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

The Interior Mathematics

Activity 11 · Two Names. Answer it here, or print it and use a pencil — both count.

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Mathematics · Activity 11

Two Names

3/4 and 0.75 are the same number wearing two names. The bar in the middle of a fraction is a division sign — divide the top by the bottom, and the decimal name appears.

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.

2/5
The bar means divide: 2 ÷ 5.
5 into 20 goes 4, remainder 0 — it stops.
Same number, two names: 2/5 = 0.4

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

  1. 11/2 = stopsrepeatscircle one first
  2. 23/4 = stopsrepeatscircle one first
  3. 31/3 = stopsrepeatscircle one first
  4. 41/5 = stopsrepeatscircle one first
  5. 52/3 = stopsrepeatscircle one first
  6. 67/10 = stopsrepeatscircle one first
  7. 75/6 = stopsrepeatscircle one first
  8. 83/8 = stopsrepeatscircle one first
  9. 91/9 = stopsrepeatscircle one first
  10. 104/5 = stopsrepeatscircle one 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
Rewrite fractions as decimals
Measure
Trials (x of y)
Independent
0 of 10
Supported
0 of 10
Hints used
0
Slips
—
Confidence
—

Six stop and four repeat in every set, mixed — a student who has only met terminating decimals decides that 0.33 is where thirds end. The row below counts stop-or-repeat slips and name slips separately, because they are different instruction: one is number sense about the denominator, the other is the division itself. Set 2 and Set 3 are the same skills with different numbers.

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