Online Practice Tests to do Hyperlinked Philip Kent QTS Info site Link to Box & Whisker Diagrams Numeracy skills tests:  Test content Box & Whisker Examples QTS Skills Tests information Stem & Leaf Diagrams Examples Online Practice Tests to do You Tube Top Tips Solutions – excellently explained G and A Numerical extra practice tests Numeracy Ready Link to website for extra practice test s Solutions – excellently explained 1 2 3 4 Numeracy skills Practice

Apps to test your mental and On- Screen Calculator skills Hyperlinked Apps to test your mental and On- Screen Calculator skills

Free apps to help improve your mental skills Hyperlinked Free apps to help improve your mental skills

Try these for more mental maths practice Hyperlinked Try these for more mental maths practice Numeracy Testbank Extra mental test from GA Numerical Extra mental test from GA Numerical - Solutions QTS Numeracy Test http://www.phillipkent.net/QTS-test http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i6/bk7_6i3.htm http://www.freeteacher.co.uk/math_games.html http://www.freeteacher.co.uk/mental_mathematics_for_key_stage_two_ks2.aspx

This slide should help your knowledge of the conversions between important fractions, decimals and percentages. You could well be asked a question where the answer comes to ⅛, however they want this given as a percentage. Don’t panic, remember that ⅛ is half of ¼ so halve 25% which is 12.5% 1 100% ¾ 0.75 75% ½ 0.5 50% ¼ 0.25 25% 1/10 0.1 10% 1/20 0.05 5% 1/100 0.01 1% ⅛ 12.5% ⅜ 37.5% ⅝ 62.5% ⅞ 87.5% ÷ by 2

Here is how you convert any fraction to a decimal to a percentage Here is how you convert any fraction to a decimal to a percentage. This is useful when answering the on-screen calculator questions. To change a fraction to a decimal (divide by the bottom number, multiply by the top number) Eg ⅝ 5 ÷ 8 0.625 To change a decimal to a percentage (multiply by 100) Eg 0.625 x 100 62.5% To change a percentage to a decimal then a fraction (divide by 100) (put the number over the value of the last digit’s column) Eg 62.5% ( 62.5 ÷ 100) 0.625 625 (cancel down) ⅝ 1000 13/11/2018

Some questions for you to try. Then click for the answers

Some questions for you to try. Then click for the answers

Change fractions into percentages x top and bottom numbers by 4 Change fractions into percentages Calculate an equivalent fraction where the denominator is 100. x top and bottom numbers by 4 x top and bottom numbers by 2 x top and bottom numbers by 2 x top and bottom numbers by 10 x top and bottom numbers by 20 x top and bottom numbers by 5 x top and bottom numbers by 5 x top and bottom numbers by 2 56 140 36 120 = ⅖ A Cancel down first A Cancel down first

To find a fraction of an amount To find a percentage of an amount (divide by the bottom number and multiply by the top number) Eg ⅝ of £40 £40 ÷ 8 x 5 £25 To find a percentage of an amount change percentage to a fraction change fraction to a decimal multiply by the amount Eg 18% of £62 18 0.18 0.18 x 62 £11.16 100 13/11/2018

This trick maybe useful

Some questions for you to try. Then click for the answers

Distance, Speed and Time Mental Question A teacher takes a school trip to the theatre. The theatre is 50 miles away and the coach travels at an average speed of 30 miles per hour. What is the latest time that the coach must leave to arrive at the theatre by 19:00 hrs. Give your answer in the 24 hour clock. 1 hour (60 mins) 30 miles 20 mins 10 miles 1 hr 40 mins 50 miles Total journey time Coach must leave by 17:20

Latest time to leave is 13:25 On-Screen Calculator To change 0.75 hr into minutes you must multiply by 60 2 x 25 = 50 mins rest breaks 11km at 4km/h (T = D/S ) = 11/4 = 2.75 hrs = 2hrs 45 mins Total time 3hrs 35mins Latest time to leave is 13:25

Latest time to leave is 13:40 On-Screen Calculator A school trip has to travel 150 miles by coach to a concert in Birmingham. The coach will travel at an average speed of 45mph and must arrive by 17:30 hrs plus they must allow a break of 30 mins. What is the latest time must the coach leave by? To change 0.3333 hr into minutes you must multiply by 60 150 miles at 45mph (T = D/S ) = 150/45 = 3.3333 hrs = 3hrs 20 mins + rest break of 30 mins Total time 3hrs 50mins (take off 4hrs and add on 10 mins) Latest time to leave is 13:40

Journey time 1 hour 26 minutes On-Screen Calculator A teacher has to travel 85 miles by car to a meeting. She will travel at an average speed of 95 km/h. Taking 5 miles to approximately equal 8 km, how long will the journey take? Give your answer to the nearest minute. To change 0.4315789 hrs into minutes you must multiply by 60 5 miles = 8 km 85 miles = 136km 136 km at 95km/h (T = D/S ) = 136/95 = 1.4315789 hrs = 1hr 25.89 mins = 1 hr 26 mins Journey time 1 hour 26 minutes

Try these yourself 4 30 4.5 hours is _____hours _____minutes 1 12 1.2 hours is _____hours _____minutes 1 1.25 hours is _____hours _____minutes 15 4 40 2.666666 hours is _____hours _____minutes 3 3.8 hours is _____hours _____minutes 48 3 3.45 hours is _____hours _____minutes 27 1 22 1.36 hours is _____hours _____minutes (to the nearest minute)

How many students gained a grade A or A*? Hyperlinked Hyperlink for explanation of Cumulative Frequency graphs by Numeracy Ready on You Tube (part 1) Hyperlink for explanation of Cumulative Frequency graphs by Numeracy Ready on You Tube (part 2) No of Pupils Q. 60 pupils took Maths GCSE and the cumulative frequency graph shows their results. How many students gained a grade A or A*?

Q. How many students gained a grade A or A˟? No of Pupils 60 – 45 = 15 students gain A or A˟ 45 Q. How many students gained a grade A or A˟? To do this you must look at the number of students who gained B or below (as this will show you the G,F,E.D,C and B)

Explanation of Box and Whisker diagrams by G&A Numerical on YouTube Hyperlinked Explanation of Box and Whisker diagrams by G&A Numerical on YouTube Top 1/4 Range Interquartile Range Top 1/4

Test 1 Test 3 Percentage Test 1 Test 2 Test 3 Test 4 A class sat 4 tests. 1) In which test did ¼ of the pupils score at least 65%? 2) Which test had the greatest range? 3) In which test did ½ of the pupils score at least 60%? Test 2 Test 1 Test 3 Test 1 Test 1 Test 1 Percentage Test 1 Test 1 Test 2 Test 3 Test 4

Explanation of Scatter Graphs by G&A Numerical on You Tube Hyperlinked Explanation of Scatter Graphs by G&A Numerical on You Tube 2015 Scatter graph showing the percentage of pupils gaining at least 5 A* to C at GCSE in 2014 and 2015 Click on the school which has the same percentage score of students gaining at least 5 A˟ - C in both 2014 and 2015 2014

Indicate the true statements. The pie chart below shows the number of pupils involved in after school activities each week. Indicate the true statements. 30 60 20 + 25 65 200 pupils 65 + 60 = 125 = ⅝ 200 200 30 + 20 = 50 = ¼ 200 200 30 = 15% 200 After school more than 15% of the pupils take Art ¼ of the pupils go to Art or Music ⅝ of the pupils are involved in Football or Drama

The table below compares the results from two mock exams. Which pupil’s marks had increased more than 10% from mock 1 to mock 2? Pupil Mock 1 (out of 20) Mock 2 (out of 50) A 15 43 B 11 35 C 16 45 D 13 38 E 14 40 F 7 22 G 17 46 x by 5 % 75 55 80 65 70 35 85 x by 2 % 86 70 90 79 80 44 92

The table below compares the results from two mock exams. Which pupil’s marks had increased more than 10% from mock 1 to mock 2? Pupil Mock 1 (out of 40) Mock 2 (out of 50) A 20 33 B 32 34 C 16 27 D 12 19 E 14 17 F 10 22 G 28 41 ÷ 4 x 10 % 50 80 40 30 35 25 70 % 66 68 54 39 34 44 82 x 2

Which grade had the biggest percentage difference? A school compared its percentage of GCSE grades with those of the national average. The results are displayed in this graph. Which grade had the biggest percentage difference? Percentage of Grades Grade E

A tricky type of question A science teacher produced the following table to show the marks achieved in an end of topic test taken by 3 Yr 9 classes. Indicate the true statements. Marks (percentage) Range Mode Median Class A 60 50 82 Class B 55 38 52 Class C 85 70 The range is always important to consider in these questions to try and determine either the highest or lowest possible values. Some pupils in Class A achieved less than 22% Even if 82 was highest mark, 82 – 60 = 22% So any mark less than 22 is not possible Range 60 82 22 At least one pupil in Class C achieved less than 15% Range 85 Even if 100 was highest mark, 100 – 85 = 15% So there must be a mark of 15 or even less 100 15 Some pupils in Class B achieved a mark of more than 95% Range 55 Even if 38% was lowest mark, 38 + 55 = 93% So a mark of more than 95% is not possible 93 38