Picture scales with fruit on the pans. Work out how many pears balance an apple, which fruit is heaviest, or which scale is drawn wrong. Six levels, a daily set and printable worksheets.
Balance scale puzzles train equality and substitution, the first steps of algebra. A scale that balances says that two piles weigh the same, so one pile can stand in for the other. If 1 apple balances 3 pears, then 2 apples balance 6 pears. A child who sees this has used a rule without writing a single equation. Problems of this kind appear in children's maths contests and in grade 1 and 2 workbooks, because they need no reading and no symbols, only pictures and careful thought. The game counts toward the skill we call balance reasoning, inside the maths group of the kids games on this site. Nothing here needs a clock: a child can think as long as they like, and the speaker button reads every question aloud.
Level 1, Starter, shows one scale: 1 apple balances 3 pears. The question scale holds 2 apples, and the child says how many pears balance them. Answers run from 2 to 8. Level 2, Swap, chains two scales: 1 apple balances 3 oranges and 1 orange balances 2 cherries, so how many cherries balance 2 apples. Answers run from 4 to 18. Level 3, Heaviest, shows three tipped scales with four fruit. The lower pan is the heavier one, and the child picks the heaviest or the lightest fruit. Level 4, Spot the slip, shows four balanced scales and one of them is drawn wrong. Level 5, Mix-up, has pans that hold two kinds of fruit, such as 1 apple and 1 pear against 3 cherries. Level 6, Brain-buster, mixes the pans on both scales and the answers go up to 16. Levels 5 and 6 are the kind of two-unknown problem found in contests for children a little older than 6.
Each puzzle starts from hidden whole-number weights for the fruit, so the scales are always true to some real set of weights. The generator draws scales that balance for those weights and picks a question. It then checks the answer by brute force: it tries every weight from 1 up to 20 for each fruit, keeps the ones that make all the scales balance, and requires that every one of them gives the same whole-number answer. If two different answers are possible, the puzzle is thrown away. For the chain and mix-up levels it also removes each scale in turn and checks that the answer is no longer certain, so no scale is spare. The heaviest-fruit puzzles try all 24 possible orderings of four fruit and need one fruit to come first in every ordering that fits the tipped scales. The slip puzzles need exactly one scale that can be removed to leave the other three consistent. The fruit are only pictures: an apple is not really heavier than a cherry here, and the puzzle says so by never relying on real weights.
The game moves up a level after 3 right answers in a row and down after 2 wrong answers in a row, and you or your child can pick a level yourselves. A wrong answer gets a gentle Try again, never a buzzer. Each day there is a set of 5 puzzles, the same for everyone with the same date on their device. To print, choose a level, 4, 6 or 8 puzzles and Letter or A4 paper. Every print makes new puzzles, and the answer key with one short reason per puzzle is on the last page. Stars and progress are saved in this browser only. This game does not teach the written symbols for equals or the names of weights, it has no timer by default, and it does not replace a teacher: it gives one kind of puzzle, done many times, in short sessions.
Level 1 is meant for a 6 year old on the first day: one scale and numbers up to 8. Levels 5 and 6 are hard for a 7 or 8 year old. The levels adjust on their own, so a younger or older child lands at a comfortable one within about 10 puzzles.
The pan that sits lower is the heavier one, and a level pan means both sides weigh the same. Level 3 states this in its question. A real kitchen scale or a see-saw at the park shows the idea in a minute.
No, only one. Each level proves it its own way. The number levels try every whole weight from 1 to 20 for the fruit and keep a puzzle only if all weights that fit the scales give one answer. The heaviest-fruit level tries all 24 orderings of the four fruit. The slip level checks that exactly one scale can be removed to leave the other three consistent. Tests repeat these checks on 500 puzzles at each level.
Yes. Pick a level, 4, 6 or 8 puzzles and Letter or A4. The sheet has the scales drawn in black and white, so it prints on any printer, and the last page is the answer key with a short reason for each puzzle.
Six fruit fit in two rows of three on a phone screen without getting tiny. Puzzles are designed around that limit, so a child counts a pile at a glance instead of squinting at it.
No. Stars, levels and streaks are saved in this browser on this device. The page counts visits with Google Analytics, never answers or scores.