The Ultimate AbacusExplore numbers. Discover why.
Learn · explore · explain

Workbook 2 · Operations, squares and roots

Answer guide

Name: ____________________   Date: ______________

For each activity: predict → explore → explain → check. Draw beads or write place-value labels when useful.

1. Explain 7 + 5 using a complement.

2. Regroup to explain 32 − 7.

3. Explain why 4 × 6 and 6 × 4 give the same answer.

4. Divide 29 into groups of 4. Give the whole-group count and remainder.

5. Find 12² using (10 + 2)². Include both cross terms.

6. Why is √49 equal to 7, although both 7² and (−7)² equal 49?

7. Bound √20 between two consecutive integers. Then try 4.4 and 4.5.

8. Can the five-place website frame display 40² exactly? Can it display √2 exactly?

9. Explain what can be displayed on the frame and what still requires a written method.

Reflection

What changed your thinking? What question would you ask next?