Fractions, Decimals and Halves

Overview

Lesson 2 of 16 in Place Value Decimal Journeys. Students connect familiar fractions to tenths and decimal notation, with a particular focus on understanding and using ( \frac{1}{2}=0.5 ).

Learning intentions

• WALT connect common fractions with decimal tenths.
• WALT recognise that the denominator 10 tells us the number of tenths.
• WALT use the equivalence ( \frac{1}{2}=0.5 ).
• WALT explain equivalent fractions using visual models, words and symbols.

Success criteria

• I can say, write and use ( \frac{1}{2}=0.5 ).
• I can convert fractions with a denominator of 10 into decimals.
• I can match a fraction, decimal and visual model.
• I can explain why ( \frac{5}{10}=\frac{1}{2} ).

Curriculum links

• Number: recognise, represent and compare fractions and decimals in familiar contexts.
• Place value: understand tenths as one part of ten equal parts and connect this to decimal notation.
• Mathematical thinking: use representations, explanations and mathematical language to justify equivalence.
• Communication and participation: work collaboratively, listen to a partner’s reasoning and share ideas clearly.

Lesson structure (60 minutes)

1. 0–7 minutes – Warm-up and learning goal

Open with the introduction and hook slides. Display a strip divided into two equal parts and another divided into ten equal parts. Ask: “How could the same amount be described using a fraction and a decimal?” Share the WALT and success criteria, and briefly revisit the meaning of numerator and denominator.

2. 7–18 minutes – Model the connection

Use the worked-example slides and draw a rectangle or number line from 0 to 1. Shade one-half, then show that the same amount covers five of ten equal parts. Record:

• ( \frac{1}{10}=0.1 )
• ( \frac{5}{10}=0.5 )
• ( \frac{1}{2}=\frac{5}{10}=0.5 )

Emphasise that the denominator 10 means “tenths” and the decimal digit in the tenths place shows how many tenths. Ask students to explain the model to a partner using the sentence frame: “I know ___ because ___.”

3. 18–30 minutes – Matching activity

In pairs, distribute the fraction-decimal-percentage matching cards, using only the fraction and decimal parts, from the fraction-decimal-percentage matching cards. Students match examples such as ( \frac{1}{10} ) and 0.1, ( \frac{3}{10} ) and 0.3, ( \frac{5}{10} ) and 0.5, and ( \frac{9}{10} ) and 0.9.

Partners must justify each match with a visual model, number line or spoken explanation. Circulate and ask: “What does the denominator tell you?” and “Where can you see the tenths in the decimal?”

4. 30–43 minutes – Guided worksheet practice

Distribute the fractions and decimals practice worksheet. Complete the first two questions together: shade tenths and write the matching decimal, then complete ( \frac{5}{10}=\frac{1}{2}=0.5 ). Students work independently for the remaining questions, with partner talk permitted before recording an answer.

Include matching, converting denominator-10 fractions to decimals, placing tenths on a 0–1 number line, and one explanation question. Pause halfway for students to compare one answer and correct their thinking in a different colour.

5. 43–52 minutes – Prove an equivalence

Return to the representation and discussion slides. Present the statement ( \frac{5}{10}=\frac{1}{2} ). Pairs prove it in at least two ways, for example:

• a shaded fraction strip or tenths model;
• a number line;
• words: “Five tenths is half of one whole”;
• division: (5\div10=0.5).

Invite two or three pairs to share. Highlight that different representations can show the same quantity.

6. 52–60 minutes – Plenary and assessment

Use the final review and exit-question slides. Students respond on mini-whiteboards:

• Write ( \frac{7}{10} ) as a decimal.
• Complete ( \frac{5}{10}=\frac{1}{2}= ___ ).
• Explain one reason that ( \frac{1}{2}=0.5 ).

Students self-assess against the success criteria using “secure”, “nearly there” or “need more practice”. Collect the worksheet and note which students need further support in the next lesson.

Resources

• the complete lesson slide deck
• the fractions and decimals practice worksheet
• the fraction-decimal-percentage matching cards
• Fraction strips or paper strips divided into halves and tenths
• Mini-whiteboards, pens and erasers
• Board and markers
• Optional 0–1 number lines
• Vocabulary cards or a displayed word bank: fraction, numerator, denominator, tenths, decimal, equivalent

Assessment

• Listen to partner explanations during modelling and card matching, checking whether students connect the denominator 10 with tenths.
• Mark the worksheet for accurate conversions and explanations, particularly ( \frac{5}{10}=\frac{1}{2}=0.5 ).
• Use the final mini-whiteboard questions and self-assessment to identify students requiring concrete models or further practice.

Differentiation

• Support: provide fraction strips, a 0–1 number line, worked examples and a reduced set of matching cards. Keep a consistent layout and colour-code tenths in both the fraction and decimal.
• Support for dyslexic learners: use a clear sans-serif font, uncluttered worksheet spacing, consistent notation, visual models, short instructions and audio instructions or teacher read-aloud. Provide vocabulary cards for fraction, decimal, tenths, numerator and denominator.
• EAL/SEN: pre-teach vocabulary with pictures and gestures; use the sentence frame “___ tenths is written as ___ because ___”. Pair students thoughtfully and allow oral explanations before written responses.
• Extension: ask students to prove ( \frac{5}{10}=\frac{1}{2} ) in three representations, or explain why ( \frac{10}{10}=1.0 ) and ( \frac{0}{10}=0.0 ). Invite them to create a matching fraction-decimal pair and justify it.