Standens Barn Primary School - Home · Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and ! ! diagrams Year 3 -

YEAR 3 Mathematics Objectives Year 3 - Using and applying mathematics

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Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out

appropriate calculations Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and

present it in context, where appropriate using .p notation or units of measure Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and

interpret the information Identify patterns and relationships involving numbers or shapes, and use these to solve problems Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and

diagrams Year 3 - Counting and understanding number

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Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to

zero in single-digit steps or multiples of 10 Partition three-digit numbers into multiples of 100, 10 and 1 in different ways Round two-digit or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences

• Read and write proper fractions (e.g. , ), interpreting the denominator as the parts of a whole and the numerator as

the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish

equivalents Year 3 - Knowing and using number facts

• • •

Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and

number pairs that total 100 Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts;

recognise multiples of 2, 5 or 10 up to 1000 Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check

calculations

Year 3 - Calculating • • •

Add or subtract mentally combinations of one-digit and two-digit numbers Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit

numbers Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect

• Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 3, 50 4); round

remainders up or down, depending on the context

• Understand that division is the inverse of multiplication and vice versa; use this to derive and record related multiplication

and division number sentences

• Find unit fractions of numbers and quantities (e.g. , , and of 12 litres)

Year 3 - Understanding shape

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Relate 2-D shapes and 3-D solids to drawings of them; describe, visualise, classify, draw and make the shapes Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side Read and record the vocabulary of position, direction and movement, using the four compass directions to describe

movement about a grid Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle;

recognise that a straight line is equivalent to two right angles Year 3 - Measuring

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Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and

millilitres; choose and use appropriate units to estimate, measure and record measurements Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to

measure and draw to a suitable degree of accuracy Read the time on a 12-hour digital clock and to the nearest 5 minutes on an analogue clock; calculate time intervals and

find start or end times for a given time interval Year 3 - Handling data

• •

Answer a question by collecting, organising and interpreting data; use tally charts, frequency tables, pictograms and bar

charts to represent results and illustrate observations; use ICT to create a simple bar chart Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion

Counting and Numbers

Objective Numbers and the number system Round any two-digit number to the nearest ten and any three-digit num-

Instruction Look for five car number plates. Write them down and then write the number rounded to the nearest 100.

Numbers and the number system Know what each digit in a three-digit number represents.

Take the last three digits of your phone number (or a friend’s) and re- arrange them to make the: Largest number you can Smallest number you can Number nearest 500 Largest odd number Smallest even number

Numbers and the number system On your way home look at the car Read whole numbers to at least 1000. number plates. Find a number as

close to 500 as you can. Jot down your number on a piece of paper. Can you work out how far away from 500 it is? Draw the car. 2

ber to the nearest 100. K457 GHW

Counting and Numbers All the Sixes Time your child while he/ she does one or more of these. • Count in sixes to 60. • • •

Count back in sixes from 60 to zero. Start with 4. Count on in sixes to 70. Start with 69. Count back in sixes to 3.

Next week, try to beat the record. Number Game Use three dice. If you have only one dice, roll it 3 times. • • •

Make three-digit numbers, eg if you roll, 2, 4 and 6, you could make 246, 264, 426, 462, 624 and 642. Ask your child to round the three-digit number to the nearest multiple of 10. Check whether it is correct, eg.76 to the nearest multiple of 10 is 80. 134 to the nearest multiple of 10 is 130. (A number ending in a 5 always rounds up). Roll again. This time round three-digit numbers to the nearest 100.

Left overs • • • •

Take turns to choose a two-digit number less than 50. Write it down. Now count up to it in fours. What number is left over? The number left is the number of points you score, eg.

Choose 27. Count: 4, 8, 12, 16, 20, 24 3 left over to get to 27 So you score 3 points

The first person to get 12 or more points wins.

Now try the same game counting in threes, or in fives. Can you spot which numbers will score you points?

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Board Games For these games you need to sketch a board like this. Notice how the numbers are arranged.

• •

Start on 1. Toss a coin. If it lands heads, move 1 place along. If it lands tails, add 10, saying the total correctly before moving. First person to reach the bottom row wins. Start anywhere on the board. Roll a dice. Even numbers move you forwards and odd numbers move you backwards. If you land on a multiple of five, you can move either 10 forwards or 10 backwards. The first person to reach either the top or bottom of the board wins.

Order, order! • Each of you should draw 6 circles in a row. • Take turns. • • •

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Roll two dice and make a two-digit number. Write the number in one of your circles. Once the number is written in a circle you cannot change it or move it! The first to get all six of their circle numbers in order wins.

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Counting Activities

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Start at any small number and count on in tens to 100, and then back again. What number is 30 after 6? What number is 20 before 89? Count in twenties to 200. Now count backwards in twenties to zero. Count in hundreds to 1000 and back again.

What is the third before 31? What number is the fourth after 48? Count in threes to 30. Count in fours to 40.

Start at 2 and count in threes. Start at 5 and count in fours. Start at 30 and count backwards in threes. Now start at 31. Can you go beyond zero? Start at 40 and count backwards in fours. Now start at 42. Can you go beyond zero?

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Objective Calculations Find a small difference between (subtract) two numbers by counting on. Calculations Understand that subtraction is the inverse of addition. Calculations Add two two-digit numbers by parti- tioning into tens and units them re- combining. Explain methods orally (and in writing) Calculations Add three or four single digit numbers mentally.

Addition and Subtraction

Instruction Ask someone at home to give you two numbers between one and nine. Make them into two two-digit numbers. Find the difference between the two numbers. How did you do it? Explain to your partner. Make up three ‘I’m thinking of a number’ problems using addition and subtraction, eg. I’m thinking of a number. When I add 27 to it I get 53. What is the number? (26) Ask someone at home to give you two numbers between one and nine. Make a two-digit number from them. Then reverse the digits to make another two-digit number. Add them together. Then ask them to give you two more numbers and do the same. What do you notice? Why do you think that happens? Write down your phone number or the school’s phone number, including the area code. Choosing just four digits try to make a total of 20. If that is not possible get as near to 20 as you can. (It can be over or under). 6

Objective Calculations Use informal pencil and paper methods to support, record or explain addition/ subtraction. Calculations Use informal pencil and paper methods to support, record or explain subtraction..

Instruction Ask a grown up you know to calculate 54 + 29 in their head. They may not write any numbers down! Find out what method of addition they used. Is it the same as yours? If not, show them your method. Ask a grown up you know to calculate 100 – 68 in their head. They may not write any numbers down! Find out what method of subtraction they used. Is it the same as yours? If not, show them your method.

Addition and Subtraction

Make 20 For this game you need to write out numbers 0 to 20 on a piece of paper. Make them big enough to put counters or coins on. • Take turns. Roll a dice. Put a coin on the number that goes with the

dice number to make 20, eg. throw a ‘4’ and put a coin on 16. • • •

If someone else’s counter is there already, replace it with yours! The first person to have counters on 6 different numbers wins. Now roll two dice, add the numbers together and look for a number to make 20. The first with coins on 10 different numbers wins.

Out and About • Choose a three-digit car number, eg 569 • • • •

Make a subtraction from this, eg 56 – 9. Work it out in your head. Say the answer. If you are right, score a point. The first to get 10 points wins.

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H569 TPK

Addition and Subtraction Number Game You need about 20 counters or coins. • Take turns. Roll two dice to make a two-digit number, eg if you roll a 4

• and 1, this could be 41 or 14. Add these two numbers in your head. If you are right, you win a counter. Tell your partner how you worked out the sum.

• The first to get 10 counters wins. Now try subtracting the smaller number from the larger one. Dicey Tens For this game you need a 1 – 100 square (a snakes and ladders board will do), 20 counters or coins and a dice. • Take turns.

• • • • •

•

Choose a two-digit number on the board, eg 24. Roll the dice. If you roll a 6, miss that turn. Multiply the dice number by 10, eg if you roll a 4, it becomes 40. Either add or subtract this number to or from your two-digit number on the board, eg 24 + 40 = 64. If you are right, put a coin on the answer. The first to get 10 coins on the board wins.

Sum it up • • • •

•

Each player needs a dice. Say ‘Go!’ then each rolls a dice at the same time. Add up all the numbers showing on your own dice, at the sides as well as at the top. Whoever has the highest total scores 1 point. The first to get 10 points wins.

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Addition and Subtraction Secret Sums • Ask your child to say a number, eg 43. • Secretly do something to it (eg add 30). Say the

• • • •

answer, eg 73. The child then says another number to you, eg 61. Do the same to that number and say the answer. The child has to guess what you are doing to the number each time! Then they can have a turn at secretly adding or subtracting something to each number that you say to them.

Number Games Roll two dice. Make two-digit numbers, eg if you roll a 6 and 4, this could be 64 or 46. If you haven’t got two dice, roll one dice twice. As your child to do one or more of the activities below. • Count on or back from each number in tens

• • •

Add 19 to each number in their head. (A quick way is to add 20 then take away 1). Subtract 9 from each number. (A quick way is to take away 10 then add back one). Double each number.

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Multiplication and Division Bingo! One person has the 2x table and the other has the 5x table. Write six numbers in that table on your piece of paper, eg

4 8 10 16 18 20 • • •

•

Roll one or two dice. If you choose to roll two dice, add the numbers, eg roll two dice, get 3 and 4, add these to make 7. Multiply that number by 2 or by 5 (that is, your table number, eg 7 x 2 or 7 x 5). If the answer is on your paper, cross it out. The first to cross out all six of their numbers wins.

Dicey division You each need a piece of paper. Each of you should choose five numbers from the list below and write them on your paper.

5 6 8 9 12 15 20 30 40 50 • •

•

Take turns to roll a dice. If the number you roll divides exactly into one of your numbers, then cross it out, eg you roll a 4, it goes into 8, cross out 8. If you roll a 1, miss that go. If you roll a 6 have an extra go. The first to cross out all five of their numbers wins.

Tables Practise the 3x, 4x and 5x tables. Say them forwards and backwards. Ask your child questions like:

What are five threes? Seven times three?

What is 15 divided by 5? How many threes in 21? 10

Objective Calculations Derive quickly diversion/ multiplication facts corresponding to the 2, 5 and 10 times table. Numbers and the number system Recognise unit fractions such as 1/2, 1/4.

Bean Race You need two dice and a pile of dried beans. • • • •

Take turns to roll the two dice. Multiply the two numbers and call out the answer. If you are right, you win a bean. The first to get 10 beans wins.

Number Game 2 • Put some dominoes face down. •

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•

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Shuffle them. Each choose a domino. Multiply the two numbers on your domino. Whoever has the biggest answer keeps the two dominoes. The winner is the person with the most dominoes when they have all been used.

Instruction Ask someone at home to write down a number fact eg 5 x 8 = 40. Then write down all the other facts you can derive because you know that, eg 40 ÷ 5 = 8 40 ÷ 8 = 5 8 x 5 = 40 Get a sheet of newspaper. Fold it in half, and then fold it in half again. Keep going. What is the smallest fraction you can fold it into? 11

Objective Recognise coins of different values.

Instruction Ask someone else to choose five coins from their purse, but they mustn’t let you see what they are. Ask them to tell you how much the five coins total. You must then guess which coins they have. Then see if you can do the same for them.

Solve simple word problems involving Write down how much pocket money money. you get this week. Then write down

everything you buy and how much it cost. At the end of the week you need to work out how much money you have left – if anything!

Choose and use appropriate operations (including multiplication) to solve problems and appropriate ways of calculating mental, mental with jottings, pencil and paper. Recognise coins of different values/

Find out the price of a first class stamp and second class stamp. Work out the cost of two first class stamps. Also two second class stamps. Work out the cost of one first class stamp plus one second class stamp. Get five coins and write down on a piece of paper how much they are worth altogether.

Solving Problems

Understand and use the £ and p. no- Find out how much your favourite tation. comic or magazine costs. Then find

out the price of the cheapest comic or magazine you can see. Work out the difference in price. 12

Objective Instruction

Use units of time and know the rela- Think of an activity that you do out- tionship between them. side school that takes about:

1 minute 5 minute 1 hour, etc Write down these activities. Note: This activity can obviously be done in different years and with different lengths of time.

Use units of time and know the rela- Look in the paper and work out the tionship between them. length of three TV programmes you

like to watch.

Make and describe shapes.

Measures, Shape and Space

Find an object at home that you can draw and then write a few sentences about. Make sure that you use mathematical language wherever you can. Use the language of shape and write down the length, width and perhaps weight of the object too. You can describe what it is made of, if that is helpful, but try to leave that unit last. Note: Encourage the children to describe household objects. You might need to give them some examples of descriptions first. 13

Objective Read and begin to write the vocabulary related to position, direction and movement and make and describe right angle turns. Measure length (of objects that are not straight) Identify lines of symmetry in simple shapes.

Instruction Write down instructions for someone in your house to get from one room to another. You will need to give them a starting place and tell them which direction to face. Then clearly tell them how many steps forward to take, which way to turn (in quarter turns) and so on. Do not make it too complicated – about six instructions should be enough. When you have tried it out on someone, ask they if they thought the instructions were good enough for them to have done it blindfolded! Give the children a piece of string or wool one metre long. Show them how to use it to measure things that are not straight, eg the circumference of the top of a waste bin. Ask the children to use their string to find things that are about one metre around or long. Look for something in your house that has a line of symmetry. Sketch it and mark in the line of symmetry. 14

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Measuring Use a tape measure that shows centimetres. • Take turns measuring lengths of different objects, eg the length of a sofa, the width

of a table, the length of the bath, the height of a door. • Record the measurement in centimetres, or metres and centi-

metres if it is more than a metre, eg if the bath is 165 cm long, you could say it is 1m 65cm (or 1.65m).

• Write all the measurements in order.

Cupboard Maths Ask your child to look at the weights printed on jars, tins and packets in the food cupboard, eg tinned tuna 185g, tinned tomatoes 400g, jam 454g. Choose six items. Ask your child to put them in order. Is the largest item the heaviest?

Up and down the scales • Guess with your child the weights of people in your home.

• Then weigh them (if they agree!) Help your child to read the scales. • Record each weight, then write all the weights in order. Repeat after two weeks. What, if any, is the difference in the weights?

Looking around Choose a room at home. Challenge your child to spot 20 right angles in it.

Can you tell the time? Whenever possible, ask your child to tell you the time to the nearest 5 minutes. Use a clock with hands as well as a digital watch or clock. Also ask: • What time will it be one hour from now? • What time was it one hour ago? Time your child doing various tasks, eg • Getting ready for school • Tidying a bedroom • Saying the 5 times, 10 times or 2 times table... Ask your child to guess in advance how long they think an activity will take. Can they beat their time when they repeat it?

Fractions Use 12 buttons, or paper clips or dried beans…. • Ask your child to find half of the 12 things • Now find one quarter of the same group • Find one third of the whole group Repeat with other numbers.

3 pencils 20 weeks 80p 50p £3.00 64p 16p 14 weeks 13 stickers 5p

Solving Word Problems Use these examples and/ or make up your own

Answers

A pencil costs 6p. How many can I buy with 20p? A model aeroplane costs £4. Jack gets 20p a week pocket money. How many weeks will he need to save his pocket money to buy the plane? Pat has a £1 coin, a 50p coin and two 20p coins. She buys an ice-cream for £1.10. How much money has she now? Ahmed bought five packets of crisps at 30p each. What was his change from £2? Jo has 17 pencils and Pete has 13 pencils. One pencil costs 10p. How much did Jo and Pete spend? Mum bought four packets of biscuits at 34p each. What was her change from £2? I have 50p pocket money. I spend 34p. How much change do I have left? Tom wants to buy a new football which costs £6.99. He gets 50 pence pocket money each week. How many weeks will he need to save up before buying his new ball? How many packs of stickers costing 15p can be bought with £2.00? How much change would you have left?

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Answers

62 cm 3.25 pm 30 cm 9.50 am 1.15 pm 8 cm 400ml or 0.4 litres 25cm 1/4m or 0.25 m 81 cm

Two rolls of tape are 25cm and 37cm long. What is their total length? A bus leaves the station at 2.45 pm. It takes 40 minutes to reach the church. What time will it arrive? A roll of wrapping paper is 5 metres long. I use 4 metres 70cms. How much paper is left? Sally arrived at school at 9.20 am. John arrived 30 minutes later. What time did John arrive at school? PE is 45 minutes. It ends at 2.00 pm. What time does it start? Joe is 1.15m, Sally is 123cms. How much must Joe grow to be the same as Sally is now? Joseph has a bottle of cherryade which contains 2 litres. If he shares his pop with 5 classmates, how much pop would each person have? A 1m long scarf is divided equally into four different col- ours. How long is each coloured part? Tim’s piece of wood is 35 cm long. Tom’s is 46 cm long. How long are the two pieces altogether?

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Answers

43 books 24 children 8 rows 14 smarties 9 boxes 16 pencils A) 17 boxes B) 34 boxes C) 84 boxes A) 42 people B) 8 people 18 days 60 vegetables 11.10

A bookshelf holds 60 books. How many are left if I take off 17? There are six chairs in a row and 4 rows, how many children could watch the show? If 48 people wanted to watch, how many rows would you need? I have 36 smarties in a tube. I eat 22. How many are left? There are 24 pencils in a box. How many boxes would be needed for a school of 200 pupils. How many pencils would be left? How many boxes would be needed if every pupil used a) 2 pencils a year, b) 4 pencils a year, c) 10 pencils each? 25 people stay for school dinners. 17 people stay for sandwiches: a) how many people altogether? b) how many more stay for dinner than sandwiches? It is the 7th December. How many days will it be until Christmas Day (25th December)? There are 16 potatoes, 25 carrots and 19 onions in a box of vegetables. How many vegetables are there in a box? A fruit cake has to bake for 40 minutes. I put it in the oven at 10.30. What time do I have to take it out?

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5 4.15 pm 15 balloons 47 20p A) 17 B) 11 1) 12 mins B) 6 mins 40 magazines 50p 27 tins

I think of a number. I double it and add 7. The answer is 17. What was my number? A cake goes into the oven at 3.30 pm. It takes 25 mins to cook and 20 mins to decorate. At what time will the cake be ready to eat? Tom blows up balloons for his party - 6 red, 5 blue, 8 green and 4 yellow. Two of each colour were burst at the party. How many are left still blown up? I think of a number, add 3 to it and divide by 5. My answer is 10. What was the number I was thinking of? A packet of biscuits cost 35p and a can of pop costs 45p. How much change would I get from £1? 7 Y5 girls stop for football practice, 20 Y5 boys stop for football practice, 10 Y6 boys stop for football practice, 6 Y6 girls stop for football practice: a) How many more boys than girls stop? b) How many more Y5 pupils stop than Y6? It takes each of the Smith family (6 people) 2 mins to brush their teeth. a) How long in total are they brushing their teeth? b) How long does it take if 2 people at a time could brush their teeth? There are 18 magazines on the top shelf and 47 magazines on the bottom shelf. 25 of the magazines are taken away. How many magazines are left on the shelves? Jim and his friend go swimming. It costs £1.25 each. How much change will he get from £3.00? There are 18 tins of red paint, 10 tins of blue paint and 6 tins of yellow paint. Sarah kicks over 7 tins of red paint. How many tins of paint are left?

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These are a little harder! A problem needing more than one step to solve it

Answers

£1.20 61 cm 30 people

£2.10

A) 30 mins

B) 2hrs 30 mins 87 people

John and Sam are in class 13. They go to the cinema and pay £2.40 altogether to get in. How much was John’s ticket? An ant walks for 35cm and takes a rest for 25 mins, he then walks another 26cm. How far does the ant walk? Dad went on the number 325 bus to work. There were 32 people at first, 8 people got off and 6 more climbed on. Dad arrived at 8 am. How many people were on the bus when he arrived? Linda bought three Twix bars at 70p each. She arrives in school at 1.00 pm, she is five minutes late. How much did she pay altogether for the Twix bars? I have to walk to school and back every day with my lunch, sports gear and homework. It takes me a quarter of an hour to get to school. How long do I spend walking: a) every day; b) every week? A train is going at 50 mph. At Stourbridge 50 people get on. At Birmingham 37 more people get on. How many are on the train altogether?

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A problem with extra (redundant) information

Answers

Documents

Standens Barn Primary School - Home · Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and ! ! diagrams Year 3 -