Counting On Hundredths

National Curriculum Links

• Mathematics Programme of Study - Year 4
  • Number - Decimals: Recognise and write decimal equivalents of any number of tenths or hundredths (4NPV-01)
  • Number - Fractions: Understand thousandths as fractions and decimal equivalents (4NPV-02)
• White Rose Maths Scheme (Summer Term, Block 4 - Decimals): Counting on in hundredths as part of developing decimal understanding.

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Learning Objectives

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

• LO1: Count forwards (count on) in hundredths from any given decimal number.
• LO2: Recognise the place value of hundredths and relate this to fractional and decimal notation.
• LO3: Explain reasoning when adding hundredths and justify their counting strategy.

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Success Criteria

I can:

• Start from any given decimal number and count forwards in hundredths accurately.
• Read and write decimals to two decimal places.
• Explain how I know I have added the correct amount when counting on in hundredths.
• Use number lines and place value grids to support my counting in hundredths.

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Resources

• Whiteboards and pens for each pupil
• Number lines showing decimals to two decimal places
• Place value grids (tenths and hundredths columns)
• Visual fraction and decimal cards (e.g. 0.01 = 1/100)
• Example worksheets/practice sheets based on White Rose style questions

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Lesson Structure (60 minutes)

1. Introduction & Engagement (10 minutes)

Objective: Hook pupils and activate prior knowledge of decimals and fractions.

• Start with a quick recap quiz on tenths and hundredths orally:
  • “If I have 0.3, what decimal comes next if I count in tenths?”
  • “How do tenths and hundredths relate?”
• Show a number line that marks decimals from 0.00 to 1.00 and model counting in tenths quickly. Then zoom into a section between 0.10 and 0.20 and explain the need to count in smaller steps — hundredths!
• Display a real-life example: “If a car travels 0.45 km and then travels another 0.07 km, where will we be on the decimal number line?”
• Emphasise the idea of adding hundredths and counting on in small steps using a number line and place value grid.

Targeted questioning:

• “Why is 0.07 the same as 7 hundredths?”
• “What do you notice about the digits when we add hundredths?”
• “Can you explain how you would get from 0.45 to 0.52 without using a calculator?”

AfL:

• Use a quick hand signal to check understanding of the terms ‘tenths’ and ‘hundredths’.
• Select 3 pupils randomly to explain tenths vs hundredths aloud (peer and teacher assessment).

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2. Modelling (15 minutes)

Teacher models counting on in hundredths with think-aloud:

• Write: 0.34 on the board. Use a place value grid splitting tenths and hundredths.
• Say: “I want to count on 5 hundredths from 0.34. So I add 0.05.”
• Demonstrate counting on the number line using small jumps of 0.01 until reaching 0.39.
• Emphasise the digits changing: Tenths stay the same (3), hundredths increase from 4 to 9.
• Repeat with a different number, e.g., 0.87 + 0.11. Show need to cross into next tenth (0.98, 0.99, 1.00, 1.01).

Example for pupils to copy:

Start: 0.34  
Count on: + 0.05 (5 hundredths)  
0.34 → 0.35 → 0.36 → 0.37 → 0.38 → 0.39  
So, 0.34 + 0.05 = 0.39  

Targeted whole-class questions:

• “Why do the hundredths digits change but tenths stay the same here?”
• “If adding 11 hundredths to 0.87 results in what number? Can you explain your steps?”
• “What happens when the hundredths go above 9? Why is this important?”

Common misconceptions to address:

• Pupils may think hundredths add only to the hundredths place without carrying over.
• Confusing tenths and hundredths places.
• Adding digits instead of values (e.g. 0.34 + 0.05 = 0.39, not 0.39 by adding 5 to 4 digit-wise).

AfL:

• Pose a counting question, then ask pupils to “stop and write their intermediate steps on whiteboards.”
• Collect whiteboards to check understanding before moving on.
• Select pupils to explain their reasoning to the class.

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3. Guided Practice (20 minutes)

• Provide pupils with a worksheet containing decimal number lines and questions such as:

  • “Start at 0.56, count on 8 hundredths. Where do you land?”
  • “Start at 0.72, add 15 hundredths. Show your steps.”
  • Use place value grids to support as needed.

• Partner talk: Pupils explain their methods to each other using sentence starters like “I know that…” and “The reason I counted like this is …”

Targeted whole-class questions (using Bloom's Taxonomy):

• Understanding: “Explain how adding hundredths affects the decimal number.”
• Applying: “If you start with 0.90 and add 0.15, how can you check your answer is correct without a calculator?”
• Analysing: “Compare adding 10 hundredths and adding 1 tenth. How are the results the same or different?”
• Evaluating: “If someone says ‘0.45 + 0.06 is 0.41’, how would you respond and explain?”

AfL:

• During partner work, circulate and listen for misconceptions or errors.
• Use mini whiteboards to quickly check answers to questions before moving on.
• Ask pupils to justify answers orally before writing final answers.

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4. Independent Practice (10 minutes)

• Pupils complete a quick quiz with decimals and counting on hundredths with varying difficulty.
• Challenge extension: “Start at 0.99, add 0.05. Write the answer and explain what happens to the tenths and hundredths.”

AfL:

• Mark quizzes live, giving instant feedback to pupils spotting misconceptions promptly.

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5. Plenary (5 minutes)

• Use a number line projected on the board starting at a given decimal (e.g., 0.23). Pupils take turns suggesting how many hundredths to add to reach a target number (e.g., 0.30). Ask pupils to justify their counting steps aloud.
• Final reflection: “What helps you when counting on in hundredths? What should you watch out for?”
• Summarise key learning points: clear place value in hundredths, using number lines, remembering to carry over when needed.

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Additional Notes on Misconceptions & Challenges

• Pupils often confuse decimals with whole numbers, especially adding digits instead of decimal values.
• Crossing from hundredths to tenths (carrying over) causes confusion and needs careful visual support.
• Place value understanding in decimals is critical; emphasise digits’ roles in a consistent way.
• Some pupils may incorrectly think 0.07 is less than 0.7 because of the way numbers look.

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WOW Factor / Outside-the-Box Ideas

• Use physical ‘Decimal Steps’ game: number lines taped on the floor; pupils “jump” in hundredths steps.
• Link to real-world contexts: Discuss money (pence as hundredths of a pound) or measurements in m.
• Digital interactive whiteboard apps: Drag and drop decimal cards to build numbers and count on.
• Math talk partners: pupils must explain and challenge each other’s counting strategies, fostering reasoning.

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This plan harnesses strong formative assessment, visual/concrete support, rich questioning, and aligns to the national curriculum and White Rose scheme effectively. It promotes conceptual understanding along with procedural fluency in counting on hundredths.