Solve problems that involve exponents and square roots.
Number Framework Stage 8
Problem: “Zoë builds a large square from 16 small square tiles.
How big is Zoë’s square?”
Get the students to build the large square out of 16 tiles. Then discuss its size. (Answer: 4 rows of 4 tiles.)
Examples: Build large squares built with these numbers of small squares and give their size: 4, 25, 9
Problem: “Zoë builds a large square from 36 small square tiles. Imagine how big the square is.”
Fold back to building the square if needed. (Answer: 6 by 6.)
Examples : Imagine large squares with these numbers of small squares and find their sizes: 49, 100, 81 ...
Using Number Properties
Problem: “Zoë builds a large square from 961 small square tiles. Describe the square Zoë builds with the aid of a calculator.”
Discuss how √x or the √ or the button helps. (Answer: = √961 = 31.)
Examples: Large squares are made with these numbers of small squares. Describe the large squares: 207 936, 2 025, 622 521, 2 217 121 ...