Tractor Subtracter portraying subtracting as separating into any amounts

Tractor Subtracter is a math character who depicts subtraction as just separating where the quantity being separated is sectioned into two parts that may or may not be equal. Use the story and follow-up below to tell about the jobs he does. Emphasize that subtraction is about separating things and that “just separating means that the result may be two groups the same size (like 6–3 = 3) or not (like 7–4 = 3). Have elementary school students mime the actions implicit in the jobs in the follow-up to acquire a literal feel for subtraction as just separating.

Tractor Subtracter is a separater. He separates things into two pieces (like breaking a stick in two) or groups (like sorting clothes into “lights and “darks before washing them). When he does, he does not care if the pieces or groups are the same size. His job is just to separate things, not to worry about the result. That is why we say he just separates things. No one knows why he does this. He just does. Do you know anyone like Tractor Subtracter? Are you ever like him? Explain.

• Peeling potatoes, mowing the lawn, and taking a bite out of a sandwich are things Tractor Subtracter would do around the house. Show me (mime) what it looks like to do those things. What are some other things Tractor Subtracter might do around the house? Show me (mime) what it looks like to do those things.

• Sharpening a pencil, taking pages out of a notebook, and abbreviating a word are Tractor Subtracter jobs at school. Show me (mime) what it looks like to do those jobs. What are some other Tractor Subtracter jobs at school? Show me (mime) what it looks like to do those jobs.

• What are some other ways to say (or imply) “just separate? Make a list of these words and post it where it can be seen and extended. In addition to the usual keywords for subtraction like “left, include words like break, carve, cut, detach, disconnect, disengage, disjoin, dissect, eject, evict, excise, exclude, expel, fragment, isolate, partition, pick, release, screen, section, segment, segregate, sever, sieve, sift, slice, split, subdivide, subtract, sunder, take, tear, wash, weed, and winnow. These words transcend the contrived language in arithmetic word problems and heighten students’ awareness of the many everyday occurrences of subtraction in and out of school.

• Optional: Write and illustrate a story about Tractor Subtracter.

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