Architecture of Grace
Mathematics · The Interior · Grades 6–8

The Interior Mathematics

Activity 5 · Sign and Size. Answer it here, or print it and use a pencil — both count.

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Mathematics · Activity 5

Sign and Size

Multiplying integers is two questions wearing one coat. The sign is the new one. The times table is not, and pretending otherwise is how a student who knows their facts still gets it wrong.

On this computer only

No score is kept. No points, no streak, no ranking — the only number anyone writes down is the one your teacher writes down, standing next to you.

Show me one first

This one is nobody's problem — it is only here to show the moves before you touch yours. Watching it costs nothing and is written down nowhere.

(−3) × (−6)
Count the negative signs: 2. Even, so the answer is positive.
Now ignore the signs: 3 × 6 = 18.
(−3) × (−6) = 18.

Now problem 1 is yours. The hint button is there the whole time, and using it is part of the lesson.

  1. 13 × (−4) = +−circle the sign first
  2. 2(−6) × 5 = +−circle the sign first
  3. 3(−7) × (−3) = +−circle the sign first
  4. 48 × 3 = +−circle the sign first
  5. 5(−9) × (−2) = +−circle the sign first
  6. 6(−24) ÷ 6 = +−circle the sign first
  7. 736 ÷ (−4) = +−circle the sign first
  8. 8(−45) ÷ (−9) = +−circle the sign first
  9. 928 ÷ 4 = +−circle the sign first
  10. 1042 ÷ (−7) = +−circle the sign first
How confident are you with these?

There is no right answer here. It only tells your teacher where to start next time.

For the teacher — this device only

One probe row, built from what happened on this screen. Nothing is sent anywhere — copy it into the Goal Builder yourself, or print this page. Independent means walked with no hints; supported means walked after a hint. Both are real evidence and neither is a grade.

Date
—
Skill
Multiply and divide integers
Measure
Trials (x of y)
Independent
0 of 10
Supported
0 of 10
Hints used
0
Slips
—
Confidence
—

Five multiply, five divide, and every set covers all four sign pairs in both — a student can pass a page of positive-times-negative and still not know what two negatives do. The row below counts sign slips and size slips separately, because they are different instruction. Set 2 and Set 3 are the same skills with different numbers.

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