Maths Year 1/2 Spring Fractions and Multiplication

Each unit has everything you need to teach a set of related skills and concepts.

Unit 1 Clever counting; multiplication (suggested as 5 days)

Planning and Activities

Day 1
Divide the class into 2 groups and rehearse ‘Whisper counting’ (alternate numbers in whispered, then normal voices; louder voices emphasise the 2s numbers). Count again, recording sequence of 2s: 2, 4, 6, … 20. Count pairs of shoes in 2s to find how many shoes in total.
Further Teaching with Y2
Highlight multiples of 2 on Number grid ITP. Discuss patterns and look at different 1s digits in odd and even numbers.
Group Activities: T with Y2
Y1 -- Count in 2s, using bodies and images, or objects in pots.
Y2 -- Sort numbers according to properties, or play heads and tails odds and evens.

Day 2
Use Number grid ITP to explore patterns of multiples of 2, 5 and 10. Describe patterns in counting sequences, e.g. 7, 12, 17, 22 ... and 8, 13, 18 and 23 …
Further Teaching with Y1
Exploring odd and even numbers with pairs of socks. Create a generalisation.
Group Activities: T with Y2
Use the in-depth problem-solving investigation ‘Multiple Madness’ as today’s group activity.
Or, use these activities:
Y1 -- Sort numbers into odds and evens by looking at the 1s digit, or by sorting pairs of socks.
Y2 -- Complete and describe number patterns that involve 2s, 5s and 10s. Or, investigate true, sometimes true or never true statements about patterns.

Day 3
Revise number doubles using fingers.
Further Teaching with Y2
Using ‘Whisper counting’ for 3s. Describe the pattern of multiples of 3 on the Number grid ITP. Use it to predict other multiples of 3.
Group Activities: T with Y1
Y1 -- Play a game to improve recall of doubles facts.
Y2 -- Identify multiples of 3; some children may use a 1–100 grid.

Day 4
Double numbers to 12 using physical objects, e.g. sweets or cubes. Note that all doubles (of whole numbers) are even numbers.
Further Teaching with Y2
Count in 2s, 3s, 5s and 10s on a beaded line, recording as multiplication sentences.
Group Activities: T with Y1
Y1 -- Calculate doubles of numbers up to 20.
Y2 -- Generate and solve times 2, times 3, times 5 and times 10 multiplication sentences. Or, solve and create x2, x3, x5 and x10 word problems.

Day 5
Halve even numbers up to 24 using physical objects.
Further teaching with Y2
Identify numbers on a 1–100 grid using a variety of properties and mathematical language.
Group Activities: T with Y1
Y1 -- Count even numbers of cubes; find and record half.
Y2 -- Decipher ‘mystery’ numbers from ‘number property’ clues.

You Will Need

  • Number grid ITP
  • Flipchart and pens
  • Labelled pots with counting objects inside
  • Hoops, Coins, Socks, Cubes, Sticky notes
  • Number cards 1–100
  • Large sheet of paper
  • ‘Odd and even numbers’ sheet (see resources)
  • ‘Patterns’ (see resources)
  • ‘1–100 number grid’ (laminated, see resources)
  • 1–10 dice, 1–6 dice
  • Sweets (or other small snack),
  • ‘Doubles’ (see resources)
  • Number shapes (e.g. Numicon)
  • Base-10 equipment (e.g. Dienes blocks)
  • ‘Spinners’ (see resources)
  • ‘Multiplying by 2, 3, 5 and 10 using beaded lines’ (see resources)
  • ‘Halve’ (see resources)
  • ’What am I?’ (see resources)
  • ‘1–50 number grid’ (see resources, preferably laminated)
  • ‘0–30 beaded line’ (see resources)

Short Mental Workouts

Day 1
Bean bag doubling

Day 2
Count in 2s (with division facts - Y2)

Day 3
Whisper counting

Day 4
Recognise multiples of 10

Day 5
Hidden numbers

Worksheets

Day 1
Y1: Count in 2s.
Y2: Using a selection of digit cards, make odd and even 2-digit, then 3-digit numbers.

Day 2
Y1: Identify odd numbers. Sort odd and even numbers.
Y2: Complete missing numbers in number sequences.

Day 3
Y1: Double numbers 1-6.
Y2: Shade multiples of 3 number grids.
Identify multiples of 3 from a set of 2-digit numbers.

Day 4
Y1: Double numbers 6 to 11. Double numbers 13 to 19.
Y2: Multiply numbers to 12 by 2, 3, 5 and 10.

Day 5
Y1: Halve even numbers to 12. Solve halving problems.
Y2: Sort numbers by one or more properties.

Mastery: Reasoning and Problem-Solving

Y1

  • Write the missing numbers in these two sequences:
    __, __, 11, 13, __, 17, __
    24, __, 20, 18, __, __, __
  • Draw an arrow from each number on the left to its matching half on the right:
    4 6
    12 10
    16 2
    8 8
    20 3
    14 4
    6 7
  • How many times can we halve 24 biscuits before we have to break a biscuit in half to share it equally
  • Jessie starts counting in 2s from 5. Will she say 25? Will she say 52? Explain your ideas.

Y2

  • Peter counts in 5s.
    When he says ‘40’, how many 5s has he counted?
  • Fran starts counting in 2s from 12: 12, 14, 16 … Will she say the number 43?
  • Poppy says that she can count in 3s or 5s, starting at zero, and reach the number 20. Do you agree?
  • Mrs Jones starts counting in 1s from zero. Annie stands up when she hears a multiple of 2, Bobby stands up when he hears a multiple of 3, Carl stands up when he hears a multiple of 5 and Dan stands up when he hears a multiple of 10.
    - Bobby and Annie stand up. What number might it be?
    - Annie and Carl stand up. What number might it be?
    - All four children stand up. What is the lowest number it could be?
    - What is the next number where they will all stand up?

In-depth investigation: Multiple Madness
Children arrange digit cards to form multiples of 2, 5 and 10 and explore different possibilities.

Unit 2 Relating multiplication and division (suggested as 5 days)

Planning and Activities

Day 1
Count in 2s, looking at the pattern on a 100 grid. Solve 2 times table problems, e.g. How many wheels on 5 bikes?
Further Teaching with Y2
Using a 3 by 5 array of counters to establish multiplication and division facts and the links between them.
Group Activities: T with Y2
Y1 -- Count pairs of items in 2s, up to 10 lots of 2.
Y2 -- Make arrays for given multiplication facts; create and solve multiplication word problems Or, write multiplication sentences to match arrays.

Day 2
Count in 10s on a 1–100 grid, solving and recording 10 times table problems, e.g. 4 sticks of 10 cubes. Move to representing ‘lots of’ on a beaded number line. Record a multiplication number sentence, i.e. 4 × 10 = 40.
Further Teaching with Y2
Arrange counters in groups to model division as grouping. Represent on the beaded line by drawing rings around groups of beads.
Group Activities: T with Y2
Y1 -- Explore grouping in 10s, using sticks of 10 cubes or a bead string image.
Y2 -- Answer division questions using grouping. Or, group ‘eggs’ into egg boxes to make groups of 6 and note any leftovers.

Day 3
Use arrays of counters and hops on the beaded number line to show commutativity of multiplication.
Further Teaching with Y1
Counting in 5s using a range of representations (arrays, hands, or on a number grid) to rehearse ‘clever’ counting in 5s.
Group Activities: T with Y1
Y1 -- Explore grouping in 5s, using arrays of 5s using counters or using hands.
Y2 -- Derive all multiplication facts for various arrays. Or, play an online array game, suggesting pairs of multiplication facts.

Day 4
Practise grouping in 5s and 10s using cubes or sweets.
Further Teaching with Y2
Represent multiplication and division facts on an array and a beaded number line.
Group Activities: T with Y1
Y1 -- Make towers of 5 and 10 cubes.
Y2 -- Explore all multiplication and division facts for various arrays.

Day 5
Model arrays of counters (rows of 2s, 5s and 10s). Know that not all numbers can be arranged in an array with a given number in each row.
Further Teaching with Y2
Model solving multiplication and division problems, recording number sentences as appropriate, using packets of buns.
Group Activities: T with Y2
Use the in-depth problem-solving investigation ‘Lots of Biscuits’ from NRICH as today’s group activity.
Or, use these activities:
Y1 -- Investigate placing 10 to 30 counters in arrays with rows of 2, 5 and 10 counters.
Y2 -- Relate multiplication and division through the creation of word problems, some based on arrays.

You Will Need

  • ‘0–20 beaded line’ (see resources)
  • Number grid ITP; Grouping ITP
  • ‘Pairs’ (see resources)
  • 1–6 dice; 1–10 spinner; 1–100 grid
  • ‘Arrays’ (see resources)
  • Pegboards and pegs; Counters; Cubes
  • Coins (2p, 5p and 10p)
  • ‘0–20 beaded line’, ‘0–50 beaded line’, ‘0–100 beaded line’ (see resources)
  • 2–6 number cards; 20–60 multiples of 10 number cards
  • ‘Division question cards’ sheets 1 and 2 (see resources)
  • 6-hole egg boxes
  • Sugar paper, markers, scissors
  • ‘0–50 beaded lines’ (see resources)
  • Small transparent bags (e.g. Sandwich bags)
  • Sweets, Buns (optional)
  • ‘Array cards’ Sheets 1, 2 and 3 (see resources)
  • ‘How many?’ (see resources)
  • Bags, party bag contents
  • Numbered cards 32, 35, 44, 49; Small cards

Short Mental Workouts

Day 1
Ten more/ten less

Day 2
Count in halves

Day 3
Odd or even?

Day 4
Bubble doubles

Day 5
Count in 10s

Worksheets

Day 1
Y1: Identify and describe patterns of 2s in a 1-30 number grid. Identify and describe patterns of 2s in a 1-50 number grid.
Y2: Match multiplication number sentences to arrays.

Day 2
Y1: Count in 10s on beaded lines.
Y2: Practise grouping numbers to 90.

Day 3
Y1: Count in 5s on beaded lines.
Y2: Write multiplication and division facts for arrays.

Day 4
Y1: Group in 5s and 10s on a beaded line.
Y2: Draw arrays; write matching multiplication and division facts.

Day 5
Y1: Identify groups in arrays.
Y2: Write division word problems based on arrays.

Mastery: Reasoning and Problem-Solving

Y1

  • 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?
  • Write the missing numbers:
    15, 20, 25, ☐, ☐, ☐
    50, ☐, 70, ☐, ☐, 100
    ☐, 10, ☐, ☐, 16, ☐, ☐
  • Write < or > or = to complete each sentence.
    (a) 4 × 5 ☐ 2 × 10
    (b) 10 × 2 ☐ 3 × 10
    (c) 3 × 5 ☐ 8 × 2

Y2

  • The same number is missing from each number sentence. What is it?
    ☐ × 3 = 15
    1 × ☐ = 5
    30 = 6 × ☐
  • Write each addition as a multiplication. Calculate the total.
    5 + 5 + 5 + 5 + 5 + 5 + 5 = ☐
    ☐ = 2 + 2+ 2 + 2 + 2 + 2
    10 + 10 + 10 + 10 = ☐
  • How many groups of 3 make 18?
  • How many groups of 6 make 12?
  • How many groups of 5 make 45?
  • Will there be any eggs left over if I put 50 eggs into boxes of 6?

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.

Unit 3 Fractions (suggested as 5 days)

Planning and Activities

Day 1
Revise doubling first for 1-digit numbers and then teens numbers using base-10 equipment (Dienes or Numicon).
Further Teaching with Y2
Physically model finding 1/2 and 1/4 of a number of objects.
Group Activities: T with Y1
Y1 -- Double handfuls of cubes. Or, play a double numbers card game using numbers to 14.
Y2 -- Explore finding 1/2s and 1/4s of various numbers; solve fraction problems.

Day 2
Briskly revisit finding 1/2 and 1/4 of 12 objects. Introduce sharing between three to find 1/3. Model using concrete resources, e.g. decorations or candles on a cake.
Further Teaching with Y1
Halve even numbers, using bar models and base-10 equipment to represent the concept.
Group Activities: T with Y2
Use the in-depth problem-solving investigation ‘Happy Halving’ from NRICH as today’s group activity.
Or, use these activities:
Y1 -- Play halves pairs with numbers up to 24 (or 34).
Y2 -- Find Smartie™ fractions through sharing. Sort numbers according to sharing results.

Day 3
Explore halving small odd numbers, e.g. 7 and 9, modelled with real objects (biscuits, sweets, etc.). Fold a paper strip of squares to provide a different representation. Record halving number sentences, e.g. half of 9 is 4½.
Further Teaching with Y2
Count in halves and quarters, modelled using paper fraction shapes and represented on a number line.
Group Activities: T with Y1
Y1 -- Halve biscuits to explore finding half of odd numbers.
Y2 -- Write, count and identify hidden numbers of 1/2s and 1/4s on a number line. Or, play a counting in 1/2s and 1/4s card game.

Day 4
Quickly revisit folding a paper circle to find halves and quarters. Then model folding a shape that can be folded in half one way, but not the other, and one that cannot be halved at all.
Further Teaching with Y2
Find fractions of numbers (including ¾) using physical objects (bananas) and relating to number facts.
Group Activities: T with Y2
Y1 -- Investigate halving and quartering shapes by folding.
Y2 -- Find and record 1/2, 1/3, 1/4 and 3/4 of given numbers. Or, calculate fraction amounts playing a ‘Find the fraction’ card game.

Day 5
Share candles between different fractional amounts of cake to find half and quarters.
Further Teaching with Y2
Finding 1/2, 1/3 and 1/4 ­ of ingredients to adjust recipes.
Group Activities: T with Y1
Y1 -- Divide a tower of cubes equally to find 1/2 of that number. Or, find 1/4 of numbers by breaking towers of cubes into half and half again.
Y2 -- Change recipe quantities to make 1/2, 1/3 or 1/4 of the given recipe.

You Will Need

  • Base-10 equipment, e.g. Dienes blocks or number shapes such as NumiconTM
  • Cubes; Play dough
  • ‘Doubling recording sheet’ (see resources)
  • ‘Doubling cards’ (3 sheets, see resources)
  • Number cards 1–10; Labels; Counters (small and large)
  • ‘Stationery problems’ (see resources)
  • ‘Number cards’ (cut out, see resources)
  • Smarties™, cupcakes, sweets, biscuits
  • ‘Cakes’ sheet (see resources)
  • ‘Halving’ bar model (see resources)
  • ‘Number cards (wholes)’ sheets 1 and 2 (see resources)
  • ‘Number cards (halves)’ sheets 1 and 2 (see resources)
  • ‘Fractions cards set 1 and set 2’ (see resources)
  • ‘Paper shapes’ (see resources)
  • ‘0–5 Number line: halves’ (see resources)
  • ‘0–5 Number lines: quarters’ (see resources)
  • ‘Paper strips’ (see resources)
  • ‘Halving recording sheet’ (see resources)
  • ‘Paper strips 2’ (see resources)
  • Large paper shapes: circle, heart, lightning bolt
  • ‘Go Bananas’ (see resources)
  • Bananas
  • Paper shapes and straws of different types/ lengths
  • ‘Finding fractions of amounts’ (see resources)
  • ‘Find the fractions’ cards sets A, B and C (see resources)

Short Mental Workouts

Day 1
Finger doubles

Day 2
Odds and evens

Day 3
Clockface halves and quarters

Day 4
Count in 3s

Day 5
Beanbag doubling

Worksheets

Day 1
Y1: Double numbers to 15. Double numbers to 21.
Y2: Halve and quarter numbers to 36.

Day 2
Y1: Halve even numbers to 22. Halve even numbers to 32.
Y2: Find 1/2, 1/3, and 1/4 of numbers to 33. Find 1/2, 1/3, and 1/4 of numbers to 60.

Day 3
Y1: Halve odd numbers to 17.
Y2: Count on and back in halves and quarters.

Day 4
Y1: Draw lines to identify halves and quarters of shapes.
Y2: Find fractions of numbers to 52, including 3/4.

Day 5
Y1: Find 1/2 and 1/4 of numbers, using supporting images.
Y2: Find 1/2, 1/3, 1/4 and 3/4 of numbers to 48, using supporting images.

Mastery: Reasoning and Problem-Solving

Y1

  • Harry says that he always gets the bigger half of pudding than his sister. Is he correct?
  • How many quarters in 1 whole cake?
  • True or false?
    - There are 2 quarters in each half.
    - Sometimes 1 quarter is larger than another quarter of the same whole.
    - Half of 8 is 4.
    - A quarter of 8 is 4.
  • Make a line of 20 cubes. Break it into quarters. How many in each quarter?
  • Make a tower of 10 cubes. Can you break it into halves? Quarters?

Y2

  • Use the image to help complete each number sentence, using <, > or =.
1/21/2
1/31/31/3
1/41/41/41/4
  • Complete each sentence.
    1/4 of 20 is _____.
    1/3 of 12 is _____.
    1/2 of 24 is _____.
  • 18 children are in a class and 1/3 are boys. How many are girls?
  • 10 of the 15 children in a class are girls. What fraction are boys?

In-depth investigation: Happy Halving
Children split shapes in half so that the two parts are exactly the same. Happy Halving from nrich.maths.org.