Counting in 6s

Skip counting in6s,7s,9s,25s and1,000s for ages8–9 uses equal groups and number patterns. Build6-jumps from two3-jumps,7-jumps from5+2,25s from four25-unit parts making100, and1,000s on a line through zero. For9,18,…,90 the digits sum to9 and the tens-up/ones-down pattern is visible; it does not extend unchanged to99, whose digits sum to18. Use patterns as checks within their stated range.

• Counting in 7s (and 6s/9s) as pure rote with no structural anchor, so a single slip cannot be repaired and the count derails.
• Missing the 9s pattern and treating each step as '+10 then −1' incorrectly, e.g. writing 9, 18, 27, 37 by adding 10 and forgetting the −1.
• Confusing adjacent tables (drifting between 6s and 8s, or 7s and 9s) because the steps feel similar and no pattern flags the error.
• Mishandling 25s past 100 (25, 50, 75, 100, 125 becoming …100, 105) by reverting to a smaller or rounder step at the hundred.
• Counting in 1,000s but stalling or reversing sign incorrectly when crossing 0 into negatives (…1000, 0, then '1000' again instead of −1000).

• Hundred square with the 9s shaded to reveal the diagonal and the digit-sum-9 pattern (and 6s to show doubled 3s)
• Aligned number lines pairing 3s with 6s (doubling) and 5s+2s composing 7s
• Equal groups / arrays for 6, 7, 9 linking each count to its multiplication table
• Money and clock models for 25s (four quarters = 100, quarter-hours) and an extended number line through 0 for 1,000s and negatives

• Lead with structure, not brute rote: teach 6s as doubled 3s, and surface the 9s pattern explicitly (each step the tens digit rises by one and the ones digit falls by one, so the digits always sum to 9) so children have a self-check when a count wobbles.
• Give the 7s the most rehearsal because they carry the weakest visible pattern — build them from known 5s and 2s (7 = 5 + 2) and from the array, and interleave them with already-secure counts rather than drilling in isolation.
• Anchor 25s in quarters and money — four 25s make 100, 25p pieces, quarter-hours — so 25, 50, 75, 100 is felt as building whole hundreds from quarters rather than a memorised list.
• Connect every count to its times table and to equal groups/arrays so counting in 6s, 7s and 9s is the fluency route into the ×6, ×7 and ×9 facts, not a parallel skill.
• Teach 1,000s alongside 1,000-more/less and backward counting through 0 into negatives, using a number line that extends past 0 so the place-value step and the negative extension are seen on one continuous track.