Solve problems that involve exponents and square roots.
Number Framework Stage 8
Square pieces of cardboard.
Calculators.
122 may be read as “12 to the power of 2” but normally it is read as “12 squared” because it represents the area of a square with sides 12. Areas of squares provide a useful geometrical introduction to squares and square roots.
Using Materials
Problem: “Matilda wants to make a square tile pattern on the floor. She draws a plan on squared paper. She wants to know how many small square tiles to buy without having to count them one by one.”
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Get the students to draw 8 rows of 8 tiles on squared paper. Discuss how multiplication can help find the number of tiles needed. (Answer: 8 x 8 = 64.)
Using Imaging
Problem: “Matilda plans another square that she describes as 10 rows by 10 tiles. Imagine how many tiles Matilda needs to build the square.” Fold back to drawing a picture on squared paper if needed. (Answer: There are 10 rows each of 10 tiles and 10 x 10 = 100.)
Examples: By imaging, find the number of tiles needed to find the area of these squares: 4 by 4, 6 by 6, 7 by 7, 9 by 9.
Using Number Properties
Problem: “Matilda plans another square that is 134 rows by 134 tiles. How many tiles will Matilda need to buy?” (Answer: 134 x 134 = 17 956.)
Problem: “Matilda notices her calculator has a x2 button. She investigates what it does.”
Get the student to input various values of x using the x2 button and discuss what it does. (Answer: x2 is a shorthand for x times x.)
Problem: “Matilda uses the x2 button to work out the number of tiles needed to build a square with dimensions 234 by 234. What is the answer? (Answer: Press 234 x2= . The display shows 54756.)
Problem: “A contractor lays concrete slabs that are 1 metre by 1 metre. He has to make a square that is 38 metres by 38 metres. Each slab costs $3. How much do the slabs cost altogether? (Answer: There are 382 tiles needed = 1 444. So the cost is 3 x 1 444 = $4,332.)
Examples: Find the area of these squares: 24 by 24, 209 by 209, 13 by 13, 900 by 900 ...
Understanding Number Properties:
The price of a tile is $ P. What is the cost of a square pattern of d rows with d tiles in each row? (Answer: d 2 x $ p)