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

Multi-step problems with larger numbers

Multiplication and division

CCSS 5.NBT.B.5CCSS 5.NBT.B.6England: Y6 Multiplication and division

Objective and success criteria

Students will: Multi-step problems with larger numbers.

  • 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: Multi-step word problems with whole numbers; Long multiplication: three-digit by two-digit

Leads to: the next skill in this area.

Materials: Counters for arrays, Multiplication grid, Base-ten blocks, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Multi-step word problems with whole numbers; Long multiplication: three-digit by two-digit). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A theatre has 18 rows of 16 seats. 257 tickets have been sold. How many seats are still free? → 31Prompt: How many seats are there altogether?
  2. 942 × 65 = ? → 61230Prompt: Multiply 942 by the ones digit of 65, then by the tens.
  3. At a swimming pool, adult tickets cost $8 and child tickets $6. Lucia's group buys 2 adult and 2 child tickets. How much do they pay in total? → 28Prompt: Work out the adult cost and the child cost separately.

Hook · 6 min

  • Show an array of chairs, eggs or windows and ask how many there are without counting one by one.
  • Share the objective: Multi-step problems with larger numbers. 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: A school has 8 classes of 32 pupils. All go on a trip by coach. Each coach seats 45. How many coaches are needed?
  • Step 1: 8 × 32 = 256
  • Step 2: 256 ÷ 45 = 5 r 31
  • Step 3: 6
  • Answer: 6
  • 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. A school has 8 classes of 27 pupils. All go on a trip by coach. Each coach seats 52. How many coaches are needed? → 5Prompt: How many pupils altogether?
  2. Felix is saving for a bike that costs $599. Felix already has $119 and saves $40 every month. After how many months will Felix have enough? → 12Prompt: How much more does the bike cost than the money already saved?

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. A school has 5 classes of 30 pupils. All go on a trip by coach. Each coach seats 57. How many coaches are needed? → 3Prompt: How many pupils altogether?
  2. Diego is saving for a bike that costs $376. Diego already has $136 and saves $20 every month. After how many months will Diego have enough? → 12Prompt: How much more does the bike cost than the money already saved?

Watch out for

  • Thinking multiplying always makes a number bigger.
  • Dropping a zero in long multiplication when moving to the tens row.

Support and stretch

Support

  • Review first: Multi-step word problems with whole numbers.
  • Use concrete materials: counters for arrays.
  • 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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Multi-step problems with larger numbers

Name

Date

Score/ 8

  1. Question 1

    Zoe is saving for a bike that costs $598. Zoe already has $142 and saves $38 every month. After how many months will Zoe have enough?

    Answer

  2. Question 2

    A school has 9 classes of 28 pupils. All go on a trip by coach. Each coach seats 52. How many coaches are needed?

    Answer

  3. Question 3

    Yuki is saving for a bike that costs $718. Yuki already has $226 and saves $41 every month. After how many months will Yuki have enough?

    Answer

  4. Question 4

    A school has 8 classes of 32 pupils. All go on a trip by coach. Each coach seats 52. How many coaches are needed?

    Answer

  5. Question 5

    Ethan is saving for a bike that costs $343. Ethan already has $103 and saves $20 every month. After how many months will Ethan have enough?

    Answer

  6. Question 6

    A school has 4 classes of 27 pupils. All go on a trip by coach. Each coach seats 52. How many coaches are needed?

    Answer

  7. Question 7

    Ben is saving for a bike that costs $718. Ben already has $226 and saves $41 every month. After how many months will Ben have enough?

    Answer

  8. Question 8

    A school has 6 classes of 30 pupils. All go on a trip by coach. Each coach seats 45. How many coaches are needed?

    Answer

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Answer key: Multi-step problems with larger numbers

  1. 1. 12

  2. 2. 5

  3. 3. 12

  4. 4. 5

  5. 5. 12

  6. 6. 3

  7. 7. 12

  8. 8. 4