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

The Interior Mathematics

Activity 7 · What Goes First. Work it here, or print it and use a pencil — both count.

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Mathematics · Activity 7

What Goes First

The order is not a tidy convention. It is the only reason one expression means one thing, and this page never asks you for the answer — only for what is allowed to happen next.

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.

5 + 3 × 2
Multiplication goes before addition — the × moves first.
3 × 2 = 6.
Then 5 + 6 = 11.

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

  1. 14 + 3 × 2 =
  2. 220 − 12 ÷ 4 =
  3. 3(5 + 3) × 2 − 1 =
  4. 42 + 3^2 =
  5. 518 ÷ 3 × 2 =
  6. 610 − 4 + 3 =
  7. 75 × (9 − 6) + 1 =
  8. 8(4 + 2)^2 ÷ 4 =
  9. 924 ÷ (8 − 2) + 5 =
  10. 103 + 2 × 5 − 4 =
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
Order of operations
Measure
Trials (x of y)
Independent
0 of 10
Supported
0 of 10
Hints used
0
Out of order
—
Confidence
—
Watched the demo
—
Stretch
—

Every set has two left-to-right traps — 18 ÷ 3 × 2 and 10 − 4 + 3 — where working right to left gives 3 for both, and 3 is nowhere near either answer. The row below counts out-of-order attempts, which is the number that actually says whether the rule is known. Set 2 and Set 3 are the same skills with different numbers.

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