Spring fever

In this activity, the students use number strategies in a measurement context to work out area, length, and rates. Multiplication of simple decimals is appropriate for students at the advanced multiplicative stage of the Number Framework. This stage also includes early proportional thinking.

The students’ first task is to calculate the area of wasted carpet. The best method is to visualise how far the carpet would extend past the boundaries of the room and see this as 1 long rectangle and 2 squares.

The students’ solutions to questions 1a and 2a should be expressed with both quantity and unit, for example, 2.48 m². Reinforce both the name and the symbol for the area unit (for example, metre x metre = square metre) and length unit.

Encourage the students to work out the cost of their chosen carpet without using a calculator. A useful way to calculate rates is to use ratio tables that help record or keep track of mental strategies and enhance accuracy. Ratio tables involve doubling and halving strategies, adding and subtracting, and multiplying. Partial calculations become obvious. A ratio table is similar to a double number line but keeps amounts compartmentalised. For example, for the first carpet: 3 metres of carpet at $115 per metre is 2 m + 1 m = 230 + 115 = $345.

Similarly, for the first wallpaper in question 2d, once the students have worked out that they need 7 rolls:

7 rolls of wallpaper at $30.80 per roll is 8 rolls – 1 roll = $246.40 – $30.80 = $215.60.

However, an efficient way of multiplying by 5 is to multiply by 10 and divide by 2, so the students could multiply by 5 and add the cost of 2 rolls.

So:

• $30.80 x 5 = $30.80 x 10 ÷ 2
• = $308.00 ÷ 2
• = $154
• $154 + $61.60 = $215.60

Note that the chart for rolls of wallpaper needed is based on the perimeter of the room excluding doors and windows. (The chart also includes an allowance for wastage when patterns are matched up.)

In question 3, encourage the students to draw a diagram of a curtain for Rebecca’s room to obtain the quantities of material she will need.

You may need to remind the students that 100 centimetres equals 1 metre. The material is 120 centimetres wide, so the quantity must be doubled for each window (2 curtains each 120 centimetres wide) and doubled again to account for the two windows. The drop must take into account the window size, a 5 centimetre hem at the top, and a 10 centimetre hem at the bottom: 145 centimetres x 2 x 2 = 580 centimetres or 5.8 metres.

You could encourage the students to try out other strategies as they solve these multiplication problems, such as experimenting with rounding, tidy numbers, and known facts. Challenge the students to explain which strategies they feel are best and why.

You could extend question 4 by asking the students to pool their information and work out what is the least or the most that redecorating Rebecca’s room will cost.

1.

a. 2.48 m2. (0.66 x 3 + 0.5 x 0.5 + 0.5 x 0.5)
b. Answers will vary depending on the carpet chosen:

i. $345
ii. $295.50
iii. $465
iv. $264

2.

a. 8.65 m
b. 7 rolls
c. $64.28. ($450 ÷ 7, with no rounding. Rounding to $64.29 would make the total $450.03.)
d. Answers will vary, depending on the wallpaper chosen:

i. $215.60
ii. $406
iii. $325.50
iv. $433.65

3.

a. 5.8 m. (1.45 for each curtain)
b. Answers will vary, depending on the curtain material chosen:

i. $229.10
ii. $120.35
iii. $108.75
iv. $150.74

4.

Answers will vary, depending on the materials chosen.