Percentage Practice | Choose the Base, Check Again Later

MATHEMATICS · A PRACTICE AND REVIEW PATHWAY

Choose the whole before you calculate.

You can calculate a percentage correctly and still use it on the wrong amount. This pack helps you notice that decision, repair it and check what you can do later. Keep a pencil and a page beside you. The first attempt comes before the explanation.

Use this route after introductory percentages have been taught. You should be able to find 10%, 20% and 25% of a positive quantity. Upper-primary and early-secondary learners can work at their taught level; the later tasks extend the same idea across successive changes. This is a focused practice pack, not a complete syllabus or a judgement about your overall Mathematics ability. All situations and prices below are invented for learning.

First attempt · Explanation · Guided practice · Fresh task · Return later · Use it elsewhere · Review and next step

1. Try before opening an answer.

Task A. Beatrice has an activity fund of $180. She spends 20% of the original fund on materials. She then spends 25% of the money remaining on printing. How much money is left? What percentage of the original fund has she spent altogether?

Show your working and explain what amount each percentage refers to. Work without hints first. If you cannot begin, write the part that is uncertain; you can then use the explanation below. There is no need to sit with confusion for a fixed time.

Keep the first attempt. Record whether it was independent, followed a question from someone else, or used the explanation. A correct answer after help is useful learning evidence; it describes a different condition from an unsupported first attempt.

2. Give each percentage an amount.

A percentage needs a reference quantity: the amount being treated as 100%. Write its name before its number. “Twenty-five per cent of the money remaining” makes the remainder the new 100% for that step.

For successive changes, record the amount after the first event before applying the next instruction. If the question asks for the overall percentage change, compare the final change with the original amount. The base for that final comparison can therefore differ from the base of the last calculation.

Worked example. A fictional $320 equipment set receives a 25% discount, then a further 10% discount on the reduced price.

Total reduction: 320 − 216 = $104. Overall percentage reduction: 104/320 × 100% = 32.5%. Both discounts lower the price, and the final price remains positive, which fits this situation.

You can also calculate the amounts retained: 75% of $320 is $240; 90% of $240 is $216. If decimal multipliers have been taught, the same route is 320 × 0.75 × 0.90 = 216. Choose a representation you can explain.

If finding a single percentage is the uncertain step, pause the sequence and use the fractions, decimals and percentage guide. For a fuller explanation of the reference quantity, open The Percentage Base, then return here for practice.

3. Practise with the decisions visible.

Task B. A club has 240 activity tokens. A delivery increases the number by 25%. The club then uses 20% of the new total. How many tokens remain? Is that more or less than the original number, or the same?

1. Name the amount represented by 100% before the delivery.
2. Find the number delivered and the new total.
3. Name the amount represented by 100% when the club uses tokens.
4. Find the number used, the final number and its difference from 240.
5. Explain why subtracting the two percentage figures would misrepresent these instructions.

Before continuing, explain one base choice aloud or in writing. If someone supplies the base, mark that support on the page. Then put this example aside.

4. Make the next decisions yourself.

Task C. A collection begins with 150 cards. Its size increases by 20%. Later, 20% of the new collection is given away. Find the final number of cards and the overall percentage change from the beginning. Explain whether the two changes cancel.

Use a clean page without the worked example or guided questions. Show the quantities your calculations refer to. This checks a fresh attempt soon after teaching; the percentage topic is still familiar, so a later check remains useful.

5. Return after a gap.

Choose a practical return time, such as two or three days later, after doing other learning. Record the date. That interval is a suggested routine, not a validated threshold. Ask someone to copy only the task onto a blank page so the example and chapter heading are absent.

Task D. A school office has 200 booklets. It distributes 15% of them. A later delivery adds a number equal to 20% of the stock left after distribution. How many booklets are there now? What is the overall percentage change from the original stock? Explain your comparison.

If help is needed, provide it and record what helped. Revisit the uncertain decision before arranging another fresh question. One difficult return does not erase all earlier progress.

6. Use the idea to make a choice.

Task E. Faith compares two invented offers for the same $260 equipment set. Offer A discounts the equipment by 20%, then adds a $12 delivery charge; the delivery charge receives no discount. Offer B discounts the equipment by 15% and includes delivery at no additional charge. No other charges apply. Which offer costs less, and by how much?

Explain what the percentage applies to in each offer and how you handled delivery. Then respond to this claim: “Offer A must save exactly 5% of $260 compared with Offer B, because 20 − 15 = 5.”

7. Review the work in three parts.

Record these dimensions separately for each task; do not turn them into a mastery percentage. Note correct or incorrect final answers as well. Calculation can be accurate within a wrongly chosen route, so inspect the bases before deciding what needs teaching.

A blank response means insufficient evidence on this task; it does not identify the cause. Keep the conditions beside the observations: independent, question supplied, example visible, calculator used, or answer already seen. These tasks are designed for manageable arithmetic; if a calculator helps, record it rather than hiding it.

For a teacher or tutor handoff, bring the original attempt, corrected work and later attempt. Add the taught school stage, dates, first uncertain line, exact help supplied, and the three observations for each task. Ask: “What should we teach or check next?”

If the base repeatedly stays unclear, use Finding the First Weak Link in Learning alongside the work. For broader Secondary practice, continue to Ratio, Percentage and the Correct Base. For repeated growth and decimal multipliers, use Repeated Percentage Change and Multiplicative Growth when those prerequisites fit.

Successful fresh, later and changed-context attempts provide several observations of this specific skill. They do not establish broad Mathematics mastery or predict an examination grade. How We Know Learning Has Really Held explains the wider review. Return to the Mathematics Hub to choose the next suitable topic or teaching route.