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Splitting: What is it?
Splitting is an addition and subtraction strategy. Splitting refers to numbers being 'split' on the place value lines in order to make computations easier.
Overview
Splitting is a way to decompose numbers based solely on the place value lines. Numbers in an equation are broken apart into their place value to make calculations easier. This involves, for example, combining 25 objects and 34 objects by breaking apart both numbers into their tens and ones, combining the tens, combining the ones, and finally combining the total of the tens with the totals of the ones. This strategy is one many students find success with and are able to use for computations quite confidently.
Supporting Students Using 'Splitting'
Students that use this strategy are developing many of the key ideas in mathematics, such as place value, part-whole relationships and commutative property. They understand that the position of a digit determines its value. As well as knowing that breaking up the numbers and moving them around still results in the same sum. Experience with making models of two-digit numbers using base ten blocks supports students' use of this strategy. When students can combine their computational strategies with an understanding of base ten grouping, they develop very efficient ways of using their understanding to mentally calculate operations.
Spending time to ensure students can accurately count by 10 over 100 is key. Often times, students will be quite confident with skip counting by 10's to 100 however, may not be as comfortable going over that benchmark. Ensure students are confident with this idea as they explore 'splitting' that may require 'regrouping'. For example, 70 + 50
Where to Next?
When students are efficient in splitting, use larger numbers to ensure they can transfer this understanding to larger numbers.
Exploring splitting with decimal numbers is also an option when ready. A natural shift from splitting may be make explicit connections to 'alternate algorithm' helping students to organize their thinking. Students may also benefit from splitting only one number and using an open number line to model thinking. (Taking jumps of 10)
Games/Activities to Support Students Using 'Splitting'
Trading Up to 1000
Trading Up to 1000
In this game, players work on their place value understanding to be the first player to 'trade up' to 1000. (GEIM)
Number Strings
Number Strings
Intentionally choosing number string to support the strategy of splitting will help students become proficient with this strategy. Refer to pg. 197 in Number Talks for examples.
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