Have you been wondering what is decomposing in math? Here is a breakdown of what composing and decomposing numbers in math means and ways to support students. Understanding that numbers can be put together and taken apart in different ways is foundational to many future mathematics concepts, including addition and subtraction.
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 and make math fun.
Students who feel successful in math class are happier and more engaged in learning. Check out The Bonus Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys for students to use in your classroom to cultivate a growth mindset in mathematics. You can also sign up for other freebies from me Here at Easternshoremathteacher.com.
As I worked with my math intervention groups each week, I realized that many students lacked a basic sense of numbers. So I started to incorporate many of these activities into my groups and started to see progress. Each week we would focus on a number and work on composing and decomposing the number. We started with using part- part- whole mats, frames, and counters. Then, connect this to our addition and subtraction facts. In addition, we made some anchor charts to help us.
Compose and Decompose Numbers Break Down
It involves helping children break numbers down into parts (decompose) and then back together ( compose). For example, a student who can compose and decompose numbers understands that 1 and 3 together make 4. In addition, can break 4 into 1 and 3.
It is important to use concrete and pictorial representations to understand that numbers can be put together and then taken apart in various ways. Students need many opportunities with numbers to 5 and later extending to 10. This forms the foundation for future work with place value and helps students develop mental images and strategies as they work with basic facts.
Compose and Decompose Numbers in Kindergarten
K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
Students develop an understanding of the meaning of addition and subtraction by modeling how they can put together (compose) or take apart (decompose) up to 10 objects in different ways.
- Compose and compose numbers up to 5, then move on to numbers up to 10.
K.OA.A.2 Solve addition and subtraction word problems and add and subtraction within 10.
- Provide addition and subtraction problems in story contents with numbers up to 5 and extend to 10.
Decompose Numbers in Kindergarten
Decomposing numbers is the ability to break down numbers into their parts.
K.OA.3 Decompose numbers less than or equal to 10 into pairs more than one way. For example, by using objects or drawings and recording each decomposition by a drawing or equation. (5= 2 +3 and 5=4 +1)
Students should have many opportunities to take apart numbers up to 10 in different ways using concrete materials and to explain their thinking and patterns that they have found. First, start with numbers up to 5 to help students develop fluency with sums to 5. Then, move to numbers up to 10.
- Use problem situations to give students many opportunities to model ways numbers can be decomposed.
- Provide a variety of materials for students to use in showing their thinking, such as five and ten frames, counters, and part-part-whole mats.
- Have students represent their concrete models using pictures.
- Once students begin to demonstrate an understanding with concrete models and pictures, begin to make connections between the models and equations. At this point, the teacher writes the equation and asks questions to make the connection.
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number. For example, by using objects or drawings, record the answer with a picture or equation.
- Have students break 10 into various combinations using models such as ten frames, part-part-whole mats, and counters. Concrete objects and Images.
- Children’s literature can offer many contexts for problems.
- Explain their thinking
K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some more ones.
- Model putting a group of 10 together (composing 10) and counting the leftover objects.
- Model written equations showing a teen number composed (10+7=17) and decomposed (17=10 +7)
Decompose Numbers in First Grade
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. In addition, understand the following as special cases:
10 can be thought of as a bundle of ten ones- called a “ten.”
The numbers from 11 to 19 are composed of a ten and some more.
The numbers 10, 20… refer to one ten, two tens….
- Use activities with ten frames, linking cubes, and counters to bundle to group 10 ones to make a ten. Place Value with Tens & Ones
- Use vocabulary to refer to a group of 10 as 1 ten.
- Given a number of objects between 11 and 19, group them into 1 group of ten and some ones.
- Describe the decade numbers (10, 20..) in groups of tens. 20= 2 tens
Decomposing numbers will continue in the upcoming grade levels, breaking larger numbers into their parts. (37= 30 + 7)
Compose Numbers
Composing numbers is the ability to put two parts together to make a whole. For example, kids will put together sets of objects of smaller numbers to make a complete set.
K.OA.A. 5 Fluency add and Subtract within 5.
By the end of Kindergarten, students should know addition and subtraction facts with sums to 5 from memory.
1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers.
Composing numbers will continue in the upcoming grade levels by putting larger numbers together.
How Do You Decompose A Number?
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 adapt it to meet different situations.
Part- Part- Whole
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. Read more… How to Use the Powerful Part-Part-Whole Strategy to Improve Number Sense.
Five Frames & Ten Frames
A Five Frame has five equal spaces in a row. For children in pre-kindergarten or Kindergarten who have not yet explored a ten frame, it is a good idea to begin with a five frame. The five frame focuses on the relationship to 5 as an anchor for numbers. These are often used before introducing a ten frame. Check out this link to find a free five-frame printable or digital version. Five Frames Template
A ten frame is a rectangle with ten equal spaces. It has five spaces on top and five on the bottom. It is used to support the development of the important landmark numbers five and ten. You often find the ten frames positioned horizontally and filled with counters placed from left to right and top to bottom.
Ten frames are a fantastic tool used in Kindergarten and First Grade to help build an understanding of counting, place value, adding, subtracting, and more. Also, you use counters or math manipulatives to represent numbers less than or equal to ten on the frame. Check out this link to find a free Ten Frames Template. Ten Frames Free Printable. Read more… Why Using Ten Frames for Math to Develop Understanding is Effective?
Math Games
Talking, playing, and solving math throughout the day- not just during math class builds number sense and the love of mathematics.
Sign up to get this Freebie of 71 Math Puzzles for fun to use with your students. These are great for warm-up, whole class, small group, or independent work. 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.. How to use Engaging Math Puzzles for Fun to Build Number Sense.
Activities for Decomposing and Composing Numbers
Decomposing Numbers
What is decomposing numbers in math? Decomposing numbers begin with objects up to 5. Use number frames, five frames, and part-part-whole mats with 2 different counters to help students decompose numbers. Then, move on to objects up to 10 and ten frames. Providing these activities as warm-ups, small groups, whole groups, and independent activities help develop students’ number sense. Furthermore, composing and decomposing numbers anchor charts can be a helpful visual for students.
Compose and Decompose Numbers Bundle
Composing Decomposing Numbers (Digital Slides & Printables)
Composing Numbers
Composing numbers begins with sums up to 5. First, use number frames, five frames, and part-part-whole mats with 2 different counters to help students compose numbers. Then, move on to sums up to 10 and ten frames. Finally, move on to sums of 20 and double ten-frames. Providing daily practice with composing numbers helps students become more fluent in their basic facts, which is essential for more complex problems.
- Math Facts Practice Bundle
- Part-Part- Whole Activities Bundle
- Math Facts Addition Bundle
- Math Fact Practice
Decomposing and Composing Numbers in PreKindergarten
Composing and decomposing numbers is a mathematical skill introduced in Pre-Kindergarten and further elaborated on in Kindergarten. Begin with numbers to 5 using five frames. Also, Compose and Decompose Numbers Anchor Chart can be a helpful visual for students.
Decomposing Numbers In Kindergarten
Students will..
- Use objects to show different ways that a given number can be broken into two sets in multiple ways. Numbers 3-10, and then 11-19.
- Connect objects to pictures.
- Describe their reasoning.
- Finally, make connections to expressions and equations provided by the teacher.
Composing Numbers In Kindergarten
Students will…
Compose and Decompose Numbers Kindergarten Worksheets
There are a lot of materials you can use to practice composing and decomposing numbers.
The resource Composing Decomposing Numbers has digital and paper versions. One option is to have the paper copies and counters while you present the slides on your screen. Then, working together, you can decompose the numbers. These resources can be used as a warm-up, whole group lesson, small group lesson, independent work, or center.
These two resources are great for practicing sums of 10 and teen numbers: Sums of 10 Freebie and Teen Numbers Freebie.
Composing and Decomposing Numbers First Grade
Students will…
- Continue to decompose numbers Numbers 3-10 and then 11-19.
- Understand that two digits of a two-digit number represent amounts of tens and ones.
- Connect objects to pictures.
- Describe their reasoning.
- Make connections to expressions and equations.
- Compose numbers with sums to 20 (fluent up to 10).
Composing and Decomposing Numbers Worksheet First Grade
Providing daily opportunities to compose and decompose numbers improves students’ number sense. Think of ways to incorporate these activities into your warm-up, whole group lessons, small group lessons, independent work, or center.
The resource Composing Decomposing Numbers has digital and paper versions to practice decomposing and composing numbers to 10.
In addition, Practicing doubles facts with Doubles Math Facts Worksheet FREEBIE, which also had digital and paper versions, helps with practicing doubles addition facts to 20.
Finally, these two resources are great for practicing sums of 10 and teen numbers: Sums of 10 Freebie and Teen Numbers Freebie.
Additional Composing and Decomposing Numbers Resources
Composing and Decomposing Numbers Kindergarten Anchor Chart
Composing Numbers & Decomposing Numbers! | Mini Math Movies | Scratch Garden– Video
10 New Math Terms Every Parent Needs to Know
Achieve the Core- Standards Progression
Addition and Subtraction Situation Types by Grade Level
How to use Engaging Math Puzzles for Fun to Build Number Sense
Why is Decomposing and Composing Numbers Important?
Understanding that numbers can be put together and taken apart in different ways is foundational to many future mathematics concepts, including place value and addition and subtraction. This is important to build students’ number sense. Number sense is a person’s ability to understand, relate, and connect numbers. It is the ability to use this understanding of numbers flexibly and develop practical, efficient strategies. Furthermore, for students to do more challenging math students, they need to have a strong sense of numbers.
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 and make math fun. Also, you can also sign up to receive other freebies from me Here at Easternshoremathteacher.com.
By providing students opportunities to play with numbers, you are building students’ number sense and helping them see the beauty in mathematics. These foundational skills will allow them to do more challenging problems and enjoy mathematics. Let me know if this clarifies what is decomposing in math and if you have additional resources to teach it?
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