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

The Interior Mathematics

Activity 6 · Both Ways. Answer it here, or print it and use a pencil — both count.

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Mathematics · Activity 6

Both Ways

Distributing and factoring are the same rectangle read in opposite directions. Nobody tells students that, so they learn two unrelated procedures and forget both.

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.

4(x + 2)
The 4 outside multiplies both things inside.
4 × x = 4x, and 4 × 2 = 8.
4(x + 2) = 4x + 8.

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

  1. 13(x + 4) =
  2. 25(x + 2) =
  3. 32(x + 7) =
  4. 44(x − 3) =
  5. 56(x + 5) =
  6. 66x + 15 =
  7. 74x + 10 =
  8. 812x + 8 =
  9. 99x − 6 =
  10. 1010x + 25 =
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
Distributive property and factoring
Measure
Trials (x of y)
Independent
0 of 10
Supported
0 of 10
Hints used
0
By direction
—
Confidence
—

Items 1–5 distribute, 6–10 factor, and each direction has one item where the constant is negative — that is where the area model earns its keep. The row below counts the two directions separately. Set 2 and Set 3 are the same skills with different numbers.

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