Junior Prep Wednesday 20 th March 2019 Kerry Walsh Lead - - PowerPoint PPT Presentation

Numeracy Coffee Morning Junior Prep Wednesday 20th March 2019

Kerry Walsh Lead Practitioner in Numeracy

“A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the

• pportunities they have to learn.”

― Jo Boaler, Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching

Aims

• To provide an overview of how maths is taught

in Junior Prep.

• Provide an overview of how teaching and

learning progresses through Junior Prep

• Provide some suggestions as to how you might

best support your child at home. Remember there is always more than one to solve a

• problem. Children are taught

multiple ways so they have a choice and can use which one Is best for the situation or works best for them

What do we teach in Reception, Year 1 and Year 2 Maths

 Number bonds from 10 and 20 ( ie 7+3=10, 18+2= 20)  Counting in 2s , 5s and 10s  Halving  Basic fractions ( ½ , ¼, 1/3 )  Addition and subtraction to 100  Place value ( ones, tens and hundreds)  Time  Measurement ( weight, length, capacity)  Money ( everyday money- calculating change)  Problem solving  Introduce statistics( graphing, tables, sorting data)  Shape and space

Years 3 and 4

 Read and write numbers up to 1000; recognise the

place value of each digit.

 Know the multiples of 5  Add numbers with up to 4 digits.  Multiply 2-digit number by 1-digit number  Find unit fractions of amounts  Recognise common equivalent fractions  Identify acute and obtuse angles.  Draw shapes with given properties.  Collect, interpret and display data in a frequency

table and bar chart.

 Read, write and convert time between analogue

and digital 12-hour clocks.

Resources

Number line Numicom Number square Counters Cusinaire Rods Place value cards Dienes Unifix cubes

Concrete, Pictorial, Abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. CPA was developed by American psychologist Jerome

• Bruner. It is an essential technique of teaching maths for

mastery. It is an highly effective framework for progressing pupils to abstract concepts like fractions. The approach involves starting with concrete materials; moving on to pictorial or representational diagrams before moving on to abstract concepts (maths with just numbers). We use concreate resources for as long as necessary and do return to them when necessary.

Concrete, Pictorial Abstract Approach

Maths Mastery

The idea of maths mastery was inspired by teaching approaches developed in Singapore and Shanghai. Mastery is an inclusive way of teaching that is grounded in the belief that all pupils can achieve in

• maths. A concept is deemed mastered when

learners can represent it in multiple ways, can communicate solutions using mathematical language and can independently apply the concept to new problems. Teaching for mastery supports Mathematics learning

• bjectives, but spends more time reinforcing number

before progressing to more difficult areas of mathematics.

Place Value

We use place value cards in combination with unifix cubes and 100 squares to recognize values of numbers. For example: - Describe the number 245 It has 2 hundreds, 4 tens and 5 ones Can you make that number with either cubes or a value card.

 Adding 5 + 3 = 8  Step 1 start on the biggest number and count on in jumps.  Subtracting 18- 4=  Step 1: start on the biggest number and count back in jumps.

Progressing to using a blank number line

 34 + 25= 59

34 44 54 55 56 57 58 59 Step 1: partition 2nd number ( 25 equals 2 tens (20) and 5 ones) Step 2: jump the 10’s ( 2 tens) Step 3: jump the 1’s ( 5)

Addition and Subtraction a with number square

 Adding 12  54 +12= 66



Step 1 :Partition the number ( one 10, two ones) 10 & 2



Step 2: add on the 10 ( down 1)



Step 3 add on the ones ( right 2)  Adding 10 go down 1  Subtracting 10 up 1  Adding 1go right 1  Subtracting 1 go left 1

Addition and Subtraction a with number square

Adding 9 : 25 + 9= 34

Step 1: find 25 on number square Step 2: simplify the equation ( add 10 -1). To add 10 simple go down one on the number Grid then then take 1 to make 9 ( go left 1 space)

Down 1 left 1

Subtracting 9: 25 -9= 16

Step 1: find 25 on the number grid Step 2: simplify the equation ( take 10 +1) Step 3: to take ten go up 1 then take 1 by going Right 1.

Up 1 right 1

Addition by partitioning

 25 + 33= 58  Step 1: partition numbers ( tens 20 + 30) (ones 5+3)  Step 2: add up the Tens (T) ( 20 + 30 = 50)  Step 3: add up the Ones (U) ( 5+ 3 = 8)  Step 4: add both (B) (50 + 8= 58)  55 + 26 ( Tens 50 + 20= 70) (Ones 5+6= 11)  70 + 11 = ( Tens 70 +10= 80 ) (Ones 0+1=1)  80+1=81

Addition – Expanded method in columns

When children’s understanding of place value is secure we progress to column addition, starting with an expanded method. 4 8 3 6 + 1 4 – adding ones first 7 0 – adding tens 8 4

Subtraction – Counting On

Counting On ‘Finding the difference’ Count on from the smallest to the largest once again bridging through ten or a multiple of ten.

+ 2 + 30 + 4 38 40 70 74 7 4 2 7 – 2 = 40 3 0 = 70 4 = 74 3 6

74 – 38 = 36

Subtraction – Counting back

Counting Backwards: Count back from the largest to the smallest once again using knowledge of number bonds. 74 – 38 = 36

• 2
• 30
• 4

74 70 40 38

Subtraction – Colum Method

Column Method – Decomposition: This method is the most efficient for subtraction. However it relies on the children’s understanding of place value due to the need to ‘borrow’ tens or hundreds if the number being subtracted is larger than the number being subtracted from.

Subtraction – Column Method

6 Column Method – Decomposition:

1 6

7

⁄ 3 9 –

3 7

Borrowing ‘ten’ not 1 1 1⁄2 3 7

8 4 – 1 5 3

Children must keep being referred back to place value – it is 3 tens not just 3.

This method is the most efficient for subtraction. However it relies on the children’s understanding of place value due to the need to ‘borrow’ tens or hundreds if the digit being subtracted is larger than the digit being subtracted from.

Using a number grid for patterns and multiplication



Colour in the even numbers to recognize odd and even



Progress to using it to learn the 5 and 10 x table

Multiplication

First recognize that multiplication is repeated addition I have 4 peas on a plate and I have 3 plates  So that is 4 + 4 + 4 = 12  Or 4 x 3 = 12  We would start with counters on a plate to work this

• ut with concrete resources.

 Pupils are always encouraged to write the sum.

Multiplication

Partitioning: 4 3 X 6 = 4 0 x 6 = (4 x 6) x 1 0 = 2 4 x 1 0 = 2 4 0 = 3 x 6 = 1 8 + 2 5 8

Once again Place Value is essential so children can understand why 40 x 6 = (4 x 6) x10

Multiplication

Grid Method: 43 X 6 124 X 32

X 6 4 0 2 4 0 3 1 8 2 5 8 X 3 0 2 1 0 0 3 0 0 0 2 0 0 3 2 0 0 2 0 6 0 0 4 0 6 4 0 4 1 5 0 8 1 5 8 3 9 9 8 This method links directly to the mental method of multiplication.

Multiplication

Expanded Short Method: 4 3 X 6 4 3 6 x 1 8 2 4 0 + 2 5 8

This method is the next step

• n from the grid method.

Multiplication

Short Multiplication: 4 3 X 6 4 3 6 x 2 5 8

1

This method is the next step

• n from the expanded

method. Once again children have to be secure with their place value and know they are carrying ‘ten’ not one.

Division

Grouping using multiplication knowledge:

This method uses children’s understanding on times tables and links to their mental calculations. e.g. 43 ÷ 7 = I know 6 X 7 = 42 so … 43 ÷ 7 = 6 remainder 1

Division

Expanded Method – Chunking: 87 ÷ 6 = 6 8 7 6 0 - 6 x 2 7 2 4 - 6 x 4 3 Answer = 14 r 3

This method is based on subtracting multiples of the divisor or ‘chunks’. Initially they subtract several chunks but with practice children will look at the biggest multiples of the divisor that they can subtract. This method reminds children the link between division and repeated subtraction.

Division

191 ÷ 6 = 6 1 9 1 1 2 0 - 6 x 20 7 1 6 0 - 6 x 10 1 1 6 - 6 x 1 5 Answer = 31 r 5 Expanded Method – chunking Hundreds, Tens and Ones ÷ Ones:

Children build up confidence, using their multiplication knowledge, to subtract larger ‘chunks’.

Divison

Short Division – Tens and Ones ÷ Ones: 81 ÷ 3 = 2 7 Answer = 27

This method is the next step after chunking. It is a more compact method.

3 8

21

Links to chunking: 3 x 20 = 60 80 – 60 = 20 which the ‘2’ represents 3 x 7 = 21 No remainder

Times Tables

Working towards all pupils being able to: -

• memorise their multiplication tables up to and

including the 12 times table by the end of Year 4

• show precision and fluency in their work

The will learn their tables to a master level at each stage before progressing to the next level.

• Learning times tables songs and rhymes
• Stage 1 – 5s and 10s
• Stage 2 – 2s, 4s and 8s
• Stage 3 – 3s, 6s, 12s and 9s
• Stage 4 – 7s and 11s

Mental Mathematics

It is essential children have secure knowledge and recall

• f mental facts including:
• Place Value including decimals
• Number bonds
• Times tables from 0 to 12 at a mastery level

Problem Solving

Using and applying knowledge and skills

Practical maths

We aim to make maths practical by using real materials. Try some

• f these at home with your child.

 Using coins using food  Using measuring cups 

cooking

Online games Children love games to engage their learning. Try some of these site links.

How you can help at home

• Lots of practice
• Counting – anything and everything
• Playing games – cards, snakes and

ladders, dominoes

• Cooking
• Telling the time
• Online Applications

Make it fun!

Celebrate their mistakes!

“Every time a student makes a mistake in math, they grow a synapse.” There” ― Jo Boaler, Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching