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

The Interior Mathematics

Activity 12 · Name the Move. Answer it here, or print it and use a pencil — both count.

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Mathematics · Activity 12

Name the Move

A property is a legal move. Both sides are always worth the same — something just changed how it looks. First say what moved. Then say its name.

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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.

9 + 5 = 5 + 9
Nothing was calculated — both sides are worth 14.
The 9 and the 5 traded seats. The move: the order swapped.
Order has a name: the Commutative Property.

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

  1. 14 + 9 = 9 + 4name the property:  
  2. 2(3 × 5) × 2 = 3 × (5 × 2)name the property:  
  3. 37 × 1 = 7name the property:  
  4. 42(x + 6) = 2x + 12name the property:  
  5. 58 + 0 = 8name the property:  
  6. 65 × 8 = 8 × 5name the property:  
  7. 7(6 + 2) + 9 = 6 + (2 + 9)name the property:  
  8. 812 × 0 = 0name the property:  
  9. 93(y + 4) = 3y + 12name the property:  
  10. 10x + 5 = 5 + xname the property:  
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
Name the property
Measure
Trials (x of y)
Independent
0 of 10
Supported
0 of 10
Hints used
0
Slips
—
Confidence
—

Every set carries all six names: two order, two grouping, two spread, and all three special-number properties. The row below counts seeing slips and naming slips separately, because they are different instruction — one is structure, the other is vocabulary. Set 2 and Set 3 are the same skills with different numbers.

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