Addition Using Objects and Pictures
Before working with written numbers, it helps enormously to understand addition using physical objects and pictures. This concrete-pictorial approach builds a genuinely deep understanding that supports all future mathematics.
Concrete (Physical Objects)
Concrete learning means using real physical items — counters, cubes, coins, fingers, stones — to model addition. You literally put two groups together and count the total.
Pictorial (Drawn Representations)
Once physical objects feel natural, you move to drawing pictures: dots, tally marks, simple shapes, or bar models. The drawing represents the objects without needing to use them physically.
The Bar Model
The bar model is a rectangular diagram used to represent addition. A long bar shows the total; two shorter bars inside show the two parts.
| Bar Model for 7 + 5 = 12 | |
|---|---|
| 7 | 5 |
| 12 (total) | |
Ten Frames
A ten frame is a 2×5 grid. You fill in circles to show a number, making it easy to see how close any number is to ten.
To show 6 + 4: fill 6 circles in one frame. Show the 4 in a second frame. Together they fill exactly 10. This is the visual proof that 6 + 4 = 10.
Why Concrete-Pictorial Matters
Research consistently shows that children (and adults) who understand the meaning behind arithmetic operations make fewer errors and adapt more easily to new mathematical ideas. Using objects and pictures before abstract symbols builds that understanding.
Key Takeaways
- Concrete: use real objects. Pictorial: draw what you'd use. Abstract: write numbers and symbols.
- The bar model shows the part-part-whole relationship in addition.
- Ten frames help link addition to place value and making tens.
- Always understand the concept concretely before working abstractly.
Practice Questions
- Draw dots to show 4 + 6 and write the answer.
- Draw a bar model for 9 + 7 = 16.
- Use a ten frame to show that 8 + 2 = 10.
- A child has 5 red bricks and 8 blue bricks. Draw a picture to find the total.
- Why is it useful to start with objects before writing maths symbols?