Name: Teacher: Form: Set: LEARNER JOURNAL Mathematics Module 2 END OF YEAR TARGET: GCSE TARGET:
MODULE 2 use a number line to represent negative numbers use inequalities with negative numbers compare and order positive and negative numbers. convert from one metric unit to another convert from one imperial unit to another. Unit 2A Number: Basic Number work out the answers to problems with more than one mathematical operation. use the four rules of arithmetic with integers and decimals. Unit 2B Geometry and Measures: Measures and Scale Drawing read and draw scale drawings use a scale drawing to make estimates. use approximate conversion factors to change between imperial units and metric units. draw nets of some 3D shapes identify a 3D shape from its net. read from and draw on isometric grids interpret diagrams to draw plans and elevations. UNIT 2A AND 2B TEST Unit 2C Statistics: Charts, Tables and Averages use tally charts and frequency tables to collect and represent data draw a line graph to show trends in data. use grouped frequency tables to collect and represent data. draw pictograms to represent statistical data work out the mode, median, mean and range of small sets of data draw bar charts and vertical line charts to represent statistical decide which is the best average to use to represent a data set. data. Unit 2D Geometry and Measures: Angles calculate angles on a straight line calculate angles around a point calculate angles in parallel lines. use vertically opposite angles. recognise and calculate the angles in different sorts of triangle. use angle properties in quadrilaterals. calculate the sum of the interior angles in a polygon. calculate the sum of the exterior angles and the interior angles use a bearing to specify a direction. of a regular polygon. UNIT 2C AND 2D TEST find multiples of whole numbers recognise multiples of numbers. identify the factors of a number. identify prime numbers. identify prime factors round a whole number. round decimal numbers to a given accuracy. Unit 2E Number: Number Properties identify the lowest common multiple (LCM) of two numbers identify the highest common factor (HCF) of two numbers. identify square numbers use a calculator to find the square of a number. recognise the square roots of square numbers up to 225 use a calculator to find the square roots of any number. use some of the important keys when working on a calculator. Unit 2F Number: Approximations identify significant figures round numbers to a given number of significant figures use approximation to estimate answers and check calculations round a calculation at the end of a problem, to give what is considered to be a sensible answer. UNIT 2E AND 2F TEST
Module 2 Grid 1- Place Value & BIDMAS (MW 1,2,3,23,138) 1) 2) 3) Improve identifying Place Value Complete Perfect! Try solving more difficult questions involving BIDMAS. Complete Write these numbers in order. Start with the Largest. -3.4, -3, -3.42, -4.1, -3.01, -2.9
Module 2 Grid 2-The Four Rules (MW 17,18,19,20,66,67) Improve using the four rules. Complete Perfect! Try solving more difficult questions involving the four rules. Complete a) 652 + 78 b) 318 82 c) 48 x 9 d) 336 8 a) 5 23 b) -17 + 39 c) -11 x -4 d) -16 8
Module 2 Grid 3- Systems of measurement & Conversion factors (MW 112) Improve converting metric and imperial units. Complete Perfect! Try solving more difficult question involving conversions. Complete
Module 2 Homework 1 Adding/Subtracting Multiplying/Dividing Integers and Decimals Reason for not submitting:
The diagram below shows some nets. Identify the name of its solid shape. Module 2 Grid 4- Scale drawings (MW 4 & 38), Nets (44), & Isometric grids (51) Draw the side elevation of the solid object from the direction of the arrow. Improve understanding of nets of solids. Complete Perfect! Try solving more difficult question using isometric grids. Complete Draw accurately the net for this cube. 1cm 1cm 1cm
Name: Class: Score: Percentage: /30 Module 2 Units 2A & 2B Basic Number Measures and Scale Drawing Qu Marks T To improve your understanding of A MW 1 5 Four rules of arithmetic 17 20 2 3 Arithmetic with negative numbers 17 / 18 3 2 Scale drawing 4 / 38 4 2 Applications of negative numbers 23 5 5 BIDMAS 75 6 3 Multiplication 19 7 2 BIDMAS 75 8 4 Application of number skills 41 9 4 Conversion of metric units 112 30 TOTAL A Complete corrections in green pen.
Module 2 Grid 5- Frequency tables & Statistical Diagrams (MW 15,16,63) The pictogram gives information about the number of goals scored by a local football team per week. a) Find the number of goals scored in the first week. b) Find the number of goals scored in the third week. c) 8 goals were scored in the fourth week 5 goals were scored in the fifth week Complete the pictogram. Improve completing a frequency table and pictogram. Complete Perfect! Try displaying data in a more complex graph. Complete The tally and pictogram show information about the number of texts sent by students last week. Draw a bar chart to represent the information about David's friends favourite crisps. (use the table from first part.) Complete the frequency table then the pictogram.
Module 2 Grid 6 - Line Graphs (MW 64) Improve interpreting line graphs. Complete Perfect! Try drawing a line graph to represent data. Complete The graph shows the number of ice creams sold each day during one week. Draw a line graph to represent this data. a) How many more ice creams were sold on Tuesday than on Monday? b) Explain what might have happened on Monday.
Module 2 Homework 2 Metric Conversion Ratio/Nets Elevations/Bar Charts Reason for not submitting:
Module 2 Grid 7- Statistical averages (MW 62) Improve calculating averages. Complete Perfect! Try solving more difficult questions involving averages. Complete
Module 2 Grid 8 Angle Facts & Triangles (MW 45,121) Improve your angle facts. Complete Perfect! Try justifying your answers. Complete a) The angles in a triangle equal. degrees. b) The angles around a point equal. degrees. c) The angles in a straight line equal. degrees. d) Vertically opposite angles are always.
Module 2 Grid 9- Polygons (MW 123) Name these regular polygons: a) Work out the size of each interior angle in this regular polygon b) c) Improve naming and calculating interior angles of regular polygons. Complete Perfect! Try solving more difficult questions involving polygons. Complete This shape is a regular. Work out the size of each interior angle of this regular polygon Work out the size of each exterior angle of this regular polygon
Module 2 Homework 3 Averages and the Range Angle Facts Angle Sums of Polygons Reason for not submitting:
Module 2 Grid 10 Angles in Parallel lines (MW 120) a Angle a equals because it is. b Angle b equals because it is. Improve calculating angles on parallel lines. Complete Perfect! Try solving more difficult questions involving angles. Complete c i) Write down the size of the angle labelled c. ii) Give a reason for your answer.
Module 2 Grid 11- Quadrilaterals & Bearings (MW 10, 124) Calculate the size of angle a. A and B are two cities. Measure the bearing of B from A Improve calculating and measuring angles. Complete Perfect! Try solving more difficult questions involving angles and bearings. Complete
Name: Class: Score: Percentage: /40 Module 2 Units 2C & 2D Charts, Tables and Averages Angles Qu Marks T To improve your understanding of A MW 1 3 Pictograms 16 2 3 Line Graphs 4 3 2 Angles round a point 45 4 6 Tally charts / Frequency tables / Charts 15 5 2 Angles on a line 45 6 2 Properties of quadrilaterals 10 7 7 Mean, Mode, Median and Range 62 8 4 Angle properties 120 / 121 9 4 Angles in triangles 121 / 122 10 4 Angle properties 120 / 121 11 3 Angles in polygons 123 40 TOTAL A Complete corrections in green pen.
Module 2 Grid 12 - Number properties (MW 28) From the numbers in the rectangle. a) Write down a multiple of 4. b) Write down a factor of 21. c) Write down a prime number. Improve identifying Multiples, Factors, and Primes. Complete Perfect! Try solving a problem involving Factors & Multiples Complete Here are six numbers: 2, 8, 9, 15, 22, 54 From these numbers find: a) A multiple of three b) A factor of 30 c) A prime number Jan writes down One multiple of 9 and two factors of 40 Jan adds together her three numbers. Her answer is greater than 20 but less than 30. Find three numbers that Jan could of written down.
Module 2 Homework 4 Parallel Lines Polygons/Bearing Factors/Squares/Cubes Reason for not submitting:
Module 2 Grid 13 - Prime factors (MW 78) Write 120 as a product of its prime factors. Find the Highest Common Factor (HCF) of 24 and 64. Find the Lowest Common Multiple (LCM) of 24 and 64. Improve finding the HCF & LCM of a pair of numbers. Complete Perfect! Try solving more difficult questions involving HCF & LCM. Complete Write150 as a product of its prime factors. Find the HCF & LCM of 120 and 150. James thinks of two numbers. He says: The Highest Common Factor (HCF) of my two numbers is 3. The Lowest Common Multiple (LCM) of my numbers is 45. Write down the two numbers James could be thinking of.
1) Without a Calculator 2) Using your calculator Module 2 Grid 14 - Squares & Calculators (MW 81, 77) a) 4 2 b) 6 2 c) 25 d) 49 e) 10 2 f) 81 Improve finding square numbers, and square roots. Complete Perfect! Try solving more difficult questions involving Squares and Calculators. Complete 1) Without a calculator a) 3 2 b) 7 2 c) 16 d) 9 + 2 2 1) Without a calculator a) 3 2 + 5 2 b) 36 x 4 2 c) 144 9 1) With a calculator a) 3.2 2 x 1.7 3 b) 529 16 2 c) (7.3 + 4.32) x (9.6 1.4)
Module 2 Grid 15- Rounding & Estimation (MW 31,32,90,91) 1) a) Round 23 to the nearest ten. b) Round 157 to the nearest hundred. c) Round 2375 to the nearest thousand. 3) Estimate the value of : 2) a) Round 2.42 to 1 decimal place. b) Round 16.45 to 1 decimal place. c) Round 8.237 to 2 decimal places. Improve rounding and estimation. Complete Perfect! Try solving more difficult questions involving estimation. Complete 1) a) Round 56 to the nearest ten. b) Round 721 to the nearest hundred. c) Round 4.66 to 1 decimal place. d) Estimate the value of 568 x 3.21 Estimate the value of : a) b)
Module 2 Homework 5 Prime Factors/Calc Skills Rounding Estimation Reason for not submitting:
Name: Class: Score: Percentage: /35 Module 2 Units 2E & 2F Number Properties Number Approximations Qu Marks T To improve your understanding of A MW 1 4 Multiples, Factors and Powers 28 2 2 Rounding to powers of 10 31 3 3 Powers and Square roots 81 4 3 Powers and Square roots 81 5 3 Prime and Square numbers 28 / 81 6 2 Rounding to significant figures 90 7 3 Application of LCM 80 8 4 Application of LCM 80 9 3 Factor problem 28 10 3 Product of prime factors 78 11 2 Calculations using approximations 91 12 3 Using a calculator / Significant figures 77 / 81 35 TOTAL A Complete corrections in green pen.
Percentage means fraction out of 100 50% = 0.5 = ½... divide by 2 25% = 0.25 = ¼... halve then halve again 10% = 0.1 = 1 /10... divide by 10 1% = 0.01 = 1 /100... divide by 100 To calculate a percentage increase (or decrease), find the percentage and add it on (or take it away) Eg to increase 120m by 15% 10% of 120m = 12m 5% of 120m = 6m 15% of 120m = 12 + 6 = 18m 120m + 18m = 138m Negative Numbers Replace - - with + eg 3 (-4) = 3 + 4 = 7 Replace + - with - eg 3 + (-4) = 3-4 = -1 + + = + eg 3 4 = 12 + + = + - + = - eg (-3) 4 = -12 - + = - + - = - eg 3 (-4) = -12 + - = - - - = + eg (-3) (-4) = 12 - - = + Fractions of To find a fraction of an amount you divide by the bottom and times by the top Eg to find 2/3 of 18m you do 18 3=6 then 6x2=12m BRACKETS INDICES DIVISION MULTIPLICATION ADDITION SUBTRACTION Laws of Indices a b a b y y y Perform calculations in the correct order Adding and Subtracting Fractions Make sure the fractions have a common denominator before you add/subtract them eg 3 2 21 10 31 5 7 35 35 35 7 1 21 4 17 8 6 24 24 24 a y a b a b ( y ) y y 0 1 b y y = mx + c (equation of a straight line) m = gradient c = y-intercept gradient (steepness) = change in y change in x y a b Types of Number odd ends in 1, 3, 5, 7, 9 even ends in 0, 2, 4, 6, 8 (is divisible by 2) factor divides exactly into a number eg 5 is a factor of 10 multiple in the times table of a number eg 20 is a multiple of 10 prime number - can only be divided by one and itself: 2, 3, 5, 7, 11, 13, 17, 19... are prime Highest Common Factor (HCF) of 2 numbers the largest value that divides exactly into both numbers Lowest Common Multiple (LCM) of 2 numbers the smallest value that is in the times tables of both numbers nth terms First find out how you get from term to term this tells you the times table the sequence is based on eg 4, 7, 10, 13,... goes up in 3s so the sequence is based on the 3x table (3n) Then find out what you need to add or subtract from this times table to get the required sequence. eg 4, 7, 10, 13,... is one more than the 3x table so the nth term is 3n + 1 To plot straight lines you can use triangle numbers 1 3 6 10 etc a table of values the cover-up method y-intercept and gradient Check the scale carefully. square numbers 1 2 =1 2 2 =4 3 2 =9 4 2 =16 5 2 =25 6 2 =36 7 2 =49 8 2 =64 9 2 =81 10 2 =100 11 2 =121 12 2 =144 13 2 =169 14 2 =196 15 2 =225 Product of Prime Factors 48 6 8 2 3 4 2 2 2 48 = 2 2 2 2 3 = 2 4 3 (index form) square roots 1 1 4 2 9 3 16 4 25 5 36 6 49 7 64 8 81 9 100 10 121 11 144 12 169 13 196 14 225 15 cube numbers 1 3 =1 2 3 =8 3 3 =27 4 3 =64 5 3 =125 10 3 =1000 3 1 cube roots 1 3 8 2 3 27 3 3 64 4 3 125 5 3 1000 10
Trial and Improvement Eg Solve x 3 + 2x = 19 to 1 dp x x 3 + 2x big/small 2 12 too small 3 33 too big 2.5 20.625 too big 2.4 18.624 too small 2.45 19.606.. too big small 2.4 big 2.45 big 2.5 Use a table for your trials Find the two whole numbers either side of the answer Then find the two numbers to 1dp either side Try halfway between these to decide which is closest so x = 2.4 (1 dp) Metric units: Length use mm, cm, m, km Area use mm 2, cm 2, m 2, km 2, (hectares) Volume use mm 3, cm 3, m 3, ml, litres Mass use g, kg Transformations (Remember Terry) Translation (moves the shape in a straight line) needs a vector eg 3 means 3 right and 1 down 1 Enlargement (makes the shape bigger or smaller) needs a scale factor and a centre of enlargement Reflection (flips the shape) needs a mirror line Rotation (turns the shape round) needs an angle, clockwise/anticlockwise and a centre of rotation Congruent shapes are exactly the same as each other (but may have been turned round or flipped) The order of rotational symmetry of a shape is the number of times it will fit on top of its original self as it completes a full turn. Metric Conversions: 1cm = 10mm 1m = 100cm 1m = 1000mm 1km = 1000m 1kg = 1000g 1tonne = 1000kg 1 litre = 1000ml 1 litre = 100cl Names of shapes: square still a square! rectangle Imperial to metric rough conversions: 5 miles = 8 km 1kg = 2.2 pounds 1 gallon = 4.5 litres Key formulae: Circumference of circle = πd Area of rectangle = length x width Area of triangle = base x height 2 Area of circle = πr 2 Volume of cuboid = length x width x height Volume of prism =cross-section area x length perimeter is the distance round the edge area is the space inside the shape rhombus parallelogram kite trapezium cuboid cone cylinder triangular prism square-based pyramid triangle-based pyramid (tetrahedron) Angle Rules: Opposite angles are equal Angles on a straight line add up to 180 Angles at a point add up to 360 Angles in a triangle add up to 180 right angle Angles in a quadrilateral add up to 360 Alternate angles in parallel lines (Z angles) are equal Corresponding angles in parallel lines (F angles) are equal Interior angles in parallel lines (C angles) add up to 180 acute obtuse reflex Quadratic Graphs Distance, Speed, Time Pythagoras theorem y = ax 2 +bx+c S D x T a c a 2 + b 2 = c 2 (c is the hypotenuse the longest side) b
Module 2 Revision List 2A & 2B Test 2C & 2D Test 2E & 2F Test Topic MW Clip Unit 2A Number: Basic Number Ordering Integers 2 Ordering Decimals 3 Negatives in Real Life 23 Inequalities on a Number Line 138 BIDMAS 75 Adding Integers and Decimals 17 Subtracting Integers and Decimals 18 Multiplying Integers 19 Dividing Integers 20 Multiplying Decimals 66 Dividing Decimals 67 Unit 2B Geometry and Measures: Measures and Scale Drawing Metric Conversions 112 Reading Scales 4 Introduction to Ratio 38 Nets 44 Plans and Elevations 51 Unit 2C Statistics: Charts, Tables and Averages Tally Charts and Bar Charts 15 Pictograms 16 Data Discrete and Continuous 63 Vertical Line Charts 64 Averages and Range 62 Unit 2D Geometry and Measures: Angles Angles on a Line and at a Point 45 Angles in a Triangle 121 Angle Sum of Polygons 123 Angles and Parallel Lines 120 Polygons 10 Bearing 124 Unit 2E Number: Number Properties Factor, Multiples and Primes 28 Product of Primes 78 Squares, Cubes and Roots 81 Calculator Questions 77 Unit 2F Number: Approximations Rounding to the Nearest 10,100,1000 31 Rounding to Decimal Places 32 Rounding to Significant Figures 90 Estimating Answers 91