Fraction Steps

Overview

Today students practise counting and locating fractions by multiples of quarters, halves and thirds. They represent these fractions as numbers on a number line, including moving between mixed numerals and improper fractions when needed.

Learning intentions

Students will:

• count forward and backward in steps of quarters, halves and thirds
• represent fractions as points on a number line
• use fraction language to describe where the fractions land (e.g., “one and a quarter”, “two thirds”)
• convert between mixed numerals and improper fractions to locate them accurately

Success criteria

Students can:

• count by quarters, halves or thirds starting at a chosen number and describe the pattern
• partition a number line between whole numbers into equal sections for the given fraction type
• place fractions in the correct order on a number line and explain why each point is correct
• write the matching mixed numeral or improper fraction for a located point

Curriculum links

• Mathematics (Year 4) — Number: counting by multiples of quarters, halves and thirds, including mixed numerals
• Mathematics (Year 4) — Number: locate and represent these fractions as numbers on number lines
• Mathematics (Year 4) — Number: convert between mixed numerals and improper fractions and represent them on a number line

Lesson structure (45 minutes)

1. 0–5 min · Hook (Fraction warm-up). Teacher displays three fraction cards: 1/4, 1/2, 1/3, plus one mixed numeral card (e.g., 1 1/4). Students give a quick vote with fingers: “Which step would you use to go from 0?” (quarter/half/third), and teacher records one example on the board.

2. 5–12 min · Direct teach (Number line and equal parts). Teacher draws a number line from 0 to 2 with the whole numbers marked, then models how to split each interval depending on the fraction type (quarters, halves, thirds). Teacher says the rule aloud (e.g., “Each quarter is one of four equal parts”) and places one example point, then asks students to name the fraction at that position.

3. 12–22 min · Guided practice (Count and place, one fraction type). Teacher chooses one focus fraction type for the class (e.g., quarters). Students work on a worksheet with a blank number line (0 to 3) and a few target placements (e.g., 2/4, 5/4, 9/4). Teacher prompts: “Start at 0. What do you count by?” Students count by the correct multiple and place each point, then label it using fraction notation and a matching mixed numeral where appropriate.

4. 22–32 min · Guided practice (Change fraction type). Teacher repeats the process for a second fraction type (e.g., halves) using the same number line idea but different partitioning (two equal parts per whole). Students complete placements such as 3/2, 1/2, 5/2. Teacher circulates prompts: “How many equal parts did you make between the whole numbers?” and “Is your point between which two whole numbers?”

5. 32–39 min · Quick check (Thirds challenge on a smaller section). Teacher reduces the scale to avoid cognitive overload: draw 1 to 2 only, then partition into thirds. Students place and label 4/3 and 5/3 on the line, explaining in one sentence where each point sits (e.g., “4/3 is one and one third”). Teacher checks accuracy and listens for correct counting by thirds.

6. 39–45 min · Exit ticket (Mixed numeral connection). Teacher gives an exit ticket showing one number line from 0 to 2 divided into quarters and two blank points. Students must:

• place the point for 1 3/4 (or 7/4)
• write the fraction name as both a mixed numeral and an improper fraction Teacher collects and uses it to plan next steps.

Resources

• Fraction number line worksheets (0–3) with whole numbers and space to partition
• Paper strips or fraction cards for quarters, halves and thirds
• Coloured pencils or markers (one colour per fraction type)
• Whiteboard or digital interactive board for modelling partitions
• Sentence starters for explanations:
• “I counted by ____ to get to ____.”
• “Between ____ and ____, I divided into ____ equal parts.”
• “This point is ____ because it is ____ of a whole after ____.”
• Improper fraction ↔ mixed numeral conversion chart (simple reference, teacher-made)

Assessment

• Formative: teacher listens during counting and checks that students correctly decide the step size (quarter/half/third)
• Formative: teacher reviews placements and asks short “why” questions about equal partitioning between whole numbers
• Exit ticket: correct location and correct naming of a mixed numeral/improper fraction on a number line

Differentiation

• Support:
• Provide partially completed number lines where the equal partitions for halves/quarters/thirds are already drawn
• Use sentence starters and a teacher model for converting between mixed numerals and improper fractions (e.g., “1 1/4 is 5/4”)
• Offer manipulatives (fraction strips) so students can physically match “one whole” with the required number of equal parts
• Extension:
• Ask students to place an additional point not listed (e.g., for quarters, “Place 3/4 and 5/4 and compare which is greater”)
• Ask students to justify ordering: “Which is larger, 7/4 or 3/2? How do you know from the number line?”
• Language/SEN considerations:
• Keep the tasks concrete by limiting to one number line at a time and using consistent fraction language (“count by”, “equal parts”, “between whole numbers”)
• Allow verbal explanations for naming if writing is still developing; check written fraction notation during the exit ticket