Oral and Mental Starters Year 6 Autumn Teaching Sequence 3

Activity 1 Objectives: To know multiplication and division facts for all tables Resources: ITP Number dials (see resources) Level of difficulty: Easy

. It is useful to make a class set of laminated cards with the number dials format on them as it can be used in a variety of ways. See resource sheet. . Use the ITP in a straightforward way to practise multiplication facts. Firstly set the multipliers in order and then randomly clicking on the pair of dice. . Use the ITP to generate division questions with the appropriate divisor. 48 divided by which number, gives a quotient of 8? . As above, the multiplier can be set up in random order to increase the challenge.

Activity 2 Objective: Know by heart division facts for the 3, 4, 5 and 6 times tables Resources: Loop cards (see resources) Level of difficulty: Easy

 Create a set of loop cards (see resources), take the first six cards out and shuffle the rest. Give two cards to each pair of children, but give the first six cards in the loop to six children who are not as confident with their division facts as others.  Ask the child whose card has the star (to denote starting card) to read what’s on their card: I have 45. How many 5s do I have? Agree the answer as a class. Who has 'Nine 5s are 45' at the top of their card? The child reads the cards: Nine 5s are 45. I have 42. How many 6s do I have? Continue until you have rehearsed the first six cards. (This has the advantage of twice the practice for the first six children, and of making them feel secure in the timed activity.)  Now we’re going to start again and time ourselves!  Time how long it takes for the class to work through the cards, ending with the card with the star at the bottom.  This is a useful activity to repeat several times over a week, challenging children to improve their time.

Activity 3

© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y6 Maths TS3 – Mental Oral Starters - Aut Objective: To know multiplication and division facts for all tables Resources: IWB calculator, class set of calculators Level of difficulty: Easy

. Distribute calculators. Only the x ÷ = and digit buttons can be used. . Put 8 into your calculator. Now, change it to 64. What did you do? . Put 64 into your calculator. Now change it to 8. What did you do? Record the calculation on the board. . Put 640 into your calculator. Now change it to 8. What did you do? Record the calculation below the one above so that the pattern can be seen. . Continue to practise multiplication and division facts.

Activity 4 Objective: To use knowledge of multiplication and related division facts for all tables to find multiples Resources: Spreadsheet – ‘Find multiples’ (see resources) Level of difficulty: Medium

. Set the multiple for the table facts that need to be practised. . Children use table facts to find the multiples and show these on whiteboards. Ask So, 88 is a multiple of 8, why isn’t 77? You’ve said that 59 isn’t a multiple of 8. What is the answer to 59 divided by 8? Which of the numbers that isn’t a multiple of 8 has the largest whole number remainder? . Continue to practise further examples by changing the sets of numbers and then the multiples

Activity 5 Objective: To make quick approximations to multiplication questions Resources: Whiteboards Level of difficulty: Medium

. Tell children that they are going to practise quickly finding approximate answers to multiplications. . Model how to use jottings to help. What is the approximate answer to 43 x 18. I’m going to round the 43 to 40 and the 18 to 20. 40 x 20 = 800 . Then start by giving children 10 seconds to find answers. If this goes well, reduce the time allowed. . Some suggested examples; 52 x 47 36 x 77

© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y6 Maths TS3 – Mental Oral Starters - Aut 27 x 35 13 x 94 . In feedback discuss whether the approximation will be larger or smaller than the product. Acknowledge that in examples where one number is rounded down and the other is rounded up, this can be quite difficult. Emphasise that the purpose of approximation is not to get as close as possible to the answer but to check whether the answers they get to multiplication questions are reasonable. They provide a check. . Then practise three-digit by one-digit examples, e.g. 426 x 17. I’ll round 426 to 400 and 17 to 20 That’s 400 x 20 = 8000 . Ask children to work in pairs to give each other calculations to approximate. They must have done the example themselves to be able to check their partner’s answer. Ask pairs to feedback their examples.

Activity 6 Objective: To make quick approximations to division questions Resources: Whiteboards Level of difficulty: Medium

. Tell children that they are going to practise quickly finding approximate answers to division questions. . Model an example, 236 ÷ 6. How many 6s do you think might be in 236? More than 10? 20? 30? 40? So the answer will be between 30 and 40. Do you think it will be nearer 30 or 40? A good estimate is just a little less than 40. . Say that you want them to make approximations in that way. The answer lies between 30 and 40. Children respond by holding up two multiples of ten. If they think the answer will be closer to one multiple than the other, they just hold up one multiple. . Practise further three-digit divided by one-digit examples where the answers are between 10 and 50, e.g. 436 ÷ 9 329 ÷ 7 157 ÷ 4 . Start by giving children 10 seconds to find answers. If this goes well reduce the time allowed. . Follow this with an example such as 160 ÷ 4 to discuss. Does this one need to be approximated? What is the answer? How did you do it? What about 250 ÷ 5?

Activity 7 Objectives: To know multiplication and division facts for all tables To practise doubling and halving Resources: Set of ‘loop’ cards (see resources) Level of difficulty: Medium

. Notice that the bottom right card ‘loops’ back to the top left card. . Give (say) 6 cards to each table. The whole group is responsible for the six cards. This prevents children relaxing if their card comes up early in the loop. It also avoids putting individuals ‘on the spot’. . Teacher starts with Nine multiplied by 4? Group with 36 says Thirty six divided by 3? . Continue until the loop finishes. . Shuffle the cards, redistribute and play at a faster pace. The loops can be timed and played on successive days to beat the record. . Alternatively, make up several copies of the loop cards, and divide (say) children into 6 groups of 5. Each child in the group is then in charge of 6 cards. They time how long it

© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y6 Maths TS3 – Mental Oral Starters - Aut takes to complete the loop. Then they shuffle the cards and redistribute to try to get a better time. Compare times to get a group winner.

It is fairly easy to make sets of loop cards to practise a range of number facts to develop quick recall. Make sure that in a loop, the number in the top left of each card is different and that the last card takes you back to the first.

Activity 8 Objective: To use knowledge of table facts for x2 x3 x4 x5 and x6 to derive multiplication facts for x20 x30 x40 x50 x60 and 0.2, 0.3, 0.4, 0.5 and 0.6 Resources: Spreadsheet Multiplication/ division facts 2 to 6 and 20 to 60 (see resources) Level of difficulty: Hard

. The spreadsheet in picture 1 can be used in a straightforward way to put in the top row and first left hand column. Children say/and or write answers to fill the grid. . It can also be used to develop reasoning and use related division facts as in the example below. 40 multiplied by a number gives a product of 120. What’s that number? 25 divided by 5 is 5, so what is 250 divided by 50? . Children complete the grid. . The grid can be made where some values cannot be worked out. Ask children to identify the additional information needed to complete the grid.

. Use the version of the spreadsheet below firstly with the values in the top row and left hand column revealed. Children complete the grid. . Then reset and reveal some of the products and some of the values in the top row and left hand column. . Children work out the missing values . Ask children to give feedback on how they worked them out.

NB. For most children, 0.1 x 0.3 = 0.03 will require some teacher explanation. It can help to think of 0.1 as one tenth, and so find one tenth of 0.3. Activity 9 Objectives: To square numbers Add mentally pairs and trios of two-digit numbers Resources: A grid on the board as in the picture below

. Ask children to work mentally to square the numbers and then add them to complete each cell as you fill them on the board. They can use whiteboards to do jottings to help if needed

+ 1² 2² 3² 4² 5² 6² 7²

1²

2²

3²

4²

5²

6²

7²

. Then ask them to use the table to write these as the sum of 3 squares

29 =  + +  90 =  + +  41 =  + + 

121 =  + +  30 =  + +  94 =  + + 

Answers:

+ 1² 2² 3² 4² 5² 6² 7²

1² 2 5 10 17 26 37 50

2² 5 8 13 20 29 40 53

3² 10 13 18 25 34 45 58

4² 17 20 25 32 41 52 65

5² 26 29 34 41 50 61 74

6² 37 40 45 52 61 72 85

7² 30 53 58 65 74 85 98

. Then ask them to use the table to write these as the sum of 3 squares

29 = 2² + 3² + 4² 90 = 4² + 7² + 5² 41 = 4² + 4² + 3²

© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y6 Maths TS3 – Mental Oral Starters - Aut 121 = 6² + 7² + 6² 30 = 1² + 2² + 5² 94 = 6² + 7² + 3²