Problem Solving Practice

Problem Solving:

​Asynchronous Session

To be completed by Monday 13th December

​Word of the Week

​Word of the Week

​"you MUST show your working out."

​This phrase indicates that marks for this question will only be given out if you show your working.

(that can be non calculator methods or what you typed into your calculator)

​Problem Solving questions:

​

• ​can appear at every grade of question.

• ​can appear for any topic.

• ​can be calculator or non calculator.

• ​are usually worth 5 marks or more.

​What do you think of problem solving questions?

Join the discussion on Padlet.

​https://padlet.com/lthorpe14/529di1j350uko8cc

Multiple Select

​Dan buys 24 packets of nuts.

​

Each packet of nuts weighs 225 g.

​

Work out the total weight of all the packets of nuts that Dan buys.

• 225 $$\div$$  24 = 9.35

• 225 x 24 = 5400

• 24 x 0.225 = 5.4

• 24 $$\div$$  225 = 0.106

​​Dan buys 24 packets of nuts.

Each packet of nuts weighs 225 g.

Work out the total weight of all the packets of nuts that Dan buys.

• ​​225 x 24 = 5400 ​Why was this answer correct?

• ​Literally we could add the bags... 225 + 225 + 225 + 225...... 24 times

• ​We say multiplication for this as 24 "lots of" 225g

​​Dan buys 24 packets of nuts.

Each packet of nuts weighs 225 g.

Work out the total weight of all the packets of nuts that Dan buys.

• 0.​​225 x 24 = 5.4 Why was this answer correct?

• ​It is exactly the same as doing 225g x 24 except we have converted 225g into 0.225kg so our answer is just in a different unit.

​There are loads of problem solving techniques:

​These slides are just a few suggestions!

​A unit of gas costs 4.2 pence.

​

On average Ria uses 50.1 units of gas a week.

She pays for the gas she uses in 13 weeks.

​

Work out an estimate for the amount Ria pays.

​#1: Identifying key information in a question:

​

​Read through the question first, underline / circle / highlight the important information in once sentence at a time

​A unit of gas costs 4.2 pence.

​

On average Ria uses 50.1 units of gas a week.

She pays for the gas she uses in 13 weeks.

​

Work out an estimate for the amount Ria pays.

​#1: Identifying key information in a question:

​

​Once you have the key information - you can use it without having to search through all the wordy sentences again.

​ unit 4.2 pence.

​

50.1 units a week.

13 weeks.

​

estimate

​#1: Identifying key information in a question:

​

​Now you can start to do the calculations you need for your answer.

​ unit 4.2 pence.

​

50.1 units a week.

​

13 weeks.

​estimate - key word means use rounded values

​use 4p

​use 50 units

​4 x 50 = 200 pence

​200 pence = £2

​£2 x 13 = £26

​ANSWER: £26

​A ticket for a seat at a school play costs £2.95

​

There are 21 rows of seats.

​

There are 39 seats in each row.

​

The school will sell all the tickets.

​

Work out an estimate for the total money the school will get.

​A ticket for a seat at a school play costs £2.95

​Estimate ticket price £3

There are 21 rows of seats. There are 39 seats in each row.

​Estimate 21 = 20, estimate 39 = 40

​20 x 40 = 800 seats altogether.

​The school will sell all the tickets.

​800 x £3 = £240

Work out an estimate for the total money the school will get.

​£240

​Let's Try a new focus question.

​Milk is sold in two sizes of bottle.

​A 4 pint bottle of milk costs £1.18

A 6 pint bottle of milk costs £1.74

Which bottle of milk is the best value for money?

You must show all your working.

​#2: Annotate diagrams with information:

​

​Look at the diagrams carefully and annotate what calculations you could do or any additional information that may help you.

​Milk is sold in two sizes of bottle.

​A 4 pint bottle of milk costs £1.18

A 6 pint bottle of milk costs £1.74

Which bottle of milk is the best value for money?

You must show all your working.

​Best value is cheapest - if I bought the same amount of milk!

​4 pinter and 6 pinter....... could buy 12 pints of either!

​#2: Annotate diagrams with information:

​Best value is cheapest - if I bought the same amount of milk!

​4 pinter and 6 pinter....... could buy 12 pints of either!

​ x 3 to get 12 pints

​

​£1.18 x 3

​= £3.54

​ x 2 to get 12 pints

​

​£1.74 x 2

​= £3.48

​6 pints is better value

​#2: Annotate diagrams with information:

​Examiners a trained to mark any information written on and around the diagram as well as on the answer lines.

​Be clear about what your final answer is.

​ABDE is a rectangle.

​

ED is 8cm.

​

BDC is a right-angled triangle.

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BC is 4.5cm.

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ABC is a straight line.

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The area of the rectangle ABDE is 40cm².

​

Work out the area of the triangle BDC.

​

​

​

​

​Check all the information given is labelled correctly

​

​

The area of the rectangle ABDE is 40cm².

​8 x ? = 40 for area of rectangle. height is 5cm

Work out the area of the triangle BDC.

​base = 4.5cm, height = 5cm (same as rectangle)

​Area = (4.5 x 5) = 22.5cm²

​8cm

​(Rectangle)

Rectangle​

Area = base x height

Triangle​

Area = (base x height)

​22.5cm²

​Let's Try a new focus question.

​#3: working out using one line of information at a time:

​Cover up the whole question..... slide down the cover so that you get one piece of information at a time and use it as you go.

​Sam buys 20 boxes of oranges.

There are 25 oranges in each box.

​try covering the rest of the question with your ruler

​20 x 25 = 500

- total number of oranges

​Sam buys 20 boxes of oranges.

There are 25 oranges in each box.

​

​Each boxes of oranges costs £7

​20 x 25 = 500

- total number of oranges

​

​20 x 7 = £140

- total cost of oranges

​Keep track of your working out and annotate exactly what it is that your have worked out.

It WILL be used in the next line or two of the question.

​Did Sam make a profit or a loss?

​Step by step working out.

​Total cost £140, Total made £80 + £50 = £130 Sam lost £10

​Sapir buys 60 bags.

​

She pays £3 for each bag.

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Sapir sells ½ of the bags for £5 each.

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She sells ¹⁄₃ of the bags for £4 each.

​

Sapir wants to make a total profit of £75

​

How much should she sell each of the remaining bags for?

​£12.50

​Be kind to your examiner -

​show clear steps of working and make your final answer obvious

​Its easier to check during the exam.

​

​Its easier to mark .

​

​Examiners have a mark scheme.

​Correct answers get full marks

​If its not completely correct examiners have to search for key calculations in your working out.

​Quizziz Completed!

​Now check out the practice questions on: