Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support
multiplication and division, including calculations with remainders
(Objective repeated in Block E Units 1, 2 & 3)
； Ask the question Q Every day at break Sam has 5 grapes for his snack. How many grapes does he eat at school during the week? Q What calculation do we need to do? ； Establish that Sam eats grapes on Monday, Tuesday, Wednesday, Thursday and Friday. Q How many days does he eat grapes? ； Explain it is 5 days. Q How many grapes does he eat each day? ； Explain it is 5. Q So how can we work out 5 lots of 5? ； Discuss 5 + 5 + 5 + 5 + 5 = 25 Q Do you know another way to write this? ； Explain it can be written as 5 lots of 5. Q Do we know a sign that represents lots of? ； Discuss the x sign and what it means. Write up vocabulary related to x eg lots of, groups of, multiply, times. Q How do we work out 5 x 5? ； Represent 5 x 5 as an array, using grapes 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ； Explain by adding 5 + 5 + 5 + 5 + 5 or we could use the 5 times table and count up in 5’s. Q So how many grapes does Sam eat during a week at school? ； Establish answer is 25 grapes. ； Discuss methods used. Activities. Children make up own problems involving the vocabulary of x and show answer using array of repeated addition.
Start with question. Q How many wheels are there on 3 cars? Q What calculation do we need to do? Discuss with partner and take responses, 4 x 3 or 3 x 4 Q Are these the same? Do they give the same answer? Discuss they are the same and prove drawing 2 arrays x x x x x x x x x x x x x x x x x x x x x x x x Q How do we work out 4 x 3?
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Children talk to partner and explain methods, ie 4 + 4 + 4, using an array, counting up in 4’s 3 times or 3 + 3 + 3 + 3, counting up in 3’s 4 times. Write 6 x 2 = ; Q What could be the possible question to go with this calculation? Discuss in pairs, take responses. Model how to work it out using repeated + and arrays. Activity Children given multiplications with ; to represent answer, which they invent own questions for. Show working in arrays and repeated +.
Q. What is double 6? ； Children to show answers using number fans. Q. How can we write the calculation to show double 6? ； Children to discuss with their partners. Ask for volunteers to come and write calculation on the board. e.g. 6 x 2 or 6 + 6 ； So we know that double 6 can be written as repeated addition or x2. ； Using whiteboards children to write calculation to represent the following questions. Q. Double 8? ； Give children time to discuss with their partners and write the answers on whiteboards. ； Ask for volunteers to write the calculation and the answer on the board and explain their methods. ； Repeat with other doubles. Q. If we know double 3 is 6, then what is double 30? ； Ask the children how they could work out this calculation and to explain their methods to the rest of the class. e.g. 3 tens and 3 tens makes 6 tens or 60 Q. How could we write this as a calculation. ； Take children’s responses and ask a volunteer to write the calculation on the board. e.g. 30 x 2 = 60 or 30 + 30 = 60 ； Repeat with other multiples of 10 Activities. Using digit cards 1 –10,20,30,40,50 children to choose a card and write the calculation to show the double and work out the answer. ； Ask a child to come out and pick two of the large digit cards. e.g. 4 and 2 ； Ask the children to use these cards to make a multiplication sum and write this on their whiteboards. Take responses. e.g. 4 x 2 or 2 x 4 ； On the board stick coloured circles to show the arrays to represent these calculations. O o o o o o O o o o o o o o o o Q. How many circles? Q. Does it matter if we do 4 x 2 or 2 x 4?
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； Children to realise that the answer is the same whichever way they do the multiplication. ； Repeat using other digit cards showing arrays and the calculations. Activities. Children to pick digit cards from the range 1 – 9 and make arrays on pegboards then write the calculations to represent the array. Q I have 8 ribbons and I want to share them between Jo and Nicola (Substitute names of 2 children in class). ； Show the children the ribbons and ask another child to come out and share the ribbons between the 2 children. ； When each child has 4 ribbons each show the children how to write the calculation 8 ？ 2 = 4 8 shared between 2 gives 4. Q I have 9 sweets to share between 3 friends. How many do they get? ； Ask children to work with a partner using whiteboards and multilink to write the calculation and find the answer. ； Work through calculation together and check answers. ； We know that ？ (division sign) can mean sharing but it can also be used for grouping - or repeated subtraction. Q There are 18 apples in the box. How many bags, each with 3 apples, can be filled? ； Do this question practically with the children using balls or multilink to represent the apples. ； Explain that this can be written as 18 ？ 3 = 6 Q How many sticks of 4 cubes can you make from a stick of 20 cubes? Children to work with partners using multilink to solve problem and writing calculation on whiteboards. Discuss methods and answers. Activities Children to work with a partner to write a sharing problem and a grouping problem and to solve problem. Swap problems with another group and solve. Using Grouping ITP Activity 1 Use the program to model real life problems and look at different contexts for remainders. Show 20 ‚ 3 and ask the children ‘If we have 20 pencils and put them into packs of 3, how many packs do we need?’ What do we have to do with the 2 pencils (dots) that are not in a group of three? Change the question to ‘If we have 20 tokens and you need 3 tokens to get a free toy, how many free toys can we get?’ What do we do with the 2 tokens (dots) that are not in a group of three? Is that the same as what we did with them last time? Explain to the children that drawing a picture or annotating is good to give us a clearer picture, but that dots or lines are good and that we don’t need to draw full tokens or pencils. Activity 2 Ask the children to think of a calculation that will give us 8 equal jumps on the number line. (16 ? 2, 24 ? 3 etc). Repeat this with other numbers of jumps. What do they notice about the calculations? They should see the relationship between multiplication and division. Activity 3 Ask the children what is the smallest number of jumps they could make to get to 30? What is the largest number of jumps they could make? How many different ways can they get to 24? Activity 4 Ask the children what calculations they can show on the number line that will give an answer of 4 remainder 1. (9 ? 2, 13 ? 3, 17 ? 4, 21 ? 5 etc). What do they notice about these numbers?
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Display the Grouping ITP with the number sentence set to 10 divided by 2, select a shape and click on 10 to display the pictures. Demonstrate how to group the pictures into 2s. As each group is completed the number line at the bottom of the screen automatically ‘jumps’ on another step. Encouraging the children to count in 2s as the number line does so. Stop when part-way through the process. How many more groups of 2 do you think we will have? Complete the process. Focus the children’s attention on the number of groups, linking to the number of steps along the number line. What is the answer to the number sentence 10 divided by 2? Display the answer by clicking the equals sign button. Reset the number sentence to 11 divided by 2, displaying the pictures. What do you know about the number 11? What do you think will be the answer to the number sentence? Why? Invite a child to group the pictures together while the class count in 2s along with the number line. Introduce the concept of ‘1 left over’ as displayed on the screen. Display the answer, introducing the term remainder as represented by r.
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