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Math lesson plan · 5th grade (Year 6 in England) · 60 minutes

Word problems with unlike denominators

Fractions

CCSS 5.NF.A.2England: Y6 Fractions

Objective and success criteria

Students will: Word problems with unlike denominators.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Add and subtract fractions with unlike denominators

Leads to: the next skill in this area.

Materials: Fraction strips or a fraction wall, Paper strips to fold, Number lines, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Add and subtract fractions with unlike denominators). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. 1/2 + 2/3 = ? Give your answer in simplest form. → 7/6 (1 1/6)Prompt: You need a common denominator first.
  2. 7/10 − 1/2 = ? Give your answer in simplest form. → 1/5Prompt: Find a common denominator.
  3. Ava ran 1/2 of a mile and then 11/12 of a mile. How far did Ava run altogether? (Simplest form; an improper fraction is fine.) → 17/12 (1 5/12)Prompt: Add the two distances.

Hook · 6 min

  • Cut a pizza or a strip of paper unevenly and ask whether the pieces are really halves or quarters.
  • Share the objective: Word problems with unlike denominators. Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Chloe spends 1/4 of an hour on maths homework and 4/5 of an hour reading. What fraction of an hour is that altogether?
  • Step 1: 1/4 = 5/20, 4/5 = 16/20
  • Step 2: 5/20 + 16/20 = 21/20
  • Step 3: 1 1/20
  • Answer: 21/20 (1 1/20)
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Ava spends 3/4 of an hour on maths homework and 1/5 of an hour reading. What fraction of an hour is that altogether? → 19/20Prompt: Use the common denominator 20.
  2. A garden is planted: 1/2 with vegetables and 3/8 with flowers. The rest is grass. What fraction is grass? → 1/8Prompt: Add the planted parts using denominator 8.

You do: independent practice · 17 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Liam spends 1/2 of an hour on maths homework and 2/5 of an hour reading. What fraction of an hour is that altogether? → 9/10Prompt: Use the common denominator 10.
  2. Without calculating exactly: is 1/4 + 2/5 less than 1, more than 1, or exactly 1? (less than 1 / more than 1 / exactly 1) → less than 1Prompt: Compare each fraction with 1/2.

Watch out for

  • Thinking a bigger denominator means a bigger fraction (1/8 > 1/4).
  • Adding the denominators when adding fractions (1/2 + 1/3 = 2/5).

Support and stretch

Support

  • Review first: Add and subtract fractions with unlike denominators.
  • Use concrete materials: fraction strips or a fraction wall.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-5.

Free lesson plan from eurekami.com/lesson-plan-builder

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Word problems with unlike denominators

Name

Date

Score/ 8

  1. Question 1

    Without calculating exactly: is 1/4 + 3/5 less than 1, more than 1, or exactly 1?

    • A. less than 1
    • B. more than 1
    • C. exactly 1

  2. Question 2

    Ravi pours 1/2 of a litre of juice and 2/3 of a litre of sparkling water into a jug. How many litres are in the jug? (Write a mixed number.)

    Answer(as a fraction)

  3. Question 3

    Priya spends 1/2 of an hour on maths homework and 2/3 of an hour reading. What fraction of an hour is that altogether?

    Answer(as a fraction)

  4. Question 4

    Sofia pours 1/2 of a litre of juice and 5/8 of a litre of sparkling water into a jug. How many litres are in the jug? (Write a mixed number.)

    Answer(as a fraction)

  5. Question 5

    Nia spends 3/4 of an hour on maths homework and 1/6 of an hour reading. What fraction of an hour is that altogether?

    Answer(as a fraction)

  6. Question 6

    Without calculating exactly: is 3/4 + 4/5 less than 1, more than 1, or exactly 1?

    • A. less than 1
    • B. more than 1
    • C. exactly 1

  7. Question 7

    A garden is planted: 3/5 with vegetables and 1/10 with flowers. The rest is grass. What fraction is grass?

    Answer(as a fraction)

  8. Question 8

    Aisha spends 1/2 of an hour on maths homework and 2/3 of an hour reading. What fraction of an hour is that altogether?

    Answer(as a fraction)

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Answer key: Word problems with unlike denominators

  1. 1. A. less than 1

  2. 2. 7/6

  3. 3. 7/6

  4. 4. 9/8

  5. 5. 11/12

  6. 6. B. more than 1

  7. 7. 3/10

  8. 8. 7/6