# Number Path

## What is a number path?

A number path is a visual tool to aid children when learning numeracy. It is similar to a number line, but uses boxes instead of lines or ticks. This is a more effective learning tool for younger learners because boxes are easier to count than lengths on a line.

## The difference between a number line and a number path

Number lines are an excellent tool for helping children understand the basic principles of numeracy:

- cardinality (one number follows another)
- addition (by using their finger or pencil to ‘jump’ to the right along the line)
- subtraction (by using their finger or pencil to ‘jump’ to the left along the line).

When children are introduced to the number line, the distance between zero and one is called ‘one unit length’. They are expected to understand that they are counting the distance between two ticks, not the ticks themselves.

The number path is the exact same concept but uses a different representational model. Simply put, it uses blocks instead of lengths. Rather than counting a unit of length, learners count 2-dimensional objects along a row.

## Why are blocks better for younger learners?

Counting a link or a length on a number line is actually quite an abstract concept. Younger learners are told to count the ‘hops’ along the line, but they can tend to focus on the tick itself rather than the line length. The tick gives them an actual thing to count.

This confusion – am I counting the hop or the tick? – means the child may not know which number they have landed on.

A child may start by hopping along the lengths, but then switch to counting ticks. Or if they count the ticks and start from zero, their answer will be out by one. Additionally, a number line which goes from zero to ten has ten links, but has eleven ticks. When a child is introduced to a number line before they have properly understood number representation, it can be very confusing.

That is why a number path can help to prevent counting errors while still introducing the key concepts of numeracy. Counting a bounded object, even a representational one, is much easier for young minds to understand.

A number path is made up of discrete objects along a row or path. There is no room for confusion. On each hop, the learner lands on a block.

## Using a number path in numeracy

A number path can be used in the exact same way as a number line to understand basic numeracy concepts.

One of the first key skills young learners need to grasp is the cardinality of numbers. This means knowing that the number three is equal to the first three blocks, not just the block labelled “3”.

The number path is a way to help learners move from the count word reference (the third block equals three) to the cardinal word reference (the first three blocks equal three).

It is more concrete to circle the first three blocks and indicate that those equal three, rather than trying to demonstrate on a line which uses length.

## A natural stepping stone

Children are usually introduced to numeracy through concrete counting games:

“Here is one doll. Here are two dolls.”

They can see the one doll, the two dolls. They may also use wooden blocks, math cubes or Cuisenaire rods.

Number paths are the next logical step after (or simultaneous with) concrete counting. A number path is made up of discrete objects, just like in the real world, that children can count along with.

Moving from a concrete to a representational model is a big step for a young learner. The number path is a natural stepping stone to help them along their numeracy path.