Multiplication and Division Times tables factors and multiples
Multiplication and Division Times tables, factors and multiples Objectives Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. Day 3 Y 3: Further revision of tables facts, commutativity. Y 4: Multiplying three 1 -digit numbers. © hamilton-trust. org. uk 1 Year 3/4
Multiplication and Division Times tables, factors and multiples Short Mental Workouts Day 1 Times tables Day 2 Think of a number – division facts Day 3 Finding unit fractions © hamilton-trust. org. uk 2 Year 3/4
Multiplication and Division Times tables, factors and multiples Short Mental Workout Times tables © hamilton-trust. org. uk 3 Year 3/4
Multiplication and Division Times tables, factors and multiples Short Mental Workout Think of a number – division facts © hamilton-trust. org. uk 4 Year 3/4
Multiplication and Division Times tables, factors and multiples Short Mental Workout Finding unit fractions © hamilton-trust. org. uk 5 Year 3/4
Multiplication and Division Times tables, factors and multiples Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). © hamilton-trust. org. uk 6 Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). This multiplication grid shows different times tables. There are lots of missing tables facts! Let’s fill the gaps for the 1, 2, 3, 4, 5, 8 and 10 times tables. We have been learning these… We can use facts we know to find other facts, such as 7 × 5 to find 5 × 7. © hamilton-trust. org. uk 7 Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). How many 3 s are there in 21? What number sentences can we write to describe the relationship between the numbers 3, 7 and 21? © hamilton-trust. org. uk 8 7 Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). 7 x 3 = 21 21 ÷ 3 = 7 3 x 7 = 21 21 ÷ 7 = 3 Just knowing one multiplication fact gives us three more facts for free! © hamilton-trust. org. uk 9 Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). The numbers in the boxes are all in the same times table. 20 5 ? 40 35 What do you think now? Why must it be the 5 s? © hamilton-trust. org. uk What times table do you think it might be? What else could it be? What can't it be? Why? 10 What do you think now? Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). What times table do you think it might be this time? What else could it be? What can't it be? Why? 18 9 ? 45 27 What do you think now? We’ve got some odd numbers on the outside here, so can the middle number be 6? 8? 9? Tell me why/ not… Why must it be the 9 s? © hamilton-trust. org. uk What do you think now? 11 Year 3/4
Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). 24 What times table do you think it might be this time? What else could it be? What can't it be? Why? 3 ? 21 18 12 What do you think now? Why must it be the 3 s? Can you be sure now? © hamilton-trust. org. uk 12 Year 3/4
© hamilton-trust. org. uk 13 Year 3/4
Challenge © hamilton-trust. org. uk 14 Year 3/4
Multiplication and Division Times tables, factors and multiples Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. © hamilton-trust. org. uk 15 Year 3/4
Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. Talk to your partner. What other arrays might be possible using 20 counters? Sketch a different array of 20 counters on your whiteboard. © hamilton-trust. org. uk 16 Year 3/4
Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. 10 by 2 5 by 4 20 by 1 So, 20 is a multiple of 1, 2, 4, 5, 10 and 20. These numbers are called its factors. Who found them all? © hamilton-trust. org. uk 17 Year 3/4
Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. What factors have you found? Do you think it is useful to list factors in pairs? With a partner, find all of the factors of 24. There are 4 factor pairs for 24: 1 and 24, 2 and 12, 3 and 8, 4 and 6. © hamilton-trust. org. uk Year 3/4
Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. Are there any numbers that are factors of both 20 and 24 ? 1, 2 and 4 These are called common factors of 20 and 24. With a partner, find all of the factors of 16 and all the factors of 18. © hamilton-trust. org. uk What common factors do these numbers have? 19 Year 3/4
Investigation Use ‘Ordering Cards’ from NRICH: https: //nrich. maths. org/8058 Children use their knowledge of times table facts to find the order of a set of loop cards. © hamilton-trust. org. uk 20 Year 3/4
Challenge © hamilton-trust. org. uk 21 Year 3/4
Day 2 Y 4: Revise factors; use to aid mental multiplication. 20 x 36 How could we find the answer? How else could we multiply by 20? We can multiply 36 by 2, then by 10 (or vice versa). Do this to calculate the answer – you are using the factors of 20! Which way did you find quicker or made more sense? Multiply 36 by 4 (doubling twice) and then by 5. Do you get the same answer? © hamilton-trust. org. uk 22 Year 3/4
Day 2 Y 4: Revise factors; use to aid mental multiplication. List ALL the pairs of factors of 14, i. e. the pairs of numbers that multiply together to make 14. 14 × 52 Use a pair of factors of 14 to calculate the answer (7 x 52 then…). © hamilton-trust. org. uk 23 Year 3/4
Investigation: Adult Sheet © hamilton-trust. org. uk 24 Year 3/4
Investigation: Child Sheet © hamilton-trust. org. uk 25 Year 3/4
Challenge © hamilton-trust. org. uk 26 Year 3/4
Multiplication and Division Times tables, factors and multiples Day 3 Y 3: Further revision of tables facts, commutativity. Y 4: Multiplying three 1 -digit numbers. © hamilton-trust. org. uk 27 Year 3/4
Day 3 Further revision of tables facts, commutativity. Multiplying three 1 -digit numbers. 2+7+8 How would you calculate this? We can add in any order, so we could add 2 and 8 to make 10, then add the 7! Multiplication can also be done in any order, just like addition, to arrive at the same answer. Calculate 1 × 2 × 3 and 3 × 1 × 2. We call this property ‘commutativity’. © hamilton-trust. org. uk 28 Year 3/4
Day 3 Further revision of tables facts, commutativity. Multiplying three 1 -digit numbers. 4× 7× 5 How could we change the order of this multiplication to help simplify the calculation? e. g. 4 × 5 × 7, i. e. calculating 20 × 7. 7× 2× 4 7 × 4 × 2 is probably a simpler order to use, because the second step involves finding double 28, rather than 14 × 4, but the choice is yours! How could we change the order of this multiplication to help simplify the calculation? © hamilton-trust. org. uk 29 Year 3/4
Challenge © hamilton-trust. org. uk 30 Year 3/4
Challenge © hamilton-trust. org. uk 31 Year 3/4
Multiplication and Division Times tables, factors and multiples Well Done! You’ve completed this unit. Objectives Day 1 Y 3: Revise times tables and division facts (1 x, 2 x, 3 x, 4 x, 5 x, 8 x, 10 x). Y 4: Revise all times tables and division facts (to 12 x 12). Day 2 Y 3: Revise factors and multiples. Y 4: Revise factors; use to aid mental multiplication. Day 3 Y 3: Further revision of tables facts, commutativity. Y 4: Multiplying three 1 -digit numbers. © hamilton-trust. org. uk 32 Year 3/4
Problem solving and reasoning questions Year 3 Write the missing numbers: ☐ × 8 = 32 6 × ☐ = 48 9 = 36 ÷ ☐ ☐ × 4 = 48 5=☐÷ 8 Write 8 × 6 = 48 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 related number sentences using this central fact. Always true, sometimes true or never true? -- 6 × 8 is the same as 4 × 12; -- Dividing a number by 3 gives an odd answer; -- Even numbers divide by 8 to leave no remainder. © hamilton-trust. org. uk 33 Year 1/2
Problem solving and reasoning questions Year 4 Find three different multiplication facts that you can multiply by 10 to give an answer of 400. Use doubling to help you solve: 23 x 4 18 x 8 141 x 4 How could you use the factors of 12 to help multiply a number by 12? Try this to find: 16 x 12 23 x 12 34 x 12 Use and explain a mental method to find: 8 x 13 7 x 16 12 x 13 © hamilton-trust. org. uk 34 Year 1/2
Problem solving and reasoning answers Year 3 Write the missing numbers: 4 x 8 = 32 6 x 8 = 48 9 = 36 ÷ 4 12 x 4 = 48 5 = 40 ÷ 8 Are children applying known times tables facts to solve divisions? Write 8 × 6 = 48 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 related number sentences using this central fact. e. g. 6 x 8 = 48; 80 x 6 = 480; 8 x 60 = 480; 800 x 6 = 4800; 8 x 600 = 4800; 80 x 60 = 4800; 48 ÷ 6 = 8; 48 ÷ 8 = 6; 4 x 6 = 24; 6 x 4 = 24; 9 x 6 = 54…. Always true, sometimes true or never true? -- 6 × 8 is the same as 4 × 12; True, both equal 48. -- Dividing a number by 3 gives an odd answer; Sometimes, when the number itself is odd e. g. 9 ÷ 3 = 3, 15 ÷ 3 = 5. -- Even numbers divide by 8 to leave no remainder. Sometimes, e. g. multiples of 8 such as 16, 24 or 32; but other even numbers will leave a remainder, e. g. 12, 20, or 22. © hamilton-trust. org. uk 35 Year 1/2
Problem solving and reasoning answers Year 4 Find three different multiplication facts that you can multiply by 10 to give an answer of 400. Any of 1 × 40, 2 × 20, 4 × 10, 5 × 8. i. e. the factor pairs of 40. Use doubling to help you solve: 23 x 4 18 x 8 141 x 4 23 × 2 = 46; 46 × 2 = 92 18 × 2 = 36; 36 × 2 = 72; 72 × 2 = 144 (Or 9 × 8 = 72; 2 × 72 = 144) 141 × 2 = 282; 282 × 2 =564 Errors may occur when children are working mentally but do not jot down the part completed solutions; some errors also possible when doubling if double the 1 s digit is greater than 10, e. g. 46 × 2 = 82 or 812. How could you use the factors of 12 to help multiply a number by 12? Multiply by 3, then by 2 again – this could be in any order. Try this to find: 16 x 12 192 23 x 12 276 34 x 12 408 Use and explain a mental method to find: 8 x 13 7 x 16 12 x 13 8 x 13 = 104, e. g. double 13 three times. 7 x 16 = 112, e. g. 7 x 8 = 56, then double 56. 12 x 13 = 156, e. g. 3 x 13 = 39, then double twice. Other methods are possible. The important thing is a) getting the right answer, and b) children being able to explain their strategy. © hamilton-trust. org. uk 36 Year 1/2
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