time yourselfCostume 2 · economy + correctionsSun 11 October1 / 4
Prices and their averages + corrections
"How many yen more" or "how many times"? An average price is an evened-out price
Name Date
Prices, and "times"Prices = how the price of the same thing changes over time.
"How many yen did it rise" (subtraction) is harder to compare across items than "how many times did it grow" (division). times = this year ÷ last year
An average price evens out the different prices of different shops. Putting things per 1 kg lets you compare different amounts.
| item | last year (yen) | this year (yen) |
|---|
| milk, 1 L | 200 | 230 |
| eggs, a box of 10 | 240 | 300 |
| rice, 5 kg | 2,000 | 2,400 |
| bread, 1 loaf | 140 | 154 |
Source: last year's and this year's receipts (made up). The basket holds these four.1 · Receipts side by side
1A box of 10 eggs cost 240 yen last year and 300 yen this year. This year is how many times last year?
2In the table, which item (1) rose most in yen, and (2) rose most in "times"? Work out the "times" for all four.
3This year, five shops sold 1 L of milk at 228, 235, 230, 224 and 238 yen. What is the average price? If last year's average was 200 yen, this year is how many times last year (rounded to two decimal places)?
4Petrol cost 165.5 yen a litre last year. This year it is 1.2 times that. What does 1 L cost this year?
First estimate: more or less than 165.5 yen?
5This year 0.45 kg of ham was sold for 360 yen. (1) How much is 1 kg of ham? (2) Last year ham cost 700 yen a kilogram. This year is how many times last year (rounded to two decimal places)?
For (1), start with the double number line.
6Put the four items in one basket. Find last year's total and this year's, and how many times last year this year is, rounded to two decimal places.
7Over five years, an item's price each year became 1.02, 1.03, 1.01, 1.04 and 1.05 times the year before. Find the average of these five numbers.
8Shop A's item went from 200 to 230 yen, and Shop B's from 120 to 150 yen. Both rose by 30 yen. Is "they rose by the same" right? Compare in "times" and give the reason.
9Rice is sold in a 5 kg bag for 2,400 yen and a 10 kg bag for 4,500 yen. Find the price per kilogram of each and say which bag is cheaper.
Putting both per 1 kg lets you compare bags of different sizes.
2 · Corrections, and one puzzle problem
10[Corrections] Pick one question from this week's notebook that you got wrong. Write all of the following.
1) the question (day and number) 2) circle why it went wrong: calculation / no diagram / calculation set-up / no estimate
3) do it again correctly 4) what you will do first next time the same question comes up
11[Difference puzzle] Sweets are handed out to children. With 6 each, 15 are left over; with 9 each, 3 are short. How many children, and how many sweets? Draw a bar diagram showing the "left over" and "short" first.
When each child gets 9 instead of 6, how many more sweets are needed in all?