Summit Climb: A Fractions, Decimals and Percents Game
Climb the mountain one ledge at a time. Every right answer about fractions, decimals and percents takes you higher.
Getting the game ready...
For grown-ups
Every ledge on this mountain is a question about one amount written in different ways. Sometimes your child matches a fraction with its decimal (1/2 and 0.5), sometimes a decimal with its percentage (0.4 and 40%), and sometimes they have to decide which of two amounts is bigger, such as 0.6 or 5/8. A right answer moves the climber up. When an answer slips, a fraction bar or a hundred grid appears so your child can see the amount instead of guessing again. It suits children in roughly Grades 4 to 7, which is when many provinces and states bring decimals and percentages in alongside the fractions children already know.
The one big idea
Before anything else, I want children to hear this sentence: a fraction, a decimal and a percentage can be three names for the same amount. Half a pizza is 1/2 of the pizza, 0.5 of the pizza and 50% of the pizza. Nothing about the pizza changes. Only the way we write it does.
Children who miss this idea treat each format as its own topic with its own rules, and they get swamped. Children who have it treat the game as a translation puzzle, which is far more manageable.
The benchmark set worth memorising
A small set of equivalents does most of the work, in this game and in daily life. Here is the table I put on the fridge.
| Fraction | Decimal | Percentage | An everyday picture |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half a dollar, 50 cents |
| 1/4 | 0.25 | 25% | A quarter |
| 3/4 | 0.75 | 75% | Three quarters, 75 cents |
| 1/5 | 0.2 | 20% | 20 cm on a metre stick |
| 2/5 | 0.4 | 40% | 40 cm on a metre stick |
| 1/10 | 0.1 | 10% | A dime |
| 3/10 | 0.3 | 30% | Three dimes |
| 1/100 | 0.01 | 1% | A penny's worth, or 1 cm of a metre |
Halves, quarters, fifths and tenths first. Once those are solid, eighths (1/8 = 0.125) can wait, and most children can work them out from quarters anyway: an eighth is half of a quarter.
Money and a metre stick
Two objects in most houses make these ideas concrete. A dollar is a hundred cents, so 0.25 of a dollar is 25 cents and 25% of a dollar is also 25 cents. When a child is unsure whether 0.3 or 0.25 is bigger, I ask: "Would you rather have three dimes or a quarter?" Almost every child knows.
A metre stick (or a tape measure) does the same job for tenths and hundredths. Each 10 cm block is a tenth. Each centimetre is a hundredth. Point at 45 cm and ask for it as a decimal of a metre (0.45) and a percentage (45%).
How to play together
Let your child read each ledge aloud. Reading "zero point six" as "six tenths" helps a great deal, because the word "tenths" tells them what the digit means. Encourage them to say which benchmark the amount is near before answering: "Five eighths. That's more than a half, because four eighths is a half."
If you are sitting with them, resist answering for them. Ask one question at a time and let the hint pictures do the explaining.
Common mistakes and what is behind them
- 0.5 versus 0.05. A child who reads both as "point five" thinks they are the same. Say "five tenths" and "five hundredths," then show both on the hundred grid: 50 squares against 5.
- Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4. Fold a strip of paper into four, another into eight. Eighths are smaller pieces, because the same strip is shared among more parts.
- Thinking 0.25 is bigger than 0.3 because 25 is bigger than 3. Write them as 0.25 and 0.30, or go back to dimes and quarters.
- Treating a percentage as a separate number. 40% is not "forty," it is "forty out of every hundred."
Talking through a wrong answer
Here is a real exchange from our kitchen table, on a ledge asking which is bigger, 0.6 or 5/8.
| Who | What was said |
|---|---|
| Child | "0.6, because six is bigger than five." |
| Me | "Okay. What is 5/8 close to? More than a half or less?" |
| Child | "More. Four eighths is a half." |
| Me | "And 0.6?" |
| Child | "Six tenths. Also more than a half." |
| Me | "So both are a bit more than a half. How much more is 5/8?" |
| Child | "One eighth more than half. And 0.6 is one tenth more than half." |
| Me | "Which is bigger, an eighth or a tenth?" |
| Child | "An eighth. So 5/8 wins. Oh." |
Notice that I never said "wrong." I asked for a benchmark, then a comparison with the benchmark. It took a minute, and the child did all the thinking.
An off-screen version
Make a set of cards from paper: one fraction, one decimal and one percentage for each amount in the table above, 24 cards in all. Play a matching game (all cards face down, turn two, keep them if they match), then a sorting game (lay them in order from smallest to biggest). For a challenge, add 5/8, 0.65 and 3/5 and ask for the order. If your child enjoys comparing amounts at speed, the Fraction War variation on the Math War card game page uses an ordinary deck for the same thinking.
What to watch for
The hint pictures are not cheating, and children who use them a lot early on are often the ones who understand best later. What you are watching for is the move from "I need the picture" to "I can see the picture in my head." A child who says "that's like 60 squares" without opening the grid has made that move.
If multiplication facts are slowing them down on percentages (20% of 40 needs 4 x 2), a spell on the Space Bricks times tables mission can help, and more ideas live in Math at Home. Then put a quarter, three dimes and a metre stick on the table, and ask which is the bigger share.
