As I began thinking about concrete and visual ways to introduce the Count Up To subtraction fact strategy, I realized that children who conceptualize subtraction as only meaning to take away would have a difficult time with this strategy.
It’s so easy to just teach subtraction as take away. We know addition involves joining quantities together. So why isn’t subtraction simply taking quantities away? Just to complicate everything, subtraction takes three forms. These forms are taking away, comparing, and finding a missing addend or part of a whole.
When a second grader reads 7-4 as 7 take away 4 rather than 7 minus or subtract 4, I know we will have a lot of work ahead. It will be necessary to rebuild a foundational understanding of subtraction.
Understanding subtraction as comparing two quantities to find the difference is an essential component of the Count Up To strategy. Comparison subtraction is useful for solving equations such as 9-6 where the two numbers are close together or “in the same neighborhood”.
The concept of comparing to find the difference between two quantities can be introduced in kindergarten. Two groups of children can line up facing each other and grasp hands (think London Bridge). They will readily see/ count the difference between the two groups. This type of activity can be repeated many times with a wide variety of objects over an extended period of time.
How to Introduce the Count Up To Subtraction Strategy
When your first or second-grade students are ready to learn this the Count Up To strategy, you might want to begin with neighbor numbers for subtraction. The equations 4-3, 7-6, and 9-8 are examples with neighbor (or right next to each other) numbers.
To introduce, display the equations. Then, ask your students what they notice that is the same about all the equations. Can they solve the equations? How did they find the difference? Model how to find the difference on a number line.
How to Practice the Count Up To Subtraction Strategy
When they understand this concept, they’re ready to move on to the Count Up To subtraction fact strategy. I typically prefer vertical number lines. But for this activity, a horizontal one made more sense. I wanted to stick with the idea of numbers or houses in a neighborhood since this is a familiar part of other resources I’ve created for this strategy. This provides a consistent visual cue.
The number line is limited to those numbers that would be used for this strategy. I did this to increase associations between the strategy and the numbers. I created number line houses 2 through 12 for group instruction and a number line strip with houses 4 through 12 for individual student use. The facts 3-2 and 4-3 can be solved by either counting down or counting up to. A number line from 4 through 12 covers the remaining basic subtraction facts for which this strategy is applicable.
How to Prepare:
Simply print the houses in color or black/ gray/ white on paper or card stock. Laminate, if desired, and cut.
Likewise, print the number line and counting strips in color or black/ gray/ white on paper or cardstock. Laminate and cut in strips.
Use any suitably sized counters.
Ways to Practice:
Place the houses in order on the carpet, a table, or a chalk/ whiteboard. Present a Count Up To basic subtraction fact with a difference of 1, 2, or 3, such as 9 – 6.
Model using counters (or button magnets on a board) how to keep 6, the lower number in your head and count up to 9, the higher number. Students can now easily visualize the difference between the two numbers!
As with the Count Up strategy for addition, you will have to find ways to keep your students from counting the number they start with. While you are modeling and practicing the process, be sure to emphasize you are finding the difference between the two numbers.
When they are ready, students can use their own number line strips to practice. Only give them three counters as this strategy is best used with a difference of 1, 2, or 3.
I have also included a three counter strip that can be used as a bridge to mental fluency, instead of using fingers. Just say the lower number. Then, place counters as you count up to the higher number.
Students who understand and apply the Count Up To strategy for basic facts will also be able to apply it to multi-digit subtraction.
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Subtraction flashcard photo is by Classroom Clicks.