Numeracy Posters Index

1. Numeracy Posters Index Measurements : Converting Weights 1 2 Measurements: Converting Units of Length 3 Measurements: Converting m/m 4 Time: 24 hour clock system 5 Time : Calculating lengths of time 6 Ratio: Using Ratios to solve problems 7 Direct Proportion 8 Rounding Round numbers to 1 decimal place 9 Order of Priority 10 Finding a percentage 11 Finding the Percentage Increase 12 Decrease by a Percentage Increase by a Percentage 13 14 Changing a Fraction to a Percentage 15 Working out percentages without calculators 16 Working out a percentage with the calculator 17 Speed Distance Time Questions 18 Drawing Bar Charts Pie Charts 19 Read information from Pie Charts Pie Charts 20 Construct Pie Charts 21 Averages Musselburgh Grammar School

2. Measurements Converting Units of Mass 1 kg= 1000g x1000 Kilogramme (kg) grams (g) ÷1000 Example 1 : Convert 2kg to g : 2 x 1000 = 2000 g Convert 4.6kg to g : 4.6x 1000 = 4600 g Convert 3000g to kg : 3000 ÷ 1000 = 3 kg Convert 650g to kg : 650 ÷ 1000 = 0.65 kg Back Musselburgh Grammar School

3. Measurements Converting Units of Length 1 km= 1000m 1m = 100cm 1cm = 10mm x1000 Kilometres (km) x100 metres (m) x10 ÷1000 centimetres (cm) ÷100 millimetres (mm) ÷10 Example 1 Convert 2m to cm : 2 x 100 = 200 cm Convert 4km to m : 4 x 1000 = 4000 m Convert 34cm to mm : 34 x 10 = 340 mm Convert 50cm to m : 50 ÷ 100 = 0.5 m Back

4. x100 metres (m) x10 centimetres (cm) ÷100 millimetres (mm) ÷10 Measurements Converting between metres and millimetres 1m = 1000mm metres (m) x1000 centimetres (cm) millimetres (mm) ÷1000 Example 1 Convert 2m to mm : 2 x 1000 = 2000 mm 3.34 x 1000 = 3430 m Convert 3.34m to mm : Convert 4000mm to m : 4000 ÷ 1000 = 4 m 7800 ÷ 1000 = 7.8 m Convert 7800mm to m :

5. Converting between the 24 hour and 12 hour clock systems Time 12/24 Hour Clock 1 am 2 am 3 am 4 am 5am 6 am 7 am 8 am 9 am 10 am 11 am midnight 0000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 midday 1 pm 2 pm 3 pm 4 pm 5 pm 6 pm 7 pm 8 pm 9 pm 10 pm 11 pm 1300 1200 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 all 24 hour clock times have 4 digits To go from 12 hour clock to 24 hour clock just add 12 to the pm hours: Example 1 8 pm becomes 2000 6:30 pm becomes 1830 To go from 24 hour clock to 12 hour clock just subtract 12 from the hours (if it is greater than 12) Example 2 2000 becomes 8 pm 1730 becomes 5:30 pm

6. Time Calculating lengths of time Example 1 : Find the time difference between 09 46 hrs and 12 32 hrs 14 mins 2 hours 32 mins 0946 1000 1100 1200 1232 Total Time = 2 hours + 14 mins + 32 mins = 2 hours + 46 mins Example 2 : Find the time difference between 02 47 hrs and 05 49 hrs 13 mins 2 hours 49 mins 0247 0300 0400 0500 0549 Total Time = 2 hours + 13 mins + 49 mins = 2 hours + 62 mins = 2 hours + 1 hour + 2 mins = 3 hours + 2 mins

7. Ratio Using Ratios to solve problems Ratios can be used to compare different quantities Example 1 The recipe for humous is as follows 2 garlic cloves, 4 ounces of chick peas, 3 ounces of olives , 5 ml of Tahina paste and 4 tablespoons of olive oil Write the ratio of chickpeas to olives olives chickpeas 4 : 3 Ratios can be used to solve problems Example 2 A chef makes more humous than normal. If he uses 16 chickpeas. How many olives will he need to use? olives chickpeas 4 3 x 4 x 4 16 12 The chef will need 12 olives

8. Direct Proportion Example 1 If it costs 85p for 5 Mars bars, what is the cost of 3 Mars bars ? Find the cost of one ! Cost of 1 mars bar :85 5 = 17 p Cost of 3 mars bars :17 x 3 = 51p Example 2 Three nights at Marton Manor Hotel cost £165. How much would five nights cost ? Find the cost of one ! Cost of 1 night :£165 3 = £55 Cost of 5 nights :£55 x 5 = £275

9. Rounding Round numbers to 1 decimal place 7 .2 3 cm 1st decimal place 2nd decimal place 7.20 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28 7.29 7.30 7.31 7.32 7.33 7.34 7.35 7.36 7.37 7.38 7.39 7.40 7.3cm 7.2cm 7.4cm 7.24 7.38 7.24 is nearer to 7.2 7.38 nearer to 7.4 The rules for rounding to 1 decimal place are: If the 2nd decimal place is 4 or less - leave 1st decimal place as it is If the 2nd decimal place is 5 or more - add 1 to 1st decimal place Example : Round the numbers to 1 decimal place • 9.04 (b) 18.08 • (c) 24.25 (d) 12.73 9.0 (1d.p) 18.1 (1d.p) 24.3 (1d.p) 12.7 (1d.p)

10. Carry out Steps Order of Priority Brackets then Multiply or Divide then Add or Subtract Example 2 3 + 4 x 6 + 8 Example 1 3 + 4 x 6 Multiply then add = 3 + 24 + 8 = 35 = 3 + 24 = 27 Example 3 18  6 + 3 x 4 Divide 18  6 = 3 then multiply 3 x 4 = 12 then add 3 + 12 = 15 = 3 + 3 x 4 = 3 + 12 = 15

11. Step 1 Step 2 Step 3 Finding a percentage Example 1 I got 30 out of 70 in my English test. What is my percentage mark? • x 100% • 70 • = 42.85…% • = 43% Divide 30 by 70 Then multiply your answer by 100% Round sensibly Does your answer make sense? Check by working out 50%

12. Finding the Percentage Increase Example 1 The volume of dough increased from 50cm3 to 74cm3 due to the effect of yeast. Work out the % increase 74 – 50 = 24 Work out the increase. Divide the increase by the starting volume. Multiply your answer by 100% Step 1 Step 2 = 24 x 100% 50 Step 3 = 48% Does your answer make sense?

13. Decrease by a Percentage Example 1 After boiling a liquid (500ml) for 5 minutes the amount of liquid has been reduced by 8%. Work out the new amount. 8 x 500 100 Step 1 Divide 8 by 100 Multiply your answer by 500 Subtract your answer from 500 Step 2 =40ml 500 – 40 =460ml Step 3 Does your answer make sense? Work out 10% mentally. Alternative method: Decrease by 8% = means a multiplier of 0.92 New volume = 500 x 0.92 = 460ml

14. Increase by a Percentage Example 1 The volume of dough increased by 18% due to the effect of yeast. At the start the volume of dough was 26cm3. Work out the new volume of dough. 18 x 26 100 Step 1 Divide 18 by 100 Multiply your answer by 26 Add your answer to 26 =4.68cm3 Step 2 26 + 4.68 =30.68cm3 Step 3 Does your answer make sense? Work out a 20% increase mentally. (i.e. 10% and double) Alternative method: Increase by 18% = means a multiplier of 1.18 New volume = 26 x 1.18 = 30.68cm3

15. 1 8 Changing a Fraction to a Percentage Example 1 Change to a percentage 1 =0.125 8 Step 1 Divide 1 by 8 Multiply your answer 100% Step 2 0.125 x100% =12.5% Does your answer make sense?

16. Working out a percentage without the calculator The 10% Route Example 1 Work out 65% of £46 10% = 4.60 50%= 23.00 5% = 2.30 65% = £29.90 85%: 10% 100% +5% -15% 15% 85% 45%: 10% 40% 20% +5% 40% 45% 5% 17 ½% = 10% +5% +2 ½%

17. Working out a percentage with the calculator Example: Work out 65% of £46? Step 1 = 65 x 46 100 =£29.90 Divide 65 by 100 Multiply your answer by 46 Step 2 Does your answer make sense? Work out 50%.

18. Speed Distance Time Questions Use the formula triangle ! To remember the formula Cover up the letter you need to find out Example 1 A car travels at a speed of 40m.p.h for 3 hours What distance does it travel? S = 40 m.p.h D = ? T = 3 hours D = S x T = 40 x 3 = 120 miles Example 2 A lorry travels a distance of 150km in 2 hours 30mins What speed did it travel at? S = ? D = 150km T = 2hrs 30mins = 2.5 hours S = D T = 150 2.5 = 60 m.p.h

19. Drawing Bar Charts Example : How do I draw a bar chart? Step 1 Draw and label the axes Freq. Plastic Paper Type Step 2 Mark an even scale on the vertical axes. Mark numbers on the lines Freq. Plastic Paper Type Step 3 Complete the graph by drawing in bars of the correct height. Each bar should have equal width. Freq. Plastic Paper Type Quantities of Litter Give the graph a title Step 4 Freq. Plastic Paper Type • Use a sharp pencil and a ruler • Colour the bars in

20. 90o 108o 36o 54o 72o Pie Charts Read information from Pie Charts Pie Charts are used to display all types of information Hint : The angles in a pie chart all up to 360º Example 1 A survey of pupils favourite sport was done. 300 pupils were asked Football Rugby This is number of pupils asked Squash Cricket Ice Hockey How many pupils liked football ? The angle for football is 108º. The total angle is 360º. Number liking football = 108 x 300 360 = 108 ÷ 360 x 300 = 90

21. Football Rugby 90o 108o 36o 54o 72o Squash Cricket Ice Hockey Pie Charts Construct Pie Charts Pie Charts are used to display all types of information Example 1 A survey of pupils favourite sport was done. 300 pupils were asked Favourite Sport Rugby 75 The results are shown in Football 90 the table Cricket 45 Display the results in a Ice Hockey 60 pie chart Squash 30 To get the angle for Football Number liking football = 90 Total number asked = 300 Angle= 90 x 360 300 = 90 ÷ 300 x 360 = 108º

22. Averages There are 3 types of Averages. Which one are you trying to find out? Mean: this is usually what people think of as average Median: this is the middle number Mode: this is the number that appears most often Example 1 Look at the following ages of children attending an after school club 5, 3 , 7, 6, 7 a)Find the mean Add up the numbers = 5 + 3 + 7 + 6 + 7 = 28 Divide this total by how many numbers are in the list so Mean = 28  5 = 5.6 b)Find the median Rewrite list in order 3 ,5 ,6, 7, 7 Middle number 3 ,5 ,6, 7, 7 Median = 6 c)Find the mode Mode = the number which appears most often Mode = 7 ( as it appears twice in list)