Counting Hundredths Fractions

Year Group

Year 4 (ages 8-9)

Duration

45 minutes

National Curriculum Links

Mathematics: Number – Fractions

• Key Stage 2 Programme of Study (Years 3 and 4):
  • Recognise and write decimal equivalents of any number of tenths or hundredths.
  • Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
  • Understand fractions as numbers and record them visually and numerically.

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Learning Objectives

By the end of this lesson, pupils will be able to:

• Count up and down in hundredths using fractions (e.g., 1/100, 2/100, ...).
• Recognise and represent hundredths as fractions and decimals.
• Use visual fraction models (such as grids or number lines) to support understanding of hundredths.
• Explain their reasoning when ordering or counting fractions in hundredths.

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Success Criteria

Pupils will be successful in this lesson if they can:

• Accurately count forwards and backwards in hundredths using fractions.
• Represent hundredths visually with partitioned grids or number lines.
• Convert between fractions (1/100, 25/100) and decimals (0.01, 0.25).
• Justify their answers when explaining how they counted or ordered hundredths.
• Identify when fractions represent bigger or smaller values and explain why.

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Resources

• Whiteboard and visualiser or projector
• Fraction grids (100 squares) printouts or on-screen
• Number lines divided into hundredths
• Mini whiteboards and pens for pupils
• Lined exercise books
• Place value counters or fraction rods (optional)

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Lesson Structure

Introduction (10 minutes)

1. Engagement Starter (Visual + Questioning)
   Show a 10x10 grid (100 squares), shaded to represent different fractions: 1/100, 25/100, 50/100, 99/100. Ask:

   • “How many squares are shaded?”
   • “What fraction does this represent?”
   • “If I take one square away, how does the fraction change?”
     Use this to introduce counting down in hundredths.

2. Big Question to stimulate reasoning:

   • “If I shade in 0.01 more, how many more squares do I add? And can you explain why it’s called one hundredth?”
   • “How do you think adding or removing one square changes the size of the fraction?”

   Use this to gauge prior understanding and activate thinking about the size and meaning of hundredths.

Whole Class Teaching & Modelling (15 minutes)

3. Explicit Modelling of Counting in Hundredths

   • Use the visualiser or projector to show a 100-square grid.
   • Shade in 1/100, then 2/100, then 3/100… up to 10/100, counting aloud.
   • Show the equivalent decimal each time and ask pupils to repeat it aloud.

4. Counting Down

   • Demonstrate counting backwards from 10/100 to 0/100 in steps of 1/100 using the grid.
   • Model how this looks on a number line labelled in hundredths (from 0 to 1).

5. Copy into Books Example
   Write the following example clearly in pupils’ books for them to copy:

   Count up in hundredths:  
   1/100, 2/100, 3/100, 4/100, 5/100, 6/100, 7/100, 8/100, 9/100, 10/100  
   As decimals:   
   0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10  
   Count down in hundredths:  
   10/100, 9/100, 8/100, 7/100, 6/100, …, 1/100, 0/100
   

6. Targeted whole-class questioning using Bloom’s Taxonomy:

   • Remembering: “What fraction comes after 5/100?”
   • Understanding: “Why does adding 1/100 make the fraction bigger?”
   • Applying: “If you are at 12/100, how many more hundredths do you need to reach 20/100?”
   • Analysing: “Between 25/100 and 30/100, which is closer to 1/3? Why?”
   • Evaluating: “Explain why 50/100 is the same as 1/2.”
   • Creating: “Create your own number line showing hundredths between 0 and 1. Mark 15/100 and 60/100 and explain your choices.”

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AfL (Assessment for Learning) Opportunities

• After modelling counting forward and backward in hundredths, ask pupils to use mini-whiteboards to write the next two hundredths after a given fraction shown on screen. (Instant check of understanding)
• Pupils explain to a partner or the class why the fraction increases or decreases by exactly 1/100 when moving one step on the 100-grid.
• Use targeted questioning and record answers and reasoning in exercise books to review pupil understanding and misconceptions.
• Observe pupils during guided practice and identify pupils struggling to convert fractions to decimals or counting accurately.

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Guided Practice (10 minutes)

• Provide pupils with 100 grids and number lines in their exercise books.
• Ask pupils to:
  1. Count up in hundredths from 13/100 to 23/100, write as fractions and decimals.
  2. Count down from 50/100 to 40/100.
  3. Shade in the corresponding squares on the grid.
• Circulate to question pupils, ensure they explain verbally or in writing how they are counting and why.

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Common Misconceptions & Difficulties

• Confusing hundredths with tenths or mistaking 1/100 and 1/10 due to similar notation.
• Mistaking fractions with different denominators as directly comparable without converting to decimals or equivalent fractions.
• Difficulty visualising 1/100 on a number line or grid because it is a very small unit.
• Counting in steps but losing track of the number of hundredths counted (off-by-one errors).
• Thinking 10/100 is a smaller fraction than 9/100 when comparing fractions.

Address these by ensuring clear visuals, consistent language, and thorough questioning prompting explanation.

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Plenary (10 minutes)

“Explain It To Me” plenary

• Select 3-4 pupils to explain to the class:
  • How we count up and down in hundredths using both fraction and decimals.
  • Why the 100 grid helps understand hundredths.
  • What changes when we add or subtract 1/100.

Final whole-class discussion questions:

• “If I shaded 75/100, what decimal is that? Can you explain how you know?”
• “Why do you think we need to understand hundredths when working with money or measures?”
• “Can you think of a real-life example where knowing hundredths as fractions might help?”

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Additional Notes for Teachers

• This lesson draws on White Rose Maths scheme’s Year 4 fraction and decimal work, specifically Week 4 "Counting in Hundredths" units.
• Carefully scaffold between visual and numerical representations to ensure deep understanding.
• Use paired and talk-partner activities to maximise verbal reasoning and confidence in fraction language.
• Use mini-whiteboards regularly for quick formative assessment (AfL) without putting pressure on written accuracy.
• Emphasise the link between fractions, decimals, and real-world contexts such as money (pence).

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This detailed and engaging lesson plan builds understanding of hundredths as fractions for Year 4 pupils, with a strong foundation in visual models, clear success criteria, reasoning-based questioning, and regular assessment for learning embedded throughout.