Sunday, July 31, 2016

Subtraction is NOT Just Take Away!

While I was updating my Subtraction Fact Mental Strategy Count Up To Free Sample, which provides practice in identifying and discriminating between basic subtraction equations, I began thinking about concrete ways to introduce this subtraction fact strategy. I also started to realize that children who view subtraction as only meaning to take away would have a difficult time conceptualizing this strategy. (Never fear, after I get off my soapbox, there will be a link to another subtraction freebie below!)

Subtraction is NOT just take away! Teaching all three forms of subtraction; taking away, comparing, and finding a missing part of the whole is critical! There are links to two subtraction fact strategy freebies in this post.



It's so easy to get stuck in a rut teaching 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; 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/ subtract 4, I know we will have a lot of work ahead to rebuild a foundational understanding of subtraction.

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, grasp hands (think London Bridge) and 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. The Teddy Bear Ten Strips, a free download, found in my post on more and less, can also be used to find the difference between two quantities, using small manipulatives. Not only will these types of activities help build an understanding of subtraction as comparing quantities, but will also lead into interpreting data in graphs by answering how many more/ less questions, a first grade standard.

The Count Up To subtraction strategy is based on finding the difference between two numbers. When your first or second grade students are ready to learn this strategy, you might want to begin with neighbor numbers for subtraction.

Introduce the Count Up To subtraction fact strategy with neighbor numbers.

One way to introduce this is to display equations and 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.

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 it is part of my anchor wall chart for this strategy. This provides a consistent visual cue. I also limited the number line to those numbers that would be used for this strategy 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.

This free resource, Numbers in the Neighborhood, provides a concrete, visual way to introduce the Count Up To subtraction fact strategy with first and second graders.


Simply print the houses in color or black/ gray/ white on paper or card stock. Laminate, if desired, and cut. Place the houses in order on the carpet, a table, or a chalk/ white board. 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.

This free resource, Numbers in the Neighborhood, provides a concrete, visual way to model and practice the Count Up To subtraction fact strategy with first and second graders.

When they are ready, students can use their own number line strips to practice. I would 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.

Enjoy these Numbers in the Neighborhood number lines for introducing and practicing the Count Up To subtraction fact strategy! The flashcards, an anchor wall chart, and two worksheets found in my Subtraction Fact Strategy Count Up To Free Sample may be downloaded from my TpT store.

These free samples, compiled from three of my subtraction resources, are for reinforcing the count up to subtraction fact strategy with first and second graders.


I am delighted to have finally finished giving my subtraction fact strategy anchor charts, flashcards, and worksheets a cosmetic makeover. I also added black/ gray/ white anchor charts and quarter page size mini-charts. The strategies covered are Subtract Zero, Subtract All, Count Down, Count Up To, Doubles, Make 10, Bridge With 10, Subtract 10, Subtract 9, and Subtract 8. These resources are available individually or as a bundle.

This set of three resources is perfect for supporting explicit strategy instruction for the basic subtraction facts to 20 in first and second grade. $


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1 comment:

  1. Great ideas. I never thought of the difference between "take away" and "minus/subtract." I always tell them to use minus or subtract because "take away" is for little kids. Now I have a better reason.

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