Year 7 Written Calculations Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 22nd July 2018 Objectives: Be able to add, subtract, multiply and divide numbers of any size (including decimals). Extension: Solve
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Year 7 Written Calculations Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com Last modified: 22nd July 2018 Objectives: Be able to add, subtract, multiply and divide numbers of any size (including decimals).
Extension: Solve problems involving missing digits within a multiplication/addition.<br>
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www.drfrostmaths.com
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Use any preferred method (but preferably long multiplication!) to multiply the following numbers. If you finish…
Put the digits from each calculation into the triangle. What do you notice? 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 This is known as Pascal’s Triangle. Each number is the sum of the two above it.
Sadly we will no longer see Pascal’s Triangle for 115 onwards (why?) ? ? ? ? ? ? ? ? ? ?<br>
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First ignore decimal points and multiply as whole numbers. Correct by counting total number of decimal place jumps.<br>
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Ensure decimal points are lined up so that the digits in each column have the same place value. Fill any ‘gaps’ with 0s.<br>
[JMC 1997 Q10] Each day throughout July 1995 I picked 300g of raspberries from my garden. What was the total weight of the raspberries I picked that month?A 10g B 9kg C 9.3kg D 10kg E 9300kgSolution: C
[JMC 1998 Q7] The Mystery Prize at the Bank of England Christmas Party was a pile of crisp new £5 notes, numbered from 659384 up to 659500. What was the value of the prize?A £116 B £117 C £580 D £585 E £1420Solution: D 9 10 [JMC 2000 Q10] Each Junior Mathematical Challenge answer sheet weighs 6 grams. If 140000 pupils enter the challenge this year, what will be the total weight of all their answer sheets?A 84kg B 840kg C 8 400kg D 84 000kg E 840 000kgSolution: B
[JMC 2000 Q14] The DISPUTOR is similar to a calculator, but it behaves a little oddly. When you type in a number, the DISPUTOR doubles the number, then reverses the digits of this result, then adds 2 and displays the final result. I type in a whole number between 10 and 99 inclusive. Which of the following could be the final result displayed?A 39 B 41 C 42 D 43 E 45Solution: E 11 12 ? ? ? ? (On provided sheet)<br>
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13 14 15 16 ? ? ? ? (On provided sheet)<br>
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[JMO 1999 A7] Before the decimalisation of money in the UK, there were 12 pence (d) in 1 shilling (s) and 20 shillings in 1 pound (£). Thus 1 pound 3 shillings and 4 pence was written £1 3s 4d. What would have been the total cost of 7 items each costing £1 6s 8d? Write your answer in simplest £ s d form.Solution: £8
[JMC 2003 Q22] Two builders, Bob and Geri, buy bricks at the same price. Bob sells 10 for £6 and Geri sells 12 for £7. Supposing they sell equal numbers of bricks, what number has each sold when Bob has gained £4 more than Geri?A 42 B 60 C 72 D 120 E 240Solution: E 17 18 ? ? (On provided sheet)<br>
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It is fine in practice to divide decimals by whole numbers.
e.g. Dividing £1.68 between 4 people.
However, we don’t in general like dividing by decimals.
e.g. Dividing £3 between 5.6 people. We can’t do that! ? ? ? ?<br>
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Ensure decimal point goes in same place in result.<br>
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? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 2 3 4 5 6 7<br>
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This lesson you will be able to work in groups on some puzzles to do with missing digits within column addition/multiplication. Clue:
We’re adding the same digits in each of the two columns, but get a different digit as the result. There therefore must have been a carry, and hence M is one more than C. Clue:
These two digits are the same. Thus J and M must add to 10. ? ? ? ?<br>
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Question 1 Get into groups of 3 or 4. Merits to the team with the most correct answers at the end.
Effective Team Maths Challenge strategy: Have two people independently work on each problem, and each ‘initial’ the problem on a shared sheet if you have a solution. When both people have solved the problem, compare your two answers. ?<br>
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Question 2 [JMC 2003 Q16] In this multiplication each letter stands for a different digit. Which letters stands for 3?A B C D ESolution: D ?<br>
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Question 3 ?<br>
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Question 4 ?<br>
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Question 5 ?<br>
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Question 6 [Junior Kangaroo 2015 Q12] In the sum shown, different shapes represent different digits. What digit does the square represent?A 2 B 4 C 6 D 8 E 9Solution: C ?<br>
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Question 7 [JMC 2002 Q24] In the multiplication on the right, each letter represents a different digit and only the digits 1, 2, 3, 4, 5 are used. Which of the letters represents 2?A B C D ESolution: E ?<br>
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Question 8 ?<br>
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Question 9 ?<br>
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Question 10 [JMO 2000 B4] How many different solutions are there to the letter sum on the right? Different letters stand for different digits, and no number begins with a zero. J M C+ J M OS U M SSolution: 6 ?<br>