Tenths To Percentages

Overview

Students connect decimal tenths and hundredths with equivalent fractions and percentages. Using place-value and hundred-grid representations, they explain that percentages describe parts out of 100.

Learning intentions

• WALT connect decimal tenths and hundredths to fractions.
• WALT convert tenths and hundredths to percentages.
• WALT explain why equivalent representations have the same value.

Success criteria

• I can write a decimal as a fraction with a denominator of 10 or 100.
• I can convert a fraction or decimal to a percentage.
• I can use a model or calculation to explain my answer.
• I can check that my fraction, decimal and percentage are equivalent.

Curriculum links

• Number: recognising and representing equivalent forms of fractions, decimals and percentages.
• Number: using place value to reason about tenths and hundredths.
• Mathsteasers: applying higher-order thinking and explaining mathematical reasoning.
• Mathsteasers / Alignment: connecting challenge questions with relevant number knowledge.

Lesson structure (13 minutes)

1. 0–2 min · Hook and notice. Teacher opens with the hook and learning intention slides and displays 0.4, asking, “Which is greater: 0.4, 4/10 or 40%? How do you know?” Students silently choose an answer, then share their reasoning with a partner.

2. 2–5 min · Model the connection. Teacher uses the place-value and hundred-grid slides to show that 0.4 means four tenths, or 4/10, and that four tenths is equivalent to 40/100 and 40%. Teacher repeats the process for 0.35, recording: 0.35 = 35/100 = 35%. Students identify the numerator, denominator and percentage in each example and explain the role of the denominator 100.

3. 5–8 min · Rapid matching activity. Teacher gives pairs a small selection of the Fraction-decimal-percentage Matching Cards and instructs them to place equivalent fraction, decimal and percentage representations together. Teacher circulates, asking, “How can you prove these match?” Students sort the cards, justify one match to their partner and correct any mismatch.

4. 8–11 min · Independent check. Teacher displays the practice questions on the guided practice and independent questions and distributes the tenths and hundredths conversion worksheet. Students complete: 0.7 = ___/10 = ___%; 0.62 = ___/100 = ___%; 9/10 = ___ = ___%; and 45/100 = ___ = ___%. Students may draw a hundred grid or place-value chart to support their thinking.

5. 11–13 min · Plenary and exit response. Teacher uses the discussion and exit-question slide to ask, “Why is 0.6 equal to 60%, but not 6%?” Students write a one-sentence explanation and hold up their worksheet or share with a partner. Teacher collects responses to identify who needs further support.

Resources

• the complete 13-minute teaching slide deck
• the tenths and hundredths conversion worksheet
• the Fraction-decimal-percentage Matching Cards
• Pencils and erasers
• Optional mini whiteboards
• Optional hundred-grid or place-value support cards

Assessment

• Listen during the hook and matching activity for whether students understand that tenths can be renamed as hundredths.
• Check worksheet answers and ask students to explain one conversion, rather than accepting answers without reasoning.
• Use the final explanation to identify misconceptions, especially confusing 0.6 with 6% or treating 0.35 as 35/10.

Differentiation

• Support learners with a visible place-value chart, a hundred grid and sentence frames: “___ tenths is ___ hundredths, so it is ___%.”
• Allow students to explain orally, point to a model or use mini whiteboards before recording written answers.
• Provide dyslexia-friendly options: clear sans-serif font, large spacing, minimal text, high contrast, numbers read aloud and no unnecessary decorative print.
• For EAL learners, explicitly teach and repeat “tenths”, “hundredths”, “fraction”, “decimal” and “percentage”, using the same visual model each time.

Extension

• Ask advanced learners to convert 0.08, 0.125 and 125/100, explaining which can be written as a percentage exactly and why.
• Challenge students to create a decimal, fraction and percentage that are equivalent to a partner’s number, then prove the equivalence using a diagram or calculation.