Equivalent Forms, Clear Comparisons

Overview

In this first lesson of Everyday Number Decisions, students connect fractions, decimals, and percentages as equivalent ways to describe the same value. They use visual models and benchmarks to compare and order values, building on prior learning about place value, fractions, and simple percentages.

Learning intentions

• WALT convert between fractions, decimals, and percentages.
• WALT compare and order values represented in different forms.
• WALT use visual models and benchmark values to justify mathematical reasoning.
• WALT explain which representation is most useful in a given situation.

Success criteria

• I can show a fraction, decimal, and percentage that have the same value.
• I can order mixed representations accurately from least to greatest.
• I can explain how I know which value is greater.
• I can choose and justify the most useful representation for a comparison.

Curriculum links

• Mathematics and Statistics — Number and Algebra: number knowledge and proportional thinking.
• Mathematics and Statistics — communicating mathematical reasoning using representations, symbols, and mathematical language.
• Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Key competencies: thinking; using language, symbols, and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Display a question from the hook and benchmark slides: “Which is greater: 0.5, 45%, or 1/2?” Students make an individual choice, then explain their thinking to a partner without being told the answer. Invite several strategies and identify useful benchmarks such as 0, 1/2, and 1.

2. 5–13 min · Make the connection. Use the visual fraction strip, hundred grid, and number line in the visual models and conversion slides to model (1/2 = 0.5 = 50%). Think aloud: a half of a whole is 50 out of 100, and 50 out of 100 is 0.50. Briefly model (1/4 = 0.25 = 25%) and (3/4 = 0.75 = 75%). Students sketch or annotate the three representations on their worksheet.

3. 13–20 min · Guided practice. Distribute the fraction-decimal-percentage matching cards to pairs. Demonstrate how to place equivalent values in the fraction, decimal, and percentage columns, using the worked example and checklist on the mat. Students complete several matches, using the number line and benchmarks to check their decisions. Confer with pairs and ask, “What evidence shows these values are equal?”

4. 20–32 min · Ordering challenge. Open the pair challenge instructions and discussion prompts and display a set such as 0.4, 35%, 1/2, 0.65, and 60%. Pairs convert where necessary, record their reasoning on the equivalent forms and ordering worksheet, and order the values from least to greatest. They must justify at least two comparisons using a visual model, benchmark, or equivalent form. Encourage students to use precise language such as greater than, less than, equal to, equivalent, and representation.

5. 32–39 min · Share and reason. Select two pairs with different methods to explain one comparison. Use the reasoning and representation discussion slides to prompt: “Could you compare these without converting everything?” and “When might a percentage be more useful than a fraction or decimal?” Students compare methods, correct any errors, and explain which representation would be clearest for a sale discount, a measurement, or a part of a group.

6. 39–45 min · Exit reflection. Display the final prompt in the plenary and exit prompt slide. Students complete the final section of the equivalent forms and ordering worksheet: convert (3/5) into a decimal and percentage, order 0.6, 55%, and (3/5), and explain which representation is most useful when describing a discount. Collect worksheets as students leave.

Resources

• the full teaching slide deck
• the equivalent forms and ordering worksheet
• the fraction-decimal-percentage matching cards
• Fraction strips or fraction bars
• Hundred grids
• Classroom number line from 0 to 1
• Coloured pencils or highlighters
• Vocabulary bank displayed on the board

Assessment

• Listen during the hook and guided matching for accurate use of benchmarks and equivalent language.
• Confer with pairs during the ordering challenge, checking whether students can justify comparisons rather than relying on guesses.
• Use the exit reflection to identify students needing further support with conversion, ordering, or explanation in Lesson 2.

Differentiation

• Provide pre-labelled fraction strips, hundred grids, and number lines, with 0, 1/2, and 1 clearly marked. Begin with familiar equivalents such as 1/2, 1/4, and 3/4.
• Use mixed-ability pairing, worked examples, colour-coded fraction/decimal/percentage representations, and a vocabulary bank. Conference with students who confuse tenths, hundredths, or percentage notation.
• For dyslexia-friendly access, use uncluttered, left-aligned worksheets in a clear sans-serif font with increased spacing. Read instructions aloud, give one direction at a time, and allow oral or recorded explanations.
• Support EAL learners with sentence frames such as “___ is greater than ___ because…” and “___ is equivalent to ___.” Provide repeated opportunities to rehearse explanations with a partner.

Extension

• Compare values with unlike denominators, such as (5/8), (2/3), and (7/10), converting only when useful.
• Create a “Which is greatest?” challenge containing at least four fractions, decimals, and percentages. Give a justified answer and explain the most efficient comparison strategy.