Decimal and Fraction Links

Overview

In this lesson (7 of 20) students begin connecting fraction meanings to decimal representations. They learn to identify terminating and recurring decimals and use digital tools to check and compare representations.

Learning intentions

• Students will recognise terminating and recurring decimals in decimal notation.
• Students will link fractions with denominators made of factors of 10 to terminating decimals.
• Students will recognise that some fractions produce repeating (recurring) decimals.
• Students will use digital tools to model, compare, and justify decimal representations.

Success criteria

• I can state whether a decimal is terminating or recurring.
• I can explain why a fraction like ( \frac{7}{25} ) becomes a terminating decimal.
• I can recognise that ( \frac{1}{3} ) becomes a recurring decimal and represent it using correct notation.
• I can use a calculator or online decimal/fraction tool to check my answer.

Curriculum links

• Number — recognise terminating and recurring decimals, using digital tools as appropriate (Year 8).
• Number — connect decimal representations to fraction understanding through recognition of terminating vs recurring behaviour.
• Cross-curriculum competence: using digital tools for checking and representing mathematical ideas.

Lesson structure (30 minutes)

1. 0–4 min · Starter (quick recall). Teacher writes two statements on the board: “0.6” and “0.333…” and asks: Which is terminating and which is recurring, and how do you know? Student answers verbally and then records a one-sentence reason in their notes.

2. 4–10 min · Direct teach (fraction → decimal idea). Teacher reviews place value meaning of decimals (tenths, hundredths) and shows that fractions with denominators like 2, 5, 4, 8, 25, 20 can match tenths/hundredths/thousandths. Students watch and copy a worked example: ( \frac{7}{25} ). They rewrite ( \frac{7}{25}=\frac{28}{100}=0.28 ) and underline where the “hundredths” appear.

3. 10–15 min · Worked comparison (terminating vs recurring). Teacher contrasts ( \frac{7}{25} ) with ( \frac{1}{3} ) and writes the key result for ( \frac{1}{3} ) as (0.\overline{3}) (recurring), emphasising that it never ends. Students participate in a short teacher-led discussion: “What patterns do you see when dividing 1 by 3?” and record the final forms: terminating vs recurring.

4. 15–22 min · Guided practice (prime-factor check using digital tools). Teacher explains a simple method: a fraction has a terminating decimal when its denominator’s prime factors are only 2s and/or 5s (so the decimal can reach tenths/hundredths/thousandths). Students use a calculator (or fraction/decimal app) to check two tasks:

• Task A: Decide terminating or recurring for ( \frac{3}{8} ), ( \frac{5}{12} ), and ( \frac{7}{20} ).
• Task B: Convert ( \frac{7}{20} ) and ( \frac{3}{8} ) to decimals and write them as decimals to the correct number of places. Students must show at least one written justification: “Denominator factors are only 2 and 5” or “Denominator includes other primes, so it repeats.”

5. 22–27 min · Independent checks (mini task + reasoning). Teacher gives a short set of 3 questions:

• Q1: Is (0.125) terminating or recurring? Write it as a fraction over a power of 10 if you can.
• Q2: Convert ( \frac{2}{5} ) to a decimal and state whether it terminates.
• Q3: Convert ( \frac{1}{6} ) to a decimal; then compare with ( \frac{1}{3} ) and describe what changes and what stays the same. Student completes independently, using digital tools only to verify.

6. 27–30 min · Exit ticket (quick evidence of understanding). Teacher asks students to answer: “Decide terminating or recurring for ( \frac{4}{15} ). Explain your reasoning in one sentence, and give the decimal form (to at least 3 decimal places if recurring).” Student submits responses; teacher checks for correct classification and a reason tied to factors of the denominator.

Resources

• Board and markers
• Student notebooks or worksheets (one page: terminating/recurring sort + 3–5 conversions)
• Calculator or tablet with a fraction-to-decimal tool
• Decimal place value chart (tenths/hundredths/thousandths)
• Fraction cards for ( \frac{1}{3}, \frac{2}{5}, \frac{3}{8}, \frac{7}{20}, \frac{4}{15} )

Assessment

• Teacher observation during the starter discussion: can students distinguish terminating vs recurring and justify briefly?
• Guided practice check: listen for correct reasoning about denominators having only 2s and/or 5s.
• Exit ticket: correctness of classification for ( \frac{4}{15} ), a reasoning sentence, and an appropriate decimal approximation/representation.

Differentiation

• Support: Provide sentence starters such as “I think it is terminating because the denominator can become a power of 10,” and “It is recurring because the denominator includes primes other than 2 and 5.”
• Support: Give a partially completed factorisation table for common denominators (2, 3, 5, 6, 8, 10, 12, 15, 20, 25).
• Extension: Ask students to justify how many decimal places are required for termination (e.g., ( \frac{3}{8} ) terminates by thousandths or hundredths depending on the denominator structure).
• EAL/SEN: Allow verbal explanations; provide visual place value chart and worked examples to reduce reading load.