Do we say “to”?
A categorical atom from mrbartonmaths.com
What this sequence teaches
Which clock times we say as “to” the next hour (20 to 4, quarter to 5), and which we say another way (o’clock, past, half past). One thing decides it: where the long hand is. If it has gone past the 6 and hasn’t reached the 12, we say “to”. Half past and o’clock are the two edges, and neither is a “to” time.
The clocks are real clocks: the short hand moves with the long hand, so at 25 to 4 it sits between the 3 and the 4.
The teaching sequence
Example 1 — 3:30, half past 3 (no). The edge itself. The long hand is on the 6 but hasn’t gone past it.
Example 1 → Example 2. The verdict clears, the stage holds still for a second, then the clock runs on five minutes. Both hands turn together.
Example 2 — 3:35, 25 to 4 (yes). The long hand has passed the 6, and now we say “to”. That is the only thing that changed.
Example 2 → Example 3. Only the short hand moves, round to between the 9 and the 10. The long hand stays where it is.
Example 3 — 9:35, 25 to 10 (yes). Still “to”: the hour doesn’t matter. It also shows a yes with the short hand on the 9 side, which Example 6 needs.
Example 4 — 9:55, 5 to 10 (yes). The clock runs on twenty minutes and the long hand goes from the 7 to the 11. Between them, the yes examples cover the whole “to” range, from just past the 6 to just before the 12.
Example 5 — 10:00, 10 o’clock (no). The clock runs on five minutes. The long hand reaches the 12: o’clock, not “to”.
Example 6 — 10:10, 10 past 10 (no). The clock runs on ten minutes. The short hand is still on the 9 side, but the long hand is on the other side of the clock, so we say “past”. This is the example to leave them with: the short hand doesn’t decide.
What this sequence doesn’t address
Which hour we say. “Quarter to 4”, not “quarter to 3”, when the short hand is just past the 3. That needs its own resource; here we only decide whether it is a “to” time.
Quarter to is left out of teaching on purpose. Most children already know it, and the examples show that “to” covers the whole of that side of the clock. It is in the testing sequence.
One-minute times and unusual clock faces (Roman numerals; only 12, 3, 6 and 9 written) are in the expansion sequence.
The rule and the script
The rule, exactly as the Show rule button displays it: For the following examples: if the long hand has gone past the 6 and hasn’t reached the 12, we say “to”.
- Example 1 — “We don’t say ‘to’. How do I know? Because the long hand is on the 6. It hasn’t gone past it.”
- Examples 2, 3 and 4 — “We say ‘to’. How do I know? Because the long hand has gone past the 6 and hasn’t reached the 12.”
- Example 5 — “We don’t say ‘to’. How do I know? Because the long hand has gone past the 6, but it has reached the 12.”
- Example 6 — “We don’t say ‘to’. How do I know? Because the long hand hasn’t gone past the 6.”
Whether students see the words is your call. Nothing appears unless you click. Show rule puts the rule above the stage and it stays until you turn it off. Why? appears after each reveal: it shows the justification, plays the find again, then turns the long hand and the number the reason names orange.
What Reveal shows. Before the tick or cross appears, the long hand pulses, then the “to” half of the clock (from the 6 round to the 12) shades in. The same half shades in on every clock, so it never gives the answer away: what decides it is whether the long hand is inside it. On Example 1 the long hand lies along its edge.
Words for later. Once this is secure, the long hand can become “the minute hand”, the short hand “the hour hand”, and “to” times “times to the hour”.
Running the sequence
Pause before each reveal: the pause is the prediction. Ask “Do we say ‘to’?” and take an answer from everyone.
Replay appears on Examples 2 to 6 and replays the change from the example before, with the same pauses. After Reveal it plays the find again as well.
It assumes students can tell the long hand from the short hand and know o’clock and half past.
About the testing sequence
Ten clocks in a new random order each time: five are “to” times, five are not. The rule decides every one. There is no Show rule button here. After each answer the same find plays as in teaching (the long hand pulses, the “to” half shades in), then the tick or cross appears. Why? shows the justification and plays it again.
What each clock is diagnosing
2:45 (yes) and 9:15 (no). The hands sit in nearly the same places, swapped. A student who goes by the short hand gets both wrong.
1:40 (yes) and 1:20 (no). Both are “20”. Only which side of the clock the long hand is on decides it.
11:30 (no). Half past is not “to”. The short hand is on the 9 side as well.
8:00 (no). O’clock is not “to”. The short hand is on the 9 side as well.
10:55 (yes). The hands are almost on top of each other, so it looks like o’clock. It is 5 to 11.
12:35 (yes). 25 to 1: the short hand is at the top, and the hour wraps round.
3:50 (yes). The short hand is on the right-hand side, and it is still “to”.
5:05 (no). Near the 12, but on the wrong side.
Discussion prompts
- “Say the rule, then use it on this clock.”
- “Which hand decides it? Show me where it is.”
- On 2:45 and 9:15: “These two look alike. What’s different?”
Reading the summary
Each cell has two channels: a green or red tint shows whether the student answered correctly; the ✓ or ✗ in the corner shows whether we say “to”.
Wrong on 2:45, 9:15, 11:30, 8:00 and 3:50 suggests the student is going by the short hand. Yes to 11:30 suggests half past is being treated as “30 to”. Yes to 5:05 suggests “close to the 12” on either side.
About the expansion sequence
The rule says “for the following examples”, and this card checks how far it reaches. Eight clocks; every one still follows the rule, on a clock that looks unfamiliar. It works exactly like the testing sequence.
The items
Roman numerals: 2:40 (yes) and 4:30 (no). VI and XII are the 6 and the 12. These need Roman numerals to XII (Year 3).
Only 12, 3, 6 and 9 written: 5:50 (yes), 2:25 (no) and 8:35 (yes). The places of the missing numbers are still there; 2:25 and 8:35 sit either side of the 6.
One-minute times: 3:31 (yes, 29 minutes to 4), 6:29 (no) and 4:59 (yes, 1 minute to 5). One minute either side of an edge. These need students who read the minute marks.
Discussion prompts
- “Where would the 6 be on this clock? Show me.”
- “How many minutes until the 12?”
Reading the summary
The same two channels as the testing sequence. Wrong on the Roman or the four-number clocks suggests the numbers, not the positions, are doing the work. Wrong on the one-minute times suggests students are reading to the nearest five minutes.