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Mental workoutIntroduction to topicIndependent /group work. PlenarySession 1Obj
Multiply mentally any two-digit number to 50 by a single-digit number.
Quickly demonstrate one way of using partitioning with jottings to aid multiplication of a two-digit number by a single-digit number. Give children similar questions to answer, writing their solutions on whiteboards.Ob:
Using place value cards make the number 746 in front of the class. Say that you want to multiply this number by 6.Partition 746 and give the 700 to one child, 40 to another and 6 to a third. Ask them each to multiply their parts of the numbers by 6 and check the answer with a friend. Together add up these partial products to find the answer to 746 x 6.Ask volunteer to show how this can be laid out on a grid. Say that you want to multiply 4746 by 6. discuss in pairs how much bigger the answer will be than the previous answer and to give an estimate (5000 x 5 = 25 000). Demonstrate grid method to record this multiplication and compare the answer with the estimate.Give the children a multiplication calculation to do in their books using the grid method. Check their answers. Ask the children to make up two of their own four-digit by single-digit multiplications, recording their use of the grid method in their books, ensure that they estimate the answer first. Check their use of the grid method is correct.
Ask for a volunteer to remind the class how to use the grid method to solve 72 x 38, estimating the answer first (70 x 40 = 2800). Get the children to use the same method for 372 x 24. Demonstrate another calculation, emphasising the need to estimate and the setting out of the grid method. Give the class a set of three-digit by two-digit calculations to do, ensure that they estimate the answer first.Write an incomplete grid on the board
What two numbers have been multiplied together in this grid. How do you know? (7642 x 6. then 7642 x 5)Session 2Obj
Use known number facts and place value to multiply mentally.
Use the counting stick to count in 5s and then in 0.5s. Point to different marker points on the stick and ask, What number would lie here?.e.g. 3.5 and How many 0.5s are represented by 3.5? Continue to reduce the intervals by counting in 0.05s and ask similar questions which encourage the children to identify multiplication facts e.g. 7 x 0.05 = 0.35.Ob:
Estimate the answer to 4.13 x 7Establish that the answer is roughly 4 x 7 = 28How would you multiply 4.13 x 7? Draw out that you could partition 4.13 into units and tenths. Demonstrate the grid method to calculate 4.13 x 7.Compare the answer of 28.91 to the estimate of 28. Ask why the answer is bigger, and by how much. Thinking of a hundred square can get the digits in the correct place in the decimals if they are unsure. Point to a hundred square say that each square a hundredth of the whole which is 0.01. Three squares represent 0.03. Multiplying the 3 squares by 7 gives 31 squares or 21 hundredths or 0.21 which would look like two rows of 10 and one left over, i.e. 2 tenths and 1 hundredth. Why cant the answer to 0.03 x 7 be 0.021? Establish that 0.021 is smaller than 0.03.Ask the children to work in pairs to use the grid method to calculate the answer to 3.23 x 3. Take feedback and ensure that the children understand the method and can interpret the difference between their estimate (3 x 3) and the answer.
Set the children other calculations, ensuring that some calculations include the crossing of the place value boundaries when adding together the partial products.Display a partially completed grid.
What two numbers have been multiplied to get this answer? How do you know?
Session 3Obj
Consolidate knowing by heart multiplication and division facts to 10 x 10. Derive quickly corresponding division facts.
Chant in 7s forwards and back. Counting stick.Stop at various multiplications and ask for other facts e.g. 9 x 7 = 63.A volunteer tells the class: 9 x 7 is 6363 7 is 963 9 is 7Ob: Use informal pencil and paper methods to support record or explain divisions.
Tell the children that self-adhesive stamps come in sheets of 24.Estimate how many sheets you would need to buy if you wanted 500.
Establish that it is roughly 500 25 = 20. How would we work it out exactly? Draw out that one way would be to subtract multiples of 24 from 500.Record on the board - How many sheets of stamps does this represent? How many sheets will you have to buy to get 500 stamps? Establish that 20 sheets will buy 480 stamps so to get 500 they will need 21 sheets. Explain that subtracting 10 lots of 24 is more efficient than subtracting single multiples. Tell the children that this method of subtracting multiples of the divisor, 24, is called chunking. How many coaches would be needed to take 780 people on coaches which hold 42 people each? Ask the children how they would use this chunking method to answer the question. Identify the divisor and what chunks they wish to subtract. Record suggestions on the board.Give the children problems to solve which involve similar calculations. Encourage the children to work with a partner and discuss the size of the chunks they are going to use.Show a solution based on subtracting 10 lots of 23.Establish that larger chunks could be subtracted.
What larger chunks could be used here?Session 4Obj
Use known number facts and place value to multiply and divide mentally. Write the number 21 and say that you want as many multiplication and division facts with an answer of 21 as possible.Encourage use of decimals.Ask children to write a question on their whiteboards. Share some of the answers. Repeat with different numbers.
Ob: Round up or down after division, depending on the context. Remind children of the calculation they carried out in the previous lesson (500 24) which they did by chunkingNow demonstrate how to do this with a calculator.Using the OHP calculator show the answer: 20.83333333.
Draw out that this means 20 sheets and some more but that we cannot tell how many more. We need to round up to 21 as the answer to the problem. How many CDs at 11.99 each could you buy with 50.Get the children to estimate an answer and establish that this is roughly 48 12 = 4 CDs. Demonstrate the division 50 11.99 on the OHP calculator and show this is 4.1701418.Discuss this answer and compare it with the earlier estimate. What does the decimal part represent?Is there enough money to buy 5 CDs? Establish that the decimal part means there will be some money left over but not enough to buy a 5th CD. the answer needs to be rounded down to 4. The decimal fraction is the remainder. Explain to children that they are now going to work in pairs solving division problems, one in each pair using the chunking method and one using a calculator. They are then to compare answers and decide whether to round them up or down and why. Tell them they have 15 minutes.Give the class problems involving division with remainders to solve in pairs.
Two pairs of children to demonstrate their problems and solutions. How do you decide whether to round up or down?
Session 5Obj
Weekly Mental maths test
Ob: Identify and use appropriate operations (including combinations of operations) to solve word problems involving numbers and quantities. Develop calculator skills and use a calculator effectively.
89 children are camping. There are 3 tents that each take 9 children and other tents that each take 4 children. How many tents taking 4 children are needed, and how many tents are needed altogether?Say that before solving the problems they need to read through all of them and decide for each one whether they would solve them mentally (M), using written methods (W) or save them for later and use a calculator (C) and record M, W or C next to each question.Allow 15 minutes to do this and solve those questions they have identified to be done mentally or using a written method.Remind the class that they should estimate their answers first and record their working. Which questions have you chosen to do on the calculator and why?Now give out calculators and allow children 10 minutes to complete the questions they saved for calculator solutions
Reinforce the step-by-step guide and emphasise the importance of estimating before calculating.
Week beginning: Sept 17th
Teacher:
Topic: Pencil and paper procedures (x and )
Year 6 Numeracy
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