Percentage, fractions and decimals 1 / 10

We are learning to read, write, compare and convert between percentages, fractions and decimals — and connect 10%, 25% and 50% to their fraction and decimal forms on a number line.

I will be successful when I can…

  • explain that per cent means "out of 100"
  • write the same amount as a fraction, a decimal AND a percentage
  • place all three forms on the same point of a number line
  • compare mixed values by converting them to one form
  • explain why 50% off means half price — and why the size of the whole matters

Mini whiteboards ready!

Equivalent fractions (last lesson!)

  • Rename 1/2 as hundredths.
  • Rename 1/4 as hundredths.

Decimal place value

  • In 0.25 — what does the 2 mean? The 5?
  • Say 0.7 as tenths. Now as hundredths.

Percentages, fractions and decimals are THREE NAMES for the SAME AMOUNT.

Per cent comes from Latin: per centum — "for every hundred". The % symbol shows a ratio out of 100.

So 25% is secretly the fraction 25/100… and 25 hundredths is exactly what the decimal 0.25 says.

Every square is one hundredth: 1/100 = 0.01 = 1%.

25 out of 100 shaded fraction: 25/100 = 1/4 decimal: 0.25 percentage: 25% Three names. One amount.
The hundred grid is the bridge between all three notations.

Quick check on whiteboards: 50 squares shaded — write it three ways.

All three labels sit on the same point — the notation changes, the position doesn't.

0 1/10 10% 0.1 1/4 25% 0.25 1/2 50% 0.5 3/4 75% 0.75 1 whole 100% 1.0 fractions in blue • percentages in red • decimals in green — same points!
The benchmark family every Year 6 student should know by heart.

SAY IT AS HUNDREDTHS → WRITE ALL THREE → CHECK ON THE LINE

Same $40 jumper, three tags: 10% off, 25% off, 50% off. Which do you grab?

  • 10% off = 1/10 off the price
  • 25% off = 1/4 off the price
  • 50% off = 1/2 off — half price!

Chant it first: "Say it as hundredths!"

  1. Shade 50 squares — write it three ways
  2. Write 10% as a fraction and a decimal
  3. Convert 3/4 to a percentage
  4. Convert 0.2 to a percentage and a fraction
  5. Order smallest → largest: 0.4,   25%,   1/2

Jai says:   5% = 0.5

Is Jai right? Prove your answer with the hundred grid.

  • Thumbs up if you agree with Jai, thumbs down if you disagree.
  • Convince your partner in 30 seconds — use the words "out of 100".

Independent work — the worksheet

  • Everyone: Sections 1–3
  • Most: Sections 4–5 (comparing & discounts)
  • Challenge: Section 6

Write all three notations for every conversion — a single answer doesn't show the connection. Hundred grids and number line strips stay on desks.

Exit ticket (last 5 minutes)