Partitioning to Add
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 doubledigit 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
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 twentysix 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 twentysix 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 twentysix 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 twentysix plus ten? Thirtysix. Now, we can add thirtysix plus five, which is fortyone. That means twentysix plus fifteen equals fortyone. "Okay, I've passed fortyone mushrooms, I can't be far." "Wait, I didn't pass green mushrooms yet." Mr. Squeaks just saw thirtytwo green mushrooms and then twelve brown ones. How many mushrooms did he pass? Start by creating an equation. We can create thirtytwo 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 thirtytwo plus ten plus two. Then, solve using the tens frame. What is thirtytwo plus ten? Fortytwo! What is fortytwo plus two? Fortyfour! So, Mr. Squeaks has passed fortyfour mushrooms. "I MUST be close now!." "MORE MUSHROOMS?" We can partition again to help Mr. Squeaks one last time. Mr. Squeaks saw fortyseven spotted mushrooms and seventeen small ones. How many mushrooms should he add? Remember to start by creating an equation. We can create fortyseven 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 fortyseven plus ten plus seven. What is fortyseven plus ten? Fiftyseven What is fiftyseven plus seven? Sixtyfour. Mr. Squeaks needs to add sixtyfour 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!"
"Iimani? That's you, right?" "Surprise! It's me!"
Partitioning to Add exercise

How do you partition to add?
HintsRemember, 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
SolutionFor Mr. Squeaks to teach Imani, he needs to show them these steps in this order:
 Create an equation.
 Partition the smaller addend.
 Add the numbers using tens frames.
 Solve the equation.

How could we solve this problem?
HintsYou 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?
SolutionTo 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?
Hints14 + 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
SolutionWhen we partition, we break the smaller number into tens and ones, like these pairs.

Show the steps.
HintsRemember, 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.
SolutionMr. 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?
HintsStart by adding the 10 to the larger addend. Then add on the ones.
31 + 10 = 41. Count on 7 more to find the answer.
Solution31 + 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?
HintsRemember, 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.
Solution43 + 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.