SPACE ACADEMY · TRY, THINK, PLAY

Class 4: Number detectives

Translate representations, use place value and solve constrained number clues.

Play missionChapters

Try a quick challenge

Just a quick try. Not saved; no game rewards.

ExploreBuilding numbers

Using ordinary digits, write the number on Dev's tablet A.

Tablet AXLITablet BXXII
  1. 51
  2. 31
  3. 41
  4. 63
Need a hint?

A smaller Roman symbol before a larger one is subtracted.

Answer & method
Answer C: 41

Tablet A, XLI, means 41.

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ReasonFactors and multiples

24 and 30 have how many common factors?

  1. 8
  2. 4
  3. 6
  4. 3
Need a hint?

A common factor divides both numbers exactly. List and count them.

Answer & method
Answer B: 4

Both numbers divide by 1, 2, 3, 6. That is 4 common factors.

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StretchComparing quantities

Which comparison is true?

  1. LII + XI > XLVIII - XIX
  2. 89 × 4 = 61 + 29
  3. 150 × 0 > 67 × 3
  4. 452 × 0 < 338 × 0
Need a hint?

Work out both sides of every statement before choosing a symbol.

Answer & method
Answer A: LII + XI > XLVIII - XIX

LII + XI = 63 and XLVIII - XIX = 29, so LII + XI > XLVIII - XIX is true.

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For grown-ups

Ideas to practise

  • Place value. A digit has a different value in each position. Count the places from the right.
  • Comparing quantities. Compare the values, not the size or spacing of their pictures.
  • Factors and multiples. Factors divide an amount exactly; multiples are repeated totals. Choose which idea the situation needs.
  • Building numbers. Combine the place-value parts, including any zero places.
  • Sorting by a rule. Check which object does not share the named property.
  • Coding and decoding. Apply the stated code consistently to each letter.
  • Working backwards. Undo the last operation first, then undo the earlier operation.
  • Number patterns. Look for the same change between neighbouring numbers.

A game mission has 8 untimed questions. Only the game saves choices and hints. A finished mission earns one launch charge and participation towards the Lab & control hub in Nebula Research Station. The chapter goal is 8 different questions in finished sets; hints and wrong answers count as participation, not mastery. Some craft systems link more than one chapter.

Choose a level

Explore

Foundations: read a representation and practise the underlying idea.

  • Find the difference between place values of digits
  • Arrange numbers in ascending or descending order
  • Choose the true comparison from four statements
  • Write numbers using ones and place-value words
  • Use factors, common factors and least or greatest factors
  • Round a marked point on a number line
  • Arrange digit cards under a lock rule
  • Calculate with Roman specimen codes
  • Find the odd number out
  • Find a code made by moving letters along the alphabet
Play Explore

Reason

Paper-style reasoning: connect clues, interpret a diagram or work backwards.

  • Find the difference between place values of digits
  • Find a number from digit clues
  • Choose the true comparison from four statements
  • Arrange numbers in ascending or descending order
  • Use factors, common factors and least or greatest factors
  • Find the smallest multiple with a given number of digits
  • Write numbers using ones and place-value words
  • Calculate with Roman specimen codes
  • Arrange digit cards under a lock rule
  • Round a marked point on a number line
Play Reason

Stretch

Higher-order practice: link conditions, test statements and avoid a tempting wrong method.

  • Find a number from digit clues
  • Choose the true comparison from four statements
  • Use factors, common factors and least or greatest factors
  • Find the smallest multiple with a given number of digits
  • Write numbers using ones and place-value words
  • Calculate with Roman specimen codes
  • Arrange digit cards under a lock rule
  • Choose equal trays or a shared signal time
  • Find the difference between place values of digits
  • Separate two interleaved number patterns
  • Round a marked point on a number line
Play Stretch

Levels change representations, clues and conditions, not just the numbers. These are practice formats, not validated exam-equivalent difficulty.

Using the feedback

Learning reports distinguish hinted answers from independent first choices. They consider up to 20 recent different, unhinted questions per skill and level, and wait for at least five before suggesting extra practice. Repeating the same question does not add evidence. Reports are practice evidence, not IQ scores, diagnoses, ranks or predictions of competition results.

Ask the learner to explain a drawing or check with objects too. Choose Explore or an earlier chapter when a step feels too large.

Sources & limits

The grade topics use SOF IMO Class 4 published topic syllabus as their primary reference. The SOF sample and CREST previous-year paper below informed representations and reasoning demands. Providers have different topic boundaries; their syllabi are not interchangeable.

Questions, diagrams, picture choices, hints and explanations are original Otterly work, not copied paper questions or publisher artwork. No Olympiad provider is affiliated with or endorses Space Academy. This is not complete exam preparation; follow classroom teaching and check the current official syllabus too. Independent educator review is still needed for difficulty and breadth.

Content and coverage notes. To report a confusing question, describe the grade, chapter, level and question on the contact page. Do not send children’s personal information.

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Original Otterly practice, not an official exam. Game progress stays on this browser.