Fraction-Decimal Links

Overview

In this lesson, students explore how simple fractions relate to decimal numbers, using models, number lines, and hundred grids. They convert common fractions (halves, quarters, thirds, fifths, tenths) to decimals and explain why the representations match.

Learning intentions

• Students will recognise fractions and decimals as two ways to show the same quantity.
• Students will convert simple fractions with denominators of 2, 4, 5, and 10 into decimals.
• Students will place fractions and decimals on number lines and explain the relationship using models.
• Students will use reasoning to check whether a conversion makes sense.

Success criteria

• I can represent a fraction using a hundred grid or area model and read the matching decimal.
• I can convert halves and quarters and fifths/tenths into decimals accurately.
• I can explain how the model supports my conversion.
• I can check my answers by comparing positions on a number line.

Curriculum links

• Fractions: connect fraction notation to quantities and to equivalent forms.
• Decimals: connect decimal notation to place value, especially tenths and hundredths.
• Number sense: use representations and compare quantities using benchmarks.
• Reasoning and communication: explain and justify mathematical choices using models.

Lesson structure (45 minutes)

1. 3 min – Quick warm-up (fraction talk)

• Display cards with “1/2, 1/4, 3/4, 1/5, 2/5, 7/10”. Students choose which is closest to 0.5 and justify using finger counts or a quick sketch.
• Teacher prompts: “How do you know which one is bigger?”

2. 7 min – Model introduction: hundred grid link

• Show a blank hundred grid. Shade 1/2, 1/4, 1/5, and 1/10 using overlays or prepared diagrams.
• Teacher explains: “A hundred grid has 10 rows of 10 squares. Tenths are one part of 10; hundredths are one part of 100.”
• Students record two examples in their books: the fraction and the decimal read from shaded squares (e.g., 1/2 = 0.5, 1/4 = 0.25, 1/10 = 0.1).

3. 10 min – Teacher-guided conversion practice

• Work through a small set together:
• 1/2 → 0.5
• 1/4 → 0.25
• 1/10 → 0.1
• 2/5 (using tenths/hundredth reasoning) → 0.4
• Teacher uses a “same quantity” statement each time: “Both show the same shaded amount, just named differently.”
• Students practise on mini whiteboards: teacher calls out a fraction; students show the decimal.

4. 10 min – Stations: number line matching

• Set up two stations and rotate after 5 minutes:
• Station A: Number line (0 to 1) with marked tenths and key points; students place fraction/decimal strips (e.g., 0.3, 3/10, 1/5, 0.2, 2/5).
• Station B: Hundred grid conversion; students shade a fraction strip and write the decimal.
• Teacher circulates, checking that students use place value language (tenths/hundredths) and can point to the model when explaining.

5. 7 min – Whole-class “Explain and compare”

• Choose 2–3 student responses (anonymised). Prompt:
• “Which model shows the same amount?”
• “How do you know it’s not another decimal nearby?”
• Emphasise common misconceptions:
• Confusing tenths with hundredths.
• Treating 1/4 as 0.4 instead of 0.25.
• Assuming all fractions have a decimal that terminates easily; for this year level, focus on fractions that align with tenths/hundredths using the model.

6. 8 min – Independent check (exit task)

• Students complete 4 items:
• Shade 1/2 on a hundred grid and write the decimal.
• Convert 1/4 and 3/4 to decimals.
• Convert 1/10 and 2/5 to decimals.
• Place one given pair on a number line: “2/5 and 0.4” (choose the correct location).
• Teacher collects for quick marking.

Resources

• Hundred grids (A4) for each student
• Fraction and decimal strip cards (prepared sets)
• Number line templates from 0 to 1 with tenths marked
• Coloured pencils or shading counters
• Mini whiteboards and markers
• Prepared shaded model slides/printouts (halves, quarters, tenths, fifths)
• Exit task sheet (4 questions) with space for working
• Visual fraction–decimal chart showing key pairs (0.1, 0.25, 0.4, 0.5, 0.75)

Assessment

• Formative observation during mini whiteboard responses and station work, focusing on accurate conversion and explanation using the model.
• Summative evidence from the exit task: correctness of decimals and appropriate placement on the number line.
• Teacher feedback in the whole-class discussion to address misconceptions about tenths vs hundredths.

Differentiation

• Support: Provide a partially completed hundred grid and a fraction-to-decimal example bank (e.g., 1/2=0.5, 1/4=0.25). Allow students to work with a partner at Station B.
• Support: Offer sentence stems for explanations: “I know because the grid shows…”, “Both names match the same shaded amount…”.
• Extension: Include a reasoning prompt: “Which decimal is larger, 3/10 or 1/4? Prove using the model.”
• SEN/EAL: Use concrete shading steps (counting shaded squares) before asking for written decimals; pre-teach key terms “tenths”, “hundredths”, “equivalent”, and “place value” in context during modelling.