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Partitioning to Add

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Basics on the topic Partitioning to Add

Add By Making 10 – Understanding Ten Frames

The ability to use appropriate tools when performing addition is critical for developing a deep understanding of addition operations. A tens frame is one such tool.

A tens frame is a rectangle with ten equal spaces, divided into two rows of five. It is used to represent numbers less than or equal to ten. Since tens frames contain ten equal spaces, they allow children to develop numbers sense and exchange skills within the base 10 number system. The tens frame can be used when using the add by making 10, or partitioning to add, strategy.

How to Use a Tens Frame

We use a tens frame by placing a single counter in each of the spaces to make the number. When adding, we can use tens frames to help us break up, or partition, numbers and count on. A double-digit number can be broken up into the tens and ones. The tens place will fill up the tens frame.

For example, the number seventeen can be broken up, or partitioned, into a ten and seven ones that can be shown on the tens frame


KS1 Add By Making 10

The tens frame can, therefore, be used to add larger numbers by breaking apart, or partitioning, the smaller addend into tens and ones.

For example, if we are asked to add 38 and 15 we can do the following:

  • Step 1: Create a number sentence → 38 + 15

  • Step 2: Break apart, or partition, the smaller addend and place it in the tens frame. The smaller addend is 15, therefore, 15 becomes 10 and 5


  • Step 3: Solve using the tens frame by adding ten and counting on. Therefore, the complete tens frame combines with 38 to give us 48. Then, we count on from there using the second tens frame to get 53.

Tens Frames – Steps for Add By Making 10 Year 2

To use make a ten to add, we can follow these steps:

Step What to do
1. Create a number sentence.
2. Break apart, or partition, the smaller addend.
3. Solve using the tens frame by
adding to the bigger number in
tens and then counting on.

Year 2 Add By Making 10 – Summary

Let’s repeat what we learnt about tens frames, partitioning and the strategy to make ten to add today.

Tens frames are useful tools in an addition strategy where the smaller addend can be broken apart, or partitioned, into a ten and the smaller number represented on another tens frame. The tens frame can then be used to find the sum by counting in tens and then counting on. Because tens frames provide a visual representation of numbers, they allow children to make sense of ‘tens’ and ‘ones’

For more, have a look at our add by making 10 worksheet Year 2, add by making 10 games and add by making 10 activity.

Frequently Asked Questions about Making 10 to Add

What is a tens frame?
Why are tens frames important?
What is number sense and how does it relate to tens frames?
What does make 10 to add mean?
How do you teach add by making 10? Can tens frames be used to teach addition and subtraction?
How can tens frames help with teaching larger numbers?
Can tens frames be used to teach number bonds?

Transcript Partitioning to Add

"The sun is so warm, it's perfect for this walk!" "And look at these mushrooms!" Mr. Squeaks and Imani are out for a walk when Mr. Squeaks sees something that catches his eye. While exploring the mushrooms he suddenly realises that he's lost! "Imani? IMANI!" Mr. Squeaks needs a strategy to help him. He can add the different mushrooms to count his way back! Let's learn about "Partitioning to add" to help Mr. Squeaks. There are different strategies that you can use to solve addition equations. One is to partition a number when adding. You may know about the tens frame and that when we fill all of the boxes, we have ten. Let's use the tens frame to help us as we partition to add! Mr. Squeaks passed twenty-six red mushrooms first and then fifteen purple mushrooms. How many mushrooms has he passed in total? We can start by creating an equation, or number sentence. Which is twenty-six plus fifteen. Next, we can take the smaller addend, or number, and break it apart, or PARTITION it, to make smaller numbers. We can take fifteen and partition it to make a ten and a five. Now we have twenty-six plus ten plus five, which may be easier to add. Then, solve using the tens frame. While there are different ways to add, in this video we will add by tens and count on. What is twenty-six plus ten? Thirty-six. Now, we can add thirty-six plus five, which is forty-one. That means twenty-six plus fifteen equals forty-one. "Okay, I've passed forty-one mushrooms, I can't be far." "Wait, I didn't pass green mushrooms yet." Mr. Squeaks just saw thirty-two green mushrooms and then twelve brown ones. How many mushrooms did he pass? Start by creating an equation. We can create thirty-two plus twelve. Next, take the smaller addend and break it apart, or PARTITION it. Here we can partition twelve and make a ten and a one. Now we have thirty-two plus ten plus two. Then, solve using the tens frame. What is thirty-two plus ten? Forty-two! What is forty-two plus two? Forty-four! So, Mr. Squeaks has passed forty-four mushrooms. "I MUST be close now!." "MORE MUSHROOMS?" We can partition again to help Mr. Squeaks one last time. Mr. Squeaks saw forty-seven spotted mushrooms and seventeen small ones. How many mushrooms should he add? Remember to start by creating an equation. We can create forty-seven plus seventeen. Next, take the smaller addend and partition it to make it even smaller. Here we can take seventeen and make one ten and seven ones. Now we have forty-seven plus ten plus seven. What is forty-seven plus ten? Fifty-seven What is fifty-seven plus seven? Sixty-four. Mr. Squeaks needs to add sixty-four mushrooms to his list. Let's review! When partitioning to add, start by creating an equation. Next, take the smaller addend and break it apart, or PARTITION it, to make even smaller addends. Don't forget to fill the tens frame with the smaller addends! Then, solve using the new equation. In this video we added by tens and counted on. Now, I wonder how Mr. Squeaks is doing. "IMANI! I missed you! I thought I was lost forever!"

"I-imani? That's you, right?" "Surprise! It's me!"

Partitioning to Add exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Partitioning to Add.
  • How do you partition to add?


    Remember, the first thing you need to do is understand what the problem is asking, and create an equation to show that in a number sentence.

    Try adding 23 + 14 on your own. What steps did you follow?

    To add 23 + 14, you can break 14 into 10 and 4.

    23 + 10 = 33

    33 + 4 = 37

    23 + 14 = 37


    For Mr. Squeaks to teach Imani, he needs to show them these steps in this order:

    1. Create an equation.
    2. Partition the smaller addend.
    3. Add the numbers using tens frames.
    4. Solve the equation.
  • How could we solve this problem?


    You will partition the number 23 (the smaller addend) into tens and ones.

    We can partition 23 into 20 + 3. How many tens are in 20?


    To use partitioning to solve 27 + 23, we could rewrite it as 27 + 10 + 10 + 3.

    • We can split 23 into 20 + 3 and then further into 10 + 10 + 3.
    • 27 + 10 = 37 + 10 = 47
    • 47 + 3 = 50
    • 27 + 23 = 50
  • How could we use partitioning to solve these problems?


    14 + 11 would be partitioned to 14 + 10 + 1.

    Remember, when partitioning we break the smaller addend into tens and ones.

    Example: 17 + 12 = 17 + 10 + 2


    When we partition, we break the smaller number into tens and ones, like these pairs.

  • Show the steps.


    Remember, we have the equation 18 + 12. Next, we need to partition the smaller addend.

    The smaller addend is 12. 12 has one ten (12) and two ones (12).

    For the second step, add 18 + 10 to fill in the blank.


    Mr. Squeaks can partition to find the answer! He will start by partitioning the smaller addend (12 = 10 + 2).

    Next, he will add the ten to the larger addend (28 + 2).

    Finally, he will add on the ones (30).

    The answer is 30.

  • How much in total?


    Start by adding the 10 to the larger addend. Then add on the ones.

    31 + 10 = 41. Count on 7 more to find the answer.


    31 + 10 + 7 = 48

    First, add the 31 + 10. 31 + 10 = 41.

    Next, add the seven ones. 41 + 7 = 48.

    The answer is 48.

  • What is 43 + 16?


    Remember, partition the smaller addend (16) into tens and ones.

    16 = 10 + 6. Add the ten to the larger number, then add the ones.

    You are adding 43 + 10 + 6.


    43 + 16 = 59

    First, Mr. Squeaks partitioned the smaller addend into tens and ones: 16 = 10 + 6.

    Then, he added the ten to the larger addend. 43 + 10 = 53.

    Finally, he added the ones to get the answer: 53 + 6 = 59.