Shears Green Infant School Welcome to the Maths Workshop

By the end of this session, we hope that you: Are better informed about the way we teach mathematics, especially calculation. Understand the progression in calculation methods taught. Know how to support your child in their maths learning at home.

The Maths Curriculum The curriculum has a large focus on number.   It is set out into the following sections for Years 1 & 2: Number – including Number and Place Value, Addition and Subtraction, Multiplication and Division and Fractions. Measurement. Geometry – including Position and Direction. Statistics.  

The Maths Curriculum The National Curriculum 2014 for mathematics aims to ensure that all pupils: 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 can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. They should also apply their mathematical knowledge to science and other subjects.

To develop efficient written calculation strategies, children need: Secure mental strategies A solid understanding of the number system Practical, hands on experiences (manipulatives) To aid children’s understanding we need to aim for ‘pictures in their heads’ through plenty of use of manipulatives.

The importance of PLACE VALUE 233 = 200 + 30 + 3 H T U 2 3 3

Partitioning This is one of the ways we teach place value and check children’s understanding. Being able to partition a number is an essential part of the calculation process and it involves splitting a number into its component parts: 579 = 500 + 70 + 9 It is important that children understand what each of the digits represents e.g. the 2 in 27 means 20 or 2 lots of 10, including 0 as a place holder, e.g. in the number 305 the 0 indicates that there are no tens and holds the hundreds and units in the correct place otherwise the number would be 35. Partitioning cards are used in school to help children understand this concept:

Dienes apparatus is also used in school to help children understand this concept: 27 = 53 = 24 72 139 248 Play partitioning games: Partitioning it! Swat! Use the partitioning cards to show these numbers as tens and units? Can you make the numbers with the dienes apparatus? What number has 3 tens and 6 units? What number has 2 hundreds, four tens and 7 units? Make the biggest / smallest 3-digit number you can with these digits: 7 3 4 9

Instantly recalling number facts Times Tables & Number Facts Doubles: Knowing instantly doubles of numbers is really helpful. Start with numbers 1-20, then the tens (30, 40, 50 etc.) and build from there. Conversely, the children will then know lots of halves of numbers. Number Bonds These are really useful for mental agility when carrying out calculations. These can be learned and practised a little like the times tables can: •Bonds to ten: 9+1; 6+4; 3+7etc. •Bonds to 100: 20+80; 50+50; 30+70; 75+25; 61+39 etc. •Bonds to 20: 17+3; 9+11; 5+15 etc.

Addition using dienes apparatus Using dienes apparatus requires children to be able to partition numbers into tens and units and recombine, and understand that ten ones are equal to a ten. Addition using dienes apparatus 27 + 22 = 49 27 + 26 = 53 (exchanging a tens) 20 + 7 + 20 + 2 = 20 + 20 + 7 + 2 = 40 + 9 = 49 20 + 7 + 20 + 6 = 20 + 20 + 7 + 6 = 40 + 13 = 50 + 3 =53

Subtraction using dienes apparatus 27 - 12 = 15 22 - 16 = 6 (exchanging a tens)

Addition using a number line Using an empty number line requires that children can add one or ten to any given number. 27 + 12 = 39 27 + 26 = 53 As children become more confident in this method they can add in jumps of 2, 5, 20 etc. 20 + 7 + 20 + 2 = 20 + 20 + 7 + 2 = 40 + 9 = 49 20 + 7 + 20 + 6 = 20 + 20 + 7 + 6 = 40 + 13 = 50 + 3 =53

Using partitioning for addition Partitioning is used to break down a calculation into manageable chunks: 36 + 27 = 20 7 36 + 20 = 56 56 + 7 = 63 Children can begin to visualise these processes and begin to do them mentally with no need for recording on paper.

Subtraction using a number line Using an empty number line requires that children can take one or ten from any given number. 27 - 12 = 15 22 - 16 = 6 As children become more confident in this method they can subtract in jumps of 2, 5, 20 etc. 20 + 7 + 20 + 2 = 20 + 20 + 7 + 2 = 40 + 9 = 49 20 + 7 + 20 + 6 = 20 + 20 + 7 + 6 = 40 + 13 = 50 + 3 =53

Using partitioning for subtraction Partitioning is used to count back: 48 - 26 = 20 6 48 - 20 = 28 28 - 6 = 22 Again, children can begin to visualise these processes and begin to do them mentally with no need for recording on paper.

Multiplication To be able to solve multiplication problems children need to be able to count forwards in 2s, 5s, 10s etc. Multiplication as an array: 5 x 2 = 10 Multiplication on a number line: 5 x 2 = 10

Division Division as sharing: 10 ÷ 2 = 5 This method of sharing is an easy concept to understand but is limited when transferring to more efficient methods of solving division.

Division To be able to solve division problems children need to be able to count backwards in 2s, 5s, 10s etc. Division as grouping: 10 ÷ 2 = 5 Division on a number line:

Useful websites Websites: http://www.amathsdictionaryforkids.com/ http://www.mathszone.co.uk/ http://www.topmarks.co.uk/Search.aspx?Subject=16&AgeGroup=2 http://www.ictgames.co.uk/

Thank you very much for coming to this workshop. Any questions?