Counting the Costs
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This is a level 3 number activity from the Figure It Out theme series.
use mental strategies to solve addition and subtraction problems
This activity gives the students further experience in calculating profit and working with more than one operation to find an answer. It is also a useful activity for students to practise estimation skills.
The students can use several tools to answer question 1:
• A table will help keep track of progress overall, give continuity to the activity, and further reinforce the concept of profit as money taken minus the costs.
The total profit in the right-hand column should balance with the total money taken minus the total costs. This is a good check for students to do on their calculators.
The calculator memory can be useful for some questions if the students make use of the M– key to calculate the profit. For example, for number 1b:
151 x 2 M+ 39 M– MR
Some students may enjoy preparing a spreadsheet to calculate the profit. If so, they could use the formula =B2-C2 and fill down to calculate profits. You could introduce the autosum function for column and row totals. The students could then explore the sort feature and the different ways the spreadsheet presents the data. They could sort the table by alphabetical order of event, by increasing or decreasing costs, and by increasing or decreasing profit. This will be a very useful skill that they will use in later work on ranking and order. If you or your students are not familiar with spreadsheets, see the teachers’ notes for pages 12–13 of Algebra, Figure It Out, Level 3.
You may need to work through an example of multiplying amounts in cents and then converting the answer to dollars. For example, to calculate the magician’s costs for question 1f: 15 cents x 110 = 1650 cents. There are 100 cents in a dollar, so the magician’s costs are 1650 ÷ 100 = $16.50.
Encourage the students to estimate the profit for each activity so that they can check whether their answer from a calculator or a spreadsheet is reasonable.
Question 4 does not require an exact answer. The question should build on the daily maintenance of sharing estimation and efficient mental strategies. The students could work in small groups of three to share solutions and then discuss with other groups which methods are best. A variety of methods could be put on a wall poster, thus reinforcing the idea that the students’ own best and varied methods are all acceptable as long as the answer is within a reasonable range.
Rounding is likely to be a strategy used by many groups. For example:
$4,231 rounded to 4 200 ÷ 100 = 42
42 x 8 may be performed mentally as (40 x 8) + (2 x 8)
= 320 + 16
= 336 (estimate)
Alternatively, rather than calculating 42 x 8, some students may round the 8 up to 10 and then compensate for this rounding by subtracting 40 x 2:
(42 x 10) – (40 x 2)
= 420 – 80
Answers to Activity
1. a. Money taken at the gumboot throwing $463
Cost of the prizes – $45
b. Money taken at the face painting $302
Cost of the paint – $39
c. Money taken at the food stall $2301
Costs – $430
d. Money taken at the plant stall ($254 + $480 + $66) $800
Costs – $210
e. Money taken at cowpat bingo ($64 x 2) $128
Cost of prizes – $20
f. The magician’s takings were $82.50
The costs were 110 x 15c – $16.50
g. Fudge money $70
Drinks money + $155
h. Mystery number money (137 x 50 cents) $68.50
Cost of the prizes – $12.00
2. The food stall was the most profitable.
3. The mystery number stall was the least profitable.
4. Estimates should be between 330 and 340 books.