Chapter 1 · Number and language

What does a number
tell us?

A number expresses a quantity or mathematical value. We can show the same value with objects, words, written symbols or beads. Let us begin with five.

Optional read-aloud uses your browser’s voice.

Five objects

five

A spoken or written name

A written numeral

Five unit beads

The bead illustration shows a count, not the complete physical frame.

Question

They look different. What is the same?

Tell someone your idea, or think it through quietly. What does each representation describe?

Think

Could you show five in another way—using your fingers, a drawing or a different word?

A small cue

Look beyond the shape of the marks. Count the quantity represented by each example.

Read the explanation

Five objects, the word “five”, the numeral 5 and five active unit beads can all represent the same value. The representation changes; the quantity remains five.

From symbols to digits

A symbol is a mark with an agreed meaning. Decimal notation uses ten digit symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

A digit’s position tells us the value it contributes to a number.

One digit in three different places
Numeral	Meaning
5	Five units
50	Five tens and zero units
0.5	Five tenths and zero whole units

Question

What changes in 5, 50 and 0.5?

The digit 5 appears in all three. Explain the difference using units, tens and tenths.

A hint about position

The count is five in each case. Ask: five of what? Five units, five tens or five tenths?

Connect the idea to beads

One bead represents one unit of its rod’s place. Five active beads on a units rod represent 5; on a tens rod they represent 50; on a tenths rod they represent 0.5. Bead count tells us how many; rod position tells us the value of each bead.

Try it

Five beads on the tens rod

Each bead represents one ten. What value do five active beads represent?

Choose an answer when you are ready.

Reflect

What must you know before reading a bead?

Could counting alone tell you its value? Explain why the rod label matters.

For teachers and parents

Invite the learner to explain in their own words. If they say “the zero moved”, ask what the digit now represents. Accept drawings, objects and spoken explanations as ways to explore the idea.