Fraction Foundations

Overview

Students build a precise understanding of fractions as equal parts of a whole. They identify the numerator and denominator, represent proper fractions with diagrams, collections and number lines, and explain the meaning of each part. This first lesson establishes language and representations needed for later fraction operations.

Learning intentions

Students will:

• define a fraction as a number representing equal parts of a whole
• identify the numerator and denominator
• represent proper fractions using area models, collections and number lines
• explain what each part of a fraction means
• communicate mathematical thinking using correct notation and vocabulary

Success criteria

• I can explain why the parts of a fraction must be equal.
• I can identify the numerator and denominator in a fraction.
• I can represent a proper fraction in a diagram, collection and number line.
• I can explain the meaning of a fraction in context.

Curriculum links

• Number — operations with rational numbers, including fractions, using efficient strategies.
• Number — mathematical modelling involving rational numbers and interpreting solutions in context.
• Number — communicating mathematical reasoning using appropriate representations and digital tools where suitable.
• This lesson supports the Western Australian Curriculum focus on representing, interpreting and communicating rational numbers.

Lesson structure (60 minutes)

1. 0–5 min · Hook and diagnostic. Teacher opens with the fraction mystery hook showing three representations of ( \frac{3}{4} ), including one incorrectly divided shape, and asks, “Which one shows three-quarters? How can you prove it?” Students respond verbally, then explain their thinking to the teacher; the teacher records prior knowledge and misconceptions.

2. 5–15 min · Define the parts. Teacher uses the fraction meaning slides to model a rectangle divided into four equal parts, shading three, and introduces whole, equal parts, numerator and denominator. Students label ( \frac{3}{4} ), state what each number means, and compare it with ( \frac{3}{5} ) to notice that the denominator describes the size and number of equal parts.

3. 15–25 min · Multiple representations. Teacher models ( \frac{2}{5} ) as an area model, a collection of five objects with two selected, and a number line from 0 to 1 divided into five equal intervals, referring to the fraction wall and strip cards as a visual reference. Students help construct each representation and explain how the denominator and numerator appear in each one.

4. 25–38 min · Guided practice. Teacher displays the prompts in the guided practice slides and works through ( \frac{1}{3} ), ( \frac{4}{6} ) as a representation rather than an operations problem, and ( \frac{5}{8} ), asking the student to predict before drawing. Teacher checks that every whole is divided into equal parts. Student completes the corresponding questions on the fraction foundations practice sheet, drawing an area model, collection and number line, and explaining each numerator and denominator.

5. 38–48 min · Reasoning and correction. Teacher presents two statements from the misconception discussion slides: “The denominator tells us how many parts are shaded” and “A fraction can be made from unequal parts.” Student decides whether each statement is true or false, creates a counterexample where appropriate, and explains the correction using mathematical language. Teacher prompts with “What is the whole?” and “Are the parts equal?”

6. 48–56 min · Individual check. Teacher gives the independent section of the individual check section and asks the student to complete it without prompts: identify the numerator and denominator in ( \frac{3}{7} ), represent ( \frac{3}{7} ) in two ways, place it on a 0–1 number line, and write one sentence explaining its meaning. Teacher observes, notes accuracy and asks only clarifying questions.

7. 56–60 min · Plenary and next step. Teacher returns to the hook using the plenary and exit prompt and asks the student to answer: “How do you know a representation shows a proper fraction?” Student gives a concise explanation and identifies one representation they found most useful. Teacher previews that the next lesson will compare and order fractions.

Resources

• the Fraction Foundations slide deck
• the Fraction Foundations practice and check worksheet
• the fraction wall and strip cards
• Whiteboard and markers
• Pencil, ruler and coloured pencils
• Optional tablet or calculator camera for photographing completed representations

Assessment

• During modelling and guided practice, check whether the student identifies the whole, divides it into equal parts and connects the numerator with selected parts.
• Use questioning to assess understanding: “What does the denominator tell you?” “Where is the numerator shown on your number line?” and “Why must the parts be equal?”
• Review the individual check for correct notation, three appropriate representations, accurate number-line placement and a clear explanation. Use errors to plan the next lesson’s retrieval task.

Differentiation

• Support with a pre-drawn 0–1 number line, highlighted labels for numerator and denominator, and sentence starters such as “The denominator tells me…” and “The numerator shows…”.
• Reduce the initial examples to unit fractions and familiar denominators such as 2, 3, 4 and 5 before introducing eighths.
• For EAL/D or students needing language support, use the visual fraction wall, gesture and repeated oral rehearsal of “__ equal parts; __ selected”.
• Extend by asking the student to represent a chosen proper fraction in three different ways and explain why an unequally divided shape is not a valid fraction model.