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Maths · Ages 9–10 · 50 minutes

Decimals and tenths

Children read and write tenths as fractions and decimals, place them on a number line and link them to place value and to hundredths.

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Success criteria

  • I can write tenths as a fraction and a decimal
  • I can place tenths on a number line
  • I can explain what the digit after the decimal point is worth

Key vocabulary

  • decimal
  • decimal point
  • tenth
  • hundredth
  • place value
  • equivalent

You will need

  • metre sticks or 0–1 number lines marked in tenths
  • place-value charts with a tenths column
  • base-ten blocks (a flat as one whole)
  • mini whiteboards

Curriculum links

  • Year 5· England
  • Grade 4· United States
  • Primary 5· Nigeria
  • Class 5· India

Practice sheets

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The lesson at a glance

50 minutes in all. Timings are a guide: follow your class.

  1. Step 1: Starter

    Count in tenths together, holding up a metre stick: "zero point one, zero point two..." up to "one".
    8 minutes

  2. Step 2: Teach

    Hold up a base-ten flat.
    14 minutes

  3. Step 3: Guided practice

    On whiteboards: Write 6/10 as a decimal.
    10 minutes

  4. Step 4: Independent practice

    Use the practice buttons above.
    14 minutes

  5. Step 5: Plenary

    True or false, with a reason: 0.3 = 3/10 0.10 is bigger than 0.9 1.5 is the same as 15 tenths Finish with: "Where would 0.65 go on our number line?"
    4 minutes

  6. Step 6: Assessment for learning

    Look for children who: read 0.6 as "zero point six" and "six tenths"; know ten tenths make one; place decimals between whole numbers on a number line.

  7. Step 7: Differentiation

    Children who need support should build every decimal with base-ten pieces and say it as a fraction first.

  8. Step 8: Common misconceptions

    Thinking 0.10 comes after 0.9.

  9. Step 9: Home link

    Measure things together with a tape measure in metres and say lengths like "1.4 metres, that's one metre and four tenths".

1.Starter

8 minutes

Count in tenths together, holding up a metre stick: "zero point one, zero point two..." up to "one". Ask, "What comes after 0.9?" Many children will say "0.10". Leave that thought in the air; it comes back in the lesson.

Quick check on place value: "In 47, what's the 4 worth? What's the 7 worth?" Then: "What happens to a number when you divide it by 10?"

2.Teach

14 minutes

Hold up a base-ten flat. "Today this is one whole. If I cut it into 10 equal strips, each strip is one tenth." Write 1/10 and 0.1 side by side.

Extend the place-value chart: tens | ones | . | tenths. "The decimal point separates whole numbers from parts of a whole. The first place after the point is tenths."

Show 0.7 with 7 strips. "Seven tenths. As a fraction, 7/10. As a decimal, 0.7. The zero says there are no whole ones."

Step by step

  1. Find the wholeWhat counts as 1?
  2. Count the tenthsHow many of the 10 equal parts?
  3. Write it both ways3/10 = 0.3. For more than one whole, the ones go before the point: 1 and 4 tenths is 1.4.

Back to the starter. "After 0.9 comes ten tenths. Ten tenths make one whole, so it's 1.0, not 0.10." Show 10 strips making a flat.

Then the link to hundredths and percent: "If I cut each strip into 10 again, the whole has 100 small squares. 3 strips is 30 squares: 3/10 = 30/100. Per cent means out of 100, so 0.3 is 30%."

The rest of the plan

Guided and independent practice, the plenary, assessment for learning, differentiation, common misconceptions and the home link are free with a Crayonbird account.

  1. Guided practice10 minutes
  2. Independent practice14 minutes
  3. Plenary4 minutes
  4. Assessment for learning
  5. Differentiation
  6. Common misconceptions
  7. Home link
See the whole plan, free

Learning Wiki

Equivalent fractions

Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.

Fractions

A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.

Perimeter

Perimeter is the total distance all the way around the outside of a flat shape. For a rectangle 5 cm long and 3 cm wide, it is 5 + 3 + 5 + 3 = 16 cm.

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