Short Blocks

Maths Year 3 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 Solve scaling problems (suggested as 2 days)

Objectives

Solve scaling problems
Unit 4: ID #3907

National Curriculum
Mult/Div (iii)

Hamilton Objectives
21. Solve problems, including (missing number and) scaling problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write a list of ingredients for a flapjack recipe. This is enough to make one tray. We need lots of flapjacks for the cake sale. What do we need to do? Together, multiply each measure by 4 by doubling twice. Repeat with a lemonade recipe, scaling it up by a factor of 10.
Group Activities
-- Scale up recipes by 4x and 10x.
-- Scale up drawings (rectangles and triangles) by 4x and 10x.

Day 2 Teaching
Show a life-size outline drawing of yourself with measurements that are all multiples of 10cm. Explain that we will make a scale drawing of this picture, scaling each measurement down to 1/10 of its original length. My height is 170cm, so what will the height be on your piece of paper…?
Group Activities
Use the in-depth problem-solving investigation ‘Follow the numbers’ from NRICH as today’s group activity.
Or, use these activities:
-- Scale down a drawing by a factor of 10.
-- Scale down Lego houses to 1/4 of their original number of bricks.

You Will Need

  • ‘Scaling up’ sheets 1 and 2 (see resources)
  • cm2 paper
  • To-scale drawing of person (prepare in advance)
  • Poster paper
  • Lego bricks
  • Rulers

Mental/Oral Maths Starters

Day 1
Double numbers to 50 (pre-requisite skills)

Day 2
Halve even numbers to 100 (pre-requisite skills)

Procedural Fluency

Day 1
Help a caterer work out how to cater for parties 4 times and 10 times the size of a standard party.

Day 2
Draw shapes according to instructions then scale them down by a factor of 4.

Mastery: Reasoning and Problem-Solving

  • The postcards in the art gallery measure 15cm by 10cm.
    One is of a painting which is 4 times bigger.
    One is of a painting which is 10 times bigger.
    One is of a painting which is 5 times bigger.
    Write the measurements of each painting.
  • A painting in the museum measures 160cm by 100cm. The gift shop sells posters of the painting at 1/4 full size and postcards at 1/10 full size. How big are posters and postcards?

In-depth Investigation: Follow the Numbers
Adapt this investigation to find the digital root and multiply by 4 or 10. Keep following this rule and see what happens. Investigate the patterns when you start with different numbers. Follow the Numbers from nrich.maths.org.

Extra Support

Double Double
Multiplying by 4 by doubling twice; Dividing by 4 by halving twice

Unit 2 Divide numbers just beyond times tables (suggested as 3 days)

Objectives

Divide numbers just beyond the times tables
Unit 5: ID #3917

National Curriculum
Mult/Div (ii) (iii)

Hamilton Objectives
16. Understand that division is the inverse of multiplication, e.g. ? × 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
21. Solve problems, including missing number and scaling problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 65 ÷ 5, then sketch a line from 0 to 65. We could draw every hop of 5, but we don’t need to! Are there more than 10 lots of 5 in 65? Draw a jotting to show 10 lots of 5 to 50 and 3 lots of 5 to 65. Add: 10 lots + 3 lots = 13 lots of 5. Repeat for 70 ÷ 5, 52 ÷ 4 and 42 ÷ 3.
Group Activities
-- Practise divisions just beyond the times tables by drawing ENL jottings.
-- Play ‘more or less than 10’ card game, predicting, then checking selected divisions by drawing empty number line (ENL) jottings.

Day 2 Teaching
Write 54 ÷ 3. How many 3s in 54? More than 10? Where do 10 lots of 3 get to on the line? How much is left? How many 3s? Draw an empty number line jotting to show this, writing 10 × 3 then 8 × 3. Repeat with other divisions, e.g. 112 ÷ 8 and 51 ÷ 3. Use an ENL to find 43 ÷ 3. Once you get to 42, point out that there is 1 left over. If we had 43 children and we wanted to put them into groups of 3, we’d have 14 groups and 1 child left over. We call this ‘left over’ number a remainder. This is an important word to remember…
Group Activities
-- Play division mini-bingo with divisions that are just beyond the times tables (no remainders).
-- Investigate numbers that will divide by 3 or 4 or both without leaving a remainder.

Day 3 Teaching
Write 46 ÷ 3. Children help you to sketch an ENL a jotting: a jump of 10 × 3 to 30, then a jump of 5 × 3 to 45. Point to the gap between 45 and 46. Label it ‘r1’ to stand for remainder 1. There is 1 left over. Repeat for 78 ÷ 5, 115 ÷ 5 and 51 ÷ 4.
Group Activities
Use the in-depth problem-solving investigation ‘Threes and Fours’ as today’s group activity.
Or, use these activities:
-- Play a game choosing and calculating divisions then collecting counters for the remainders.
-- Division with remainders card game.

You Will Need

  • ITP: Number Dial
  • ‘Division jottings’ sheet (see resources)
  • ‘Number cards’ sheet (see resources)
  • 1–9 and 1–6 dice
  • ‘Recording table’ sheet (see resources)
  • Additional activity sheets (see resources)
  • Mini-whiteboards and pens
  • Counters
  • ITP: Tell the Time

Mental/Oral Maths Starters

Day 1
Division facts for the 3 and 4 times tables (pre-requisite skills)

Day 2
8 times table (pre-requisite skills)

Suggested for Day 3
Find a time later (simmering skills)

Procedural Fluency

Day 1
Complete division calculations that sit slightly beyond the times tables.

Day 2
Complete division calculations that sit slightly beyond the times tables: some with remainders.

Day 3
Division calculations with remainders for just beyond the 3-, 4-, 5- and 8-times tables.

Mastery: Reasoning and Problem-Solving

  • How many 3s in each number?
    45
    52
    39
  • Will the remainder be the same in these divisions?
    (i) 53 ÷ 4
    (ii) 66 ÷ 5
    (iii) 40 ÷ 3
    Guess first and then work each one out to check.

In-depth Investigation: Threes and Fours
Children explore multiples of 3 and 4 to find divisibility patterns.

Extra Support

Flip-flops
Dividing within tables by 3, 4 and 5 (no remainders)

Unit 3 Gain fluency using multiplication & division (suggested as 3 days)

Objectives

Gain fluency using multiplication and division
Unit 6: ID #3923

National Curriculum
Mult/Div (iii)

Hamilton Objectives
19. Multiply a 1-digit number by a 2-digit number using partitioning.
16. Understand that division is the inverse of multiplication, e.g. ? × 3 = 21 ≡ 21 ÷ 3 = ?
21. Solve problems, including missing number and scaling problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a grid on the board and ask children to explain each stage to a partner. Take feedback. Ensure children remember how this method works. Children work out 7 × 35. Ask a pair up to the board to model solving the calculation: one to write, the other to ‘commentate’.
Group Activities
-- Practise multiplying numbers between 20 and 40 by 1-digit numbers.

Day 2 Teaching
Say that 4 shells decorate each sandcastle. We have 18 shells, how many sandcastles can they decorate? Sketch a 0–18 line and draw 4 hops to 16. Point out the remainder (2). Agree that 4 castles can be decorated and 2 shells are left over. Repeat to solve other problems.
Group Activities
-- Complete divisions and score for each reminder. Reason about possible remainders for a given divisor.

Day 3 Teaching
Write names of 4 roller coaster rides on cards. 4 children each hold one. Imagine we are at a theme park and we are deciding which two rides to go on, and in which order. Together, we will find all the possible options. Work systematically to find all 12 possible combinations.
Group Activities
Use the in-depth problem-solving investigation ‘Yuck or Yum!’ as today’s group activity.
Or, use these activities:
-- Investigate all possible combinations for 3 beach holiday activities.
-- Investigate the possible combinations of children and cats there could be for a given number of legs.

You Will Need

  • 1–6 dice
  • 1–9 dice
  • Mini-whiteboards and pens
  • ‘Blank multiplication grids’ sheet (see resources)
  • ‘Finding remainders’ sheet (see resources)
  • 4 large cards
  • ‘Holiday activities’ sheet (see resources)

Mental/Oral Maths Starters

Day 1
Division facts for the 4 times table (pre-requisite skills)

Day 2
8 times table (pre-requisite skills)

Suggested for Day 3
40 times table (simmering skills)

Procedural Fluency

Day 1
Complete calculations using the grid method: 2-digit numbers to 25.
Complete calculations using the grid method: 2-digit numbers to 40.

Day 2
Divide a big box of cakes into smaller bags. How many bags can be made; how many cakes left over?
Divide a big box of chocolates into smaller gift boxes. How many gift boxes can be made; how many chocs left over?

Day 3
Work out all possible clothing outfit combinations.

Mastery: Reasoning and Problem-Solving

  • Start with 11.
    Multiply by 4 and then multiply the answer by 5.
    Halve your answer.
    Divide that answer by 10.
    What do you notice?
    Start with 12. Repeat the steps. Does the same thing happen? Can you explain why?
    Challenge! Repeat, starting with 13.
  • Tim uses four wheels on each Lego car. He counts up and sees that he has 54 wheels. How many cars can he make?
  • There are three ice-cream flavours: strawberry, chocolate and vanilla. You choose any two and have one on top and one underneath. How many possible ways can we choose the pair?

In-depth Investigation: Yuck or Yum!
Children find all possible food combinations from given lists and then decide which are ‘yuk’ and which are ‘yum’!

Extra Support

Multiplication Tables - Matching Cards
Use this game from NRICH to gain fluency with recall of tables facts. Matching Cards from nrich.maths.org.