Multiple Strategies, Number Lines & Other Mysteries: Why Maths Looks Different Now?

If you’ve ever muttered “just carry the one!” under your breath, this one’s for you. Today’s strategies might look unfamiliar, but they’re designed to build deeper understanding.

Traditional methods focused on memorisation; modern ones build number sense.

I don’t know about you, but when I reflect on how I learnt maths in primary, what I remember was lots of repetition/memorisation of facts - at school and at home.

A quick story…

When I was in primary, I was ‘good’ at maths. I completed pages and pages of my workbook - red ticks everywhere, and I was great at reciting my multiplication tables. I distinctly remember having competitions in class to see who could rattle off a set of tables the fastest … hello! That was me! But my fact nemesis was 7 x 8. I mixed up the answer often, so mum, being mum, put that fact and its answer on post-it notes, or the equivalent back then, and put them everywhere in the house. I’d open the fridge … and there it was… bathroom, cupboard, inside my shoe … everywhere … and it didn’t take me long to remember the right answer. And off I went to ‘win’ the speed tests again, knowing that I knew them all!

Well, that feeling came crashing down when I went through secondary. I thought I was good at maths, but it turned out that all I really knew were the facts, and the process of how to do things. I didn’t have the understanding of why they worked, so when I needed to build on them … you get the picture!

Today, your child is taught the WHY behind the how so they can apply it in different situations. It’s about understanding beyond the surface. it’s about looking for, noticing and using relationships between and within numbers.

It gives them the confidence to understand, be more flexible and manipulate numbers for their benefit when needed.

So, while you may not adopt the post-it note strategy to help them memorise their multiplication facts, don’t forget to discuss with them WHY 7 x 8 is 56. Let them tell you, draw a picture or make a model. it all helps them represent their thinking which is an important part of their learning journey.

Learning multiple strategies helps kids see how numbers work, not just follow steps.

Imagine you’re a tradie and you only had a screwdriver, but the job required a hammer. You could attempt the job, and you might even get it completed, but it’s not the right tool for the situation, so it will take longer than it should, be frustrating - for everyone - and it’s not likely to fill you with confidence for the next job.

Teaching your child multiple strategies is about building a ‘toolkit’ of strategies so they will always have the right one for the situation.

Having a selection allows them to attempt the problem another way if the strategy they initially chose doesn’t work, or can’t be used in that scenario. It gives them flexibility AND it builds their confidence. It also gives them choice.

Returning to the tradie analogy, imagine being told that you HAD to use the one tool for every job. Not functional and not inspiring!

Also, the strategy one person chooses doesn’t mean it is the strategy of choice for everyone, and ‘making’ them use a strategy they don’t like, find efficient or understand only adds frustration to the situation.

In the classroom, kids will choose a range of strategies, and it is in the discussion of the pros and cons of those choices, that they work out more efficient ways of solving certain problems. It also opens their eyes to other ways of solving problems. They learn that there is no ‘right’ or ‘wrong’ way, just more efficient ways to solve problems.

At home, you could discuss with them their choices, ultimately letting them decide. Talking with them about it afterwards is a great way to help them reflect on and justify their choice and helps them use the required mathematical language.

Win, win!

Number lines, and other manipulatives, support all learners and flexible thinking.

There used to be a real stigma around using something - a number line, blocks, counters, etc - to help with maths once the child started Year 3, and to a degree, there still can be because their use is not understood, but consider this …

Every year, your child builds upon previous concepts, extends concepts and learns new concepts, and as expected there is a structure to that learning.

Officially it’s known as the Concrete–Representational–Abstract (CRA) instructional approach, and it’s widely used in maths to build deep, transferable understanding. Here's how it breaks down:

• Concrete Stage

  • Learners use physical objects (manipulatives like blocks, counters, fraction tiles) to explore mathematical concepts.

  • This stage is tactile and experiential which is ideal for building foundational understanding.

  • Eg: Using base-ten blocks to build the number 126.

• Representational Stage

  • Learners move from physical models to visual representations—drawings, diagrams, tallies, or sketches.

  • This bridges the gap between hands-on experience and abstract thinking.

  • Eg: Drawing a picture of base-ten blocks to represent 126.

• Abstract Stage

  • Learners use numbers and symbols to represent mathematical ideas.

  • This is where formal notation and operations come into play: 126, +, –, ×, ÷.

  • Eg: Solving 126 + 34 using written numerals and standard algorithms.

This progression isn’t always linear. Your child may move back and forth between stages as needed. But it’s a powerful framework for ensuring that maths isn’t just memorised, but truly understood.

And if your child needs to use manipulatives - and they’re not ‘allowed’ - well, let’s not go there. Simple put, if they need them, they should have access to them.

At home, this doesn’t mean rushing out to buy resources, just use what you have. Then ask them to explain their models, drawings or written method to you as this is an important part of their learning.

You’ve got this!

You absolutely have. My takeaway tip today is to talk more with your child about maths.

Instead of muttering “just carry the one!” under your breath, ask: “Can you show me how your teacher taught you?” or “Can you tell me how you worked this out?” It invites conversation, not conflict. it builds curiosity and connection, for both of you.

And if you want to know exactly what your child is learning so you can REALLY hone in on those concepts and strategies that will build their capacity and confidence, then I’m ready to help.

After all, it’s what I do.