We often hear parents say, “My child knows their times tables perfectly.” They can chant them, answer rapid-fire questions, and pass their weekly tests.
But there is a big difference between memorisation and understanding.
In schools today, from Year 3 onwards, the curriculum encourages children to use “manipulatives” (physical objects) to understand maths. However, as children get older, these visuals are often taken away too early, replaced by abstract written methods. This leaves a gap in their understanding.
We built our new Multiplication Array Visualiser to fill that gap. Whether your child is just starting to learn their 3 times table, or is preparing for the 11+, this tool demonstrates that multiplication isn’t just about memorising numbers—it’s about understanding patterns.
Why All Primary Children Need This (Not Just for Exams)
Before we talk about exams, we need to talk about the fundamental laws of mathematics. These are concepts that every child is taught in school but often finds confusing when written down as algebra or rules.
Our app makes these laws visible:
1. The Commutative Law (The “Switch”)
This simply means that the order doesn’t matter:
4 × 5 = 5 × 4
In our Free Play mode, a child can swap the Rows and Columns and see instantly that the total number of counters never changes, only the shape does. This builds the confidence to rearrange numbers to make them easier.
2. The Distributive Law (The “Split”)
This is the ability to break a difficult multiplication into two easier ones. For example, if a child struggles with 7 × 6, our Task Mode teaches them to start with 5 × 6 (which is easy: 30) and just add 2 more rows of 6.
30 + 12 = 42
This isn’t just a “trick”; it is the foundation of mental arithmetic and algebra.
The 11+ Superpower: “Working Smart, Not Hard”
For parents looking at the 11+ or entrance exams, this visual understanding is a brilliant way to support your child understand this concept, which later on can help solve some questions we’ve seen many children struggle with. These exams are time-pressured. A student doing long, written multiplication for every question will run out of time. A student who visualises arrays will spot the shortcuts.
Here are two examples of how using our Show Me (Level 2) tool trains the brain for high-level exam success.
Example 1: The “Impossible” Calculation
Question: Calculate (678 × 567) + (322 × 567) without using column multiplication.
The Hard Way: A student relying on rote learning sees two huge sums. They try to work out 678 × 567 on paper (prone to error), then 322 × 567 on paper, and then add them up. This takes 5 minutes.
The Visual Way: A student who has used our Array Visualiser sees this differently. They don’t see numbers; they see “Groups of counters.”
- Imagine a grid. You have 678 rows of 567.
- You add another 322 rows of 567.
- How many rows do you have in total?
678 + 322 = 1000 rows
Now the sum is simple:
1000 × 567 = 567,000
By understanding that they can “add the rows together” before multiplying, the question becomes solvable in 10 seconds.
Example 2: The “Nearest Ten” Strategy
Question: Calculate 29 × 14.
The Hard Way: The student attempts mental column multiplication, trying to hold multiple carry-over numbers in their head. It is stressful and risky.
The Visual Way: In our app’s Task Mode, we practice adding and removing rows. The student visualises that 29 is nearly 30.
- Round up to 30 rows of 14. (3 × 14 = 42) … so 30 × 14 = 420
- But we have 1 row too many. We need to remove one group of 14. 420 – 14 = 406
Answer: 406
Summary
The Multiplication Array Visualiser isn’t just for testing times tables.
- For Year 3/4: It cements the link between “groups of” and the multiplication sign.
- For Year 5/6 & 11+: It trains the brain to spot the distributive law, allowing students to combine and manipulate numbers mentally to solve complex problems in seconds.
Try our newly released Multiplication Array tool to help your child gain conceptual understanding of Distributive Law for multiplication.