Fraction Wall

What your child will figure out

• Build equivalent fraction bars and justify equivalence from their aligned endpoints.
• Compare fractions by lining up equal wholes rather than judging one numerator or denominator alone.
• Simplify a fraction by dividing numerator and denominator by the same common factor while preserving its length.
• Solve generated fraction-wall challenges as an adaptive staircase scales denominator size and structure.

The levels

1. Build the wall

   Predict and snap 2/4 beneath 1/2, observe identical endpoints, and explain that splitting pieces did not change the covered length.

2. Stack equivalents

   Predict and build 4/6 beneath 2/3, then explain why multiplying both fraction numbers by two preserves the amount.

3. Triple the pattern

   Build 9/12 beneath 3/4 and explain why scaling both numbers by three preserves the endpoint.

4. Compare matching pieces

   Compare 3/8 and 5/8 using equal-size pieces and aligned endpoints.

5. Same count, new sizes

   Compare 3/4 and 3/7 to see that equal numerators can cover different lengths.

6. Check the reach

   Line up 3/5 and 2/3 on equal wholes, compare their endpoints, and explain why 2/3 is larger.

7. Spot a hidden tie

   Compare 4/6 and 2/3 and recognize that differently labelled bars can share one endpoint.

8. Use fewer bricks

   Replace 6/8 with the simplest equivalent fraction 3/4 and justify dividing both numbers by two.

9. Find the full factor

   Simplify 12/18 all the way to 2/3 rather than stopping at a partially simplified bar.

10. Reverse the build

    Build 15/18 beneath 5/6 and explain equivalence under a scale factor of three.

11. Inspect a close call

    Compare 5/8 and 7/12 by their nearby endpoints and verify the result using twenty-fourths.

12. Master wall transfer

    Transfer all three ideas by simplifying 18/24 to 3/4 while preserving the endpoint and using the fewest pieces.