A part part whole mat is a simple picture tool that helps children see how numbers can be made and broken apart. The two smaller spaces are the parts, and the larger space is the whole. When the parts join together, they make the whole number.
This helps young learners build a strong understanding of addition and subtraction.
Understanding Early Learners: Part Part Whole
Children learn number best when they can touch, move, and count real objects. Put a small group of buttons, blocks, or toy animals in each part space. Then have the child count every object in both groups to find how many there are altogether.
At first, many children will count both groups from one again. With practice, they begin to hold one amount in their mind and count on from it. This is an important step toward faster addition.
The objects show that a number is not only a spoken word or a written mark. It tells how many things are in a group.
A whole stays the same even when its objects are moved into different groups. This idea can take time to understand. A child may think a spread out row has more objects than a close row, even when both rows have the same amount.
Encourage them to line up, touch, and count each item once. Moving the same counters from one part space to another can show that the total amount has not changed.
Only the groups have changed. This builds a foundation for understanding that numbers can be rearranged without changing the total.
Part part whole thinking appears in ordinary routines. A child might notice how many red socks and blue socks are in a basket. They might split snacks between two plates, count children wearing boots and children wearing shoes, or sort crayons by color.
At home or school, adults can say the total first and ask the child to make two groups. This is often more useful than giving a worksheet straight away.
When children create the groups themselves, they see that several different pairs can belong to one total. They begin to notice useful number patterns, especially pairs that make five or ten.
When learning this topic, pay attention to counting carefully and using the correct role for each number. The whole is the total number of objects before or after they are separated. Each part is only one group.
A common mistake is to count an object twice, skip an object, or treat a part as if it were the total. Pointing to each counter while saying one number word helps. Drawings can help too, but each drawing must stand for one object.
Later, children can replace counters with number cards and mental pictures. The goal is not to rush away from materials. The goal is to understand the relationship so clearly that the child can explain what happened when an object is added to, removed from, or moved between groups.
Key Facts
- part + part = whole
- whole - part = other part
- If one part is 3 and the other part is 2, then the whole is 5.
- If the whole is 8 and one part is 5, then the other part is 3.
- The same whole can be split in different ways, such as 6 = 1 + 5, 6 = 2 + 4, and 6 = 3 + 3.
- A part part whole mat can show addition and subtraction with counters, drawings, or numbers.
Vocabulary
- Part
- A part is one smaller group that helps make a whole.
- Whole
- A whole is the total amount made when all parts are put together.
- Join
- To join means to put parts together to make a bigger group.
- Split
- To split means to break a whole into smaller parts.
- Total
- The total is the number of objects altogether.
Common Mistakes to Avoid
- Putting the whole in a part space is wrong because the whole is the total, not one smaller group.
- Adding only one part is wrong because both parts must be joined to find the whole.
- Forgetting that parts can be different sizes is wrong because a whole can split into many pairs of parts.
- Counting the same counter twice is wrong because each object should be counted one time when finding the whole.
Practice Questions
- 1 There are 4 red counters in one part and 3 blue counters in the other part. How many counters are in the whole?
- 2 The whole is 9 counters. One part has 6 counters. How many counters are in the other part?
- 3 A child moves 2 counters from the whole space into one part and 5 counters into the other part. Explain how the mat shows that the whole was split into two parts.