Numbers to 1000 & skip-counting
Count, read, write & order to ~1000; skip-count (2s, 3s, 5s, 10s).
Once you can count and order numbers to 100, the next move is to stretch that skill to about 1000 — and to learn a faster way to count than one-at-a-time: skip-counting in steps of 2, 3, 5 or 10.
What it means
Numbers to 1000 are still the ordinary whole numbers — the counting numbers with no fractions — just carried further. Writing them takes up to three digits, and position still decides value. In 473 the 4 means four hundreds (400), the 7 means seven tens (70), and the 3 means three ones, so 473 is 400 + 70 + 3. This is the same place-value idea you met with two-digit numbers (N1.2), with a new column — hundreds — added on the left.
Reading and writing means matching the spoken name to the digits: you hear “six hundred and five” and write 605 (six hundreds, no tens, five ones — the 0 holds the tens place empty). Ordering means deciding which number is larger by comparing from the left: check hundreds first, then tens, then ones. 518 beats 489 because 5 hundreds beat 4 hundreds, before you even look at the rest.
Skip-counting is counting in equal jumps instead of by ones. Counting by 5s you say 5, 10, 15, 20, 25 — each number is 5 more than the one before. You can skip-count in 2s (2, 4, 6, 8…), 3s (3, 6, 9, 12…), 5s (5, 10, 15…) or 10s (10, 20, 30…). It matters because it is faster, it reveals number patterns, and it is the seed of multiplication: counting seven 5s (5, 10, 15, 20, 25, 30, 35) is exactly 7 × 5.
A number line makes skip-counting physical: instead of tiny one-steps, you take equal-sized hops. Counting by 10s is a hop of ten each time; the landing points are 10, 20, 30 and so on.
Worked examples
Skip-count by 5s to 40. Each step adds 5:
5 → 10 → 15 → 20 → 25 → 30 → 35 → 40The ones digit alternates 5, 0, 5, 0 — a rhythm you can hear and see.
Skip-count by 3s, ten times:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30Ten hops of 3 land on 30, so 10 × 3 = 30.
Order these numbers from smallest to largest: 407, 74, 470, 47.
| position | 1st | 2nd | 3rd | 4th |
|---|---|---|---|---|
| number | 47 | 74 | 407 | 470 |
The two three-digit numbers are automatically bigger; between them, 407 has 0 tens and 470 has 7 tens, so 407 comes first.
The generative-art connection
Skip-counting is a pattern, and patterns want to be drawn. In dot-multiplier, dots are added in fixed groups spread symmetrically around a centre — so a starburst with 8 arms of 5 dots is a skip-count of 5 made visible, and also a picture of 8 × 5. Add another arm and the total jumps by exactly one group.
The hundred board is even more direct: colour every 5th square and a clean pattern of vertical stripes appears; colour every 2nd square and you get the alternating comb of even numbers; every 10th square marks a single column. The child isn’t told the pattern — they make it, and the mathematics is the shape that emerges. This is the mathartcademy premise in miniature: the structure of the art is the counting rule.
Common misconceptions
- Losing the empty column. Writing “six hundred and five” as
65instead of605. The0isn’t nothing — it holds the tens place so the 6 stays in the hundreds column. - Comparing by length of digits alone, or right-to-left. Compare from the left, hundreds first:
90is smaller than100even though 9 feels big. - Starting a skip-count from the wrong place. Counting by 3s means 3, 6, 9 — not 1, 3, 6. Every landing point must be an equal jump from the last; check that each gap is the same.
What a learner should be able to solve
The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.
-
Write these number names as digits: (a) "three hundred and sixty", (b) "seven hundred and four", (c) "nine hundred and ninety".
Answer
(a) `360` (3 hundreds, 6 tens, 0 ones — a trailing zero because there are no ones). (b) `704` — the `0` holds the empty tens place. (c) `990`. The tricky ones have a zero standing in a column with nothing in it: you must keep that column so the other digits stay put.
Art hook A 3-column place-value grid (hundreds, tens, ones). The child types a number and Canvas draws that many dots stacked in each column; a `0` leaves a column visibly empty, so `704` shows a full hundreds column, a blank tens gap, and 4 lone dots.
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Put these four numbers in order from largest to smallest: `970`, `907`, `97`, `790`.
Answer
`970, 907, 790, 97`. Compare from the left. `97` is the only two-digit number, so it is smallest. Among the rest: `970` and `907` both have 9 hundreds and beat `790` (7 hundreds); between them `970` has 7 tens and `907` has 0 tens, so `970` is biggest.
Art hook Draw a horizontal number line 0–1000 with tick marks every 100. The child drops each number as a coloured dot at its position; when sorted correctly the dots read left-to-right (largest at the right end near 1000), and a line connects them into a staircase.
-
Skip-count by 5s starting at `5` and by 10s starting at `10`. Which numbers do BOTH counts land on, up to `50` — and why must that always happen?
Answer
By 5s: `5, 10, 15, 20, 25, 30, 35, 40, 45, 50`. By 10s: `10, 20, 30, 40, 50`. Both land on `10, 20, 30, 40, 50`. It must happen because one 10-hop equals two 5-hops, so every landing point of the 10s count is also reached by the 5s count.
Art hook On a hundred board (10x10), colour the 5s squares blue and the 10s squares yellow with transparency. Where they overlap the colour turns green — the green squares are exactly the shared landing numbers, a colour-mixing proof that the 10s are a subset of the 5s.
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Carla skip-counts by 3s: `3, 6, 9, 12, 15`. How many hops has she taken to reach `15`, and what multiplication does that show?
Answer
5 hops (`3→6→9→12→15`). Five 3s make 15, so this shows `5 × 3 = 15`. Skip-counting a fixed step is repeated adding, which is exactly multiplication.
Art hook Place a dot every 3 units along a number line and draw a curved hop-arc between each pair. Each completed arc increments a counter; landing on 15 lights up '5 hops = 5 × 3' — skip-count arcs as animated multiplication.
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
-
Count on by ones out loud: `697, 698, 699, ___, ___, ___`. What are the next three numbers?
Answer
`700, 701, 702`. After `699` the ones roll over and make a new hundred: `700`.
Art hook An odometer-style Canvas of three spinning digit wheels. As the count rises past 699 the ones and tens wheels roll to 0 and the hundreds wheel clicks up — showing the carry as motion.
-
In the number `352`, what is the value of each digit? Say what the `3`, the `5` and the `2` are worth.
Answer
The `3` is worth `300` (3 hundreds), the `5` is worth `50` (5 tens), the `2` is worth `2` (2 ones). So `352 = 300 + 50 + 2`.
Art hook Tap a digit and Canvas 'explodes' it into its true value as dots: tapping the 3 in 352 scatters 300 tiny dots grouped into 3 hundred-blocks, the 5 into 5 ten-rods, the 2 into 2 singles.
-
Write these as digits: (a) "two hundred and thirty", (b) "five hundred and nine".
Answer
(a) `230`. (b) `509` — the `0` holds the empty tens place, so the 5 stays in the hundreds column.
Art hook A 3-column place-value grid (hundreds, tens, ones): the child types the number and Canvas fills each column with that many dots, so the empty tens column in `509` stays visibly blank — the zero you can see.
-
Which is larger, `409` or `421`? How do you know without counting up?
Answer
`421` is larger. Both have 4 hundreds, so compare the tens next: `421` has 2 tens, `409` has 0 tens. More tens wins, so `421 > 409`.
Art hook Two vertical bar-towers side by side (hundreds, tens, ones stacked). The taller total glows; the comparison highlights the first row where the towers differ — teaching 'compare from the top'.
-
Fill in the skip-count by 2s: `2, 4, __, 8, __, 12, __`.
Answer
`6, 10, 14`. Each number is 2 more than the one before.
Art hook Light up every 2nd dot on a ring of 20 dots; the lit dots form a perfectly even alternating pattern — the visual signature of counting by twos.
-
Order these from smallest to largest: `199, 91, 219, 190`.
Answer
`91, 190, 199, 219`. `91` is the only two-digit number (smallest). Then `190` and `199` both have 1 hundred and 9 tens — `190` (0 ones) before `199` (9 ones) — and `219` has 2 hundreds, so it is largest.
Art hook Drop each number as a dot on a 0–250 number line; when placed correctly they climb left-to-right, and the close pair 190/199 sit almost touching, showing how nearby numbers cluster.
-
Fill in the skip-count by 10s: `30, 40, __, __, 70, __`.
Answer
`50, 60, 80`. Add 10 each hop; only the tens digit changes.
Art hook A number line with big 10-sized hop arcs; the ones digit stays 0 the whole way, so every landing point sits in a tidy vertical column on a hundred board.
-
Ravi counts by 5s and writes: `5, 10, 15, 25, 30`. He made one mistake — spot it and fix it.
Answer
He skipped `20`. Between `15` and `25` the gap is 10, not 5. The correct count is `5, 10, 15, 20, 25, 30`.
Art hook Draw each written number as a hop on a number line; a wrong-sized hop flashes red because its arc is a different width from the others — the mistake is literally a bigger jump.
-
Start at `12` and skip-count by 3s four more times. What numbers do you say?
Answer
`15, 18, 21, 24`. Keep adding 3: `12→15→18→21→24`.
Art hook Place dots on a circle of 30 positions and connect every 3rd dot; the chord pattern draws a repeating triangle-like star as the count wraps around.
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A necklace has beads in a repeating pattern of 5. If there are 7 groups of beads, how many beads are there? Skip-count to find out.
Answer
Skip-count by 5s seven times: `5, 10, 15, 20, 25, 30, 35`. There are `35` beads (and this is `7 × 5`).
Art hook Draw a circular necklace and add beads 5 at a time in a new colour per group; a running total updates each group — a skip-count bracelet that is also 7 × 5 made visible, in the dot-multiplier spirit.
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Reasoning: Mia says "when I skip-count by 10s, only the tens digit ever changes." Try `10, 20, 30... 90, 100`. Is she always right?
Answer
She is right up to `90`, but at `100` a hundreds digit appears and the tens go back to `0`: `90 → 100`. So counting by 10s across a hundred changes more than just the tens digit.
Art hook An odometer where the tens wheel spins each hop; watch the moment it rolls from 90 to 100 and the hundreds wheel wakes up — the exception to Mia's rule shown as a gear turning over.
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Open-ended: pick a start number and a step (2, 3, 5 or 10) and write down six numbers of your count. Then tell a friend the rule so they can continue it.
Answer
Any correct constant-step sequence works, e.g. start 7, step 5: `7, 12, 17, 22, 27, 32` — rule 'add 5 each time'. Success = every gap is equal and the child can state the step.
Art hook A 'pattern maker': the child sets start and step with sliders and Canvas draws the count as evenly spaced glowing dots on a line; equal spacing confirms a valid skip-count, and changing the step re-spaces every dot at once.