to match that value.
Discuss efficient ways to do this, like removing a 10p and a 5p coin.
Show the same calculation on a number line to connect the coins with a visual model.
Emphasize that this is not about counting in ones, but using known facts.
Skill Check
I can use coins or objects to help me subtract.
5. Subtracting Across a Tens Boundary
Move on to problems where subtracting the ones does cross a tens boundary.
Start with simpler examples where the difference is a multiple of ten: 86 – 26
Then increase the ones by 1 to create bridging problems: 86 – 27
Use number lines to show how the ones can be partitioned further to cross the tens boundary.
Model additional examples: 73 – 35; 62 – 49
Discuss why subtracting tens and ones separately (partitioning both numbers) won’t always work here. For example: 63 – 17
If your learner tries subtracting tens from tens and ones from ones, point out what happens when the ones digit is larger in the subtrahend.
If needed, count back to confirm which method is correct.
Skill Check
I can subtract two-digit numbers when the ones cross a tens boundary.
6. Practice and Real-Life Contexts
Provide varied practice to help your learner become confident and fluent. Include missing number problems such as equations and part–part–whole diagrams. Also use real-life problems such as:
I got sixty-two pounds for my birthday. Then I spent thirty-five pounds. How much do I have left?
There are thirty-two children in the class. Seventeen have put on their coats. How many have not?
Tara’s sunflower is seventy-seven centimeters tall. Akesh’s is fifty-eight centimeters tall. How much taller is Tara’s?
Introduce challenge problems where the minuend is a multiple of ten:
I had eighty centimeters of ribbon. Then I used twenty-three centimeters to wrap a present. How much is left?
If your learner is ready, include problems with two subtrahends or those that require bridging tens in different ways.
Skill Check
I can solve subtraction problems in many different ways.
Summary
By the end of this lesson, your learner should feel confident subtracting two-digit numbers by partitioning. They will understand how to subtract in steps, bridge tens when needed, and avoid common mistakes like subtracting tens from tens and ones from ones separately. Practicing with coins, number lines, and real-life examples will help reinforce these skills.
Skill Check