eduKatePunggol · Name the whole, then calculate

Which amount represents 100%?

Sometimes a percentage question gives you the whole and asks for a part. Sometimes it gives you a part and asks you to recover the whole. The percentage symbol appears in both, but the calculation has a different job.

Use this practice companion to identify the amount represented by 100%, match the known amount to its percentage, and check your answer against the story. Keep the first response, try unfamiliar work after teaching, and return later.

Begin after introductory percentages have been taught. You should understand percentages as parts per hundred and be able to multiply and divide. Upper-primary and early-secondary learners can use the tasks when those prerequisites fit. All situations and amounts are invented for learning.

Read how to use the questions before beginning. Optional questions near the end introduce an increase and a case with missing information.

Keep the work and the help used

Write on paper before opening the corresponding answers. For each task, name the quantity represented by 100%, show the calculation and include units. Keep agreed reading support available. If a calculator helps with arithmetic, record that use so the review can distinguish calculation from choosing the relationship.

The headings and questions already direct attention to percentages. They are part of the task’s support. Record additional help in ordinary words: “pointed to remaining”, “supplied 65%”, “showed a similar example”, or “no hints”. A correct response after a prompt describes a different condition from a response produced without that prompt.

If the meaning of 25% or multiplication and division is still uncertain, ask for a smaller teaching step. The relationships-before-operations companion helps with quantities and units. The Primary 5 proportional-reasoning guide explains how fractions, percentages and ratios connect.

P1: Same numbers, different unknowns

First attempt. Keep the answers closed. The repeated numbers are deliberate: explain what each calculation is finding.

1. A tray holds 160 labels. Twenty-five per cent of the labels are blue. How many blue labels are there?
2. Another tray has 40 blue labels. These blue labels are 25% of all the labels in that tray. How many labels are there altogether?
3. For question 2, a learner writes 40 × 25 ÷ 100 = 10. What does that calculation find, and why does it not answer the question?

Write the date and any help used. A final number without its meaning leaves part of the reasoning unrecorded.

Open P1 answers and explanations

1. Find the part: all 160 labels represent 100%. The blue labels represent 25%, so 160 × 25 ÷ 100 = 40 blue labels. A quarter of 160 is also 40.

2. Recover the whole: the 40 blue labels represent 25%, not 100%. Since 25% is one quarter, the whole contains four such parts: 40 × 4 = 160 labels altogether. The unitary method gives the same result: 40 ÷ 25 × 100 = 160.

3. Explain the wrong route: 40 × 25 ÷ 100 finds 25% of the 40 blue labels. It treats 40 as the base for that calculation. The question asks for the total of which 40 is already 25%, so it requires scaling up to 100%.

Question	What is known?	What is required?
P1.1	100% = 160 labels	25% = 40 blue labels
P1.2	25% = 40 blue labels	100% = 160 labels

Check the answer to question 2 by applying the original statement: 25% of 160 is 40. The total is larger than its positive 25% part, which fits the situation.

Give the known amount its correct percentage

Before choosing an operation, write two labels: “100% is the original whole” and “the known amount represents ___%”. That second label matters when the amount given is what remains after something has been used.

Worked example: a fictional activity fund has $84 left after 30% of the original fund is spent. How much was in the fund at the beginning?

The $84 belongs to 70%, because 100% − 30% = 70%. Ten per cent is $84 ÷ 7 = $12, so 100% is $12 × 10 = $120. Another route is 84 ÷ 70 × 100 = 120.

Check in the story: 30% of $120 is $36, and $120 − $36 = $84. Both the percentage relationship and the remainder now agree. Dividing $84 by 30 would assign the remaining money to the percentage spent.

If decimal multipliers have been taught, the same relationship is 0.70 × original amount = 84, so the original amount is 84 ÷ 0.70. Choose a method you can explain; no single layout is compulsory.

When using the 1% method, the amount corresponding to 1% can be a decimal even when the final count is a whole number. It is a proportional calculation, not an instruction to cut physical objects into hundredths. Keep the units and check the final result in context.

P2: Use the relationship on fresh work

After teaching, close the P1 answers and worked example. Use a clean sheet and record the task code, date and help used.

1. A club uses 35% of the ribbon on a roll for a display. There are 78 metres of ribbon left. How many metres were on the roll originally?
2. A different roll contains 18 metres of blue ribbon. This is 15% of the ribbon on that roll. What is the total length of ribbon on that roll?
3. Check each answer against its original statement. For question 1, also find the length used and check that used plus remaining equals the original length.

Name the whole in words before writing its value. If someone supplies the percentage for the 78 metres, keep that prompt in the record.

Open P2 answers and explanations

1. Original length: 35% was used, so 65% remains. The known 78 metres represents 65% of the original length. The original length is 78 ÷ 65 × 100 = 120 metres.

2. Total length: the known 18 metres represents 15% of this roll. The total is 18 ÷ 15 × 100 = 120 metres. You can also reason that 5% is 6 metres, so 100% is 6 × 20 = 120 metres.

3. Check both relationships: for question 1, 35% of 120 is 42 metres. Then 42 + 78 = 120 metres. For question 2, 15% of 120 is 18 metres.

The totals happen to match, but the known amounts represent different percentages. In question 1, 78 metres is the remainder, or 65%. In question 2, 18 metres is the stated 15% part.

If a response uses 78 ÷ 35 × 100, inspect how the learner matched 78 to the wording. If the match is correct but the division is inaccurate, the next teaching step concerns arithmetic. Keep those observations separate.

P3: Return later and choose the direction

Agree another day and record the actual date. Keep the earlier answers and worked example closed. These questions mix finding a part with finding a whole.

1. After a group uses 40% of its original labels, 132 labels remain. How many labels did the group have originally?
2. Another pack contains 90 labels. Twenty per cent are green. How many green labels are there?
3. In a third pack, 42 blue labels represent 35% of all the labels. How many labels are in the pack altogether?

For each question, show the relationship, calculate and check the answer in the original statement. Record any related practice since P2 and any help used today. The chapter heading remains a cue, so later teacher-selected mixed work can provide a different check.

Open P3 answers and review notes

1. Recover the original count: 60% remains after 40% is used. The original count is 132 ÷ 60 × 100 = 220 labels. Check: 40% of 220 is 88, and 220 − 88 = 132.

2. Find a part of a known whole: 100% is already given as 90 labels. The green part is 90 × 20 ÷ 100 = 18 green labels. Check: 18 ÷ 90 × 100% = 20%.

3. Recover the total: 42 labels represents 35%, so 100% is 42 ÷ 35 × 100 = 120 labels. Check: 35% of 120 is 42.

Question 2 changes the direction. Dividing by 20% would recover a whole if 90 represented a 20% part, but the question says that 90 is the complete pack. A habit of always dividing is as unreliable here as a habit of always multiplying.

Look at the label attached to the known amount, the calculation and the check. A correct number with no clear relationship may need a further explanation. If a prompt was needed, record the exact prompt before choosing another task.

Optional: a larger amount and a missing amount

Use these after the core relationship is clear. The first question assumes that percentage increase has been taught. Treat the extension separately when reviewing progress on P1–P3.

1. A fictional activity fund increases by 20% of its original amount and becomes $144. What was the original amount? Explain why subtracting 20% of $144 would use a different base.
2. Forty per cent of a different activity fund is spent. No starting amount or spending amount is given. What can you say about the remainder, and can you determine its dollar value?

Open the optional answers and explanations

1. The final amount is 120% of the original: the original 100% plus an increase of 20% gives 120%. The original amount is 144 ÷ 120 × 100 = $120. Check: 20% of $120 is $24, and $120 + $24 = $144.

Subtracting 20% of $144 would remove $28.80 and give $115.20. That percentage uses the final amount as its base, while the stated increase uses the original amount. The reverse calculation must undo the relationship actually given.

2. The remainder is 60% of the original fund. Its dollar value cannot be determined from the percentage alone. For example, an original $100 would leave $60, while an original $200 would leave $120. Both fit the statement. You need enough further information to establish the whole or an equivalent amount-per-percentage relationship.

The first example uses more than 100% because the fund grew. The second has a clear percentage relationship but no monetary scale. Neither can be solved by treating every visible percentage question as the same calculation.

Use the work to choose the next teaching step

Keep P1, P2 and P3 together with dates and conditions. A missed later check is recorded as missed. Choose a new time or a smaller task; the absent response does not tell you whether learning has held.

• The wrong amount is treated as 100%: label the whole in words and match the known amount to its percentage.
• The remainder is matched to the amount used: show the original, used and remaining quantities together.
• The relationship is correct but arithmetic slips: practise the uncertain calculation and use a fraction, unitary route or multiplication check.
• The explanation and check work on unfamiliar tasks: ask which changed context or mixed question is suitable next.

Use the weekly practice record to name the next action, helper and review date. If this began with a marked paper, the Returned Paper Review and its two-page printable sheet keep the original response beside the later attempts.

These tasks provide observations of a specific skill under recorded conditions. They do not establish whole-subject mastery or predict an examination grade. Bring the actual working to a teacher or tutor when the base choice remains uncertain.