See and Build Equivalence

Overview

In this first lesson of Equivalent Fractions in Action, students connect familiar sharing situations to equivalent fractions. They use fraction strips and fraction walls to build, match and explain equivalent fractions, focusing on halves, quarters, eighths and related fractions.

Learning intentions

• WALT identify equivalent fractions using visual models.
• WALT represent fractions as equal parts of a whole.
• WALT use fraction walls to compare related fractions.
• WALT explain equivalence using mathematical language and diagrams.

Success criteria

• I can build or shade a fraction model.
• I can match equivalent fractions.
• I can explain why two fractions are equivalent using words and a diagram.
• I can use the words numerator, denominator, equal parts and equivalent correctly.

Curriculum links

• Partitioned fractions: represent and compare halves, quarters, thirds and fifths, including related fractions formed by halving such as eighths.
• Partitioned fractions: model equivalent fractions as equal lengths.
• Partitioned fractions: represent fractional quantities equal to and greater than one.
• Decimals and place value: begin connecting fractions with equal-sized parts to later decimal representations, particularly tenths and hundredths.

Lesson structure (60 minutes)

1. 0–7 min · Engage: sharing fairly. Teacher displays a chocolate bar or paper strip divided into equal parts using the sharing hook slide and asks, “Is one-half the same amount as two-quarters?” Students think independently, discuss with a partner and justify their answer using a drawing or gesture. Invite several explanations without confirming every answer immediately.

2. 7–17 min · Build the language. Teacher introduces or revisits whole, equal parts, numerator, denominator and equivalent, using the vocabulary and model slides. Fold or overlay fraction strips to show that 1/2, 2/4 and 4/8 cover the same length. Students repeat sentence frames, label a quick model and identify what the numerator and denominator tell us. Emphasise that the whole must stay the same size.

3. 17–27 min · Model with a fraction wall. Teacher demonstrates how to read a fraction wall and align strips to compare lengths, using the fraction wall and strip cards and the fraction wall demonstration slides. Model 1/2 = 2/4 = 4/8, then briefly show related examples such as 1/3 = 2/6 and 1/5 = 2/10. Students build each example with strips and record one matching equation in the equivalence modelling worksheet.

4. 27–43 min · Pair matching investigation. Teacher gives each pair a fraction wall and strip cards, explains the matching routine on the pair investigation instruction slide, and circulates with questions: “How do you know?”, “What stayed the same?” and “Can you prove it another way?” Students match fraction names or symbols to equal-length representations, then record at least three matches and a diagram in the worksheet. Partners take turns as builder and explainer, using: “___ is equivalent to ___ because ___.”

5. 43–53 min · Reasoning journals and share. Teacher selects two or three examples, including one misconception such as 1/2 = 2/6, for discussion using the reasoning and discussion slides. Students write a short collaborative reasoning entry in the worksheet: draw or shade both fractions, write an equation and explain why the lengths are or are not equal. Pairs share their reasoning with another pair, who check the use of equal parts and mathematical vocabulary.

6. 53–60 min · Exit check and review. Teacher presents an unfamiliar equivalent pair, such as 3/6 and 1/2, on the plenary and exit-check slide. Students independently complete the exit item on the worksheet: match the pair and justify the match with a diagram and sentence. Finish by asking students to name one equivalent fraction pair they can now explain.

Resources

• the complete lesson slide deck
• the equivalence modelling worksheet
• the fraction wall and strip cards
• Paper strips or magnetic fraction pieces for teacher modelling
• Coloured pencils or markers
• Mini-whiteboards and pens
• Collaborative reasoning journals or maths books
• Word bank displayed on the board: numerator, denominator, equal parts, equivalent, whole

Assessment

• Listen for accurate use of numerator, denominator, equal parts and equivalent during partner explanations.
• Check models and equations during the investigation, especially whether students preserve the same whole and compare lengths rather than only numbers.
• Collect the exit check to identify students who can match an unfamiliar pair and justify equivalence with a diagram.

Differentiation

• Support students with concrete strips, colour coding, a completed example and the sentence frame “___ is equivalent to ___ because the fractions show the same ___.”
• Provide an illustrated word bank and allow EAL/D learners to rehearse explanations orally with a partner before writing. Use mixed-ability pairs and explicitly model turn-taking language.
• Work with a teacher-guided group using only halves, quarters and eighths before introducing thirds, sixths, fifths and tenths.
• Extend confident students by asking them to find multiple equivalent forms for one fraction and investigate the pattern in the numerators and denominators, such as doubling both numbers.

Extension

• Find three different fractions equivalent to 1/2 and represent each on the fraction wall.
• Investigate whether multiplying both numerator and denominator by the same number always preserves the length. Explain with a diagram and an example.