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.

Saved on this computer only.

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.

If you share this computer, erase before you go. Anyone who uses this same browser profile could open the page and see your work. That is what the erase buttons are for, and using them is completely normal.

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.

  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
—
Watched the demo
—
Stretch
—

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.

Saved on this computer