Teaching flexible maths strategies through hands-on learning
In episode three of the AAMT x We Support Hands-On Learning video series, Allan Dougan and Professor Catherine Attard dig into addition. And as with counting and number lines, it turns out there’s a lot more going on beneath the surface than you might expect.
Why addition strategies matter
“There is a lot to consider when children are first learning to add,” Catherine says. Addition isn’t just about getting the right answer, it’s about building mental flexibility, developing reasoning and understanding that numbers are made up of parts that can be combined and rearranged in all sorts of ways.
The goal is to give children time and space to explore those relationships through concrete materials and hands-on reasoning, before moving towards abstract algorithms.
Understanding addition and number relationships
A key concept underpinning early addition is the part-part-whole idea – the understanding that any number is made up of parts, and that those parts can look different every time. Seven can be five and two. It can also be three and four. Or six and one. Same whole, different parts.
This is also where the equals sign comes in. Many children come to understand = as meaning “the answer goes here.” But what it actually means is sameness. Equality. Three plus four is the same as four plus three. That’s the commutative property of addition, and establishing it early through play and physical materials, not just symbolic notation, makes a real difference down the track.
Another concept worth establishing early is number bonds (previously called “friends of ten,” though the updated language allows children to think beyond ten and explore part-part-whole relationships more broadly). Strong fluency in number bonds to ten is, as Catherine says, “the foundation of so much of the algebraic thinking that’s developed later.”
Hands-on maths: Exploring addition with materials
Allan and Catherine work through several hands-on resources in this episode:
Two-colour counters are a great starting point. Take ten counters, throw them on the table, and see what combinations come up. Each throw is a different way of seeing ten, and over time children begin to recognise those combinations without having to count every one. Alongside this, you start to see whether a child counts every object from one, or whether they can recognise a group and count on from there. That tells you a lot about where they are.
Ten frames are another powerful tool for building number sense and reinforcing those bonds to ten. When a child can look at a ten frame with seven dots and immediately know that three are missing (without counting) they’re subitising and demonstrating fluency with number bonds at the same time.
MAB (Base Ten) blocks come into play as children begin to move from concrete to more abstract thinking. One concept that trips many children up at this stage is understanding that ten individual units and one “long” (a ten-block) represent the same quantity.
Teacher takeaway: Ideas for your classroom
A few key things to take away from this episode:
- Give children time to explore relationships before moving to abstract symbols or formal algorithms. This is where the real understanding is built
- Don’t always start from one. Encourage children to recognise a quantity and count on from there
- Remember what the equals sign means – equality, not just “the answer.” Build this understanding early and explicitly
- Use number bonds to ten as a foundation. Fluency here underpins so much of what comes later, including algebraic and multiplicative thinking
- Watch the language you use, and make sure children are exposed to all the different words that mean addition
To wrap it up in one sentence: addition is about relationships, not rules. Don’t rush the algorithm.