Multiply mentally any two-digitnumber to 50 by a single-digit number.
Quicklydemonstrate one way of using partitioning with jottings to aidmultiplication of a two-digit number by a single-digit number. Givechildren similar questions to answer, writing their solutions onwhiteboards.
Using place valuecards make the number 746 in front of the class. Say that you wantto multiply this number by 6.Partition 746 and give the 700 to onechild, 40 to another and 6 to a third. Ask them each to multiplytheir parts of the numbers by 6 and check the answer with afriend. Together add up these partial products to find the answerto 746 x 6.Ask volunteer to show how this can be laid out on agrid. Say that you want to multiply 4746 by 6. discuss in pairshow much bigger the answer will be than the previous answer and togive an estimate (5000 x 5 = 25 000). Demonstrate grid method torecord this multiplication and compare the answer with theestimate.
Give the childrena multiplication calculation to do in their books using the gridmethod. Check their answers. Ask the children to make up two oftheir own four-digit by single-digit multiplications, recordingtheir use of the grid method in their books, ensure that theyestimate the answer first. Check their use of the grid method iscorrect.
Ask for avolunteer to remind the class how to use the grid method to solve72 x 38, estimating the answer first (70 x 40 = 2800). Get thechildren to use the same method for 372 x 24. Demonstrate anothercalculation, emphasising the need to estimate and the setting outof the grid method. Give the class a set of three-digit bytwo-digit calculations to do, ensure that they estimate the answerfirst.
Write anincomplete grid on the board
What two numbershave been multiplied together in this grid. How do you know?
(7642 x 6. then 7642 x 5)
Use known number facts and placevalue to multiply mentally.
Use the countingstick to count in 5s and then in 0.5s.Point to different marker points on the stick and ask, What numberwould lie here?.
e.g. 3.5 and How many 0.5s are represented by 3.5? Continue toreduce the intervals by counting in 0.05s and ask similar questionswhich encourage the children to identify multiplication facts e.g.7 x 0.05 = 0.35.
Estimate theanswer 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 couldpartition 4.13 into units and tenths. Demonstrate the grid methodto calculate 4.13 x 7.Compare the answer of 28.91 to the estimateof 28. Ask why the answer is bigger, and by how much. Thinking ofa hundred square can get the digits in the correct place in thedecimals if they are unsure. Point to a hundred square say thateach square a hundredth of the whole which is 0.01. Three squaresrepresent 0.03. Multiplying the 3 squares by 7 gives 31 squares or21 hundredths or 0.21 which would look like two rows of 10 and oneleft over, i.e. 2 tenths and 1 hundredth. Why cant the answer to0.03 x 7 be 0.021? Establish that 0.021 is smaller than0.03.
Ask the childrento work in pairs to use the grid method to calculate the answer to3.23 x 3. Take feedback and ensure that the children understandthe method and can interpret the difference between their estimate(3 x 3) and the answer.
Set the childrenother calculations, ensuring that some calculations include thecrossing of the place value boundaries when adding together thepartial products.
Display apartially completed grid.
What two numbershave been multiplied to get this answer? How do youknow?
Consolidate knowing by heartmultiplication and division facts to 10 x 10. Derive quicklycorresponding division facts.
Chant in 7sforwards 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 63
63 7 is 9
63 9 is 7
Ob: Use informal pencil and papermethods to support record or explain divisions.
Tell the children that self-adhesivestamps come in sheets of 24.
Estimate how many sheets you wouldneed to buy if you wanted 500.
Establish that it is roughly 500 25= 20. How would we work it out exactly? Draw out that oneway would be to subtract multiples of 24 from 500.Record on theboard - How many sheets of stamps does this represent? How manysheets will you have to buy to get 500 stamps? Establish that 20sheets will buy 480 stamps so to get 500 they will need 21 sheets.Explain that subtracting 10 lots of 24 is more efficient thansubtracting single multiples. Tell the children that this methodof subtracting multiples of the divisor, 24, is called chunking.How many coaches would be needed to take 780 people on coacheswhich hold 42 people each? Ask the children how they would use thischunking method to answer the question. Identify the divisor andwhat chunks they wish to subtract. Record suggestions on theboard.
Give the childrenproblems to solve which involve similar calculations. Encouragethe children to work with a partner and discuss the size of thechunks they are going to use.
Show a solutionbased on subtracting 10 lots of 23.Establish that larger chunkscould be subtracted.
What larger chunkscould be used here?
Use known numberfacts and place value to multiply and divide mentally. Write thenumber 21 and say that you want as many multiplication anddivision facts with an answer of 21 as possible.
Encourage use of decimals.
Ask children to write a question on their whiteboards. Share someof the answers. Repeat with different numbers.
Ob: Round up or down after division,depending on the context. Remind children of the calculation theycarried out in the previous lesson (500 24) which they did bychunkingNow demonstrate how to do this with a calculator.Using theOHP calculator show the answer: 20.83333333.
Draw out thatthis means 20 sheets and some more but that we cannot tell how manymore. We need to round up to 21 as the answer to the problem. Howmany CDs at 11.99 each could you buy with 50.Get the children toestimate an answer and establish that this is roughly 48 12 = 4CDs. Demonstrate the division 50 11.99 on the OHP calculator andshow this is 4.1701418.Discuss this answer and compare it with theearlier estimate. What does the decimal part represent?Is thereenough money to buy 5 CDs? Establish that the decimal part meansthere 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 isthe remainder.
Explain tochildren that they are now going to work in pairs solving divisionproblems, one in each pair using the chunking method and one usinga calculator. They are then to compare answers and decide whetherto round them up or down and why. Tell them they have 15minutes.
Give the class problems involving division with remainders to solvein pairs.
Two pairs ofchildren to demonstrate their problems and solutions. How do youdecide whether to round up or down?
Weekly Mental maths test
Ob: Identify and use appropriateoperations (including combinations of operations) to solve wordproblems involving numbers and quantities. Develop calculatorskills and use a calculator effectively.
89 children arecamping. There are 3 tents that each take 9 children and othertents that each take 4 children. How many tents taking 4 childrenare needed, and how many tents are needed altogether?
Say that before solving the problems they need to read through allof them and decide for each one whether they would solve themmentally (M), using written methods (W) or save them for later anduse a calculator (C) and record M, W or C next to eachquestion.
Allow 15 minutes to do this and solve those questions they haveidentified to be done mentally or using a written method.
Remind the class that they should estimate their answers first andrecord their working. Which questions have you chosen to do on thecalculator and why?Now give out calculators and allow children 10minutes to complete the questions they saved for calculatorsolutions
Reinforce thestep-by-step guide and emphasise the importance of estimatingbefore calculating.