Session 2: Multiplication TA Maths Course Session 2: Multiplication

Aims of the session: To build understanding of mathematics and its development throughout KS2 To have a stronger awareness of how to support struggling learners and stretch those who are secure To enhance subject knowledge of the pedagogical approaches to teaching mathematics

Models of multiplication I had four bags and they each contained six books. How many books do I have? I had six pens. Tom had four times as many? How many did Tom have?

Number sense v memorisation 18 x 5 Jo Boaler video https://www.youcubed.org/what-is-number-sense/

14th November 2012 Mathematics Across the Curriculum 14/11/2012 6 6 6 6 6 6 + 6 + 6 + 6 Additive reasoning 6 6 6 6 6 x 1 6 x 4 Multiplicative reasoning Secondary mathematics team, Babcock 4S

Models for multiplication Scaling This can be generalised to include any multiplier including those less than one – i.e. making smaller 3 times as tall 6

Models for multiplication Arrays 2 lots of 3 make 6 3 lots of 2 make 6 There are two 3s in 6 There are three 2s in 6 2 x 3 = 6 3 x 2 = 6 6 divided by 2 = 3 6 divided by 3 = 2

An image for 7  8 = 56

Multiplication At the heart of success of this topic is clearly mastery of times tables. It is the one area where deviating from your year group and extending has value. Fluency with tables opens up so many other topics in maths (e.g. fractions and area) and conversely closes off success in other topics if they haven't been mastered at a young age. Guide: Yr 2 (2, 5, 10) Yr 3 (3, 4, 8) Year 4-6 (up to 12 x 12) Practice, practice, practice is the key. Use every (daily throughout the year) opportunity open to you, especially: - Lining up to assembly, getting changed for PE, etc. - Parents! They can really support the regularity of practice. Note: DK Times Table App – many can access at home.

Building the Journey Year 3 Autumn two-digit x one-digit informally Spring/Summer developing two-digit x one-digit formally Year 4 Autumn/Spring term two-digit & three-digit x one-digit formally Year 5 Autumn/Spring term up to 4-digit x one-digit or two-digit formally (including long multiplication) Multiply whole numbers and decimals by 10, 100, 1000 Year 6 All of the above should now be fluent

Arrays to Solve Multiplication 13 x 4 = 10 3 4 10 x 4 = 40 3 x 4 = 12 40 + 12 = 52 13 x 4 = 52

Year 3 (set questions involving their tables targets; in autumn change to 34 x 8 or 85 x 3) Autumn Spring Summer 34 x 2 45 x 3

Year 4 (set questions involving all their tables targets - though this will need differentiation throughout the classes) Always go back to the kinaesthetic example when re-introducing (even if only for a few seconds) 43 x 6 247 x 3 40 3 6 200 40 7 3

Try these out: Model these using both grid multiplication and short multiplication: 31 x 2 26 x 3 279 x 4

Year 5 Multiply up to 4 digits by one-digit or two-digit, using a formal written method, including long multiplication for two-digit numbers. re-visit: Hands-On? Short-Multiplication Long-Multiplication 4253 x 7 4253 x 7 253 x 37

Year 5 Multiplying (and Dividing) by 10, 100 and 1000 4 x 10 13 x 10 6 x 100 4.3 x 10 0.12 x 1000 U T H 1 10 1 100 http://www.topmarks.co.uk/Flash.aspx?f=MovingDigitCards

Year 5 Multiply multi-digit numbers up to 4 digits by a 2-digit whole number. 10 18 18 8 10 100 80 13 13 3 30 24

Progressing towards the standard algorithm 1 0 8 1 0 1 0 0 8 0 3 3 0 2 4

10 8 3 100 80 30 24 When? ? 1 8  3 5 4 2 How?

Year 6 Multiply multi-digit numbers up to 4 digits by a 2-digit whole number. 2361 x 53 9 x 5.4

Deeper thinking 1 1

Deeper thinking 3 5 4 x 9 3 2

Using Inequalities 1 < 3 2 = 2 3 > 1 3 x 42 5 x 21

Where now? Reflect on the addition and subtraction journey. What are the most important messages you are going to take away? * Where next? Progress in division