Using the part-part-whole model helps learners see the relationship between the whole number and its parts and helps build number sense which is the foundation for mathematical learning. For students to develop an understanding of math concepts, flexible and fluent thinking with numbers is necessary. The part-part-whole strategy is easy to incorporate into your teaching and helps to improve number sense. Who else is always looking for ways to enhance their student’s number sense?
Get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. Providing opportunities to do math puzzles daily is one way to help students develop their number sense. CLICK Here to sign up for 71 Math Number Puzzles, and check out my website for more resources I use.
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Using the part-part model has helped me show students the relationship between the whole and its parts. It has helped students become more fluent in their math facts and see the connections between addition and subtraction. In addition, this strategy has been beneficial when solving word problems.
I was tired of students just taking the two numbers in the problem and adding or subtracting them without regard to the actual problem. Using the part-part-whole model helped them visualize what was happening and start to make sense of the problem.
What is Number Sense in Mathematics?
Number sense refers to understanding number concepts, operations, and applications of numbers and operations. It is the ability to be flexible with numbers and have a variety of strategies to use. Students know how to use the strategy and how to adapt it to meet different situations.
For students to develop an understanding of math concepts, flexible and fluent thinking with numbers is necessary. It is the building block of mathematics.
The Importance of Number Sense
Good number sense helps children manipulate numbers to make calculations more accessible and gives them the confidence to be flexible in their problem-solving approach.
It is so crucial for young mathematicians because it promotes confidence and encourages flexible thinking. In addition, It allows young children to create a relationship with numbers and talk about math.
How to Build Number Sense
Children with good number sense enjoy playing with and exploring numbers. Putting numbers together and taking them apart (composing and decomposing numbers), and finding the parts of a whole (part-part-whole) are both ways to help students become flexible in their thinking. These Part-Part-Whole activities are a great way to practice this strategy. Click HERE to see them.
Talking, playing, and solving math throughout the day- not just during math class builds number sense and the love of mathematics.
Get this Freebie of 71 Math Puzzles to use with your students. These are great for warm-up, whole class, small group, or independent work. In addition, You can also print and put the puzzles up on a bulletin board. Then, have strips of paper for students to write down their answers. It is a great early-finisher activity and allows students to see math as fun.
Read more about it at How to Use Engaging Math Puzzles for Fun to Build Number Sense.
What is Part-Part-Whole Math?
The part-part-whole model is a pictorial representation of a problem that helps students see the relationship between a “whole” and its components. The act of splitting a number into parts is known as partitioning.
The part-part-whole diagram shows that you know some information but still need to find additional information. The bar can be split into as many parts as you need, depending on the amount of information you’ve been given. The whole or any of the parts can be missing.
Children using this model will see the relationship between the whole number and its parts, helping learners to make the connections between addition and subtraction.
The part-part-whole model can be connected to number bonds with the whole and its parts. Using the part-part-whole mat to solve problems gives students a way to represent the problem. Click HERE to get a digital and printable part-part-whole mat.
Why Use the Part-Part-Whole Model?
When learners have experience using the part-part-whole model in math, it will further develop their understanding of numbers. For example, they will realize that addition and subtraction are related and that word problems can often be solved by addition and subtraction.
By breaking down numbers into smaller chunks, they can learn how numeracy relates to other math skills, including addition, subtraction, multiplication, and division. This helps them to become flexible and fluent with numbers and improve their number sense. And having a solid number sense helps them understand math concepts. It sounds like a win-win to me!
Examples of Part- Part-Whole
In the part-part-whole model below, you can see that the whole is 5, and one of the parts is 3. Before learners use abstract numbers, it is essential to use objects representing cardinality (the amount in a group), as this will be easier for young children to manipulate.
With part-part-whole models, it is important to remember that the parts combine to make the whole. The parts and the whole should not be combined to create a new whole. Rather, the point of the part-part-whole model is to look at what the other missing part would be when combined with the other part that makes the whole. To write this model as a number sentence, it would be 3 + __ = 5 or 5 = 3 + __.
Using Part-Part-Whole with Word Problems
Problem-solving is always going to be difficult for primary students. Applying mathematical knowledge can be hard when learners don’t understand which operation they need to use. A part-part-whole model shows learners the problem in an accessible way.
It helps students to interpret, visualize, and solve word problems. For example, students can use the part-part-whole mat to identify the parts they know and what they need to find out.
This allows the students to visualize the problem and prevents them from just adding or subtracting the numbers without understanding the relationship of the numbers.
Part- Part-Whole Activities to Build Number Sense
Using the part-part-whole mat to solve problems gives students a way to represent the problem. Click HERE to get a digital and printable part-part-whole mat.
Concrete-Representational-Abstract (CRA) model is an instructional approach that is effective in teaching math concepts. Students use counters and a part-part-whole mat during the concrete stage. Then, progress to drawing the counters on the mat in the representational stage. Then finally, progress to the abstract stage, where students write the numbers on the part-part-whole mat.
A part-part-whole worksheet could be used with basic addition and subtraction problems or addition and subtraction word problems. In addition, you can use fact families to teach your children about the part-part-whole method.
For example, give your student a whole number and ask them to break the whole into all its possible parts. To help them, you can provide counters or blocks to represent the whole number. Then, encourage your children to split their whole number into as many different parts as they can and get them to count and record each possible pair.
These Part-Part-Whole activities are a great way to practice this strategy. Click HERE to see them.
Some part-part-whole activities are part of my Freebie of 71 Math Number Puzzles that will be e-mailed to you when you sign up.
Additional Resources:
- Video of the concept of number sense
- Demystifying Math: What Is Number Sense?
- CRA: An Instructional Strategy for Math
- How to use Engaging Math Puzzles for Fun to Build Number Sense
- Part- Part-Whole Mat
- Common addition and subtraction problem structures
Part- Part-Whole Model Improves Number Sense
Strong number sense helps build a foundation for mathematical understanding. Focusing on number sense in the younger grades helps build the foundation necessary to compute and solve more complex problems in older grades. Creating a love for math in your children begins with building an understanding of numbers.
Teachers can promote number sense by providing rich mathematical tasks and encouraging students to decompose and compose numbers using the part-part-whole model.
Sign up on my webpage to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. Slides using the part-part-whole model are included. CLICK Here to sign up for 71 Math Number Puzzles and check out my website Here at Easternshoremathteacher.com
Using the part-part-whole model helps learners become more fluent and flexible with numbers which helps to build number sense, the foundation for mathematical learning. Let me know how you use the part-part-whole strategy in the comments.
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