Pears Make Squares

Topics: Starter | Arithmetic | Number

• COLA, London Y9 Set 1
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• ☆, ☆, ☆ .
• Matthew, 3D, Craigslea State School
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• I figured out another solution. All the pears' numbers are 0!
• R G, City Of Leeds
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• I believe it works for all values to equal a square number divided by 2. eg ☆, ☆, ☆ or ☆, ☆, ☆ .
• Transum,
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• As you can see there are many answers below. It may be interesting to group the answers to help understand the patterns. There are some answers where all three numbers are the same. How would you describe these solutions? The comment above suggests the rule for even square numbers. What about odd square numbers? Must the pears be thinking of integers or could they have mixed numbers in their fruity minds (as proposed in the first comment above)?
• Y4GB, Leigh, England
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• My Year 4 primary top set found ☆, ☆, ☆ to work. Mr B.
• Wendover C.E Junior 6J,
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• Freddy found ☆, ☆, ☆ and 0, 16, 9! Connor found ☆, ☆, ☆ !
• 4W, Wendover C E Junior School
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• Dylan found ☆, ☆, ☆ .
• Sam, Carnoustie
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• - half a square number, write it twice subtract that from any other square to find the third number eg. ☆ , ☆ , ☆ ☆, ☆, ☆ ☆ , ☆ , ☆ ☆ , ☆ , ☆ , ☆ ☆ ... ☆ , ☆ , ☆ ☆ , ☆ , ☆ ☆ ☆ , ☆ , ☆ ☆ ☆ , ☆ , ☆ ☆ ... ☆ ☆ . ☆ , ☆ ☆ . ☆ , ☆ . ☆
  if you want three different numbers
  - find two numbers with an odd difference which add up to an odd square: write them down
  - find the two squares with that same odd difference
  - subtract the numbers you wrote down from the two squares you just found: you should get the same answer twice. write it down.
  eg. ☆ , ☆ ☆ , (with a difference of ☆ ☆ : just like ☆ ☆ ☆ and ☆ ☆ ☆ ) ☆ ☆ ☆
  ☆ , ☆ ☆ (with a difference of ☆ ☆ : just like ☆ ☆ ☆ and ☆ ☆ ☆ ) ☆ ☆
  ☆ , ☆ ☆ (with a difference of ☆ ☆ : just like ☆ ☆ and ☆ ☆ ☆ ) ☆ ☆
  ☆ , ☆ ☆ (with a difference of ☆ ☆ : just like ☆ ☆ and ☆ ☆ ) ☆ ☆
  ☆ , ☆ ☆ , ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆
  notice the pattern: first number increases by ☆ second number decreases by ☆ third number decreases by previous even number
  ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ ☆ , ☆ ☆ , ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆ ☆ ☆ , ☆ ☆ ,- ☆ ☆
  the solutions are infinite!
• Class 4 Highfields, Twitter
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• 2 of my pupils in @Class4Highpri completed the square number task before me. JP was really quick. Totally fascinated by their ideas/ strategies . https://t.co/VjY8GIHgHx pic.twitter.com/nuiN3UUFWk

  — Class 4 Highfields (@Class4Highpri) January 13, 2021

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