Maths Year 1 Summer Multiplication, Division, Fractions

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Counting in 2s, 5s and 10s (suggested as 3 days)

Objectives

Counting in 2s, 5s and 10s
Unit 1: ID# 1889

National Curriculum
Num/PV (ii)
Mult/Div (i)

Hamilton Objectives
2. Count in 2s, 5s, 10s.
14. Solve simple problems involving multiplication/division. Find answers with support using objects, pictorial representations or arrays.

Teaching and Group Activities for Understanding

Day 1 Teaching
Ask three children to stand at the front of the class and hold up their hands. Count in 5s to count the total number of fingers. Draw six jumps of 5 on a 0–50 beaded line. Write on the board: 6 lots of 5 is 30. Repeat, counting the number of fingers by counting in 10s. Draw three jumps of 10 on 0–100 beaded line. Write on the board: 3 lots of 10 is 30. Repeat for six children and twelve hands.
Group Activities
-- Count in 2s, 5s or 10s and record on a beaded line.
-- Count sweets for cookies in 2s, 5s or 10s.

Day 2 Teaching
Show five 10p coins. Count in 10s pointing at each coin. Write on the board: 5 lots of 10p is 50p. Repeat with seven 2p coins and six 5p coins. Swap 20 pennies for a number of 10ps, 2ps and 5ps. Record: • lots of 10p is 20p, • lots of 2p is 20p, • lots of 5p.
Group Activities
-- Count in 2s, 5s and 10s to ‘decorate’ clown images.
-- Roll a dice and count out that many 2p, 5p or 10p pieces.
-- Play ‘Big Saver’ game by counting ‘lots of’ 2p, 5p or 10p pieces.

Day 3 Teaching
Show children some rubbers. Explain that each rubber costs 10p. How many 10p coins would we need to buy four rubbers? So, how much would four rubbers cost? Discuss in pairs. Good mathematicians like us always try to find efficient ways to do things, so instead of writing 4 lots of 10 is 40 which uses quite a lot of words, we can write 4 × 10 = 40. We read this as ‘4 times 10 equals 40’. Repeat for six rubbers.
Group Activities
Use the ‘Trains’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Sort objects, counting ‘lots of’ 10p and recording as hops on a penny line and as multiplication number sentences.
-- Play ‘buying bears’ game, counting ‘lots of’ 5p and 10p, recording as hops on a penny line and as multiplication number sentences.

You Will Need

  • 0–50 and 0–100 beaded line (see resources)
  • Cubes
  • Dice (1–10 and 1–6)
  • 0–100 landmarked line (see resources)
  • Additional activity sheets (see resources)
  • Rubbers and 2p, 5p and 10p coins
  • ‘Clown’ sheets 1–3 (see resources)
  • Buttons, gummed paper spots and pom-poms
  • Dice (adapted to show 2p, 5p and 10p)
  • 1–10 number cards
  • Range of objects in tubs, e.g. counters, pencils, multilink, beads, straws, etc.
  • Counting bears, price labels

Mental/Oral Maths Starters

Day 1
Count in 2s (pre-requisite skills)

Day 2
Count in 5s to 50 (pre-requisite skills)

Suggested for Day 3
Doubles and halves (simmering skills)

Procedural Fluency

Day 1
Count in 2s, 5s and 10s, recording hops on a beaded line to 50.
Record repeated addition as a multiplication sentence.

Day 2
Calculate the cost of multiple items priced at 2p, 5p or 10p. Record jumps on a penny line to 50p

Day 3
Calculate the cost of multiple bears priced at 2p, 5p or 10p. Record hops on a penny line to £1.

Mastery: Reasoning and Problem-Solving

  • James has five of each coin in three separate piles.
    2p 5p 10p
    How much does he have in each pile?
  • Write the missing numbers:
    15, 20, 25, ☐, ☐, ☐
    50, 60, 70, ☐, ☐, ☐
    8, 10, 12, ☐, ☐, ☐, ☐
  • Write < or > or = to complete each sentence.
    (a) 4 × 5 ☐ 2 × 10
    (b) 10 × 2 ☐ 3 × 10
    (c) 3 × 5 ☐ 8 × 2

In-depth Investigation: Trains!
Children use the same size ‘carriages’ (number rods, e.g. Cuisenaire) to make a ‘train’ of 20 units.

Extra Support

Smelly Socks!
Counting in 2s – ‘clever counting’ and early multiplication

NB The multiplication symbol is not introduced until Day 3 of this unit. Avoid the temptation to use it during this activity.

Unit 2 Division by finding how many sets (suggested as 2 days)

Objectives

Division by finding how many sets
Unit 2: ID# 1907

National Curriculum:
Num/PV (ii)
Mult/Div (i)

Hamilton Objectives
14. Solve simple problems involving multiplication/ division; find answers with support using objects, pictorial representations or arrays.

Teaching and Group Activities for Understanding

Day 1 Teaching
Draw 10 rabbits. Two rabbits live in a hutch. How many hutches do we need for ten rabbits? How can we work this out? Draw around groups of two rabbits. How many groups? Five, so we need five hutches. Repeat with 14 rabbits, and agree we need 7 hutches.
Group Activities
-- Group different quantities of rabbits into 2s and work out how many hutches are needed for them.

Day 2 Teaching
On the IWB, show children ten counters arranged randomly. How many groups of 5? Circle the groups and agree we can make two groups. Underneath show a 0–30 beaded line. Circle groups of 5 to show two groups of 5 in 10. Repeat with 20 and then 30 counters.
Group Activities
Use the in-depth problem-solving investigation ‘Lots of Biscuits’ from NRICH as today’s group activity.
Or, use these activities:
-- Group different quantities of cakes into 5s and work out how many boxes are needed for them.
-- Calculate how many groups of 2, 5 and 10 there are in given numbers.
-- Make up word problems for how many groups there are of 2, 5 and 10 in given numbers.

You Will Need

  • ‘Rabbits’ sheet (see resources)
  • ‘How many hutches’ sheets 1–3 (see resources)
  • Number cards with multiples of 5 on them (5–60)
  • Cubes and counters
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Counting in 2s to 30 (pre-requisite skills)

Day 2
Counting in 5s and 10s to 100 (pre-requisite skills)

Mastery: Reasoning and Problem-Solving

  • True or false?
    40p is eight 5p coins.
    If we have 10 gloves, we can make 5 pairs.
    12 is 8 groups of 2.
    35 beads can be made into 7 necklaces, each with 5 beads.
  • How many 10p coins are in my purse if I have 60p? (I only have 10p coins!)
  • How many 5p coins are in my purse if I have 25p? (I only have 5p coins!)
  • How many 2p coins are in my purse if I have 26p? (I only have 2p coins!)

In-depth Investigation: Lots of Biscuits
Green class have been baking. Can you help them share out the biscuits? Lots of Biscuits from nrich.maths.org.

Extra Support

Good Dog
Using grouping to divide by 2, then 5

Unit 3 Doubling and halving (suggested as 2 days)

Objectives

Doubling and halving
Unit 3: ID# 1913

National Curriculum
Fr (i)

Hamilton Objectives
13. Recognise doubles to double 6 and find related halves (half even numbers up to 12).
15. Recognise, find, name a half as 1 of 2 equal parts of a quantity.

Teaching and Group Activities for Understanding

Day 1 Teaching
Explain that when we double a number we add the same amount again, e.g. 2 doubled is 2 + 2 = 4, 3 doubled is 3 + 3 = 6, etc. What is double 10? 10 + 10 = 20. Double 11? We double the 10, (20) and then double the 1 (2). Recombine these amounts to give a total of 22. Provide a visual representation to support visualisation, using base-10 equipment (e.g. Dienes cubes or number shapes such as Numicon) to model the partitioning, doubling and recombining steps. Repeat with 12, 13 and 14.
Group Activities
-- Double handfuls of cubes.
-- Play double numbers card game using numbers up to 14.

Day 2 Teaching
Explain that halving is sharing the number between two. Demonstrate by sharing four sweets between two children. Repeat with other even numbers up to 20. Odd numbers are harder to share as there is always one left over. Display a bar model to show double 8 is 16. Use this to halve 16. As last time, providing a visual representation using base-10 equipment will support partitioning, halving and recombining.
Group Activities
Use the ‘Halving Chains’ in-depth problem-solving investigation (below) as today’s group activity.
Or, use these activities:
-- Play halves pairs game with numbers up to 24.
-- Play halves pairs game with numbers up to 34.

You Will Need

  • Cubes
  • Base-10 equipment, e.g. Dienes blocks or number shapes such as Numicon
  • ‘Doubling recording sheet’ (see resources)
  • 'Doubling cards' (see resources)
  • Number cards 1–10
  • Additional activity sheets (see resources)

Mental/Oral Maths Starters

Day 1
Doubling numbers to 6 (pre-requisite skills)

Day 2
Odd/even numbers (pre-requisite skills)

Procedural Fluency

Day 1
Double numbers to 15; record as an addition sentence.
Double numbers to 21; record as an addition sentence.

Day 2
Halve numbers up to 22.
Halve numbers up to 32.

Mastery: Reasoning and Problem-Solving

  • Draw lines from each double to its matching half.
146
1210
167
288
2013
2414
2612
  • Double 3, double the answer, and double the answer!
    Halve 28 and halve the answer. Is the answer more than 10?

In-depth Investigation: Halving chains
Children investigate which numbers from 1 to 20 will give the longest ‘halving chain’, where each ‘link’ is a whole number.

Extra Support

Copycat
Finding doubles from double 1 to double 10

Be Fair!
Halving even numbers up to 10

Unit 4 Multiplication and division as sets (suggested as 3 days)

Objectives

Multiply as 'sets of' and divide as 'how many sets'
Unit 4: ID# 1931

National Curriculum
Num/PV (ii)
Mult/Div (i)

Hamilton Objectives
2. Count in 2s, 5s, 10s.
14.Solve simple problems involving multiplication/ division; find answers with support using objects, pictorial representations or arrays.

Teaching and Group Activities for Understanding

Day 1 Teaching
Sit children in a circle and place four bags of 5 buttons in the middle. How many buttons in total? Model counting in 5s: 5, 10, 15, 20. Write on the board: 4 × 5 = 20. Repeat with three bags of 5 buttons, six bags of 5 buttons and then eight bags of 2 counting bears.
Group Activities
Use the ‘Balancing Act’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Calculate multiplications by creating multiple ‘sets of’.
-- Create multiple ‘sets of’ counting bears.

Day 2 Teaching
Build three towers of 10 cubes. How many cubes in total? Count in 10s to establish 30. Then record on the board: 3 × 10 = 30. Repeat to find five towers of 10 cubes. Then show 40 cubes on the floor and ask how many towers of 10 cubes can children make from these.
Group Activities
-- Make multiple towers of 5 or 10 cubes and calculate how many cubes are needed in total.
-- Work out how many towers of 5 (or 10) can be made from a given multiple of 5 (or 10).

Day 3 Teaching
I have five 2p coins in my purse. How much money do I have altogether? Discuss, then count in 2s to 10p. Record on the board: 5 x 2p = 10p. Repeat for eight 2p coins in the purse. I have 8p in my purse. All of the coins are 2p coins. How many 2p coins are there? On a 0-50p penny line, circle groups of 2p up to 8p. There are four groups of 2 in 8p, so I must have four 2p coins! Repeat with other problems like this.
Group Activities
-- Draw sets of 2 on a penny line to work out how much money is in a purse.
-- Find and record the number of 2ps, 5ps or 10ps needed to make a multiple of 10p.

You Will Need

  • Buttons (or any other small objects)
  • Counting bears and transparent bags
  • ‘Multiplication sets’ sheet (see resources)
  • Cubes and dice (1–6 and 1–10)
  • Number cards 2–10
  • Number cards (multiples of 5 from 10-50)
  • 2p and 5p coins and purses/small bags
  • 0–50p penny line (see resources)
  • Additional activity sheets (see resources)
  • Number cards (multiples of 10 from 10-100)

Mental/Oral Maths Starters

Day 1
Counting in 2s (pre-requisite skills)

Day 2
Counting in 5s (pre-requisite skills)

Day 3
Count on/back in 10s (pre-requisite skills)

Procedural Fluency

Day 1
Solve ×2 and ×5 multiplications using cubes or landmarked lines.

Day 2
Solve multiplication problems using cubes to make towers.

Day 3
Work out how many 2p or 5p coins are in a purse from a given total amount.

Mastery: Reasoning and Problem-Solving

  • Maia has eight 2p coins, Teddy has two 10p coins, and Jon has three 5p coins. Who has the most money? Who has the least money?
  • There are eight towers with 5 cubes in each tower? How many cubes altogether? How many in total if there are 10 cubes in each tower?
  • Tom has 30p in his purse. He has six coins all the same. What coin does he have?
  • Anna has 24p in her purse. She has 12 coins all the same. What coins does she have?

In-depth Investigation: Balancing Act
Children balance multiple number shapes to find equivalent multiplications.

Extra Support

Lots of Biscuits
Can you help the children share out the biscuits they have baked? Lots of Biscuits from nrich.maths.org.

NB This activity was suggested as the investigation for Unit 2, but there is no harm in revisiting it. Read the teachers’ notes at nrich.maths.org for key questions and ideas for possible extension.