Block Builder

What your child will figure out

• Build a requested multiplication array by resizing its rows and columns, then verify the product by skip-counting equal rows.
• Read the product represented by a completed rectangular array and connect the factors to its two dimensions.
• Find a missing factor by holding one array dimension fixed and resizing the other until the target area is reached.
• Transform arrays by turning, resizing, doubling, and matching equivalent areas; connect missing factors to division and develop flexible fluency across factors 1–12.

The levels

1. Plan a 3 × 4 floor

   Predict 12, build three rows of four, skip-count 4, 8, 12, and explain that rows × columns counts every square.

2. Read the rectangle

   Name the product shown by a completed 4 × 6 array and verify 24 by counting equal rows.

3. Finish the 42-tile wall

   Solve 6 × ? = 42 by keeping six columns fixed and resizing the array to seven rows.

4. Add one whole row

   Transfer the rectangle model from 5 × 8 = 40 to 6 × 8 = 48 and explain why one new row adds eight squares.

5. Turn the window wall

   Rebuild 4 × 9 as 9 × 4 and establish that turning an array preserves its 36 squares.

6. Remove two seat rows

   Change 8 × 7 = 56 to 6 × 7 = 42 by removing two complete groups of seven.

7. Complete the 72-panel roof

   Solve 9 × ? = 72 by holding nine rows fixed and finding the eight-panel width.

8. Raise a square tower

   Build and verify the square fact 11 × 11 = 121.

9. Double the banner

   Double 4 × 12 = 48 to 8 × 12 = 96 and connect doubling one factor with doubling the product.

10. Rebuild the same courtyard

    Show that 6 × 10 and 5 × 12 are equivalent arrays with area 60.

11. Reverse the 96-block plan

    Connect division and missing factors by solving 96 ÷ 12 = 8 as an 8 × 12 array.

12. Complete the master grid

    Integrate prediction, two-axis building, skip-counting, and explanation in the 12 × 12 = 144 capstone.