KS2 Maths Parent Workshop BK 6th November 2017

Aims of today To find out about the KS2 Maths Curriculum To use some of the resources we use in school to teach Maths To find out about how calculations are taught in KS2 To take away some ideas to support your children at home. BK

The New Maths Curriculum Children should: Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations and developing an argument, justification or proof using mathematical language. Solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. BK

Year Five Add and subtract numbers mentally with increasingly large numbers. Fluency Reasoning Problem Solving Work out this missing numbers: ____ - 92 = 145 740 + ___ = 1039 ____ = 580 – 401 True or False? Are these number sentences true or false? 8.7 + 0.4 = 8.11 6.1 – 0.9 = 5.2 Give your reasons. If 2541 is the answer, what’s the question? BK

Depth not acceleration… The old curriculum, measured in terms of levels, encouraged undue pace. Children were accelerated onto more complex concepts before really mastering earlier ones. The new curriculum encourages a study of fewer skills in greater depth – mastery. BK

Teaching principals Whole class teaching - no differentiation by acceleration Support and challenge through scaffolding, questioning and intervention How, why and efficient methods are explored Precise language Variation promotes deeper learning Intelligent practice develops fluency Sufficient time is spent on key concepts to embed learning Additional practice consolidates learning BK

Lesson Design Fewer topics in greater depth One learning aim per lesson Small connected steps Misconceptions are identified in advance and planned for Questions are planned to challenge thinking Context and representations are chosen to help students link concrete to abstract High quality resources are used BK

What is “depth”?… Procedures Vs Concepts DE

Learning Key Number Facts

Concrete, Pictorial and Abstract DE

Resources DE

Progression in Calculation DE

Addition and Subtraction Singapore Bar Model 100 75 25 75 Inverse Commutative Part Part Whole Model 100 25

The Four Operations Addition – Lower KS2 Number Lines: 48 + 36 = DE You can see the two methods children are taught either partitioning and adding on the tens firat or bridging through multiples of ten – using the number bonds they learnt in KS1

The Four Operations Addition – Lower KS2 Partitioning: Partitioning means splitting the number into the tens and units. 48 + 36 = 40 + 30 = 70 40 + 8 8 + 6 = 14 30 + 6 = 84 70 + 14 = 84 DE You can see the different layouts here, the one in blue leading into the formal column method of addition.

The Four Operations Addition – Lower KS2 Expanded methods in columns: Children’s understanding of place value has to be secure. 48 + 36 = 84 4 8 3 6 + 1 4 – adding ones first 7 0 – adding tens 8 4 DE It is vital children are secure with their place value so they can put the digits in the correct column.

The Four Operations Addition – Lower and Upper KS2 - Column Method This method remains efficient when adding larger numbers and decimals. It is a quick and reliable method. 379 + 92 = 471 3 7 9 9 2 + 4 7 1 1 1 carrying ‘ten’ and ‘one hundred’ DE This is extended to addition od decimals where children learn to use a zero as a place holder e.g. 34.5 + 27.43 needs to be 34.50 + 27.43

3 7 9 9 2 + 4 7 1 1 1 H T O

3 7 9 9 2 + 4 7 1 1 1 H T O

Concrete Pictorial

Using the place value counters, dienes or jottings solve the following number sentence 2 8 9 4 3 + _____ DE

The Four Operations Subtraction – Lower KS2 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 BK Due to the larger numbers involved children learn to subtract by finding the difference. They use a number line to assist them – continuing from Year 2. 38 40 70 74 74 – 38 = (2 + 30 + 4) = 36

The Four Operations Subtraction – Lower KS2 Partitioning: BK Children will partition the smaller number. First subtracting the tens and then the ones.

The Four Operations Subtraction – Lower KS2 Partitioning: BK And also partitioning both numbers. Obviously this method only works when the number being subtracted is smaller than the number it is being taken from.

The Four Operations Subtraction –Upper KS2 BK BK Chn need to be taught to be careful how they set out the numbers when calculating with decimals. They are taught the decimals REMAIN in the SAME PLACE

T O 1 10 100

T O 1 10 100

Use the place value counters, dienes or jottings to solve the following number sentence. 57. 12 - 32.76 _____ BK

The Four Operations Multiplication – Concepts First 18 6 3 18 = 3 + 3 + 3 + 3 + 3 + 3 18 = 3 x 6 18 = 6 + 6 + 6 18 = 6 x 3 CR

The Four Operations Multiplication – Concepts First 18 3 6 180 30 60 CR 1800 600 300

The Four Operations Multiplication – Concepts First 18 3 3 3 3 3 3 6 6 CR

The Four Operations Multiplication – Lower & Upper KS2 Grid Method: CR

The Four Operations Multiplication – Lower & Upper KS2 Grid Method: 43 X 6 124 X 32 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 X 6 4 0 2 4 0 3 1 8 2 5 8 CR

The Four Operations Multiplication – Year 4 & Upper KS2 4 3 X 6 Expanded Short Method: 4 3 6 x 1 8 2 4 0 2 5 8 Grid Method: X 6 4 0 2 4 0 3 1 8 2 5 8 CR

The Four Operations Multiplication – Year 4 & Upper KS2 4 3 X 6 Expanded Short Method: Short (Compact) Method: 4 3 6 x 1 8 2 4 0 2 5 8 4 3 6 x 2 5 8 1 CR

The Four Operations Multiplication – Upper KS2 Short Multiplication for 2-digit x 2 digit: 5 6 x 2 7 = 5 6 2 7 x 3 9 2 1 1 2 0 + 1 5 1 2 4 CR 1

The Four Operations Now it’s your turn! 1. Calculate 602 × 57 CR SATs example

The Four Operations Division – Lower KS2 : Concepts First 18 = 3 x 6 18 ÷ 6 = 3 18 ÷ 3 = 6 CR 6 ÷ 18 = 3

The Four Operations Division – Lower KS2 : Concepts First Division as repeated subtraction 18 ÷ 3 = 6 18 15 12 9 6 3 0 -3 -3 -3 -3 -3 -3 CR 39

The Four Operations Division – Lower KS2 : Concepts First Grouping using multiplication knowledge: This method uses children’s understanding of times tables and links to their mental calculations. e.g. 43 ÷ 7 = I know 6 X 7 = 42 so … 43 ÷ 7 = 6 remainder 1 CR

The Four Operations Division – Lower KS2 : Concepts First Grouping using jottings This enables the introduction of remainders CR 41

The Four Operations Division – Upper KS2 Short Division – HTU ÷ U: 291 ÷ 3 = 9 7 3 2 9 1 2 CR

The Four Operations Division – Upper KS2 (Year 6) Long Division – HTU ÷ TU: Dangerous Divide Monkeys Multiply CR Snatch Subtract Bananas Bring Down

The Four Operations 2 1 2 12 12 2 5 4 4 4 4 24 1 12 2 Dangerous Division – Upper KS2 (Year 6) Long Division – HTU ÷ TU: 2 1 2 12 Dangerous Monkeys Snatch Bananas Divide Multiply Subtract Bring Down Repeat 12 2 5 4 4 4 4 24 1 12 2 CR 12 24 36 48 60 Let’s start by dividing 25 by 12 as they are both a 2 digit number. What is 14 minus 12? Now drop down the 4. How many 12s are there in 24? Write 2 above the 4 and there is your final answer! Write 1 above the 4 and 12 below the 14. How many 12s are there in 14? Write 2 above the 5 and write 24 below the 25. What is 25 minus 24? Now drop down the 4. How many 12s are there in 25?

The Four Operations Now it’s your turn! 1. Calculate 816 ÷ 24 2. A school buys some yo-yos as prizes. The yo-yos cost £4.25 each. The school has £40 to spend on prizes. They buy as many yo-yos as they can. How much money is left? CR KS2 SATs Question

Key Stage 2 SATs BK

Reasoning and Problem Solving