Squaring

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.”

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)