Subtraction Timed Test

Addition read backwards, and harder for it

Every subtraction fact on these sheets is an addition fact turned around: 14 − 6 is the question "six plus what makes fourteen". That is why the set has no shortcut of its own and why subtraction sheets come back slower than addition sheets from the same child.

The facts here run from 0 − 0 to 24 − 12 and never produce a negative answer, because the minuend is built from the two operands rather than picked independently. A sheet of 100 problems therefore stays inside the same fact set a classroom would call "subtraction within 20" plus the twelves.

Borrowing across ten, and the count-back trap

Counting back works up to about three and collapses after that. 13 − 4 by counting back is four steps and usually correct; 13 − 8 is eight steps and usually wrong. The fix is not more counting but the other direction: 13 − 8 becomes 13 − 10 + 2, or "eight plus five". A timed sheet is useful here precisely because it makes counting back too slow to survive.

The second trap is order. A child who has learned that subtraction means "take the small from the big" will answer 4 − 13 as 9 without noticing anything is wrong. These sheets never present that problem, which means the habit goes undetected here — worth knowing, because it is the most common wrong idea in the whole operation.

Where to start with subtraction

Start with the ranges a child can reach by counting back, then leave them. Subtracting 1, 2 and 3 will look fluent whether or not the facts are memorized, so a fast sheet there tells you very little. They are useful as a warm-up and as a way to keep a week's sheet from being uniformly discouraging.

The sheets that carry information are subtracting 6 through 9, where counting back is too slow to finish inside a minute. Subtracting 10 is worth its own sheet for the opposite reason — it is the anchor every other bridge move goes through, and it should be instant. Run 0–12 or mixed once the single ranges are fast, not before.

Thirteen sheets for subtraction

Each of these is its own sheet with its own fact table and its own trouble spots. The single ranges hold one operand steady; 0–12 and mixed draw from the whole set.

• All subtraction facts from 0 − 0 to 24 − 12, with no negative answers. 0–12
• Subtracting 2, from 2 − 2 to 14 − 2. 2s
• Subtracting 3, from 3 − 3 to 15 − 3. 3s
• Subtracting 4, from 4 − 4 to 16 − 4. 4s
• Subtracting 5, from 5 − 5 to 17 − 5. 5s
• Subtracting 6, from 6 − 6 to 18 − 6. 6s
• Subtracting 7, from 7 − 7 to 19 − 7. 7s
• Subtracting 8, from 8 − 8 to 20 − 8. 8s
• Subtracting 9, from 9 − 9 to 21 − 9. 9s
• Subtracting 10, from 10 − 10 to 22 − 10. 10s
• Subtracting 11, from 11 − 11 to 23 − 11. 11s
• Subtracting 12, from 12 − 12 to 24 − 12. 12s
• Subtraction facts drawn across the whole 0–12 range in random order. Mixed

Three that come up

Do these subtraction sheets ever give a negative answer?

No. The minuend is constructed from the answer plus the number being subtracted, so the result is always between 0 and 12 and the sheet never asks for something a child has not been taught.

Why is subtraction slower than addition for the same child?

Because most children recall subtraction by finding the matching addition fact, which is two steps rather than one. The gap between an addition sheet and a subtraction sheet is usually a good estimate of how automatic the addition really is.

What is the hardest group of subtraction facts?

The ones that cross ten with a subtrahend of 6, 7, 8 or 9 — 15 − 7, 16 − 8, 14 − 6. They are too far to count back and they have no pattern to lean on.

What the standards and the critics actually say