Series route: This guide belongs to the complete PSLE Learner’s Guide volume directory. The original PSLE Learning Guide supplies the wider English, Mathematics and Science route, while PSLE Mathematics provide verified subject-specific continuation.
Find your route through this guide
This volume solves one precise learner problem: the learner sees two large numerators, compares them directly, or assumes that the fraction missing the smaller numerator count is closer to one without considering denominator-sized parts. The aim is not to memorise a slogan. It is to understand the mechanism well enough to recognise the idea when the wording, numbers, diagram or context changes. A Primary 6 learner should be able to explain the decision, perform it under time pressure, and detect a tempting answer that only looks familiar.
- Understand the mechanism before memorising a form.
- Study the worked examples and compare near-misses.
- Repair common misconceptions with targeted tests.
- Complete graded independent practice before reading the answers.
- Use delayed transfer and examination control to make the skill durable.
- Use the parent and tutor notes only after the learner has attempted the work.
The problem beneath the mistake
The fractions 11/12 and14/15 are both close to one. Converting them to decimals works, but a quicker exact comparison notices what each is missing: 1/12 and1/15.
Because 1/15 is smaller than1/12, the fraction missing1/15 is closer to one. Therefore14/15 is greater than11/12.
The method depends on equal whole units. One whole minus a smaller gap leaves a larger remainder. This reverses the comparison of the gaps.
The numerator alone is unsafe. Fourteen is greater than eleven, but that fact is not the reason the fraction is larger. Different denominators divide the whole into different-sized parts.
The number of missing pieces is also unsafe without size. The fractions8/10 and17/20 are missing2/10 and3/20. Three pieces can represent a smaller amount because twentieths are smaller than tenths.
A complement can be found by subtracting the numerator from the denominator. For a/b, the missing amount is (b−a)/b when0 Unit-fraction gaps are especially easy. Among1/12 and1/15, the larger denominator produces the smaller unit fraction. This denominator rule applies only after confirming that each numerator is one. When gaps have different numerators, compare the missing fractions properly. For2/9 and3/14, use common denominators, cross-products or another exact method. The complement route is efficient when fractions are near one. For fractions near one-half or zero, another benchmark may produce simpler reasoning. Improper fractions require a new reference. A value greater than one has an excess above one rather than a missing part. The same distance idea can work, but the direction must be stated correctly. An estimate is a useful check. Both11/12 and14/15 should be above0.9, and the final ordering should agree with a cross-product comparison. A complete answer writes the complements, compares them with a reason, reverses the gap order for the original fractions, and verifies by a different route. Core decision: For proper fractions near one, rewrite each as one minus its missing fraction; the fraction with the smaller missing amount is the larger original fraction. A useful rule has three parts: a trigger, an operation and a check. The trigger tells you when the rule applies. The operation tells you what to do. The check tells you whether the result still matches the meaning of the question. Learners who remember only the operation often apply it in the wrong place; learners who remember only an example often freeze when the surface details change. Fractions can be compared by distance from one only when one represents the same-sized whole in both quantities. Diagnostic question: Do the fractions refer to one equal whole? Reliable response: State the common benchmark. For a/b, calculate (b−a)/b. Diagnostic question: How much must be added to reach one? Reliable response: Write a/b=1−(b−a)/b. Use unit-fraction reasoning, common denominators or cross-products as appropriate. Diagnostic question: Which gap is genuinely smaller? Reliable response: Include denominators and units. A smaller gap below one means a larger original fraction. Diagnostic question: Which fraction lies closer to one from below? Reliable response: State the larger original explicitly. Confirm that both are proper fractions near enough to one for the route to simplify rather than complicate. Diagnostic question: Would another benchmark be easier? Reliable response: Choose efficiency without changing logic. Use cross-products, equivalent fractions or decimals after the complement argument. Diagnostic question: Does another exact route give the same order? Reliable response: Repair any sign or reversal error. Do not race through these examples. Before reading each explanation, name the evidence that matters and the information that does not. Then compare the correct route with the tempting route. That comparison is where the transferable learning sits. Task. Compare11/12 and14/15. Reasoning. Their gaps are1/12 and1/15. Since1/15<1/12, the second fraction is closer to one. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 14/15>11/12. Independent check. Cross-products give14×12=168 and11×15=165. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Compare17/20 and18/20. Reasoning. The gaps are3/20 and2/20; the smaller gap belongs to18/20. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 18/20>17/20. Independent check. With equal denominators, numerator comparison agrees. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Compare7/9 and11/14. Reasoning. The gaps are2/9 and3/14. Cross-multiplying gaps gives2×14=28 and3×9=27, so3/14 is smaller. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 11/14>7/9. Independent check. Direct cross-products give11×9=99 and7×14=98. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Compare8/10 and16/20. Reasoning. The gaps are2/10 and4/20, both equal to1/5. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. The fractions are equal. Independent check. Both simplify to4/5. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Order5/6,9/10 and13/15. Reasoning. The gaps are1/6,1/10 and2/15. In thirtieths they are5/30,3/30 and4/30. Smaller gaps mean larger fractions. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 9/10>13/15>5/6. Independent check. Direct decimal estimates are0.9, about0.867 and about0.833. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Compare2/7 and3/8. Reasoning. Complements are5/7 and5/8, which can be compared, but direct cross-products are simpler. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 3/8>2/7. Independent check. 3×7=21 exceeds2×8=16. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Compare13/12 and16/15. Reasoning. These are1+1/12 and1+1/15. A larger excess above one gives the larger number, reversing the below-one rule. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. 13/12>16/15. Independent check. Cross-products give195>192. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. Task. Tank A is11/12 full and Tank B is14/15 full, with equal capacities. Reasoning. A is missing1/12 of a tank; B is missing1/15. The smaller missing volume is B’s. The controlling idea is the actual size of each complement to one, not the number of missing pieces without their denominators. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example. Answer. Tank B contains more water. Independent check. Equal capacities are necessary for the volume conclusion. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption. A method becomes independent when you can say where it applies, where it stops and which change would alter the conclusion. The cases below deliberately vary one structural feature at a time. For each case, pause before the analysis and predict whether the core rule remains available. Then name the exact condition that controls the decision. This is harder than repeating a worked solution, but it is also closer to what an unfamiliar examination item demands. Case. Fractions of the form(n−1)/n are one unit fraction below one. Analysis. The larger denominator gives the smaller gap. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Order9/10,11/12,19/20. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. A fraction such as13/15 is2/15 below one. Analysis. The numerator of the gap and its denominator both matter. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare with7/8. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Compare1−2/11 and1−2/13. Analysis. With equal gap numerators, the larger gap denominator makes the gap smaller. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. State the original order. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Compare1−3/20 and1−5/20. Analysis. With equal denominators, fewer missing parts means a smaller gap. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Write both fractions. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. 2/10 and4/20 are equal missing amounts. Analysis. The original fractions are therefore equal. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Find both originals. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Gaps2/9 and3/14 can be converted to126ths. Analysis. Exact equivalence makes the reversal clear. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Complete the conversion. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Compare a/b and c/d gaps without decimals. Analysis. Cross-products preserve exactness for positive denominators. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Explain which product belongs to which gap. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. A decimal approximation can check but need not drive the proof. Analysis. Rounding must not erase a small difference. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Use three decimal places. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Near-one fractions can be expressed as percentages. Analysis. Percent conversion supplies another benchmark. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare95/100 and19/20. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Two equal-capacity tanks make fullness fractions comparable. Analysis. Different capacities break the direct volume conclusion. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Construct a counterexample. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Half of a large cake can exceed three-quarters of a small cake. Analysis. Fraction order and absolute amount are different questions. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Name the requested quantity. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. A gap of zero identifies the whole1. Analysis. No proper fraction can exceed it. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare1 and999/1000. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. A fraction0 is one whole below one. Analysis. The complement method remains true but is not efficient. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Use direct comparison. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Values above one have excesses rather than gaps. Analysis. Larger excess means larger value. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare9/8 and10/9. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Any positive amount above one exceeds any proper fraction below one. Analysis. Benchmark location settles the order. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare17/16 and31/32. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Below one, smaller distance means larger value. Analysis. This reversal is the heart of the method. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Explain on a number line. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Fractions close to1/2 may be easier to compare by doubling. Analysis. Choose a benchmark that simplifies structure. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare7/15 and8/17. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Small numerators may favour direct unit-fraction reasoning. Analysis. A method is useful only when it reduces work. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Compare2/101 and3/150. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Convert all gaps to a common unit before reversing the list. Analysis. A table prevents losing ownership. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Order four given fractions. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Case. Whole, complement, exact gap comparison, reversal and independent check complete the method. Analysis. Each step blocks a different error. Notice that the answer depends on the actual size of each complement to one, not the number of missing pieces without their denominators; changing a decorative detail would not be enough to change the reasoning. Challenge. Audit five examples. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid. Finish the lab with a blank-page recall. Write the rule, its conditions, one confirming example, one near-miss and one independent check from memory. Compare that page with the article only after finishing. If the rule is correct but the condition is missing, the learning is not yet safe: an overgeneralised rule can produce confident errors. If the condition is correct but no example can be generated, practise construction rather than rereading. What the learner may think. Compare numerators even when denominators differ. Why it fails. The parts have different sizes. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Use complements or cross-products. Use this short test immediately: What is one part worth? What the learner may think. Count the missing numerator only. Why it fails. Three twentieths can be less than two tenths. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Compare missing fractions, not piece counts. Use this short test immediately: Which gap is larger? What the learner may think. The fraction farther below one must be larger. Why it fails. Subtracting more from the same whole leaves less. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Reverse the gap order. Use this short test immediately: Draw a number line. What the learner may think. Use denominator size without checking the numerator pattern. Why it fails. The rule works for matched unit gaps, not arbitrary fractions. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Identify the gap form first. Use this short test immediately: Are gap numerators equal? What the learner may think. Fullness fractions directly compare litres in unequal tanks. Why it fails. The same fraction of different capacities gives different amounts. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Confirm equal wholes or compare actual volumes. Use this short test immediately: What is the whole? What the learner may think. Two rounded decimals match, so fractions are equal. Why it fails. A small exact difference may disappear. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid. Targeted repair. Use exact arithmetic for close cases. Use this short test immediately: Do cross-products agree? Attempt each item without looking ahead. Write one line that identifies the controlling evidence before writing the final answer. Items 1–3 check recognition, 4–7 require explanation, and the later items change the surface form so that memory alone is insufficient. Question. Compare23/24 and19/20. Explained answer. 23/24>19/20. Why this answer earns trust. The gaps are1/24 and1/20, and1/24 is smaller. Transfer variation: Verify by cross-products. Question. Compare13/15 and20/23. Explained answer. 20/23>13/15. Why this answer earns trust. Gaps are2/15 and3/23;2×23=46 while3×15=45, so3/23 is smaller. Transfer variation: Check direct products. Question. Compare21/28 and15/20. Explained answer. They are equal. Why this answer earns trust. Their gaps7/28 and5/20 both equal1/4. Transfer variation: Simplify both originals. Question. Order7/8,16/18 and9/10. Explained answer. 9/10>16/18>7/8. Why this answer earns trust. Gaps are1/10,1/9 and1/8; smaller gaps give larger values. Transfer variation: Plot approximate positions. Question. Tank A is9/10 full and B is11/12 full; capacities equal. Which holds more? Explained answer. B. Why this answer earns trust. Its gap1/12 is smaller than A’s1/10. Transfer variation: State why equal capacity matters. Question. A10-L tank is9/10 full; a20-L tank is3/4 full. Which holds more? Explained answer. The20-L tank:15 L versus9 L. Why this answer earns trust. Absolute amount requires multiplying by capacity. Transfer variation: Separate fraction order from volume order. Question. Compare17/16 and21/20. Explained answer. 17/16>21/20. Why this answer earns trust. Excesses are1/16 and1/20; above one, the larger excess gives the larger number. Transfer variation: Explain why the rule direction changes. Question. Is complement to one efficient for3/11 and4/13? Explained answer. It is valid, but direct cross-products are simpler. Why this answer earns trust. Their gaps are not simpler than the originals. Transfer variation: Choose and justify a method. Question. State the complement rule in one sentence. Explained answer. For proper fractions below one, the smaller missing amount corresponds to the larger fraction. Why this answer earns trust. Both fractions share the same benchmark one. Transfer variation: Recall after two days. Question. Order five close fractions without decimals. Explained answer. List exact complements, compare them, reverse the order and verify the closest pair. Why this answer earns trust. The whole route is visible and checkable. Transfer variation: Repeat after one week. Build a table for twenty fractions near one. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation. Success criterion. Every row shows original, exact gap, gap order and original order. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter. After one week, explain why gap order reverses below one. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation. Success criterion. The proof uses subtraction from the same whole, not a memorised slogan. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter. Compare fractions near zero, one-half, one and above one. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation. Success criterion. The learner selects a useful benchmark and states the direction correctly. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter. 1. Read the job before the story. Underline the command and the noun it governs. “Explain the change,” “state the word,” “find the fraction” and “identify the evidence” are different jobs even when the surrounding context is similar. 2. Separate given information from remembered information. Use only the facts supplied for the current task plus secure subject knowledge. Do not let a previous question, a familiar worksheet or an expected pattern silently become new evidence. 3. Write enough working to expose the decision. A marker or teacher should be able to see the relationship that justifies the answer. Extra sentences are not automatically stronger; the strongest working is concise, relevant and checkable. 4. Reserve a different-route check. For language, read the sentence for meaning and grammar. For mathematics, estimate or reverse the operation. For science, check the claim against the stated observation and a conservation or fair-test principle. 5. Stop when the requested job is complete. Unrequested speculation can contradict a correct answer. Add detail only when it explains the mechanism or satisfies another explicit part of the question. Under time pressure, use a compact four-part margin routine: trigger → evidence → operation → check. Trigger names the feature that activates the method. Evidence identifies the exact words, values or observations allowed. Operation performs the language, mathematical or scientific step. Check asks whether the final statement answers the requested job, preserves units or referents, and avoids a stronger claim than the evidence supports. After practice, do not record only “careless mistake.” Name the broken decision. Useful labels include trigger missed, evidence imported, relationship reversed, referent lost, unit dropped, operation correct but job wrong, and check repeated the same route. Add one prevention cue beside the label. A short accurate log is more useful than a long emotional account because it tells the learner what to do on the next item. Review the log after two days and again after a week. Reattempt only one or two representative items first. If the method transfers, move to a mixed set. If it fails, repair the exact link between trigger and operation. This spacing matters because a solution can feel obvious while it is still visible and disappear when the page is closed. Use a number line from zero to one and mark the missing distance. Ask which mark leaves the shorter walk to one before asking for any calculation. Do not praise a correct order without the reversal explanation. The durable idea is that subtracting a smaller gap from the same whole leaves a larger amount. Mix equal and unequal wholes in word problems. The learner should distinguish comparing fractions from comparing actual quantities such as litres or metres. The adult’s most useful question is not “Why were you careless?” but “Which decision did the evidence require?” Ask the learner to point to the controlling word, value, relationship or observation. If the learner can explain that link, reduce support. If the learner cannot, model one example and then change the surface details for the next attempt. The amount that must be added to a fraction to make one. Subtract the numerator from the denominator: the gap is(b−a)/b. From the same whole, subtracting a smaller amount leaves a larger remainder. No. Denominators determine the size of the missing parts. Use excess above one instead; there, a larger excess gives a larger number. Cross-multiply the original fractions or convert them to exact equivalent fractions. Return to the complete volume directory to locate the series, use the original PSLE Learning Guide for the foundation route, and continue through PSLE Mathematics for verified subject guidance. The next useful task is a mixed set in which this idea is sometimes relevant and sometimes irrelevant; that is the point at which a learner must choose, not merely copy.Mechanism: why the rule works
1. Confirm the same whole
2. Find each complement
3. Compare the missing amounts
4. Reverse the order
5. Check the range
6. Verify independently
Worked examples: make the decision visible
Worked example 1: Unit gaps
Worked example 2: Same denominator
Worked example 3: Different gap numerators
Worked example 4: Equal fractions
Worked example 5: Three fractions
Worked example 6: Not near one
Worked example 7: Above one
Worked example 8: Word context
Deepening lab: compare cases, conditions and limits
Deepening case 1: One missing piece
Deepening case 2: Two missing pieces
Deepening case 3: Same gap numerator
Deepening case 4: Same gap denominator
Deepening case 5: Equivalent gaps
Deepening case 6: Common denominator
Deepening case 7: Cross-products on gaps
Deepening case 8: Decimal check
Deepening case 9: Percent check
Deepening case 10: Same whole
Deepening case 11: Different wholes
Deepening case 12: Exactly one
Deepening case 13: Zero
Deepening case 14: Improper fractions
Deepening case 15: Mixed below and above
Deepening case 16: Distance reversal
Deepening case 17: Near half
Deepening case 18: Near zero
Deepening case 19: Ordering many
Deepening case 20: Final audit
Common misconceptions and targeted repairs
Misconception 1: Larger numerator wins
Misconception 2: Fewer missing pieces always wins
Misconception 3: Larger gap means larger fraction
Misconception 4: Larger denominator always gives larger fraction
Misconception 5: Different wholes do not matter
Misconception 6: Decimal rounding proves equality
Graded independent practice
Practice 1: Unit gaps
Practice 2: Two gaps
Practice 3: Equality
Practice 4: Order three
Practice 5: Same whole
Practice 6: Different whole
Practice 7: Above one
Practice 8: Method choice
Practice 9: Rule recall
Practice 10: Transfer
Delayed transfer: prove that the learning lasts
Transfer test 1: Complement table
Transfer test 2: Delayed proof
Transfer test 3: Mixed benchmark set
Examination control
A compact error log
Notes for parents and tutors
Frequently asked questions
What is a complement to one?
How do I find it for a/b?
Why does the order reverse?
Can I compare only missing numerators?
Does the method work above one?
What is a good check?
Next routes