Counting Hundredths

---

Overview

Age group: Year 4
Duration: 60 minutes
Class size: 30 students
Curriculum link:

• Mathematics Program of Study (Number - fractions and decimals) - Key Stage 2 National Curriculum England
• “Recognise and write decimal equivalents of any number of hundredths,” and “Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.”
• Aligned with White Rose Maths – Summer Block 3 (Decimals) focusing on hundredths.

---

Learning Objectives

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

• Count forwards and backwards in hundredths using both fractions and decimals.
• Understand the relationship between hundredths as fractions and decimals (e.g., 15/100 = 0.15).
• Represent hundredths with correct notation and equivalence.
• Explain and justify their counting strategy clearly using mathematical language.

---

Success Criteria

Pupils will:

• Successfully count in hundredths forwards and backwards from any number.
• Correctly write hundredths as fractions and decimals.
• Explain their reasoning when converting between fractions and decimals in hundredths.
• Demonstrate understanding by completing a structured example independently.

---

Resources

• Whiteboard and markers
• Number line (0 to 1, marked in hundredths)
• Individual mini whiteboards and pens
• Printed worksheet with fraction-decimal pairs and blanks
• Visual aids showing grids of 100 squares shaded to represent hundredths

---

Lesson Structure

1. Introduction (10 minutes)

Engaging Hook:
“Imagine you have 100 tiny pieces of chocolate. If you eat 1 piece, that’s one hundredth of the chocolate gone! How would you write that as a fraction? How would you write it as a decimal?”

Display a 10x10 grid to visually represent hundredths. Shade 15 squares, write “15/100” and “0.15”.

Key Questioning:

• What does the denominator 100 tell us about these fractions? (Understanding)
• How is the decimal 0.15 connected to the fraction 15/100? (Understanding)
• If I shaded 23 squares, what fraction and decimal would that be? (Applying)

Interactive activity:
Model counting up in hundredths on the number line from 0.00 to 0.10 (0/100 to 10/100) pointing out decimal and fractional forms aloud.

---

2. Teaching and Modelling (20 minutes)

Explicit modelling:

Model writing:

• "Start here at 0/100 or 0.00."
• "Now add one hundredth: 1/100 or 0.01"
• Continue through to 15/100 or 0.15 with reasoning for each step.

Example to copy into books:

Fraction	Decimal	Explained Reasoning
5/100	0.05	Five parts out of hundred, decimal moves two places left of the decimal point.
12/100	0.12	Twelve hundredths means twelve parts out of hundred, decimal is 0.12.
30/100	0.30	Thirty hundredths is the same as 3/10, decimal form 0.30 shows this easily.

---

Targeted Whole Class Questions (incorporating AfL)

• Remembering: What is one hundredth written as a decimal?
• Understanding: Why does the fraction 23/100 equal 0.23? Can you explain this relationship?
• Applying: If I start at 0.70 and count on 4 hundredths, what decimal am I at? Explain your thinking.
• Analysing: How are tenths and hundredths connected when counting on the number line?
• Evaluating: Which is greater: 53/100 or 0.5? How do you justify your answer?
• Creating: Can you write a sequence of five numbers counting backwards in hundredths from 1.00? How do you know your decimal equivalents are correct?

AfL points:

• Use mini whiteboards for pupils’ instant responses.
• Note misconceptions seen in responses.
• Encourage peer discussion for reasoning.

---

3. Guided Practice (15 minutes)

Children complete worksheet activities:

• Count forwards/backwards in hundredths starting from various decimals (e.g., 0.27 up to 0.37).
• Match or write the equivalent decimal for given hundredths fractions and vice versa.
• Identify mistakes in sample answers and explain why errors are incorrect (focusing on common misconceptions).

---

4. Common Misconceptions & Difficulties

• Confusing hundredths with tenths (e.g., thinking 0.1 = 1/100).
• Misplacing the decimal point; writing 0.3 instead of 0.03 for 3/100.
• Thinking the numerator always represents tenths instead of hundredths depending on the denominator.
• Counting in steps of 0.1 when asked to count in 0.01 (hundredths).
• Challenges in visualising hundredths on a number line or grid.

Strategies:

• Reiterate decimal place values with visual aids.
• Model number line alongside fraction and decimal notation explicitly.
• Deliberately check pupils’ decimal placement in their writing.

---

5. Plenary (10 minutes)

Game & Reflect:
Play “Decimal Detective” — say a decimal aloud (e.g. 0.14), pupils hold up mini whiteboards with equivalent fraction or vice versa. Pupils explain their reasoning aloud.

Summary Discussion:

• What did you find easiest or hardest about counting in hundredths today?
• How does understanding hundredths help you in real life?

Final pivotal question:
If someone says “0.1 is the same as one hundredth,” how would you politely correct and explain why?

---

Additional Notes

• Ensure language is clear and consistent with White Rose Maths terminology (e.g., “hundredths”, “decimal equivalents”).
• Cross-reference pupils' work with National Curriculum attainment targets for Year 4 fractions and decimals.
• Use regular AfL throughout to adapt questioning and scaffolding as required.

---

This approach balances concrete visual modelling, reasoning-rich questioning, and scaffolded practice to deeply embed the concept of counting in hundredths as fractions and decimals for Year 4 students, aligned tightly with the National Curriculum England and White Rose guidance.