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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How do I know that's true?

There is no send button, no upload, no account, no sign-in. Your work is saved on this one computer so you can come back to it — and you can erase it whenever you want.

This page has no way to send anything. It saves your work in this browser's own storage on this machine. It loads nothing from the internet and sends nothing out, so there is no copy anywhere else — not with your teacher, not with the school, not with anyone.

This one is different from the Wednesday worksheets. Those are your own thinking and nobody reads them. This is math, and math is meant to be looked at together — your teacher may stand next to you and read this screen, and may write down how it went. Nothing travels on its own; a person has to be standing here.

Asking for a hint is not cheating. The hints are part of the lesson. Using them tells your teacher what to teach next, which is exactly what they are for.

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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.

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.

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
—

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.

Saved on this computer