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Crookham Infants School

Parents’ Curriculum WorkshopMathematics

““They didn’t do it that way when I They didn’t do it that way when I was at school!”was at school!”

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Maths is about ...

– problem-solving– patterns and relationships (generalising lies at the

heart of mathematics)

... and involves using richrich mathematical tasks (rather than pages of sums!)

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Mathematics education 2012 ...

– focussing on learning skillslearning skills– developing children’s thinkingthinking skills– developing children’s problem-solvingproblem-solving

capability– developing a “feel” for number“feel” for number

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Your days are numbered

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Counting

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Learning to count • Knowing the number word sequence• Linking the number word sequence and numeral

(recognising numbers out of context)• Linking the number word sequence to counting

objects accurately (1 : 1 correspondence)• Understanding the cardinal value of numbers

(when counting objects the last number name recited is the sum of objects in the set)

• Knowing that symbols can represent objects (concrete and then abstract)

• Knowing that symbols can represent operations

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Jack and Jill went up the hill To fetch a pail of water.

Jack fell down and broke his crown, And Jill came tumbling after.

Jack and Jill

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Now backwards!

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after tumbling came Jill and crown his broke and down

fell Jack water of pail a fetch

to hill the up went Jill and Jack

Jill and Jack

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Alphabetland

• In Alphabetland letters are used instead of numbers.

• The new number names are A, B, C, D ... instead of 1, 2, 3, 4 etc.

• You may use your fingers, or anything else you can think of to help you, BUT don’t work out the corresponding number.

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Number lines & tracks

Now let’s try some calculations!

D + C = K – B D x F

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Maths should be fun!

“Learning for young children should be all about play with emphasis on counting in as many different contexts as possible.”

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Addition Early stages

• Practical activities and discussions. Recognising numbers.Count objects up to 20. Find one more than a number.Count in ones and tens.Relate addition to combining two groups of

objects.Count along a number line to add numbers.Begin to use + and = signs in a number sentence

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Progressing to:• Mental Strategies & Informal Methods

Counting on from the largest number, recognising addition can be done in any order.

Looking for pairs that make 10 then 20, 100 - Number bonds. 7 + 3 = 10 70 + 30 = 100 17 + 3 = 20

Partitioning a number, and then adding on the tens and units (100s).

Adding ‘nearly’ numbers – To add 9 add 10 then subtract 132 + 9 = 32 +10 =42 -1 =41

Using known number facts and partitioning numbers further, bridging through a multiple of 10(100) eg 27+8

+3 +5

27 30 35

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SubtractionEarly stages

• Practical activities and discussion. Count backwards in number rhymes or stories. Count back from a given number. Begin to relate subtraction to take away. Find one less than a number. Counting back in tens Count backwards along a number line to take away. Begin to use the – and = signs to record mental additions.

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Progressing to:•Mental Strategies & Informal Methods

Looking for the inverse, the subtraction facts that match Number bonds.

7 + 3 = 10 so 10 – 7 = 3

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MultiplicationEarly stages

• Practical Activities

Counting in twos, fives and tens.

Using activities to recognise doubles and halves.

Using equipment to give lots of practice of making groups of.

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Progressing to:

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• Practical Activities. Counting back in tens, twos and fives.

Sharing

Know halves ... half of 6 is 3

Division Early stages

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• Mental Strategies & Informal Methods Counting on and back Understanding division as sharing between more than two e.g if 20

sweets are shared between 4 people:

Understanding division as grouping e.g. How many groups of 5 are there in 20? (Using apparatus and then our tables)

Using arrays ●●●●● 10 divided into 2 groups = 5 in each group

●●●●● ●●

OR 10 divided into 5 groups = 2 ●●

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Progressing to:

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• Mental Strategies & Informal Methods (Contd)

Repeated subtraction 12 ÷ 3 means how many 3’s in 12, therefore keep subtracting 3’s : 12 - 3 = 9, 9 – 3 = 6 etc.

-3 -3 -3 -3 How many 3’s? = 4

________________________0 3 6 9 12

Understanding division as the inverse of multiplication and using known multiplication facts to solve sums/problems.

Start to understand remainders and if you need to round up or down

e.g. If I have 14 eggs, how many egg boxes will I need? 14 ÷ 6 = 2 remainder 2 So 3 boxes needed.

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Using and applying – can children demonstrate and use what they have learnt in a variety of contexts.

Problem Solving

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Bowling   

• Zoe scored 13 points. Which pins did she knock down?•  • If Imogen knocked down 3 pins. What might she have scored?•  • If you knocked down 4 pins. What might you have scored?•  • What is the highest / lowest score you could get by knocking

down 3 pins?•  • Could you score all the numbers in between the highest and

lowest score?

1 23

4

57

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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico, who first discovered the planet, saw a crowd of Zios and Zepts. He managed to see that there was more than one of each kind of creature before they saw him. Suddenly they all rolled over onto their backs and put their legs in the air. He counted 52 legs. How many Zios and how many Zepts were there?

Zios and Zepts

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How to help you child

Keep it fun and practical – learning to be a good mathematician is not about completing pages of sums! Instead…

• Count and manipulate sets of objects in all sorts of contexts – for example, adding one more cake to a plate of cakes. Ask: how many cakes are there? If we add one more, how many will there be? If I eat one, how many well be left? If we share the cakes, how many will have each?

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Day to day patterns & numbers• What do you see? What is the same?

What is different?

• Door numbers• Telephone dials• Dvd timers/oven clocks/microwave timers• Remote controls• License plates• What shapes can you see outside?• Repeating patterns

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Board and card games

• What number are you on? (number recognition)

• I’m on 3. If I roll 4 what number will I land on? • How many spots can you see on the dice?• Who is in first place? Second place, etc?• “Snap”/ “Go Fish” with playing cards

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Stories, songs, rhymes …

• Five Speckled Frogs• Ten Green Bottles• 5 Little Ducks• 5 Currant Buns

• Number chanting…count forward and backward to 10 and beyond. Practise known number facts (eg 1 and 1 is 2)

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Cooking and Shopping

• Which apple is bigger, heavier, lighter, smaller?

• Coin recognition• What shapes can you see? • How many bananas on the bunch? If we

buy one more, how many will there be? • Calculating change, finding totals, what is

the fewest number of coins we could pay with?

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Construction toys (Lego, K’nex, Mobilo …)

• Great for making and extending patterns – using only 3 lego blocks, each a different colour, how many different towers can you make? What if I add another colour?

• Introducing shapes, varying sizes, and introducing terms such as length, height, width, counting bricks

• Describing patterns built using words such as “next to”, “above”, “below”.

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Outdoor play and games

• How many times can you catch a ball in one minute? How many more times than me did you catch the ball?

• Hopscotch• Counting paving slabs/steps. Count forward

then backward. Count in 2s, 5s, 10s• In the sandpit, how many cups of sand fit in

the bucket? Which bucket is bigger/smaller. Why do you think that?

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Time

• Look at the time and mention what the time is whenever you can.

• Immerse your children in the language of time but make it real.

• Encourage your child to tell you what the time is.

• Play games that are timed, mention how many seconds, minutes and hours have passed.

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Mistakes are learning sites

“A problem is a question which, initially, you have no idea how to solve.”

• Children need to struggle with problems and need to understand that the struggle is a natural part of the learning process.

• Children need to experience success and recognise the struggle to achieve it.