Round to one decimal place

What this sequence teaches

The whole routine for rounding to one decimal place, one step per click. It assumes students have met each step on its own: Cut after the first decimal place, Does it round up?, Recall the rounding rule and Add 0.1. None of those names appears on screen, so say as much or as little as you like. The rule itself does appear, at step 3, because saying it is part of the routine. The stage is set out like a whiteboard: every line on it is a line students write.

The steps

1. Cut. The number is copied down and cut after the first decimal place.
2. Decide. The digit straight after the cut lights, then “Rounds up” or “Doesn’t round up” appears.
3. Say the rule. Before you click, ask students to say the rounding rule, or write it: “Keep what’s before the cut, and add 0.1 only if it rounds up.” The click then shows the sentence. It appears instantly, with no fade, so there is no glimpse of it beforehand. This step is easy to skip, and it is the one that usually stays hidden: knowing whether it rounds up is not the same as knowing what to do about it.
4. Use the rule. What’s before the cut is written underneath. If it rounds up, “+ 0.1” is set out below it. Nothing is added up yet.
5. Add 0.1, only if it rounds up, one column at a time.
6. Write the answer.

The button never says how many steps are left, because that would give away whether the number rounds up.

The two examples

Example 1 — 8.2476 → 8.2. It doesn’t round up, so what’s before the cut is the answer.

Example 2 — 8.2576 → 8.3. One digit changes, the 4 to a 5. The cut stays where it was, the decision flips, and this time 0.1 is added. On Next the old working fades first, the stage pauses, and only then does the 4 change to a 5, so nobody misses it. While you work through it, the previous answer (8.2476 = 8.2) stays at the bottom of the stage, dimmed and labelled, so you can ask students to predict whether the answer will change. It is replaced only when the new answer is shown.

Running the sequence

• Nothing moves between steps until you click, so you can talk or check boards for as long as you want.
• Replay shows the last thing again. Why? gives the reason for the step on screen.

About the testing sequence

Seven numbers in a fixed order. Students write every line on their whiteboards. There is no scoring; the whiteboards are the data. Early on you might check boards after each step. Later, ask for all the working at once and click through to compare.

What each item catches

• 305.472 → 305.5. A cut after the first digit, 3 | 05.472, gives a wrong answer.
• 305.422 → 305.4. One digit changed, and the previous answer stays on screen, dimmed, until the new one is shown. A student who always adds 0.1 writes 305.5 again.
• 3.9728 → 4.0. Catches 3.10, and 4 with the zero left off.
• 49.3207 → 49.3. The 9 just before the point tempts “rounds up”.
• 40.039 → 40.0. Catches 40 and 40.00.
• 0.0829 → 0.1. Skipping the zero gives 0.08.
• 29.964 → 30.0. Two 9s change. Catches 29.10 and 30.

Reading the boards

• Cut line wrong: go back to cutting after the first decimal place.
• Decision wrong: go back to “Does it round up?”
• 0.1 added when it doesn’t round up, or left out when it does: rehearse the rounding rule.
• The sum is right but its answer is wrong: go back to adding 0.1.

About the expansion sequence

The same routine for other decimal places, with no new teaching. The instruction at the top changes, the cut moves with it, and the amount added matches the last place kept: 0.01 for two decimal places. The rule at step 3 changes to match (“add 0.01 only if it rounds up”).

1. 5.0649 to 2 decimal places → 5.06.
2. The same number to 1 decimal place → 5.1. Only the instruction changes. The previous answer, 5.06, stays on screen, dimmed, until the new one is shown.
3. 85.6074 to 2 decimal places → 85.61. 0.01 is added.
4. 3.996 to 2 decimal places → 4.00. Both zeros are written.