MULTIPLICATION. Year Objective Method / Example Solve simple practical problems that involve doubling Rote counting in rhythm

Transcription

1 MULTIPLICATION Year Objective Method / Example Solve simple practical problems that involve doubling Rote counting in rhythm Rec E.g. 2 3 pause (Working Using objects in sets and on number line towards L) Number line + Numicon (Working towards and within L) Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 0 to the tenth multiple Counting patterns, what comes next? E.g 2 4 6? ? Using objects to make equal sets or groups. 2 lots of 3 butterflies. Introduce vocabulary: Lots of Groups of Sets of Solve practical problems that involve combining groups of 2, 5 or 0, How many fingers are there altogether on four hands? There are 0 crayons in each box. How many crayons are there altogether? 2 (Levels 2c Represent repeated addition and arrays as multiplication; use practical and informal written methods and related vocabulary to support multiplication Using practical equipment or objects as a starting point, children understand that repeated addition can be represented using the multiplication symbol. For example, they record four lots of five fingers as and use the multiplication sentence 4 5 to record this. They understand that 'multiplied by 5 or ' 5' means lots of or groups of 5. Use a number line to support repeated addition, recording the equal jumps on the line and writing the repeated addition statement and the matching multiplication statement = = 30 Language

2 6 multiplied by 5 equals 30 6 groups of 5 make 30 6 hops of 5 make 30 6 lots of 5 are 30 Multiply Times They use arrays of pegs in pegboards, patterns on squared paper or hops on a number line to show that 3 5 = 5 3 or that 4 2 = 2 4. This array shows 3 lots of 5 or 3 x 5 = 5 This array shows 5 lots of 3 or 5 x 3 = 5 Commutativity Children should know that multiplication can be done in any order e.g. 5x3 has the same answer as 5x3. This can be shown on a number line or as an array or on a beadstring

3 3 (Levels 2a Use practical and informal written methods to multiply two-digit numbers (e.g. 3 3) Using times tables to count up in required multiples and informal jottings. E.g. Paul buys 2 lollies that cost 5p each. Work out how much this will cost altogether. How did you find the answer? Did you jot anything down? Using known / given facts to work out related answers: E.g. What is 4 2? What is 0 2? How could we use these facts to work out 4 2? Children continue to use repeated addition 4 times 6 = = 24 or 4 lots of 6 or 6 x 4 Use of arrays, number line or bead string to support understanding x 4 = 36 and 4 x 9 = 36 Moving on to partitioning based on known tables facts -TU x U : e.g. 3 x 3 0 x 3 = 30 3 x 3 = 9 3 x 3 = = 39 Or 3 x 3 = (0 x 3) + (3 x 3) = = 39 0 x 3 3 x Using times tables to count up in 5s, etc. E.g. How many 5-minute cartoons can I watch in 20 minutes? What multiplication fact can help you to find the answer? Understand that division is the inverse of multiplication and vice versa; use this to derive and record related multiplication and division number sentences and solve problems Using times tables facts and knowledge of inverse operations Consider problems such as: 4 x 2 = 5 x = 30 x 6 = 8 x = 32 4 (Levels 3c Develop and use written methods to record, support and explain multiplication of TU x U (e.g. 5 9) Knowing times tables facts and being able to x0 is a prerequisite for being able to use the grid method for multiplication. Continuing partitioning based on known tables facts -TU x U e.g. 27 x 9 = 20 x 9 = 80 (because 2x9=8) 7 x 9 = = 243 Or 27 x 9 = (20 x 9) + (7 x 9) = = 243 This method presumes that children can use their knowledge of multiplying by 0, that they know their times tables and that they can add 2 and 3 digit numbers together.

4 Grid method - TU x U 38 x When setting up addition, children will be encouraged to order the numbers, starting with the largest. 5 (Levels 3b Refine and use efficient written methods to multiply HTU U, TU TU, U.t U Grid method - H TU x U 28 x When setting up addition, children will be encouraged to order the numbers, starting with the largest. Leading to formal multiplication. e.g. 346 x Extend grid method to TU x TU e.g. 37 x 25 x Moving on to U.t x U E.g. 4.9 x Once grid method is secure, they can move onto the vertical compact method for multiplication. 76 x If necessary, start with the vertical expanded method for multiplication (if chn don t grasp compact method) 76 x5 30 (6 x 5) 350 (70 x 5) 380

5 When multiplying with decimals, use formal method and put the decimal point ready in the answer box, then multiply as normal. e.g x 8. _ 6 (Levels 4c Use efficient written methods to multiply integers and decimals by a one-digit integer, and to multiply twodigit and three-digit integers by a two-digit integer Continue to use grid method going on to ThHTU x U and HTU x TU E.g x Gelosia method (useful for up to 3 digits by 2 digits) See example below -Set up grid -Multiply out putting tens digit in top half of box and units digit in bottom half of box -Starting with bottom right corner, add up digits along the diagonal (carrying as you would with column addition) Formal long multiplication e.g. 32 x (x 5) 6420 (x20) 8025 If necessary, start with the vertical expanded method for multiplication (if chn don t grasp compact method) e.g. 32 x25 5 ( x 5) 00 (20 x 5)

6 500 (300 x 5) 20 ( x 20) 400 (20 x 20) (300 x 20) 8025