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Multiplication and Division. 2003 Presented by D & A. Learning Outcomes. To reflect on Addition and Subtraction. Look at the strategies for Multiplication and Division. Use the Mult/Div book to plan a lesson. Look at equipment to assist in the teaching of Mult/Div. Reflection.
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Multiplication and Division 2003 Presented by D & A
Learning Outcomes • To reflect on Addition and Subtraction. • Look at the strategies for Multiplication and Division. • Use the Mult/Div book to plan a lesson. • Look at equipment to assist in the teaching of Mult/Div.
Reflection How was Addition and Subtraction? What were the highlights? What are the challenges so far? Bright Ideas
Solve using a variety of strategies • There are 89 people in a restaurant and 12 leave. How many people are left? 89 – 12 = • Anna won $347 in lotto and then her parents gave her $343 for her birthday. How much money does she have altogether? 347 + 343 =
Addition and Subtraction Strategies • Counting All Objects 5 + 4 = 1,2,3,4,5,6,7,8,9 • Counting On 8 + 5 = 9, 10, 11, 12, 13 • Counting Backwards 37 – 4 = 36, 35, 34, 33 • Doubles 8 + 7 = (8 + 8) – 1 25 + 27 = (25 + 25) + 2 = 52 • Making 10s 5 + 4 + 5 = 10 + 4 15 + 18 + 5 +2=10+10+10+10 = 40 • Place Value 43 + 25 = (40 + 20) + (3 + 5) Partitioning 69 – 43 = (60 – 40) + (9 – 3) so 20 + 6 = 26
Addition and Subtraction cont’d • Compensation 63 – 39 = 63 – 40 + 1 = 24 • (Rounding, Tidy Numbers) 198 – 20 can be:200 – 20 – 2 = 178 398 + 30 = 400 + 30 – 2 = 428 • Reversibility 63 – 39 = so 39 + ? = 63 Therefore 39 + 20 + 4 =63 so answer is 24 • Compatible Numbers 247 + 243 = (247–2)+(243 +2) =245+245=490 • Equal Additions 63 – 39 = 63 + 1 = 64, 39 + 1 = 40 so 64 – 40 = 24 865 – 590 = 875 – 600 = 275 • Algorithm 865 +432 1297
How would each stage solve the following? • There are 6 cars outside the school, they are going on a school trip. There are 5 children in each car. How many children would go on the trip? • If we have 4 shopping bags and 12 apples, how many in each bag? What if one bag breaks?
And this….? • I gave 3 lollies to every child in my class. I have 18 children in my class, how many lollies did I need to buy altogether?
Model these concepts with equipment. • Why does 4 x 3 give the same answer as 3 x 4? • There are 12 lollies and 3 friends. How many lollies each? • There are 12 lollies. How many packets of 3 can you make?
Strategies For Multiplication and Division • Counting All objects eg 4 x 2 = 1, 2, 3, 4, 5, 6, 7, 8 • Skip Counting – eg 4 x 5 = 5, 10, 15, 20 • Repeated Addition eg 3 x 4 = 4 + 4 + 4, 4 + 4 = 8 + 4=12 • Doubling eg 2 x 6 = 12 so 4 x 6 = 24 • Adding and Subtracting eg 2 x 6 = 12 so 3 x 6 = 12 + 6 • Reversibility eg 7 x 4 = 28 so 28 ÷ 4 = 7
More Mult/Div Strategies • Compensation - Rounding (Tidy Numbers) eg 6 x 998 = (6 x 1000) – (6x2) • Place Value eg 4 x 38 = (4 x 30) + (4 x 8) • Proportional Adjustment eg 3 x 12 = 6 x 6 = 36 or (Doubling and Halving) 44 x 5 = 22 x 10 = 220 • Algorithms eg. 42 X32 84 1260 1344
Times Tables?? • Knowing times tables does not mean children know multiplication • If children understand commutativity ie 6 x 2 = 2 x 6 then there are only 55 facts left. • X 0 – now only 45 facts left. • X 1 – now only 36 facts left. • X 2 (doubles) – now only 28 facts left • X 5 – now only 21 facts left • X9 – with fingers or add to 9 rule or from 10 x tables – now only 15 facts left. 15 facts are: 3 x 3, 4 x 3, 6 x 3, 7 x 3, 8 x 3, 4 x 4, 6 x 4, 7 x 4, 8 x 4, 6 x 6, 6 x 7, 6 x 8, 7 x 7, 7 x 8, 8 x 8
Where to now?? • Re look at your groups • Teach a 5 week block on Multiplication and Division • Provide whole class warm ups that have multiplication and division as the focus.
