Fraction Circles

Overview

Students revisit the fundamentals of fractions and use fraction circles to identify the numerator and denominator, distinguish proper and improper fractions, and represent fractions greater than one. The lesson builds from concrete models to drawings and mathematical language, suitable for one Year 5 student working with the teacher.

Learning intentions

Students will:

• identify the numerator, denominator and fraction bar.
• explain that the denominator names the equal parts in one whole and the numerator names the parts selected.
• represent proper and improper fractions using circles.
• compare a fraction with one whole and explain whether it is less than, equal to or greater than one.

Success criteria

• I can name the numerator and denominator in a fraction.
• I can use a fraction circle to show a fraction.
• I can explain that a proper fraction is less than one.
• I can explain that an improper fraction is equal to or greater than one.

Curriculum links

• Number — compare and order fractions, including mixed numerals, and represent them on a number line.
• Number — solve problems involving addition and subtraction of fractions with the same or related denominators.
• Mathematical modelling — represent and explain practical situations using diagrams and efficient strategies.
• General capabilities: Numeracy, critical and creative thinking, and communicating mathematical reasoning.

Lesson structure (30 minutes)

1. 0–4 min · Hook and prior knowledge. Teacher opens with the fraction pizza hook and asks, “If a circle is cut into four equal pieces and I have three pieces, what fraction do I have?” Students discuss the whole, equal parts and how they would write the fraction. Teacher briefly plays the supplied proper-and-improper-fractions video segment, pausing after the explanation of numerator and denominator.

2. 4–9 min · Fraction fundamentals. Teacher uses the numerator and denominator slides to model (\frac34), pointing to the numerator, denominator and fraction bar. Students label (\frac25), saying, “The numerator is __ because I have __ parts; the denominator is __ because the whole is divided into __ equal parts.” Emphasise that the denominator cannot be zero and that the parts must be equal in size.

3. 9–16 min · Build with circles. Teacher provides the fraction circles cut-out pack and models building (\frac14), (\frac24) and (\frac44). Students use the circles to make each fraction, then explain that (\frac44) equals one whole. Teacher asks: “What does the denominator stay responsible for?” and “What changes when the numerator increases?” Record key ideas on the slides.

4. 16–22 min · Proper and improper fractions. Teacher displays the proper and improper fraction comparison slides and models (\frac34), (\frac44), (\frac54) and (\frac73) with circles. Explain that a proper fraction has a numerator less than its denominator and is less than one; an improper fraction has a numerator equal to or greater than its denominator and is equal to or greater than one. Students build one example of each, draw the circles on the worksheet and complete the sentences: “My fraction is proper/improper because…”

5. 22–27 min · Guided practice. Teacher distributes the fraction circles practice worksheet and guides the student through questions involving identifying parts, shading circles, classifying fractions and converting simple improper fractions to mixed numerals, such as (\frac54=1\frac14) and (\frac73=2\frac13). Students use the circles before recording symbolic answers. Include a challenge: “Make an improper fraction greater than one using quarters and show it with circles.”

6. 27–30 min · Explain and assess. Teacher returns to the final reflection slides and asks the student to explain why (\frac38) is proper and (\frac{10}{8}) is improper. Students complete the worksheet exit task: draw a model for (\frac65), classify it, and write its mixed-numeral form. Student verbally justifies the answer using numerator, denominator and whole.

Resources

• the fraction foundations and comparison slide deck
• the fraction circles practice worksheet
• the fraction circles cut-out pack
• Scissors and glue, if needed
• Pencils, coloured pencils and eraser
• Whiteboard and marker
• Supplied proper-and-improper-fractions video segment
• Optional number line drawn from 0 to 3

Assessment

• Listen for accurate use of numerator, denominator, equal parts, proper and improper fraction during questioning.
• Check whether the student’s circle models match the written fractions and whether they recognise (\frac44) as one whole.
• Use the exit task to assess classification, representation and conversion of an improper fraction to a mixed numeral. If errors occur, rebuild the fraction with circles and recount complete wholes.

Differentiation

• Support with pre-cut circles, colour-coding the numerator and denominator, a sentence frame, and repeated modelling of one denominator at a time.
• Keep the student working with denominators 2, 3, 4 and 5 before introducing eighths or larger numerators.
• For EAL/D or language support, pair each term with an action and visual: denominator divides the whole; numerator counts the selected parts.
• Extend by asking the student to place (\frac34), (1), (\frac54) and (\frac73) on a number line and explain how the circle model and number-line position show the same value.