Short Blocks

Maths Year 5 Summer Multiplication and Division (B)

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Division problems with short division (suggested as 3 days)

Objectives

Solve division problems with short division
Unit 3: ID #5827

National Curriculum
Mult/Div (vi) (x)
Add/Sub (iv)

Hamilton Objectives
18. Divide 2, 3, 4-digit numbers by 1-digit numbers above tables range; choose and use efficient methods; interpret remainders appropriately according to context.
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Model short division to find 2381 ÷ 3. Cover the digits 3, 8 and 1 with a sticky note. Make 2381 using base-10 equipment or use the ‘Short division 1’ presentation. Point out that we cannot make a group of three 1000s blocks from the two 1000s blocks available. Move the sticky note to reveal the 3. Change the two 1000 blocks for twenty 100 blocks. How many 3s in 23? Continue the division to give answer 793 r 2. Repeat with 1381 ÷ 6 and 1281 ÷ 5 using just the sticky notes.
Group Activities
-- Investigate short division of given 4-digit numbers. Explain a pattern in the remainders.

Day 2 Teaching
Use the ‘bus shelter’ short division layout to model calculating 5466 ÷ 4. Agree the remainder as 2. We can divide 2 by 4 to give 2/4. How can we simplify this? Agree the answer as 1366¹/2. Repeat for 5120 ÷ 6, agreeing an answer of 853¹/3. Write 5118 ÷ 6. What do you think will be the answer to this? Can you suggest other divisions by 6 that will not have a remainder? A division that will have 1/6 in the answer?
Group Activities
Use the in-depth problem-solving investigation ‘Remainder runners’ as today’s group activity.
Or, use these activities:
-- Make a 3-digit number; divide by a fourth number. Score the remainder.
-- Divide 4-digit numbers by single-digit numbers, investigating largest possible fraction remainders.

Day 3 Teaching
Write: 472 ÷ 4, 3958 ÷ 3, 2786 ÷ 4, 7975 ÷ 4. Children agree an estimate for each. Take feedback on how they did this. Model a calculation of 2786 ÷ 4 using base-10 equipment or use the presentation provided. Express the remainder as fraction and simplify to 696¹/2. Children calculate 2054 ÷ 3 on their whiteboards. Challenge children to write a division with an answer of more than 1000 and one with an answer of less than 1000.
Group Activities
-- Practise short division of 3- and 4-digit numbers, creating calculations with number cards.

You Will Need

  • ‘Short division 1’ presentation (see resources)
  • 1000s, 100s, 10s and 1s base-10 equipment
  • Sticky notes
  • ‘Short division 2’ presentation (see resources)
  • Mini-whiteboards and pens
  • ‘Short division 3’ presentation (see resources)
  • 0–9 digit cards

Mental/Oral Maths Starters

Day 1
Division facts for the 6 times table (pre-requisite skills)

Suggested for Day 2
Place value in 6-digit numbers (simmering skills)

Day 3
Division facts (pre-requisite skills)

Procedural Fluency

Day 1
Practise short division of 3-digit numbers with remainders.
Practise short division of 4-digit numbers with remainders.

Day 2
Calculate multiplications; use them to choose 3-digit numbers to divide by 3, 4 and 5 to give answers within given ranges.
Practise dividing 4-digit numbers, expressing remainders as fractions, simplifying where possible.

Day 3
Use short division to divide 3-digit and 4-digit numbers by 1-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Find:
    581 ÷ 7 = ☐
    3456 ÷ 5 = ☐
    5400 ÷ 9 = ☐
  • A farmer is packing eggs. Each box holds six eggs. The farmer has 890 eggs to pack. How many boxes will the farmer fill?
  • Fill the missing boxes to give an answer with fraction remainders as follows:
    187 ÷ ☐ = ____1/2
    331 ÷ ☐ = ____3/4
    ☐ ÷ 10 = ____2/5

In-depth Investigation: Remainder Runners
Children divide 1234, 2345, 3456 by 3, 4, 5 … 12 and look for patterns in the remainders.

Extra Support

Chunking Champs
Using chunking to divide, answers between 10 and 30, with remainders.

Unit 2 Solve long multiplication problems (suggested as 3 days)

Objectives

Solve long multiplication problems
Unit 5: ID#5851

National Curriculum
Mult/Div (iv)

Hamilton Objectives
16. Multiply 2, 3, 4-digit numbers by numbers ≤26 using long or short multiplication.
21. Solve problems involving multiplication and division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Remind children how to use long multiplication to calculate 57 × 16. They then work out 14 × 38. Write 26 × 57. What is an efficient way to multiply by 20? (Double, then multiply by 10) Write this in the multiplication, work out the next row, then add to find the answer. Discuss multiplying by 30. Children then try using long multiplication to find 24 × 57 and 34 × 57. Children working towards ARE can use the grid method, comparing products with long multiplications scribed for them.
Group Activities
-- Continue to develop understanding of long multiplication for 2-digit by 2-digit multiplications.
-- Consolidate use of long multiplication for 2-digit by 2-digit multiplications.
-- Consolidate use of long multiplication for a sequence of 2-digit by 2-digit multiplications where one number is less than 40. Describe and explain patterns in answers.

Day 2 Teaching
Write 25 × 37 and 27 × 35. Do you think they will give the same answer? Children work in pairs to find the 2 answers. Agree that they do not give the same answer. Show children how to find the digital root of each number in the first multiplication and the answer. Children multiply the digital roots in each multiplication and find the digital root of the product. Compare with the digital root of the answer to find that it is the same. Children repeat for the second multiplication. What do they find?
Group Activities
-- Apply long multiplication in an investigative context. Explore digital roots and explain observations.

Day 3 Teaching
Write 18 × 324 and 13 × 368. Which do you think will have the bigger answer? Use rounding to make estimates. Ask children what is different about these calculations from those they did last time (there is a 100s digit in one of the numbers). Model using long multiplication to find 324 × 18. Compare with the grid method. Ask children to work in pairs to find 368 × 13. Model using long multiplication to find 28 × 324; ask children to calculate 23 × 368, estimating the answer first.
Group Activities
-- Create a Top Tips poster for using long multiplication. Use to scaffold calculation.
-- Multiply 3-digit numbers by numbers between 40 and 60.

You Will Need

  • Mini-whiteboards and pens
  • ‘Multiplying 2-digit numbers’ (see resources)
  • Flipchart and pens
  • ‘Multiplying 3-digit numbers by 2-digit numbers’ (see resources)

Mental/Oral Maths Starters

Day 1
Multiplication facts (pre-requisite skills)

Suggested for Day 2
Rockin’ remainders (simmering skills)

Day 3
Multiply multiples of 10 by multiples of 100 (pre-requisite skills)

Procedural Fluency

Day 1
Use long multiplication to multiply pairs of 2-digit numbers. Are the children fluent enough to finish the Multiplication Marathon?

Day 2
Choose pairs of 2-digit numbers to multiply together to give answers within given ranges.

Day 3
Use long multiplication to multiply 3-digit numbers by 2-digit numbers up to 30.
Use long multiplication to multiply 3-digit numbers by 2-digit numbers up to 60.

Mastery: Reasoning and Problem-Solving

  • Alan saves 50p coins. He has saved 93 of them. How much money has Alan saved?
  • Mel’s hotel swimming pool is 33 metres long and 12 metres wide. On every day of her 3-week holiday, she swam 15 lengths. How far did she swim in total? Each day, her brother Sammy swam 35 widths. Who swam farthest?
  • Write the missing digit:
    2☐3 × 7 = 1981
    46☐ × 13 = 6097

In-depth Investigation
Use the Whole class investigation on Day 2.

Extra Support

Root Revelation
Using the grid method to multiply 3-digit numbers by 1-digit numbers