At a glance. One lesson of about 60 minutes. Students convert a currency in both directions, find the rate for the reverse direction, and compare prices across currencies and pack sizes.
Calculator: no calculator. The rates are chosen to divide exactly, and the invented currencies keep the arithmetic in whole numbers where it matters. The work is in choosing what to multiply or divide.
What students will learn
Know
- An exchange rate is a conversion factor between two currencies.
- Multiply to change into the currency with the smaller unit value, divide to change back.
- Prices are compared in one currency and for one amount.
Understand
- The rate in the other direction is the reciprocal: 1 dirham = 20 rupees means 1 rupee = 0.05 dirham.
- A comparison across currencies can change when the rate changes.
- Totals for different pack sizes cannot be compared: only a price for one can.
Do
- Convert a price from one currency to another and back.
- Compare prices in different currencies and pack sizes.
- Find the exchange rate at which two prices are equal.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: converting both ways and finding the price for one (questions 1 to 7).
- Criterion B. Investigating patterns: the figure. Move the rate across the break-even and ask what the answer depends on, and at what rate it flips.
- Criterion C. Communicating: explaining why both the currency and the amount must match before two prices are compared (question 9).
- Criterion D. Applying mathematics in real-life contexts: shopping across borders, changing money, pack sizes (the hook and questions 3 to 8).
The one thing to do with the figure
Ask for a prediction before the slider moves. “15 dirhams or 330 rupees: which is cheaper?” Most students say 15. Ask what fact they would need, and keep the answer (the exchange rate) on the board.
Then move the rate slowly through 22 and ask the room to say “now” when the answer flips. Ask what the rate would have to be for the two prices to be exactly equal, before the slider reaches it.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook: headphones in two currencies, with predictions. The figure on the board. |
| 10 min | Key idea; the break-even rate; the reverse conversion as a reciprocal. |
| 10 min | Both worked examples; students finish the faded tea example in pairs. |
| 5 min | Question 1, the check. If many choose A, ask which currency has the bigger numbers for the same price. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 2400 mL; 100 rupees; 36 rupees. |
|---|---|
| Worked example 1 | 35 dirhams. |
| Worked example 2 | The 2 kg pack, 75 against 80 rupees per kilogram. |
| Faded example | The 1 kg pack, 360 against 380 rupees per kilogram. |
| 1. Which way to convert | B, divide by 20. A converts the other way; C and D mix the currencies. |
| 2. Dirhams to rupees | 264. 12 × 22 = 264 rupees. |
| 3. Rupees to dirhams | 20. 440 ÷ 22 = 20 dirhams. |
| 4. Comparing across currencies | 30. 15 × 32 = 480 taka, and 480 − 450 = 30. |
| 5. A rate and its reverse | 20. 1 ÷ 0.05 = 20, because 20 × 0.05 = 1. |
| 6. Price per litre | 10. 180 per litre and 170 per litre; 180 − 170 = 10. |
| 7. Break-even exchange rate | 20. 560 ÷ 28 = 20 rupees per dirham. |
| 8. There and back again | 160. 200 × 20 = 4000 rupees, and 4000 ÷ 25 = 160 dirhams. |
| 9. One currency and one kilogram | C. A compares raw numbers; B changes the currency but not to one kilogram; D finds one kilogram but not in one currency. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A, C or D in question 1; 9680 in question 3 | Multiplied or added when converting to the currency with the larger unit value. | Ask which currency has the bigger number for the same price, then which operation makes a number smaller. |
| 34 or 10 in question 2; 418 in question 3 | Added or subtracted the exchange rate. | Say it as “22 rupees for each dirham” and ask how many dirhams there are. |
| 480 or 435 in question 4 | Stopped after converting, or compared the numbers in different currencies. | Underline what is asked: how much cheaper. Put both in taka first. |
| 0.05 or 0.95 or 5 in question 5 | Did not invert the rate, or subtracted. | Check by multiplying: 20 × 0.05 should make 1. |
| 180 or 250 in question 6 | Gave one bottle's price per litre, or the difference of the totals. | Fill in a two-row table of litres and rupees, and work out the price for one litre in both. |
| 588, 15680 or 532 in question 7 | Added, multiplied or subtracted the two prices. | Write 28 × rate = 560 and ask what the rate must be. |
| 200, 5000 or 4000 in question 8 | Used one rate for both steps, or stopped in the middle. | Draw the two steps as a chain and label each arrow with its rate. |
| A, B or D in question 9 | Compared raw numbers, or matched only the currency, or only the amount. | Ask for both: one currency and one kilogram, then compare. |
Questions worth asking
- Why does a lower number of dirhams not mean a lower price? Because a dirham is worth many rupees. Listen for “different units”.
- If 1 dirham = 22 rupees, what is 1 rupee in dirhams? 1 ÷ 22, about 0.045. Listen for “the other way, divide”.
- Why might the shop that is cheaper today not be cheaper next month? The exchange rate moves. Link to the break-even figure.
- How is comparing pack sizes like comparing currencies? Both need one common unit first. Listen for “same units”.
Differentiation
A way in for anyone stuck
- Give a two-column table with headings dirhams and rupees, and fill 1 dirham, then the amount asked.
- Use rates such as 1 dirham = 10 rupees until the direction of conversion is secure.
- Colour the two currencies differently on every line of working.
Stretch
- Question 7, then: at 25 rupees to the dirham, which shop is cheaper, and by how much? (Chennai, 700 against 560, by 140.)
- Question 8, then: with the same two rates, how many dirhams must Ravi start with to finish with 200? (250, because 250 × 20 = 5000 and 5000 ÷ 25 = 200.)
Students learning in English as an additional language
Money words can be confused with each other. Show a coin or note of each currency, or a picture, with its name written below.
| Word | Plain meaning | Example |
|---|---|---|
| exchange rate | how much of one currency one unit of another is worth | 1 peso = 5 rupees |
| currency | the money of a country | dirham, rupee, taka |
| convert | change from one unit or currency to another | 12 pesos to rupees |
| reciprocal | the number you multiply by to get 1 | 4 and 0.25 |
| break-even | the point where two things are equal | 10 dirhams = 250 rupees at 25 |
| per kilogram | for each one kilogram | 80 rupees per kilogram |
Sentence starters for explaining aloud or in writing:
- At 1 dirham = … rupees, … dirhams is … × … = … rupees.
- To compare them I changed both to …, then I …
- The pack that is cheaper per kilogram is … because …
Two things not to say
“Always multiply by the rate.” It depends on which currency you are going to. Ask which has the bigger numbers.
“The bigger pack is always better value.” Sometimes it is, but only the price per kilogram says so.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- Currency1 dirham = 22 rupees. Change 9 dirhams to rupees.
198 rupees. - Back againChange 660 rupees to dirhams at the same rate.
30 dirhams.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ShoppingA kettle costs 45 dirhams in Sharjah and 1050 rupees in Kochi. At 1 dirham = 22 rupees, which is cheaper, and by how many rupees?
Sharjah: 45 × 22 = 990 rupees, which is 60 rupees cheaper than 1050. - Per kilogramSugar is sold as 2 kg for 124 rupees or 5 kg for 300 rupees. Which is cheaper per kilogram?
5 kg: 62 rupees against 60 rupees per kilogram. - Earlier work (Lesson 3)A bottle holds 0.75 litres and a jug holds 3 litres. How many bottles fill the jug?
4 bottles: 3 ÷ 0.75 = 4.
3Challenge
Reasoning, generalizing and working backwards.
- Chain of rates1 dirham = 22 rupees and 1 rupee = 1.5 taka. How many taka is 1 dirham?
22 × 1.5 = 33 taka. - Which wayThe rate moves from 1 dirham = 22 rupees to 1 dirham = 24 rupees. Is a 12-dirham item cheaper or dearer in rupees, and by how much?
Dearer: 12 × 24 = 288 against 12 × 22 = 264, which is 24 more.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
The slider works with the keyboard (tab to it, then the arrow keys) and by touch. Under the figure, “Show me the steps” gives the same states in words.
No device? Write the rates on the board and give each pair a price card in one of two currencies; they swap and convert.