Numeracy Coffee Morning Junior Prep Wednesday 20 th 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 opportunities 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 Approach 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.
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 objectives, 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 2 nd 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 c hildren’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. + 30 + 4 + 2 38 40 70 74 7 4 2 7 – 2 = 40 74 – 38 = 36 3 0 = 70 4 = 74 3 6
Subtraction – Counting back Counting Backwards: Count back from the largest to the smallest once again using knowledge of number bonds. - 30 - 4 - 2 38 40 70 74 74 – 38 = 36
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 Column Method – Decomposition: Children must keep being 1 1 6 1⁄ 2 3 7 6 referred back to ⁄ 3 9 – 7 place value – it is 8 4 – 3 tens not just 3. 1 5 3 3 7 Borrowing ‘ten’ not 1 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 out with concrete resources. Pupils are always encouraged to write the sum.
Multiplication Partitioning: Once again Place Value is essential 4 3 X 6 = 4 0 x 6 so children can understand why 40 x 6 = (4 x 6) x10 = (4 x 6) x 1 0 = 2 4 x 1 0 = 2 4 0 = 3 x 6 = 1 8 + 2 5 8
Multiplication This method links directly to the Grid Method: mental method of multiplication. 43 X 6 124 X 32 X 3 0 2 X 6 1 0 0 3 0 0 0 2 0 0 3 2 0 0 4 0 2 4 0 2 0 6 0 0 4 0 6 4 0 3 1 8 4 1 5 0 8 1 5 8 2 5 8 3 9 9 8
Multiplication This method is the next step on from the grid method. Expanded Short Method: 4 3 X 6 4 3 6 x 1 8 2 4 0 + 2 5 8
Multiplication This method is the next step on from the expanded Short Multiplication: method. 4 3 X 6 4 3 Once again children have to 6 x be secure with their place 2 5 8 value and know they are carrying ‘ten’ not one. 1
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 This method is based on Expanded Method – Chunking: subtracting multiples of the divisor or ‘chunks’. 87 ÷ 6 = Initially they subtract several chunks but with practice children will look at the biggest 6 8 7 multiples of the divisor that they 6 0 - 6 x can subtract. 2 7 2 4 - 6 x 4 3 This method reminds children the link between division and repeated Answer = 14 r 3 subtraction.
Division Expanded Method – chunking Hundreds, Tens and Ones ÷ Ones: 191 ÷ 6 = Children build up confidence, using their 6 1 9 1 multiplication knowledge, to 1 2 0 - 6 x 20 subtract larger ‘chunks’. 7 1 6 0 - 6 x 10 1 1 6 - 6 x 1 5 Answer = 31 r 5
Divison Short Division – Tens and Ones ÷ Ones: This method is the next step after chunking. It is a more compact method. 81 ÷ 3 = Links to chunking: 2 7 3 x 20 = 60 2 1 3 8 80 – 60 = 20 which the ‘2’ represents 3 x 7 = 21 No remainder Answer = 27
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
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