Decimal Place Value Mastery

Overview

• Duration: 60 minutes
• Class size: 1 student (Year 6, working at Year 5 level)
• Learning context: 1:1 tuition, supporting a struggling learner
• Focus: Decimal place value, multiplying & dividing decimals by powers of 10, and equivalence of fractions and decimals
• Curriculum links: National Curriculum for England, Mathematics, Years 5 & 6: Number - Decimals and Fractions

---

National Curriculum References

• Y6 Number - Decimals
  • "Read, write, order and compare numbers with up to three decimal places."
  • "Multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places."
• Y6 Number - Fractions (including decimals)
  • "Associate a fraction with division and calculate decimal fraction equivalents (for example, 0.375) for a simple fraction (for example, 3/8)."
• Y5 Number - Decimals (to support student’s current level)
  • "Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents."

---

Learning Objectives

By the end of this session, the student will be able to:

1. Identify the value of each digit in numbers given to three decimal places.
2. Multiply and divide decimals by 10, 100 and 1000, giving answers up to three decimal places.
3. Understand the link between fractions and division, and convert simple fractions to decimal equivalents.
4. Solve SATs-style questions related to these topics with increased confidence.

---

Resources Needed

• Whiteboard and markers or notepad and pen
• Base-10 decimal place value chart (printed or drawn)
• Decimal place value slider strips (visual aids for movement with powers of 10)
• Mini-whiteboard and pen for the student
• Fraction-to-decimal conversion cards (example: 1/2, 3/8, 1/4, 5/10)
• Number cards (digits 0–9)
• Dice or spinner (for game element)
• SATs-style question worksheets (custom-designed for rapid feedback)

---

Lesson Breakdown

Activity 1 – Decimal Place Value Exploration (15 minutes)

Objective: Identify the value of digits up to three decimal places.

Activity details:

• Begin with a visual place value chart displayed (thousands | hundreds | tens | units | tenths | hundredths | thousandths).
• Present various numbers (e.g., 4.375, 23.048, 0.962) verbally and write them on a mini-whiteboard.
• Using the base-10 slider strips, physically move the digits to show where each digit sits in the chart.
• Quiz the student by showing a number and asking, "What is the value of the digit 7 in 4.375?" (Answer: 7 hundredths or 0.07).
• Use number cards and ask the student to build numbers with specific values, e.g., create a number with a 5 in the hundredths place.
• Use “I see, I say” method—student verbalises each digit value aloud.
• Curriculum link: Y6 Number - Decimals (reading and writing decimals).

---

Activity 2 – Multiplying and Dividing by 10, 100 and 1000 (15 minutes)

Objective: Multiply/divide decimals by 10, 100 and 1000, up to 3 decimal places.

Activity details:

• Introduce the concept using the decimal place value slider strips to physically move digits right or left.
• Example: Multiply 4.375 by 10 → slide digits one place to the left (43.75).
• Do the same for division by 10, 100 and 1000.
• Use a hands-on game format: spin/roll a dice to select a power of 10 (10, 100, 1000) and choose to multiply or divide.
• Given a starting decimal, the student uses the slider strips and mini-whiteboard to find the answer.
• Record answers and explain digit movement.
• Highlight place-holder zeros introduced after division.
• Curriculum links: Y6 Number - Decimals (multiplication and division by 10, 100, 1000 with decimals).

---

Activity 3 – Fraction and Decimal Equivalence (15 minutes)

Objective: Associate fractions with division and calculate decimal equivalents for simple fractions.

Activity details:

• Use fraction-to-decimal cards and number line visuals showing fractions and their decimal equivalents.
• Explain how dividing numerator by denominator gives the decimal equivalent, e.g., 3 ÷ 8 = 0.375.
• Work through examples together using a whiteboard:
  • 1/4 = 1 ÷ 4 = 0.25
  • 3/8 = 3 ÷ 8 = 0.375
  • 7/10 = 7 ÷ 10 = 0.7
• Use the hands-on approach: student uses mini-calculator or long division to see the fractions converted.
• Encouraged to verbalise why decimals result from division.
• Create a matching game: match fractions to their decimal cards.
• Curriculum link: Y6 Number - Fractions (associate fractions with division and decimal equivalents).

---

Activity 4 – SATs-Style Question Practice (15 minutes)

Objective: Apply learned skills solving SATs-style questions focused on decimals and fractions.

Activity details:

• Provide 5–7 tailored, scaffolded SATs-style questions concentrating on:
  • Identifying digit values in decimals to 3 places.
  • Multiplying/dividing decimals by 10, 100, 1000 with answers up to 3 decimals.
  • Converting fractions to decimal equivalents by division.
• Questions examples:
  • "What is the value of the 4 in 12.496?"
  • "Divide 5.432 by 100. Write your answer to three decimal places."
  • "Write 3/8 as a decimal."
• Use mini-whiteboard to work through each question together, encouraging thinking aloud.
• Give immediate feedback and strategies for tricky questions.
• After completion, identify areas for further reinforcement.
• Curriculum link: All relevant Y6 objectives relevant to decimals and fractions.

---

Assessment & Feedback

• Continuous formative assessment through questioning during activities.
• Verbal and written feedback focusing on understanding of decimal places and fraction-decimal equivalences.
• End-of-session reflection with student self-assessment: Which activity did they find easiest/hardest and why?
• Record progress against the national curriculum objectives for future sessions.

---

Differentiation & Support Strategies

• Visual aids and hands-on resources to support understanding.
• Use of physical movement of digits ensures kinaesthetic learning.
• Step-by-step modelling followed by guided practice.
• Scaffolded questioning and prompts if student struggles.
• Use of ‘think aloud’ techniques to verbalise reasoning.
• Minimise abstract notation; use concrete representations.

---

Extension Ideas for Future Lessons

• Exploring comparing and ordering decimals beyond three decimal places.
• Converting repeating decimals from fractions.
• Practical problem-solving involving measurements with decimals (e.g., money, length).
• Using real-life contexts for multiplying/dividing decimals by powers of 10.

---

This structured, multisensory approach combined with targeted practice will help the student gain confidence and fluency with decimals and fraction-decimal equivalence in alignment with the National Curriculum requirements for Year 6.