The shape of the lesson
By the end of the lesson, learners can
- Calculating with money: Bills, change and wages are a chain of simple steps.
- Converting currencies: Open the lab on Exchange rate and move the rate and amount sliders.
- Comparing prices in different currencies: To compare, change both prices into the SAME currency first, then subtract.
- One unit throughout: all dollars or all cents.
- Exchange rate \(\$1 = k\) units: multiply dollars by \(k\); divide the other currency by \(k\).
- Sense check: does the answer have more or fewer units than you started with?
- Compare prices only after changing them into the same currency.
- Commission: take it off before converting, unless told otherwise.
One picture every idea returns to
If $1 = €0.92, then dollars \(\times 0.92\) gives euros and euros \(\div 0.92\) gives dollars. Check the answer makes sense: one dollar buys LESS than one euro, so the number of euros is smaller.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Dollars, euros and cents.. Money questions are everyday arithmetic done carefully: bills, change, wages and prices, always to the nearest cent. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Calculating with money | Bills, change and wages are a chain of simple steps. Model the worked example Change from a note on the board, one line at a time. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Converting currencies | Open the lab on Exchange rate and move the rate and amount sliders. Project tab 2 of the lab (Ratio, rates and percentages lab, exchange rates) and let a student drive it while the class predicts. Model the worked example Both directions on the board, one line at a time. Your turn: Using $1 = €0.92, change €115 into dollars. | Pairs |
| 21 to 30 min | Teach and check: Comparing prices in different currencies | To compare, change both prices into the SAME currency first, then subtract. Model the worked example Where is it cheaper? on the board, one line at a time. | Connect-Extend-Challenge |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Comparing prices in different currencies, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Connect-Extend-Challenge
After the new idea, each student writes three lines: how it connects to what they knew, how it extends their thinking, and what still challenges them. Pairs compare, then the challenges become the plenary.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Mixing dollars and cents in one calculation causes errors of 100 times. | Work entirely in dollars (\(85\) cents \(= \$0.85\)) or entirely in cents. |
| Multiplying when you should divide gives \(230 \times 0.92 = \$211.60\) for part (b). | Sense-check first: $1 buys only €0.92, so a euro is worth MORE than a dollar, and €230 must be MORE than 230 dollars. |
| Do not subtract prices in different currencies: \(185 - 150 = 35\) has no meaning because dollars and pounds are different units. | Return to Comparing prices in different currencies: ask a pair to state the correct version and show it on the lab before moving on. |
Money and currency conversion: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
Tom buys 3 games at \(\$12.99\) each. He pays with a \(\$50\) note. How much change does he receive?
The exchange rate is \(\$1 = 83.2\) rupees. (a) Change \(\$250\) into rupees. (b) Change 5000 rupees into dollars.
An electricity bill is a fixed charge of \(\$18.50\) plus \(\$0.21\) for each unit used. Calculate the bill for 640 units.
A watch costs \(\$185\) in the USA and £150 in the UK. The exchange rate is £1 = $1.27.
In which country is the watch cheaper, and by how many dollars?
Zoo tickets cost \(\$14.50\) for an adult and \(\$8.75\) for a child. A family ticket for 2 adults and 3 children costs \(\$52\). How much does a family of 2 adults and 3 children save by buying a family ticket?
Ravi changes \(\$1200\) into yen. The rate is $1 = ¥148.6, and the bank keeps 2% of the dollars as commission.
He spends ¥150 000 on holiday and changes the rest back into dollars at ¥1 = $0.0065, with no commission. How many dollars does he get back?
Answer key and marking notes
- Cost: \(3 \times 12.99 = \$38.97\).
- Change: \(50 - 38.97 = \$11.03\).
- (a) \(250 \times 83.2 = 20\,800\) rupees
- (b) \(5000 \div 83.2 = 60.096... = \$60.10\)
- \(640 \times 0.21 = \$134.40\)
- \(134.40 + 18.50 = \$152.90\)
- UK price in dollars: \(150 \times 1.27 = \$190.50\).
- USA is cheaper, by \(190.50 - 185 = \$5.50\).
- Separate tickets: \(2 \times 14.50 + 3 \times 8.75 = 29 + 26.25 = \$55.25\).
- Saving: \(55.25 - 52 = \$3.25\).
- Dollars changed: \(1200 \times 0.98 = \$1176\).
- Yen received: 1176 × 148.6 = ¥174 753.60.
- Left after spending: 174 753.60 - 150 000 = ¥24 753.60.
- Back to dollars: \(24\,753.60 \times 0.0065 = 160.898... = \$160.90\).
6 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Ali buys 4 drinks at \(\$1.65\) each and 3 sandwiches at \(\$3.20\) each. He pays with a \(\$20\) note. How much change does he receive?
- A\(\$3.80\)
- B\(\$15.15\)
- C\(\$10.20\)
- D\(\$4.80\)
A gas bill is a fixed charge of \(\$22.40\) plus 18.5 cents for each unit used. A household uses 820 units. Find the total bill.
- A\(\$174.10\)
- B\(\$151.70\)
- C\(\$15\,192.40\)
- D\(\$1539.40\)
The exchange rate is \(\$1\) = €0.88. Change \(\$420\) into euros.
- A€369.60
- B€477.27
- C€50.40
- D€419.12
A camera costs \(\$640\) in the USA and £520 in the UK. The exchange rate is £1 = \(\$1.25\). In which country is the camera cheaper, and by how much in dollars?
- AIn the USA, by \(\$10\)
- BIn the UK, by \(\$120\)
- CIn the UK, by \(\$224\)
- DIn the USA, by \(\$130\)
A bank changes dollars to Japanese yen at \(\$1\) = ¥151.2. It takes 2.5% of the dollars as commission. Ravi changes \(\$750\). How many yen does he receive?
- A¥110 565
- B¥113 400
- C¥113 022
- D¥85 050
Kai changes \(\$640\) into pounds at £1 = \(\$1.28\). He spends £320 on holiday, then changes the rest back into dollars at £1 = \(\$1.20\). How many dollars does he get back?
- A\(\$216\)
- B\(\$150\)
- C\(\$230.40\)
- D\(\$320\)
Quiz key
Drinks: \(4 \times 1.65 = \$6.60\). Sandwiches: \(3 \times 3.20 = \$9.60\). Total \(= \$16.20\), so change \(= 20 - 16.20 = \$3.80\). The tempting \(\$15.15\) subtracts the price of just one drink and one sandwich. \(\$10.20\) counts only one sandwich, and \(\$4.80\) is a subtraction slip.
18.5 cents \(= \$0.185\). Units cost \(820 \times 0.185 = \$151.70\); add the fixed charge: \(151.70 + 22.40 = \$174.10\). The tempting \(\$15\,192.40\) mixes cents and dollars, using 18.5 as if it were dollars. \(\$151.70\) forgets the fixed charge, and \(\$1539.40\) uses \(\$1.85\) per unit.
Each dollar buys €0.88, so \(420 \times 0.88 = 369.60\): €369.60. The tempting €477.27 divides by 0.88, which is the conversion from euros to dollars. Sense check: one dollar buys LESS than one euro, so the number of euros must be smaller than 420. €50.40 is 12% of 420, and €419.12 subtracts 0.88.
UK price in dollars \(= 520 \times 1.25 = \$650\). This is more than \(\$640\), so the USA is cheaper by \(650 - 640 = \$10\). The tempting 'UK, by \(\$120\)' subtracts \(640 - 520\), mixing pounds and dollars. 'UK, by \(\$224\)' divides by 1.25 instead of multiplying, and \(\$130\) subtracts 520 from the converted price.
Dollars after commission \(= 750 \times 0.975 = \$731.25\). Yen \(= 731.25 \times 151.2 = 110\,565\). The tempting ¥113 400 forgets the commission. ¥113 022 takes off 2.5 dollars instead of 2.5%, and ¥85 050 takes off 25%.
Pounds bought: \(640 \div 1.28 = 500\), so £500. After spending, he has \(500 - 320 = 180\), so £180. Changing back: \(180 \times 1.20 = \$216\). The tempting \(\$150\) divides by 1.20 instead of multiplying (pounds are worth MORE than dollars, so he should get more than 180 dollars). \(\$230.40\) uses the first rate, and \(\$320\) subtracts pounds from dollars.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.