cippenham infant school maths workshop number and calculations 6 th february 2013 believe and...

Cippenham Infant SchoolMaths Workshop

Number and Calculations6th February 2013

Believe and Achieve Together

We all use Maths all day everyday!

• We look at the clock to tell the time before we get out of bed.

• We estimate how far it is to the floor!

• We know how many degrees to turn the tap so that we get enough water without getting soaked!

• We measure the cornflakes in our bowl so they don't spill over!

• We go to the shops, pay bills, pay for the bus…you get the picture!

• Today we will focus on number and calculating and aim to show you how we develop your child’s mathematical knowledge at school and provide some ideas how you can best support them at home.

• A document called Development Matters is used to plan relevant activities and learning

opportunities at age related expectations.

• All activities are working towards the final aim, the Early Learning Goal.

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Foundation Stage - How its Done!Development Matters

FS - Number

Children count reliably with numbers from one to 20, place them in order and say

which number is one more or one less than a given number.

Using quantities and objects, they add and subtract two single-digit numbers and count

on or back to find the answer.

They solve problems, including doubling, halving and sharing.

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What are the Early Learning Goals?

• Many support materials such as ‘The Primary Strategies’ have been produced to help teachers plan effectively and with

progression.

• All support materials work towards the final goal to achieve National Curriculum expectations.

• At Cippenham Infant School we use the National Curriculum and School Targets to plan effectively for every child.

• Nationally pupils are expected to achieve level 2b at the end of year two, although at Cippenham Infant School we always

aim higher!5

Key Stage One - How its Done!The National Curriculum

KS1 – NumberLevel 1

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Count up to 10 objectsRead, write numbers to 10Order numbers to 10Understand addition as finding the total of two or more sets of objectsUnderstand subtraction as ‘taking away’ objects from a set and finding how many are leftAdd and subtract numbers or objects to 10Begin to know some addition factsSolve addition and subtraction problems involving up to 10 objects (practically)Record work with objects, pictures, diagramsBegin to use + and =

KS1 – NumberLevel 2

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Count sets reliably (10’s, 2’s 5’s)Know place value of 2 digit numbersRecognise odd and even numbers Use the knowledge that subtraction is the inverse of additionUnderstand halving as a way of ‘undoing’ doubling and vice versa Use mental recall of addition facts to 10Use mental calculation strategies to solve number problems including those involving money and measuresChoose appropriate operation when solving addition and subtraction problemsSolve number problems involving money and measuresRecord their work number sentences

First, we begin with fun practical activities.

You have 2 sweets. I give you 1 more. How many do you have altogether?

You have 4 pencils. I take one away.How many pencils do you have left?

Addition and Subtraction

Then, we learn how to write it as a number sentence.

2 + 1 = 3

4 - 1 = 3

Addition and Subtraction

Using a numberline8 + 5 = ?

Put your finger on 8….jump on 5…What number did you land on?

15-7=?Put your finger on 15….jump back 7….

What number did you land on?

Addition and subtraction

Have a go!

8 + 7 = We always remind the children to count

the jumps not the numbers!

Addition and subtraction

Mental methods 15+3=18“Put 15 in your head, count on 3.What number did you land on?”

19-6=13“Put 19 in your head, count back 6.What number did you land on?”

The teachers like to call it ‘Grab and Chin It!’

Addition

Have a go!

18+6=?‘Grab and Chin It!’

Addition

Using a hundred squareOnce there is understanding of the value of Tens and Units we use the 100 Square to work out the answer.

15+12=?“Put you finger on 15. Add 10

by jumping down one row, then add 2 by jumping along 2. What number did you land on?”

27-14=?“Put your finger on 27. Take

away 10 by jumping up one row, then take away 4 by jumping back 4. What number did you land on?

Addition and Subtraction

Mental methods and number sentencesOnce there is understanding of the value of Tens and Units then we use this method but remember we always keep the first number whole!

15+12= 37-2615+10=25 37-20=1725+2=27 17+6=11

The children use Dennes blocks to support their understanding. Also, until they are confident at counting on and back in Tens and Units in their head they can use a 100 square to check their answers.

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Addition and subtraction

Have a go at the long written method!

17+14=? 35-22=?

Remember we always keep the first number whole!

Addition and subtraction

Explain Multiplication

First, we begin with fun practical activities.I have 5 friends coming to a party and each

friend needs 2 slices of pizza for dinner. How many slices do I need?

Multiplication

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Then, we learn how to write it as a number sentence.

First of all we teach the children to understand ‘x’ as ‘lots of’

So

So: 5 lots of 2 = 10

Then, record with the multiplication operation symbol. So:

5 x 2 = 10

Multiplication

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Repeated additionMultiplication

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When the children are still developing their number skills, it can be useful to show them how to work out multiplication as repeated addition.So 4 lots of 5 or 4 x 5 would become 5 + 5 + 5 + 5And the answer is 20!

MultiplicationI can multiply using arrays.

MultiplicationI can multiply using arrays.

I have 12 counters.

How could you arrange them

into 2 equal rows?

There are 2 lots of 6….

There are 2 lots of 6….

…..6 + 6 = 12

Or there are 6 lots of 2….

…. 2 + 2 + 2 + 2 + 2 + 2 = 12

Then you can convert these repeated additions into multiplication number sentences using ‘lots of’.

6 + 6 = 12

How many ‘lots of’ 6 are there?

So this becomes

2 lots of 6 = 12

or 2 x 6 = 12

Then you can convert these repeated additions into multiplication number sentences using ‘lots of’.

2 + 2 + 2 + 2 + 2 + 2 = 12

How many ‘lots of’ 2 are there?

So this becomes

6 lots of 2 = 12

or 6 x 2 = 12

Can you think of any other ways to arrange the counters?

Write your repeated addition and corresponding multiplication on your board!

Multiplication

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Mental methodsAs the children progress in their

learning of mathematics, they will develop mental strategies that will allow them to solve multiplication

problems without written methods.

So calculating 5 x 2involves counting in 2’s 5 times!

First, we begin with fun practical activities.

I have 8 cookies and need to share them with my friend. How many cookies do we get

each?

Division

We share the cookies between the 2 people.

How many cookies do they get each?4

Division

Then we teach the children to write this as a number sentence.

First of all we explain the division operation symbol as meaning shared between.

So 8 shared between 2 = 4

Division

Then, record with the multiplication operation symbol. So:

8 ÷ 2 = 4

Division

Mental methodsAs the children progress in their learning of

mathematics, they will develop mental strategies that will allow them to solve

division problems without written methods.

They can actually use their knowledge of multiplication to help them with this.

Start on 4 and count in 4’s until you get to 8. Count on your fingers how many times

you count. That’s your answer!

Division

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When the children are still developing their number skills, it can be useful to show them how to work out division as repeated subtraction.So you start on 8 and jump back in 2’s until you can’t go any further!How many jumps do you make?2!So 8 ÷ 2 = 4

DivisionRepeated Subtraction

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During all maths activities the children need to be able to use and apply what they know.

We have to ask the right questions to support the children in learning how to use and apply their knowledge.

This is really important when solving real life problems.

Using and Applying

I spend 35p at the shops. If I pay with 50p how

much change will I get?

Have a go!Using any of the methods we have looked at today, what would be the best method for the children to use to work

out the answer?

Using and Applying

What are the important numbers?

How do you know?

?What are the

important words?

What do you need to do to work out the

answer?

What can you do check your answer is right?

Level 1Use mathematics as an integral part of classroom activities, (with support)- engage with practical mathematical activities involving sorting, counting and measuring by direct comparison- begin to understand the relevance of mathematical ideas to everyday situations by using them in role-play

Level 2Select the mathematics they use in some classroom activities (with support)- find a starting point, identifying key facts/relevant information- use apparatus, diagrams, role-play, etc. to represent and clarify a problem- move between different representations of a problem, e.g. a situation described in words, a diagram, etc.- adopt a suggested model or systematic approach- make connections and apply their knowledge to similar situations- use mathematical content from levels 1 and 2 to solve problems and investigate

Using and Applying

Questions

Learning is a journey!

At CIS learning is exciting, challenging and personal.

Children should rarely stop on their school journey. If and when they do we all need to be

there to ensure they continue rapidly and confidently to enable them to be the best they

can be.

How can you support your child on their learning journey?

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How can you support your child on their learning journey?

•Use school methods when completing homework.•Share mathematical experiences that are fun – look at your hand out for help!•Day to day tasks are a mathematical opportunity!

Count the stairs to bed, look at even and odd numbers on houses, add together the numbers on a car number plate, cutting a cake into even slices…•Play relevant learning games on the computer.•One of the most valuable things you can do is to ask the magic question...”How did you work it out?” If children can explain what they have done they will consolidate their own understanding and misconceptions can be addressed.•Always ask the teachers if you have any questions.

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Tuesday 12th and Thursday 14th February9.15am - 10.15am

We look forward to welcoming you into school.

Families into maths