Rewarding Tuition · Real, Repeatable, Relevant
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Rewarding Tuition · 01/06

Start here

You already know enough to help.

This isn't about knowing more maths. It's about knowing what's worth doing with the ten minutes you've got.

Rachael Ward
Hi, I'm Rachael. I've spent ten years teaching, most recently as Head of Year 4 at an independent prep school, and I now run Rewarding Tuition, an online maths programme for Year 3 and Year 4 children.

If you've opened this, you already want to help. That's not what you're short on.

What you're short on is knowing what's worth doing, and trusting yourself enough to do it.

Here's what I want you to know before we go any further: you don't need to relearn how they teach maths now. You need one way of deciding what's worth ten minutes of your evening, and permission to trust your own judgement once you've got it.

Tick whatever's true for you right now:

Whichever you ticked, you're not the only one. I don't think I've met a parent who hasn't felt at least one of these. None of them needed to know more maths. They needed a filter.

Rewarding Tuition · 02/06

Translate the new maths

Translate the new maths

You already recognise more of this than you think.

The methods look different to how you learned them. That's not a gap in you. The national curriculum for primary maths had its last big rewrite in 2014, which makes it twelve years old now, and if your child is in Year 3 or 4, you were at primary school considerably longer ago than that yourself. Tick whatever you already recognise in each group below.

Remember, if you ticked more than zero, you're translating and not starting from scratch :)

Rewarding Tuition · 03/06

The filter

The filter

Two questions to ask yourself, in this order, before you use any maths resource, including what you already own.

Step one: where does this need to start? Concrete, pictorial, or abstract, always in that order, never the other way round.

Concrete

Real objects your child can touch and move: actual sweets, actual coins, actual counters.

Pictorial

A drawing or picture that stands in for those objects: a bar, an array, a quick sketch.

Abstract

Numbers and symbols alone, on a page, with nothing to picture.

Most resources jump straight to abstract, because that's what fits on a worksheet. That's usually why kitchen-table practice turns into a fight: a child's been handed the last step before they've had the first two.

Step two: once you know the stage, ask three questions about what you're about to do at that stage.

RealIs this something my child can picture or touch, not just a number on a page?
RepeatableCan we do this in ten to twenty minutes, more than once, without it becoming an overwhelming event?
RelevantDoes this match what's actually being taught in their class this term?

Try it now, on something you already own

Rewarding Tuition · 04/06

The filter in action

The filter in action

Not new teaching. The same two questions, applied to three things parents ask about most.

Fractions

Fractions

Fractions trip children up because they usually meet them as abstract first, two numbers stacked on a page with nothing to picture. Once a fraction is something they can see or hold, the numbers stop being strange.

Concrete: an actual pizza, actual sweets, an actual four-pack of yoghurts, split out loud. Pictorial: draw the pizza as a circle and shade the slices you're talking about. Only once that's landed, put the numbers on the page.

By Year 3, children are finding fractions of amounts and spotting that fractions can be equivalent. By Year 4, they're finding fractions of larger amounts and starting to connect them to decimals.

Run it through the filter: real (an actual pizza, not a worksheet pizza), repeatable (two minutes at tea time, not a Sunday project), relevant (ask what fractions work has come home this week, then ask how they got the answer, not just whether it's right).

If your child says "I can't do it," that's not a sign something's wrong. Most children find fractions hard at first. Naming that out loud does more than reassurance does.

Multiplication

Multiplication

Multiplication gets treated as something to memorise, and that's usually where it goes wrong. A child who's learned 7 x 8 = 56 without a picture behind it loses it under pressure. A child who's seen it as groups can work it out even when they've forgotten.

Concrete: actual eggs in a box, actual wheels on cars in the car park. Pictorial: an array, drawn as dots in rows and columns. Abstract: the times table fact itself, once the other two have landed.

By the end of Year 4, children are expected to know every times table up to 12 x 12. That's the multiplication tables check, the MTC: 25 questions, 6 seconds each. Worth knowing about in September, not finding out in May.

Run it through the filter: real (things you can actually count, not just numbers), repeatable (five questions in the car, little and often, not a long session), relevant (check which table their class is currently focused on, and use that one rather than guessing).

If your child says "I'm rubbish at times tables," treat that as a confidence issue first. Ending on a table they already know well does more than another five minutes on the one they're stuck on.

Division

Division

Division is where children who are otherwise doing fine start to wobble, because it's the first time the answer doesn't always come out even. A remainder feels like a wrong answer, when it's actually the right one.

Concrete: actually sharing sweets between friends, with one left over. Pictorial: drawing the groups and circling what's left. Abstract: the written method, once sharing and grouping both make sense.

By Year 3, children are dividing two-digit numbers by a single digit and starting to understand remainders. By Year 4, they're using more formal written methods and applying remainders to real situations, not just leaving the number on the page.

Run it through the filter: real (23 sweets, not 23 as a number), repeatable (once a week, thirty seconds, sharing something out loud and asking what happens to what's left), relevant (ask your child to explain what the remainder means in that specific question, not just what the number is).

If they say "there's a bit left over and I don't know what to do with it," that's not them failing. That's the actual hard part of division, and it's worth saying so.

Rewarding Tuition · 05/06

Keep this one visible

What to do in the moment

Not for reading now. For reading when it's actually happening.

When your child says "I can't do it":
Don't say: "Yes you can, keep trying."
Say: "This bit is hard for lots of people. Show me what you can do first."
When your child says "I'm rubbish at maths":
Don't say: "No you're not."
Say: "You're finding this bit tricky at the moment but I want you to go step by step and think about what you do know."
When you feel the ten minutes turning into a battle:
Stop. Ending on something they can do is worth more than finishing the worksheet.
When you don't know if you're helping or making it worse:
You're not. Showing up with an open mind, ten minutes of your time and no pressure on your child is a massive help.
Rewarding Tuition · 06/06

Keep this page

Your filter, in one place

Keep this page after everything else has been read once.

  • Concrete, then pictorial, then abstract, always in that order.
  • Real, repeatable, relevant, always about the specific thing in front of you, not the topic in general.

Maths sticks in a child's head best when it is made real, repeatable and relevant. That's the whole method. It works on fractions, multiplication and division because it works on anything. Whatever comes home next, run it through the same two questions.

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Rachael x