So far for mental maths strategies we’ve looked at: counting on, near doubles and compatible numbers. Today we’re moving on to the partitioning numbers strategy. You can use the partitioning strategy for subtraction, multiplication and division, but for today I’ll share with you some of my ideas for using partitioning for addition.
What is partitioning for addition?
When we add numbers, sometimes it helps to break these numbers up into parts which helps to simplify what is being added.
When working with little kids, this can be demonstrated using numbers that can make a group of 10. For example: 7 + 5 can be solved by first adding 7 and 3 to total 10. Then adding on the 2. So the 5 is partitioned into 3 and 2. Or for older students adding 38 + 6 can be solved by first adding 38 and 2 to total 40. Then adding on the 4 for a total of 44. The 6 was partitioned into 2 and 4. The below picture uses a number strip to show how this can be done.
It’s also important for your students to practice other ways of partitioning. You can model to students all the ways that partitioning can be used to solve the following problem.
For this activity you will need a large 100 grid for the class to be able to view.
- Circle two different numbers on the 100 chart, such as 37 and 47. Get your students to solve mentally and share their strategies.
- Highlight the partitioning strategy. For example, (30 + 40) + (7 + 7) = 70 + 14 = 84. Discuss other ways students may have partitioned the numbers.
- Get your students to work in pairs. One student selects 2 different numbers from the 100 grid; both students must use the partitioning strategy to add the numbers. Students take it in turns to pick the numbers. Get them to check if they partitioned the numbers in the same way.
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Graphic Credits: Graphics From the Pond
If a student first learns that 7+8=15, than a student will see that 17+8=25, 27+8=35, and 37+8=45, and in fact, they can practice that pattern.