Equivalent Decimal Fractions

Overview

In this third lesson of the unit Decimal Fractions and Operations, students build on place-value understanding to recognise and create equivalent decimal fractions. They use hundred grids, money and place-value language to explain why changing the number of decimal places does not necessarily change the value.

Learning intentions

• WALT recognise equivalent decimal fractions.
• WALT create equivalent decimals using tenths and hundredths.
• WALT explain equivalence using models, place value and money contexts.
• WALT communicate mathematical thinking clearly and respond to the ideas of others.

Success criteria

• I can show that 0.5 = 0.50.
• I can convert between tenths and hundredths.
• I can use a model to explain why two decimal fractions are equivalent.
• I can find more than one equivalent representation and connect decimals with percentages or common fractions.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen understanding for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks connected to relevant textbook and unit content.
• Mathematics and Statistics — Mathsteasers: additional challenge and enrichment for advanced learners.
• Mathematical communication, reasoning and representation through models, discussion and justification.

Lesson structure (60 minutes)

1. 0–6 min · Hook and retrieval. Teacher displays 0.5 and 0.50 on the hook and retrieval slides, asks, “Which is greater, or are they equal? How could you prove it?”, then revisits tenths, hundredths and the value of each place. Students make an individual choice, justify it to a partner, and share different representations.

2. 6–18 min · Explicit teaching with models. Teacher models 0.5 on a 10-by-10 hundred grid, shading 50 squares, then labels it as 5 tenths, 50 hundredths, 0.5 and 0.50 using the hundred-grid modelling slides. Link this to $0.50 and 50 cents, carefully emphasising that the final zero changes the number of parts named, not the value. Students use mini-whiteboards to complete prompts such as 0.7 = __ hundredths and explain the place-value relationship.

3. 18–30 min · Guided representation practice. Teacher distributes the equivalent decimal fractions worksheet and completes the first two examples with the class: 0.3 = 0.30 and 0.08 = 0.08. Demonstrate how to draw or shade a hundred grid and how to write a sentence such as, “3 tenths is the same as 30 hundredths.” Students solve the first section independently, then compare methods with a partner. Pause for a targeted check before moving on.

4. 30–43 min · Paired reasoning task. Teacher displays the task instructions on the paired reasoning slides: “Are these pairs equivalent? Prove your answer using a model, place-value chart, money or a number line.” Use pairs including 0.4 and 0.40, 0.25 and 0.250, 0.6 and 0.06, and 0.09 and 0.90. Students work in pairs, record a representation and explanation for each, and identify the pair that is not equivalent. Teacher circulates, asking, “What does each digit represent?” and “How does your model prove it?”

5. 43–53 min · Independent application and challenge. Teacher directs students to the remaining worksheet questions, displayed on the independent practice and challenge slides. Students complete equivalent-decimal conversions and explain at least two answers. Students ready for extension find three representations of one value, for example 0.5 = 0.50 = 50% = 1/2, then create a new set for a partner to solve. Provide targeted small-group support using hundred grids, money notation and a worked example.

6. 53–60 min · Plenary and exit check. Teacher revisits the WALT and asks students to complete the final prompt on the worksheet: “Explain why 0.70 = 0.7, but 0.70 ≠ 0.07.” Invite two students to share contrasting explanations, then use the plenary and exit-check slide for a final response. Students self-assess against the success criteria and hand in their explanation as they leave.

Resources

• the equivalent decimal fractions lesson deck
• the equivalent decimal fractions worksheet
• Hundred grids, one per student or pair
• Mini-whiteboards and pens
• Place-value charts
• Play money or images of dollar and cent amounts
• Pencils, rulers and coloured pencils
• Projector or interactive whiteboard

Assessment

• Listen to partner explanations and check whether students distinguish the value of a digit from its position.
• Use mini-whiteboard responses to identify misconceptions, especially confusing 0.06 with 0.60 or believing that a longer decimal is always larger.
• Collect the worksheet and final explanation to assess representation, conversion and mathematical justification.

Differentiation

• Support learners with partially completed place-value charts, hundred grids, money contexts, the sentence frame “___ tenths is the same as ___ hundredths because…”, and a teacher-led group during independent practice.
• Provide a worked example before each new question type and allow students to explain orally, draw or use materials before recording symbolic notation.
• For EAL learners, pre-teach and display tenths, hundredths, equivalent, value, digit, equal to; pair words with diagrams and gestures.
• Extend advanced learners by requiring multiple representations, connections to percentages and common fractions, and a proof of why adding zeros to the right of a decimal does not change its value.