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Overview
Overview
Splitting is a common strategy for multi-digit calculation that students may do naturally, or that a teacher can introduce.
In Grade 1, students need to add and subtract to 50, and in grade 2 up to 100, but standard algorithms are not introduced until Grade 3. This is one of the strategies that students may use to add and subtract without the algorithm. Also, they help address the Grade 3 expectation that asks students to "Demonstrate an understanding of algorithms for adding and subtracting whole numbers by making connections to and describing the way other tools and strategies are used to add and subtract."
This strategy also helps meet the mental math expectations in the curriculum.
These strategies are precursors to the alternative or standard algorithm. When using these strategies, children split the numbers along place value lines, then work with the numbers to find partial sums or differences (Lawson, p. 89).
Splitting in Addition
If time has been spent learning the earlier strategies for the working with numbers section of the continuum, students may come up with splitting as a mental math strategy.
The teacher can scribe that strategy in one of the two ways shown here.
For example, students may say, “First I added the 20 and 30 to get 50. Then I added 5 and 7 and got 12. So, 50 + 12 = 62.”
Splitting in Subtraction
When students are using “splitting” in subtraction, they are not regrouping (or “borrowing”).
In the first version, the numbers are decomposed by place value. Then the student subtracts 30 from 60, adds back the 2, then subtracts the 7.
In the second version, the first number, 62, is kept whole, 30 is subtracted, then the 7 is subtracted after that.
Watch to see how students subtract the final 7. They should be using a strategy like “Down over 10”, not counting back on their fingers or in their head.
Supporting Students with Splitting
Supporting Students with Splitting
Various models can be used to support students with this strategy.
Base 10 blocks are not recommended in Grade 1 and for at least the start of Grade 2. Small ten-frames may provide a better model, as students are used to filling a ten frame, and know a full one contains ten single counters.
Rekenreks also provide a more concrete visual for understanding groups of 10.
See these 2 visuals for the calculation 35 + 18.
Games to Promote Splitting
Games to Promote Splitting
Closest to 100
Closest to 100
Players each roll four dice, make two 2-digit numbers, and add them using splitting. The winner for each round is the player whose total is closest to 100.
Other Games to Promote Splitting
Other games - Make sure students are applying the Splitting strategy as they play:
Advanced Dollar Digit (found under variations)
Big Pig (found under variations)
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