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

2. Back Musselburgh Grammar School Converting Units of Mass Kilogramme (kg) ÷1000 x1000 grams (g) 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 1 kg= 1000g Measurements Example 1 : Back Musselburgh Grammar School

3. Back Musselburgh Grammar School Converting Units of Length Kilometres (km) centimetres (cm) millimetres (mm) ÷ 1000 x1000 x100 x10 metres (m) ÷ 100 ÷ 10 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 1 km= 1000m 1m = 100cm 1cm = 10mm Measurements Example 1 Back

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

5. Back Musselburgh Grammar School 2300220021002000190018001700160015001400 1300 1200 11 pm10 pm9 pm8 pm7 pm6 pm5 pm4 pm3 pm2 pm1 pmmidday 110010000900080007000600050004000300020001000000 11 am10 am9 am8 am7 am6 am5am4 am3 am2 am1 am midnight 12/24 Hour Clock Time To go from 12 hour clock to 24 hour clock just add 12 to the pm hours: Converting between the 24 hour and 12 hour clock systems 2000 1830 Example 1 8 pm becomes 6:30 pm becomes To go from 24 hour clock to 12 hour clock just subtract 12 from the hours (if it is greater than 12) Example 2 8 pm 5:30 pm 2000 becomes 1730 becomes all 24 hour clock times have 4 digits

6. Back Musselburgh Grammar School Calculating lengths of time Example 1 : Find the time difference between 09 46 hrs and 12 32 hrs 09461000110012001232 14 mins2 hours32 mins 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 mins2 hours49 mins 02470300040005000549 Total Time = 2 hours + 13 mins + 49 mins = 2 hours + 62 mins = 2 hours + 1 hour + 2 mins = 3 hours + 2 mins Time

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

8. Back Musselburgh Grammar School 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. Back Musselburgh Grammar School Round numbers to 1 decimal placeRounding 7.2cm 7.3cm 7.4cm 7.2 3 cm 1 st decimal place 2 nd decimal place 7.24 7.38 7.24 is nearer to 7.27.38 nearer to 7.4 If the 2 nd decimal place is 4 or less - leave 1 st decimal place as it is If the 2 nd decimal place is 5 or more - add 1 to 1 st decimal place The rules for rounding to 1 decimal place are: Example :Round the numbers to 1 decimal place (a) 9.04(b) 18.08 (c)24.25(d) 12.73 9.0 (1d.p) 24.3 (1d.p) 18.1 (1d.p) 12.7 (1d.p) 7.217.227.237.257.267.277.287.297.317.327.337.347.357.367.377.387.397.247.307.207.40

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

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

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

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

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

15. Back Musselburgh Grammar School Changing a Fraction to a Percentage Change to a percentage Divide 1 by 8 Multiply your answer 100% Does your answer make sense? 1 =0.125 8 0.125 x100% =12.5% Step 1 Step 2 1818 Example 1

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

18. Back Musselburgh Grammar School Speed Distance Time Questions Example 1 A car travels at a speed of 40m.p.h for 3 hours What distance does it travel? Use the formula triangle ! To remember the formula Cover up the letter you need to find out 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. Back Musselburgh Grammar School Step 1 Step 2 Step 3 Drawing Bar Charts Example : How do I draw a bar chart? Give the graph a title Draw and label the axes PlasticPaper Mark an even scale on the vertical axes. Mark numbers on the lines Plastic Paper Type Freq. Step 4 Complete the graph by drawing in bars of the correct height. Each bar should have equal width. PlasticPaper Type Quantities of Litter Freq. Use a sharp pencil and a ruler Colour the bars in Freq. PlasticPaper Type Freq.

20. Back Musselburgh Grammar School Read information from Pie ChartsPie 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 Hint : The angles in a pie chart all up to 360º Rugby Football Cricket Ice Hockey Squash 90 o 108 o 54 o 72 o 36 o How many pupils liked football ? The angle for football is 108º. Number liking football = 108 x 300 360 = 108 ÷ 360 x 300 = 90 The total angle is 360º. This is number of pupils asked

21. Back Musselburgh Grammar School Construct Pie ChartsPie Charts Pie Charts are used to display all types of information Example 1A survey of pupils favourite sport was done. 300 pupils were asked Rugby Football Cricket Ice Hockey Squash 90 o 108 o 54 o 72 o 36 o Display the results in a Total number asked = 300 Number liking football = 90 To get the angle for Football Rugby Football Cricket Ice Hockey 75 90 45 60 Favourite Sport Squash30 The results are shown in the table pie chart Angle= 90 x 360 300 = 90 ÷ 300 x 360 = 108º

22. Back Musselburgh Grammar School Averages Example 1 Look at the following ages of children attending an after school club 5, 3, 7, 6, 7 There are 3 types of Averages. Which one are you trying to find out? 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 a)Find the mean Mode = the number which appears most often Mode = 7 ( as it appears twice in list) 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 b)Find the median c)Find the mode Rewrite list in order 3,5,6, 7, 7 Middle number 3,5,6, 7, 7 Median = 6