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Partitioning Explained For Teachers, Parents And Kids

Partitioning is a phrase that even the youngest elementary school child will probably know. Here we show you how kindergarten and 1st grade children are taught this skill to help them break down any number into its component parts.

What is partitioning?

Partitioning is a way of splitting numbers into smaller parts to make them easier to work with. This can also be called decomposing.

Partitioning links closely to place value: a child will be taught to recognize that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4.

By moving tens and ones between the two parts, the number can be partitioned in many other ways:

partitioning numbers example

When shown a number (up to 7+ digits by 5th grade), children should be able to partition them independently to show a good understanding of place value. For example, 5,202,086 = 5,000,000 + 200,000 + 2,000 + 80 + 6.

When will my child learn about partitioning in elementary school?

Children will most likely learn about partitioning very early on in their math lessons.

Schools that follow the Common Core State Standards will introduce students to partitioning in Kindergarten. Students will compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings.

Students will also be expected to write an equation to record their composition or decomposition, such as 10 + 8 = 18. Students expand on this concept in 1st grade, using larger numbers and beginning to apply the same concept to digits within a number.

Students should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasize the value of each digit in two-digit numbers. They begin to understand zero as a placeholder.

In second grade, children use larger numbers to at least 1000, applying partitioning related to place value using varied and increasingly complex problems, building on work in 1st grade (for example, 146 = 100 + 40 and 6, 146 = 130 + 16).

Students in schools who are not following Common Core Standards will also begin to learn how to partition, or compose and decompose, numbers in Kindergarten and build upon that through 1st and 2nd grade. The standards may vary slightly, though.

partitioning with 4-digit numbers
Using partitioning with 4-digit numbers in a Third Space Learning online math lesson.

How does partitioning relate to other areas of math?

Children will use partitioning in many other areas of math:

  • Introducing column addition, also known as the standard algorithm: 56 + 78 may be first calculated as (50 + 70) + (6 + 8)
  • Introducing column subtraction, also known as the standard algorithm: 56 – 22 may be first calculated as (50 – 20) + (6 – 2)
  • Understanding exchanging in column subtraction: 32 – 18 may be first calculated as (30 – 10) + (2 – 8) until children realize that they can’t subtract 8 from 2 without reaching a negative number. Partitioning is important here in understanding why exchanging works. 32 can be partitioned into 20 + 12, so this subtraction can be recalculated as (20 – 10) + (12 – 8)
  • Introducing multiplication: 34 x 6 may be first calculated as (30 x 6) + (4 x 6) which represents the Distributive Property of Multiplication
  • Area Model: Students decompose numbers to make them easier to multiply.

Wondering how to explain other key math vocabulary to your children? Check out our Math Dictionary For Kids And Parents, or try these other terms:

Practice questions

1) Write the missing numbers.

361 = ___ + 60 + 1 300

945 = 900 + __ + 5     40

2) If

partitioning practice question 2a

Write the value of each diagram. (1st = 1,231)    (2nd = 2,013)

partitioning practice question 2b
partitioning practice question 2c

3) Match the sums that have the same answer.

partitioning practice question 3

(2nd box to 1st box; 3rd box to 2nd box; 4th box to 4th box)

4) 700 + 20 + 3 =             (723)

3,000 + 40 + 2 =         (3,042)

2,000 + 300 =             (2,300)

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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

Sophie Bartlett
Sophie Bartlett
Year 6 Teacher
Sophie teaches mixed age classes at a small school in central England. She is a self confessed grammar pedant and number nerd so we've welcomed her as a regular author and editor for Third Space Learning.

[FREE] Fun Math Games and Activities Packs for Kindergarten to Grade 5

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