Decimal Drop

Where does 0.35 land? And what fraction is that?

Game Adjusts as you go Equivalent fractions and decimals 4.NF.C.64.NF.C.7 MagPI · Number line estimation ALPACA · Elementary operations
New to fractions? Start here. A short lesson where one bar gets cut up while you watch, so you can see for yourself that one half and two quarters are the same amount. About about 5 minutes.
Show me how fractions work → Why are one half and two quarters the same?
▤ Print this All of 4th grade

For grown-ups

  • How long: 5 to 10 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
  • The strategy to reinforce: “Tenths first” — The first digit after the point is tenths. 0.35 is between three tenths and four tenths. If they stall, remind them of this rather than giving the answer.
  • When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
  • It adjusts as you go: this one gets harder while they are getting them right and easier if they are not, aiming to keep them succeeding about four times in five — hard enough to be worth doing, not hard enough to stop being fun. The score is how deep they got rather than how many they answered, because the difficulty moved. Nothing is stored — it starts fresh every time the page loads.
  • On the timer: it is off unless you turn it on, and it is never needed. Use it only once the skill is comfortable, never to introduce it.
  • Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.

What this practises

Placing a decimal between 0 and 1, and matching it to its fraction.

Decimals and fractions on the same number line, so they read as one idea in two notations rather than two unrelated topics. Matching 0.25 to a quarter is the link that makes both easier.

The underlying idea
Decimals and fractions as one idea in two notations, on one line.
Where this sits in Illustrative Mathematics
4th grade Unit 4: From Hundredths to Hundred-thousands
Sources
Institute of Education Sciences / What Works Clearinghouse (2021) · Schneider et al. (2018) · Riconscente (2013)  all references →

Related measured skills: MagPI · Number line estimation, ALPACA · Elementary operations. What this means

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