Fraction Steps

Overview

In this lesson, Year 4 pupils solve multi-step word problems involving fractions, building on prior learning of adding and subtracting fractions, finding fractions of amounts, and working with improper fractions and mixed numbers. They will also practise explaining their reasoning, not just giving answers.

Learning intentions

• Students will solve multi-step problems involving fractions by choosing the correct operations.
• Students will use fraction methods accurately, including adding/subtracting like denominators.
• Students will convert between improper fractions and mixed numbers to write final answers.
• Students will explain their thinking using clear mathematical sentence stems.

Success criteria

• I can break a multi-step fraction problem into smaller steps.
• I can calculate the fraction of an amount and then combine results correctly.
• I can add/subtract fractions with the same denominator accurately.
• I can justify my final answer and write it as a mixed number when appropriate.

Curriculum links

• Number: fractions (including decimals) — solve increasingly harder problems involving fractions and calculate quantities.
• Solve problems involving fractions to divide quantities and include non-unit fractions where the answer can be a whole number.
• Use and understand improper fractions and mixed numbers in multi-step reasoning.
• Add and subtract fractions with the same denominator.

Lesson structure (35 minutes)

1. 0–5 min · Hook and active reasoning

• Teacher shows the problem on the board: “A recipe uses 3/4 of a bag of flour. You use 2/3 of that amount for cookies, then you add 1/6 of the original bag for chocolate cake. How much flour is used in total (write as a mixed number if needed)?”
• Teacher asks: “What do you notice first? What is the first thing we must find?”
• Pupils do quick think-time, then pair-share. Teacher circulates and selects a few verbal strategies.

2. 5–12 min · Modelling + prove it (reasoning before writing)

• Teacher models the solution with a clear “steps” structure, using sentence stems and a timer for verbal reasoning.
• Sentence stems (display): “First, I find … because …” “Next, I calculate … by …” “I know the denominator stays … because …” “My answer is a mixed number because …”
• Timer routine: “You have 20 seconds to talk to your partner before we write any calculations.”
• Modelling example (copy-ready in children’s books will be provided after this plan’s resources section).
• Teacher explicitly verbalises common choices: fraction-of-amount comes before final addition; only add/subtract after getting same-denominator totals; convert to mixed number for final answer.
• AfL (during modelling): teacher uses 3 targeted calls to probe method (“Which step gives you the part of the bag? Which part do we add?”). Capture misconceptions verbally.

3. 12–18 min · Targeted whole-class questioning (layered, justified)

• Teacher poses layered questions; pupils answer with reasoning, using stems.

• Q1 (Understand): “What does ‘2/3 of that amount’ mean in this problem—what calculation must we do first?” (Explain in your own words.)

• Q2 (Apply): “When you find 2/3 of 3/4, why do we multiply the numerators and denominators? Show the fraction structure.”

• Q3 (Analyse): “Before adding 1/6, what do we need to make sure of? How do you know?”

• Q4 (Reason about errors): “Common mistake: pupils add 3/4 and 2/3 directly. Why is that wrong here?”

• Q5 (Evaluate): “How can you check your mixed number answer makes sense without doing everything again?”

• AfL: use cold call + hands-up “reasoning check” where pupils must include “because…”. Teacher listens for correct operation selection and denominator reasoning.

4. 18–28 min · Guided practice task (gradual complexity)

• Pupils work on a staged worksheet (or board task) in 3 increasing steps.
• Step A (single multi-step): Same context type, smaller numbers with like denominators after fraction-of-amount.
• Step B (add improper/mixed conversion): One result becomes an improper fraction that must be converted.
• Step C (more steps): Add both a fraction-of-amount and an extra adjustment fraction, then combine and simplify.
• Teacher provides a worked “checklist” on the board:

1. Find the fraction-of-amount
2. Convert if needed (improper to mixed)
3. Add/subtract with same denominator
4. Check: does it match a sensible size?

• AfL points:
• Teacher uses a quick mid-task stop at minute 23 to ask two pupils to explain their chosen operations verbally before continuing.
• Marking focus: correctness of each step and clear working—not just final answer.

5. 28–33 min · Plenary (prove it + misconceptions)

• Teacher returns to a “wrong answer” example (display): “Flour used = 5/6 + 1/6 = 1” (but the given fractions require fraction-of-amount first).
• Questions:
• “What is the first step this person missed?”
• “Which operation did they choose incorrectly, and why?”
• “How would you correct it—what would you do next?”
• Pupils give verbal corrections using stems, then one pupil writes the corrected start on the board.
• AfL: traffic-light (verbal): “Green = I can explain the first step; Amber = I need help with operation choice; Red = I’m unsure how to justify.”

6. 33–35 min · Exit ticket (short, justified)

• Exit ticket: “A treasure map shows 5/6 of the area is “land”. Jamie uses 3/5 of the land area and then adds 1/3 of the remaining area. What fraction of the whole map is used? Write as a mixed number if needed.” Pupils must include one sentence: “I chose to … because …”
• AfL: collect to assess reasoning quality and operation selection.

Resources

• Copy-ready worked example (teacher and pupils)
• Whiteboards/slates or scrap paper for 20-second partner reasoning
• Fraction wall / bar model images (tenths/hundredths optional; use for fraction-of-amount support)
• Sentence stem cards for modelling and explanations
• Worksheet with 3-step increasing complexity task
• “Wrong answer” slide/poster for plenary
• Exit ticket slips

Assessment

• During modelling: teacher listens for “because…” explanations tied to operations (fraction-of-amount vs add/subtract).
• During questions: teacher checks misconceptions (adding fractions that aren’t like parts; incorrect denominator handling; skipping conversion to mixed numbers).
• During task: teacher uses a step-by-step checklist to judge accuracy and method choice.
• Exit ticket checks both final answer and one-sentence justification.

Differentiation

• Support:
• Provide a step template (“First… Next… Then… Finally…”) and sentence starters.
• Offer a model bar/area sketch for fraction-of-amount and allow fraction manipulation reminders.
• Provide worked examples of converting improper fractions to mixed numbers.
• Challenge/extension:
• Include an extra line in the problem: “How many more bags would be needed to use 2 whole bags?” (pupils justify with subtraction/addition of mixed numbers).
• Ask pupils to create and explain a second solution method (e.g., different order of combining when valid), justifying why it works.
• EAL/SEN:
• Use visual step labels on the board and allow verbal responses first; provide language frames and key words (“of”, “then”, “in total”, “remaining”).

Copy-ready example (for pupils to copy)

Problem: “A recipe uses 3/4 of a bag of flour. You use 2/3 of that amount for cookies, then you add 1/6 of the original bag for chocolate cake. How much flour is used in total (write as a mixed number if needed)?”

Working:

1. Cookies: “2/3 of 3/4” ( \frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2} )

2. Chocolate cake: “1/6 of the original bag” ( \frac{1}{6} )

3. Add parts (same denominator): ( \frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3} )

Final answer: ( \frac{2}{3} ) of the bag is used in total.

Reasoning sentence (to write after your working): “I found the cookies part first because it says ‘2/3 of that amount’, then I added the extra 1/6 using a common denominator.”