Making Maths Meaningful Every Day: Time, Tools and Trajectories
Why it matters
The evidence is unequivocal: early maths is one of the strongest predictors of later academic success (Duncan et al., 2007). But early years provision is not about rushing children into worksheets — it’s about purposeful daily exposure, hands-on tools, and teaching that builds step-by-step on children’s developmental progressions.
In this post, we’ll explore three research-backed ways to strengthen everyday practice:
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Dedicate time for maths each day and integrate it into daily routines.
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Use manipulatives and varied representations to make abstract concepts visible.
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Build on children’s existing knowledge using developmental progressions and counting principles.
1. Dedicate Time for Maths Each Day — and Weave It Through Routines
Think of maths as something children live every day, not just a 20-minute slot after phonics. The research is clear: daily maths time builds fluency (Frye et al., 2013; EEF, 2020). Disadvantaged children, in particular, make the most progress when given regular, structured opportunities (Ramani & Siegler, 2011).
How this looks in practice:
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Morning maths moments: During register, count how many children are present and compare with yesterday. Predict: “If three more friends arrive, how many will we have?”
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Snack time maths: Share fruit fairly. Ask, “We have 8 bananas and 5 children — will there be leftovers?” This prompts one-to-one correspondence, simple subtraction, and problem-solving.
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Outdoor maths: Use a hopscotch number line. Children “count on” as they jump. Or collect sticks and compare lengths — bigger/smaller, longer/shorter.
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Game time: Board games like Snakes and Ladders encourage “counting on” and number recognition. Siegler and Ramani found such games accelerate number development for children with less prior knowledge.
👉 The golden rule? Make it daily, playful, and purposeful. Maths doesn’t need a special corner — it’s everywhere.
2. Use Manipulatives and Representations to Make the Invisible Visible
Children learn best when they can see and touch maths. Manipulatives (cubes, counters, ten-frames) are more than classroom clutter — they are bridges between concrete experience and abstract ideas. A major meta-analysis found manipulatives improve learning, especially long-term retention (Carbonneau et al., 2013).
How this looks in practice:
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Counting with meaning: Give children 10 counters. Say, “Show me 5.” They place counters, then draw 5 circles, then write the numeral. Concrete → pictorial → abstract (CPA).
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Ten-frames for number sense: Put 7 counters on a frame. Ask: “How many spaces are empty? If we add 2 more, what happens?” Patterns become visible (“5 and 2 makes 7”).
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Walking the number line: Lay a floor number line. A child stands on 6 and jumps forward 3. “Where did you land?” Record together: 6 + 3 = 9.
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Teacher modelling: Narrate your thinking: “I’m putting 2 counters here and 3 here. Together, that makes 5.” Children see the link between action and idea.
👉 The key is explicit connections. Manipulatives alone don’t “teach” — but when adults model, question, and guide, they unlock understanding.
3. Build on Children’s Existing Knowledge: Progressions and Principles
Children don’t all learn numbers at the same pace, but they do follow predictable progressions (Clements & Sarama, 2014). If we skip stages, understanding becomes shaky. That’s where counting principles come in (Gelman & Gallistel, 1978):
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One-to-one – each object gets one number word.
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Stable order – numbers are always in the same order.
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Cardinality – the last number said is the total.
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Abstraction – anything can be counted (toys, claps, jumps).
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Order-irrelevance – objects can be counted in any order.
How this looks in practice:
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One-to-one correspondence: Give a child cups to hand out at snack. Do they double-count or skip? Scaffold as needed.
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Cardinality check: After counting 7 cars, ask, “So how many cars are there?” If the child recounts, they haven’t yet grasped cardinality.
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Stable order: Sing counting rhymes and gently correct errors (“It goes 6, then 7, then 8”).
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Order-irrelevance: Count a pile, rearrange it, and count again. Ask, “Did the number change?”
👉 Keep an observation grid to note which principles each child demonstrates. Tailor small-group activities to the “next step.” A child secure with rote counting but shaky on one-to-one may need more hands-on tasks, not worksheets.
Observation Grid
| Counting Principle | What to Look For | Prompt Questions (Teacher → Child) | Example Tasks / Activities |
|---|---|---|---|
| 1. One-to-One Correspondence (Each object gets one number word) | Child gives exactly one count per object (no skipping or double-counting) | “Did you give one cup to each friend?”“Can you check if anyone has two?” | Snack time: Hand out one cup per child.Lining up: Place one foot on each step while counting. |
| 2. Stable Order (Number words said in the same order each time) | Child uses a consistent number sequence (1, 2, 3, …) | “What comes after 5?”“Can you count from 3 up to 8?” | Number rhymes: “One, Two, Buckle My Shoe.”Number line jump: Step along floor numbers in order. |
| 3. Cardinality (The last number said tells “how many”) | After counting, child recognises the total without recounting | “So how many are there altogether?”“If we counted again, would the number change?” | Car counting: Count 7 toy cars, then ask total.Dice game: Roll, count dots, then say the total. |
| 4. Abstraction (Anything can be counted: toys, sounds, actions) | Child applies counting to different types of objects/events | “Can we count the jumps/claps?”“What else could we count in the classroom?” | Clap and count: Clap 5 times together.Mixed objects: Count pens, chairs, and blocks together. |
| 5. Order Irrelevance (Objects can be counted in any order) | Child understands rearranging doesn’t change the total | “If we move the blocks around, will there still be 6?”“Does it matter if we start counting from this one or that one?” | Block piles: Count 5 blocks, rearrange, recount.Snack bowls: Mix order of fruit pieces, recount. |
Pulling It All Together
The strongest early maths classrooms do three things every single day:
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Make time for maths. Not as an add-on, but as a natural part of daily life.
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Use tools and representations. Make abstract ideas visible and accessible.
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Follow the developmental ladder. Start from what children already know, and scaffold the next step.
When combined, these practices don’t just teach numbers — they foster curiosity, reasoning, and confidence, laying a rock-solid foundation for all future learning.
References
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Carbonneau, K. J., Marley, S., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. PDF link
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Clements, D. H., & Sarama, J. (2014). Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed.). Routledge. Learning Trajectories resource
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Duncan, G. J., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. PubMed abstract
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Education Endowment Foundation (2020). Improving Mathematics in the Early Years and Key Stage 1. EEF Guidance Report PDF
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Frye, D., Baroody, A., Burchinal, M., Carver, S., Jordan, N. C., & McDowell, J. (2013). Teaching Math to Young Children: A Practice Guide (NCEE 2014-4005). Washington, DC: IES. Full guide PDF
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Gelman, R., & Gallistel, C. R. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.
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Ramani, G. B., & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between low- and middle-income preschoolers. Journal of Applied Developmental Psychology, 32(3), 146–159. PDF link
