Maths Workshop for Year 4 Parents and Carers 16 March 2015 Mrs Claire Searle – Maths Leader

 New National Curriculum introduced September 2014, for all year groups (except Years 2 and 6 – they are from September 2015).  Expectations have been increased, and some of what was in the Year 5 curriculum is now in Year 4.  All multiplication tables up to 12 x 12 need to be learnt by the end of Year 4.

 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate Steps: Recognise ones, tens, hundreds and thousands digits and know their values. Know how to set out each column in an addition question. Know to start adding from the right side of the addition (ones.) Th H T U

Children in Year 4 often still need to use the column headings to help them set calculations out correctly = They need to remember to use 0 as a place-holder!

Adding and subtracting decimals - money What do children need to know to work these out? How would you set these calculations out? Need to know that numbers after the decimal point are smaller than 1. Need to know that numbers must be lined up in columns including the decimal points.

Multiplication and Division

 What do you understand by:  Multiplication?  Division?  What vocabulary can you think of that applies to each of them?  What methods do you use to multiply and divide? Are they mental or written?

 X  repeated addition eg 5 x 3 is the same as (equals)  times  lots of  groups of  multiplied by  multiply  times tables  double

 ÷  Repeated subtraction eg 20 ÷5 = 20 – 5 – 5 –  Divide  Divided by  Share  Share equally  Groups  Lots  Halve

Recall multiplication and division facts for multiplication tables up to 12 × 12 By the end of the summer term in Year 4, all children should know all multiplication tables off by heart. This includes multiplication facts out of order eg what is 8 times 3? Also corresponding division facts for all multiplication tables, eg how many 7s in 42? They need to know these instantly! No fingers or chanting through the tables.

Practising objectives on Numeracy Passports will help. If they have completed North America by the end of Year 4 then they have met this requirement. All Numeracy Passports and parent helpsheets are on the Longfield School website. Knowing tables and their multiplication and division facts is really important as they are a vital part of being able to problem-solve and reason. How would you do? This is one way we test times tables in school – have a go! You will have 30 seconds to work out the answers to 10 questions.

Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers Children need to be able to: derive and recall multiplication tables (including multiplying by 0 and 1) derive and recall division facts use known facts to derive new facts, for example: 3 x 5 =15 so 3 x 50 =150 Try this! What other facts can you derive from 4 x 6 = 24? : 4 x 60 = x 6 = x 60 = x 600 = x 6 = 2400

Multiply two-digit and three-digit numbers by 10 When multiplying by 10, 100 or 1000, we teach children to ‘move all the digits to the left’ according to the number of zeros. So to multiply a whole number by 10, move all the digits one place to the left, and then place a zero in the space left as a placeholder. To multiply by 100, move all the digits 2 places to the left and place 2 zeros as placeholders.. To multiply by 1000, move all the digits 3 places to the left and place 3 zeros as placeholders.

The decimal point does not move – we never teach children to ‘move the decimal point’. 632 x 10 = zero as a placeholder x 10 zero not needed as placeholder

With enough practice and visualising, children will learn to ‘see’ place value boards in their minds and be able to move the digits to the left, to multiply, or to the right, to divide, using zero as a placeholder when necessary. Try this! For each number and calculation, said, say whether the digits need to move the left or to the right, and then write the final number.

Multiply three numbers together; use my knowledge of number facts and regrouping to make calculating easier, for example: (2 x 6) x 4 = 2 x (6 x 4) Multiplications can be done in any order, so it is possible to regroup numbers in a calculation to make the numbers easier to calculate. So 9 x 10 x 7 can be regrouped as (9 x 7) x 10. Times tables should mean that a child can work out 9 x 7 = 63, and knowledge of place value means that 63 can be easily multiplied by 10 mentally: 63 x 10 = 630

Try this! Regroup these numbers to make them easier to multiply. 6 x 7 x 5 (6 x 5) x 7 6 x 5 = x 7 = 7 x 30 7 x 3 is 21, so 7 x 30 is 210

Recognise and use factor pairs and commutativity in mental calculations Children need to understand that factors are whole numbers you can multiply together to get another number, for example: 2 and 3 are factors of 6 (because 2 x 3 = 6). Understand that factors come in pairs. Try this! What numbers can you multiply together to get 24? 1 x 24 2 x 12 3 x 8 4 x 6

 Addition and multiplication are commutative operations. This means that for these operations the numbers can be added or multiplied in any order and the answer will still be the same. (You can think of it like the word ‘commuter’ – like people the numbers can go back and forth or change place and still be the same!)  So = 12 is the same as = 12  And 8 x 5 gives the same answer as 5 x 8.  But subtraction and division are not commutative.  8 – 4 (= 4) is not the same as 4 – 8. (=-4)  And 40 ÷ 5 (= 8) is not the same as 5 ÷ 40 (= 0.125)  Children need to be taught this – they don’t automatically know or recognise it, and often won’t notice or realise that they have written the calculation the wrong way round.

Use factor pairs and commutativity to multiply mentally for example: 15 x 6 = 15 x 2 x 3 15 x 2 = 30 and 30 x 3 = 90 so 15 x 6 = 90 Your turn! Try working out this calculation mentally using a factor pair: 18 x 5 18 x 5 = 9 x 2 x 5 2 x 5 = x 9 = 90

Use factor pairs and commutativity to divide mentally for example: 90 ÷ 6 = 90 ÷ (3 x 2) 90 ÷ 3= 30 and 30 ÷ 2 = 15 so 90 ÷ 6= ÷ (4 x 2) 120 ÷ 4 = ÷ 2 = 15 So 120 ÷ 8 = 15 Try this! Use factor pairs to divide this mentally. 120 ÷ 8 =

Multiply two-digit and three-digit numbers by a one-digit number using formal written layout Understand that the phrase 'formal written layout', probably does not include the 'grid method' but refers to a column method for multiplication.

What is the grid method? The grid method is a method of multiplying using partitioning. 2-digits (or more) are split up and each number multiplied separately, before being added together again. It is a step on the way to short and long multiplication.

Try the grid method! 84 x 7 =

Short multiplication Multiplication of a 2-digit (or more) number by a single-digit number. Children need to understand when they need to carry tens and hundreds, and to add them on once carried. Numbers need to be lined up in columns according to place value. Place value headings should be used at first. H T U

Short multiplication Your turn! 58 x x 5 Need to remember to use zero as a place-holder, and to carry both tens and hundreds. This calculation goes into the thousands column.

Division Chunking 85÷ x x x ÷ 5 = 17 Chunking involves repeatedly taking away ‘chunks’ of easily calculated numbers from the number being divided (dividend – here the dividend is 85). They need to be chunks of the divisor (here the divisor is 5). Once zero is reached, the number of chunks added together gives the answer.

Your turn – try chunking! 245 ÷ x x x x x So 245 ÷ 5 = 49 In this calculation, children need to be confident taking away chunks of 50 that go over the hundreds barriers. More confident children will be able to take away groups of 20 x 5 to carry out the calculation more quickly.

Solve problems involving multiplying and adding, including using the distributive law to multiply 2 digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects. Children need to know that if you are scaling up you will be using multiplication for example: to make 7 kg of concrete you need 1kg of cement, 2kg of sand and 4kg of gravel. So how much cement, sand and gravel would you need to make 21 kg of concrete? Can you work it out? What do you need to do? There are 3 lots of 7 in 21, so you need to multiply all the amounts by 3. So 3kg cement, 6kg sand, 12kg gravel. All those added together make 21kg.

Know that if you are scaling down you will be using division for example: how can you share 12 sweets between 4 children so each child has the same number of sweets? So 12 divided by 4 = 3. Each child has 3 sweets.

Use the relationship between multiplication and division to solve problems, for example:  X 5 = 45 60÷  = 5 What needs to happen here to solve these problems? Use the inverse operation – division. So 45 ÷ 5 = 9 9 x5 = 45 Divide 60 by 5 = ÷ 12 = 5

Solve multiplication and division problems in context including measuring and scaling contexts, for example: 4 times as high, 8 times as long, 12 sweets shared between 4 children. Apple pudding – serves 4 400g cooking apples 50g soft brown sugar 1 egg Grated rind of 1 lemon 80g self-raising flour 90g caster sugar 75g butter 100ml milk If this recipe makes enough for 4, how much flour would you need to make enough for 12 people? How much sugar?

Make use of opportunities to give your child practical experience of mathematics in the home and everyday life, such as: following recipes and changing them for different numbers of people; working out quantities of different parts to make diluted drinks, colours of paint or cement; comparing prices for single and multi- buy packs to decide which is better value.

Example questions Calculate 453 × 8. Calculate 942 ÷ 6

Fractions

What is a fraction? Talk to someone else – what do you think?

Why do children find fractions difficult? Difficulties with fractions often stem from the fact that they are different from natural numbers in that they are relative rather than a fixed amount - the same fraction might refer to different quantities and different fractions may be equivalent (Nunes, 2006). Would you rather have one quarter of £20 or half of £5? The fact that a half is the bigger fraction does not necessarily mean that the amount you end up with will be bigger. The question should always be, 'fraction of what?'; 'what is the whole?'. Fractions can refer to objects, quantities or shapes, thus extending their complexity.

Numerators and Denominators A fraction is made up of 2 numbers. The top number is called the NUMERATOR and the bottom number is called the DENOMINATOR. In the fraction ¾, 3 is the numerator and 4 is the denominator. DENOMINATOR This number shows how many equal ‘pieces’ something has been divided into. In the fraction ¾, 4 is the denominator showing that there are 4 equal pieces making up the whole. NUMERATOR This number shows how many of those pieces there are. In the fraction ¾ there are 3 pieces out of the total of 4.

Numerators and Denominators For example, if a pizza is cut into 4 equal slices there will be 4 pieces on the plate. This makes a fraction of 4/4 (1 whole). If I eat one of those pieces, ( ¼) then there are 3 pieces left. ( ¾ ). The denominator stays the same, there are still 4 parts that made up the whole pizza, but the numerator has changed, as there are only 3 parts of the pizza left.

What fraction is each part of the whole? What other fractions can you make? What equivalences can you find? Exploring equivalence using a tangram

Use your strips of paper to: Make some different fraction strips. What fractions can you find that are equivalent to 1/4? Which is larger, 5/8 or ¾?

Equivalent fractions ½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 =... ¼ = 2/8 = 3/12 = 4/16 = 5/20 =... 1/3 = 2/6 = 3/9 = 4/12 = 5/15 =... Make fraction strips showing quarters, thirds, sixths, eighths.

How can fraction strips help children make sense of problems like this?

Your turn! Write these fractions as decimals 4 / / 100 Write these decimals as fractions / 10 = / 100 = = 7 / = 86 / 100

 Some fractions with the same denominator will add to a total of 1, eg 1 / / 3 = 1  If fractions have the same denominator then you just need to add the numerators together.  Some answers will be less than 1 eg  3 / / 10 = 7 / 10 Some answers will be greater than one. The answers can be given as an improper (top-heavy) fraction or a mixed number. 8 / / 10 = 17 / 10 = 1 7 / 10 Remember not to add the denominators.

 Children need to know that one tenth or one hundredth is one of ten or one hundred equal parts of an object or quantity  They need to record tenths as fractions 1 /10, 2 /10 etc  They need to understand that 0.1 is the same as one tenth, 0.2 = two tenths, etc  They need to record hundredths as fractions 1/100, 2/100, etc  They need to know that 0.01 is the same as one hundredth, 0.02 = two hundredths, etc.

 Subtracting fractions with the same denominators is very similar 9 / / 10 = 7 / 10 If the first number in the subtraction is an improper (top-heavy) fraction, just subtract in the same way. 20 /8 – 6 /8 = 14 /8 = 1 6 /8

Your turn! Add or subtract these fractions. Give the answers as mixed numbers 7 / / / 10 = 20 / 7 – 9 / 7 = 23 / 10 = 2 3 / / 7 = 1 4 / 7

 Go back to the fraction strips Label the fraction strips with their decimal equivalents – for ¼ (0.25) ½ (0.5) and ¾ (0.75) Children need to remember and recall these decimal equivalents to fractions.

 Need to remember that numbers that end in 1, 2, 3 or 4 round down.  Numbers that end in 5,6, 7, 8 or 9 round up.  So 76, rounded to the nearest 10 is 80.  Likewise 7.6 rounded to the nearest whole number is 8. The 0.6 rounds up.  7.4 would round down, to 7.

 lication_division/read/1/ lication_division/read/1/  junior.kent.sch.uk/maths/timestable/interactive.htm junior.kent.sch.uk/maths/timestable/interactive.htm   years/multiplication-and-division years/multiplication-and-division  years/fractions-and-decimals years/fractions-and-decimals  ns_basic/play/ ns_basic/play/  maths/fractions/index.htm maths/fractions/index.htm