Reasoning · Grade 3-2 Weighing Applications

Problem

Order objects by weight from comparisons

Blue, red and green marbles go on a balance, and same-colour marbles weigh the same. The pan that dips is heavier. 1 blue against 1 red dips to the red; 2 blue against 1 red dips to the blue; 1 green against 2 blue dips to the green. Find the single heaviest marble.
Your answer
How to solve
Strategy Draw a Diagram — Picturing each balance gives a 'heavier than' comparison. Lining the comparisons up in order lets us chain them so the single heaviest marble stands out.
1STEP 1

Compare red and blue

The first shows red beats blue.

red > blue
2STEP 2

Compare two blue with one red

The second shows two blues beat one red.

blue + blue > red
3STEP 3

Compare green with two blue

The third shows green beats two blues.

green > blue + blue
4STEP 4

Chain the comparisons in order

Chained together, green also beats red — green is heaviest.

green > blue+blue > red > blue
Answer
the green marble
Green > 2 blue > red > blue makes a consistent order with no contradictions, so green being the single heaviest marble is sensible.
Takeaway

If green beats two blues, and two blues beat a red, then green wins overall — you can order things by chaining 'heavier than' clues like a Grade 1 comparison!

  • Compare red and blue
  • Compare two blue with one red
  • Compare green with two blue
  • Chain the comparisons in order