Beaconhouse / Middle / Mathematics / Class 6 / Subject Guide / Suggested Scheme of Work Term I (15 Weeks) ● ● ● ● ● ● ● ● ● ● ● Term II (15 Weeks) ● Square and cube roots Orientation ● HCF and LCM Number System ● Time and Average speed Number Properties ● Algebraic expressions and factorization Integer and Decimals ● Equations and Inequalities Fractions and Percentages ● 2D and 3D shapes Ratio, rate and Proportion ● Area and Volume Sequence and Patterns ● Introduction to coordinate geometry Lines and Angle Properties ● Measure of Central Tendency Angle properties, bisectors and construction of polygons ● Introduction to Set Theory Transformation* ● Probability* Frequency distribution and statistical graphs* * The highlighted sections/ topics in this document will not be covered in the academic year 2020-2021 Suggested Time 0.5 week Strand Titles/ Topics Orientation 1.5 weeks Numbers Attainment Targets Suggested Strategies Suggested Vocabulary Suggested Resources Spend the week recapping on number work - counting, square numbers, fractions, looking at the 100 square grids to look for number patterns through games and fun worksheets ● Generate a discussion ● Numeral ● Number lines Understanding ● Read, write, order and Number compare whole number with students on why and ● Numeric marked in ● Natural numbers Systems including greater than how man first felt the positive & 1000000 need to have numbers in ● Whole numbers negative numbers ● Know different types of ● Large his life and what type of ● Integers ● Positive integers Real Numbers’ subsets ( numbers do they see thermometer or a ● Negative integers Natural, Whole, Integers, around them and the picture of ● Even Rational, Irrational numbers they see in thermometer that ● Odd numbers) Mathematics that they is numbered ● Convert whole numbers cannot see in real life (e.g ● Prime numbers above and below ● into rational numbers negative numbers) to be Composite numbers zero ● Recognize Rational and ● Rational numbers ● Abacus able to categorize ● Decimal place Irrational numbers different kinds of numbers ● Irrational numbers ● With increasing degree of ● Use number cards with ● Less than value chart ● Greater than ● Number line challenge, understand and various multi-digit ● ● ● ● ● use the concept of place numbers (smaller and value for any real numbers greater than one million) of any size written on them and ask Use number line to students to read them and illustrate the position of compare their sizes ● Group discussion on the any Real number Use negative numbers in pros and cons of rounding context, and calculate off amounts. When is it intervals across zero okay to round off? When Use symbols <, >, =, =, ?, is it not? ● Use number line for = to compare and order different types of real ordering and comparing numbers real numbers ● Round any number to a Investigate real life required degree of situations where accuracy and significance rounded/approximate Use knowledge of numbers are given and rounding to give an figure out possible estimate to a calculation original numbers and uses it to check the reasonableness of the solution. Suggested Online Resources: http://www.softschools.com/math/classifying_numbers/ (classification of numbers/ number system using Venn diagram) http://www.math-play.com/rational-and-irrational-numbers-game/rational-and-irrational-numbersgame.html (differentiation of rational and irrational numbers) ● Reinforce application of ● Using multiplication grids 1 week Number Properties divisibility tests for 2, 3, 4, investigate patterns in 5 & 10 to identify the multiplication tables to numbers that are divisible identify numbers that are by the given numbers divisible by the different ● Multiply multi– digit tables ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Number line Unit Ten Hundred Thousand Ten thousand Hundred thousand Million Ten million Hundred million Tenth Hundredth thousandth Large numbers Ordering Rounding ● ● ● ● ● ● Approximation Significant number Index numbers Full form Approximate Place value ● ● ● ● ● ● ● ● ● ● ● marked in tenths/hundredths Decimal number cards Numbered cards Base ten material Thermometer Weather chart Number line Fraction wall/number line Square and cube root bingo cards Fraction dominoes Online games Calculator where necessary whole numbers by a multi- ● digit whole number using the formal written method of long multiplication ● Divide multi-digit whole ● numbers by a 2-digit whole number using the of long division and short division, interpreting ● remainders as whole number remainders, fractions, or by rounding, as appropriate for the context ● Multiply and divide whole and decimal numbers by multiples of 10 (up to 1000000000) Display a number and have ● ● different groups run different divisibility tests ● on that number (Including ● ● division by 1 and 0) ● Online games on multiplication and division ● ● of multi-digit whole numbers Use a number line with place value headings and moveable cards with single digits on them to discuss place value. Investigate how the digits move in relation to the decimal point when multiplied or divided by multiples of ten. ● Cross curricular links: Include contexts that lend themselves to using large numbers (such as astronomical data or demographic data) and small numbers (e.g. concept of microorganism) divisible digit remainder quotient divisor dividend short division long division Suggested Online Resources: http://www.mathplayground.com/index_multiplication_division.html (For multiplication and division of large numbers) https://www.studyladder.com/games/activity/multiply-by-multiples-of-10-22221 (for multiplication with multiples of 10s) ● Quick mental tests on ● Whole numbers 1.5 weeks The Four Integers and ● Perform mental ● Integers Operations Decimals calculations, including mixed operation (e.g ● ● ● ● ● ● ● ● ● ● Positive integers mixed operations and 22/11x10, 50+60x5, ● Negative integers integers <100 50/5+4x3 etc. ● Use vocabulary and Choose set of counters in ● Less than ● Greater than symbols related to addition different colours to ● Number line and subtraction, represent positive and ● Decimal multiplication and division negative integers. ● Place value of integers and decimal Matching sets of both numbers to describe and colours represent zero. For ● Unit ● Ten record number sentences. example, blue chips Order, add and subtract represent negative integers, ● Hundred ● Thousand (with or without number while red chips represent lines), multiply and divide positive integers. To solve ● Ten thousand positive and negative the problem of (+3) + (–7), ● Hundred thousand integers set out three red chips and ● Million Understand and use seven blue ones. Physically ● Ten million commutative and match up pairs of red and ● Hundred million associative and distributive blue chips to equate them ● Tenth ● Hundredth laws of the four operations to zero, and remove the ● thousandth in whole numbers – no remaining chips. The definitions remaining four blue chips ● Large numbers Identify the value of each represent the solution, (–4). ● Ordering ● Number sentences digit in decimal numbers ● Review the concept of ● Terminating Differentiate between multiplication by asking ● Non-terminating terminating, recurring and students how they can non-recurring decimals represent 4 x 2. Include a ● Recurring Use the symbols > and < to discussion of commutative ● Non-recurring compare integers and property, multiplication as ● Product ● Sum decimals repeated addition, and ● addition Round places of decimal to multiplication as groups. the nearest whole number Ask students whether they ● total ● subtraction and up to 3 decimal place can apply their ● difference Multiply a decimal number understanding of with a whole number and a multiplication of positive ● operation ● digit decimal number (up to 3 integers to model (–5) • decimal places only). (+3). Discuss their thinking ● calculation Divide decimal numbers by and bring in the definition ● multiplication a whole number and by a of commutative property, ● division decimal number up to 3 so that the question can be ● divisor decimal places(by understood as (+3) x (–5) converting decimals to or three groups of –5. And fractions and by direct apply the knowledge for division) division of integers. ● Use BODMAS to solve ● Online math games on numerical expressions integer and decimal involving integers and addition, subtraction, decimals multiplication and division ● Solve word problems that ● Present the class with call for addition, scenarios requiring subtraction, multiplication addition, subtraction, and division of any multiplication and division numbers in context of by decimals, and ask money, length and weight. students to record their estimates and the strategies they used to arrive at them ● ● ● ● dividend Remainder brackets BODMAS Suggested Online Resources: http://www.sheppardsoftware.com/mathgames/fruitshoot/FS_Mixed_Integers.htm (For mixed operations on Integers) http://www.math-play.com/decimal-math-games.html (for different games related to decimals including rounding, adding, subtracting, place value etc.) http://www.sheppardsoftware.com/mathgames/decimals/CompareDecimals.htm (for comparing decimals) ● Ask students to use factor ● Prime numbers 1.5 weeks Square and ● Recognize prime and Cube Roots composite numbers < 200 trees to identify prime and ● Composite numbers ● Calculate squares and ● Perfect square composite numbers ● To develop concept of ● Perfect cube cubes, square roots and cube roots of larger roots, tell students that a ● Square root numbers dance floor is square and ● Cube root ● Use calculator methods to ● Rounding has an area of 81 m2 . find squares and cubes, What are its dimensions? ● Approximation ● Powers/index/exponent square roots and cube roots. ● Explain why the v30 is ● Use knowledge of the between 5 and 6 or 3v100 ● Inverse ● Rational roots relationship between is between 4 and 5. ● Online games on square ● Irrational roots powers and roots to evaluate whole number and square roots, cubes and ● Prime number ● Composite numbers powers of any appropriate cube roots. ● ● Prime factor number, for example, 34 = Online games on 81 and vice versa (e.g. 3v27 identification of square or ● Prime factorization ● ● ● = 3) Understand that the square root and cube root is the inverse process of squaring and cubing a number respectively. Estimate squares and square roots to solve problems on Square roots, cubes and cube roots of small numbers (e.g. 3v27, 3v8 and v64 etc.) Describe principal roots and tell if they are Rational of Irrational (e.g. v4=2 is rational number 3v2 or v3 = decimal are irrational numbers Use approximation to the nearest perfect square and perfect cube numbers to find square root and cube roots of non-square and non-cubic numbers (e.g. v1000) Use estimation to check answers to calculations and determine an appropriate degree of accuracy in context of a problem cube root of a number being a rational or irrational number ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Suggested Online Resources: ● https://www.mathgames.com/skill/8.6-square-roots-of-perfect-squares (for practicing square root) https://www.mathgames.com/skill/8.8-estimate-cube-roots (for estimating cube roots of non-perfect cube ● ● numbers) ● http://www.mathopolis.com/games/estimate-sqroot.php ( for estimating square roots of non-perfect ● square numbers) ● ● Factor tree Index Power Exponent Factor Divisor Multiple Common factor Common multiple Common divisor lowest (least) common multiple(LCM) Highest Common Factor(HCF) Greatest Common Factor (GCD) Numerator Denominator Rational number Irrational numbers Fraction proper fraction improper fraction Mixed number Equivalent fractions Reciprocal Cancellation Integers Reduce Simplest form common denominator Quantities Percentage Relationship Interest Principal Amount Time Interest Rate ● Ask students to use Venn ● LCM and HCF ● Recognize prime and composite numbers < 200 diagram to find common ● ● Find common factors and multiples and factors and ● ● common multiples of a set eventually choose HCF ● of multi – digit numbers and LCM from them. ● Online games on multiples, ● (up to 4 digit numbers) ● ● Find prime factors of any factors, LCM and HCF number using division and factor tree methods ● Write prime factors in the index/power notation ● Use LCM and HCF in simple problem solving Suggested Online Resources: http://www.bbc.co.uk/education/guides/zp6p34j/test (for practising factors and multiples) http://www.bbc.co.uk/bitesize/quiz/q65495764 (for practising LCM and HCF) ● Online game on rational 2 weeks Fractions and ● Recognize Rational and Percentages Irrational numbers and irrational numbers ● Convert whole numbers ● Have all students make up into rational numbers one multiple-choice ● Identify and convert question to ask the class between various forms of and let them collect the fractions (e.g. proper data on to be able to fractions, improper calculate the fraction, fractions, equivalent decimal and percentage of fractions, mixed number students choosing a etc.) particular answer. ● Simplify fractions by ● Hold speed competitions to cancelling all common calculate different speeds. factors and generate Compare two given parts, equivalent fractions. convert them to ● Compare and order percentages and check fractions, including which is larger? ● Compare, which is bigger fractions > 1 , by converting them into 20% of 50kg or 15% of equivalent fractions or 70kg etc. to compare two decimal notations quantities by percentages 1 weeks Annual Equivalence Quotient Inverse Operation Simplify Product Sum ● ● ● ● ● ● ● 1 week Ratio, Rate and ● Proportion Add, subtract, multiply and divide simple and mixed fractions by integers and fractions, writing the answer in its simplest form Use BODMAS to solve numerical expressions involving fractions Calculate simple percentages of quantities and vice versa, with and without a calculator and solve simple problems involving percentages Compare two quantities by calculating their percentage (simple cases) Use the knowledge of percentages to solve problems related to simple interest (simple cases) Convert and use equivalences between simple fractions, decimals, ratios and percentages, including in different contexts. Solve word problems related to fractions and percentages in context of money, length and weight. Use the concept of fraction to express quantities as ratio (two or more) and rate, simplifying where appropriate to find equivalent ratios (simple ● Online games on proper, improper, equivalent fractions ● Online games on percentages Online games on equivalent ● ● fractions ● Place a variety of the three colours (e.g. blue, white, red) ● of poker chips into beakers and ● ● ask students to compare the Quantities Fractions Ratio Rate Unit Equivalent ratios ● Ratio table cases) number of red chips to blue Find the missing term in a chips or number of red chips to ● Unit rate pair of equivalent ratios. white chips etc. to develop the ● percentages ● Recognize and use common concept of two and three term measure/units of rate ratio. Also ask students to ● Convert and use divide the chips in a given equivalences between ratio. simple fractions, decimals, Give students examples from ratios and percentages, daily life to understand how including in different different quantities can be used contexts. together to form a rate (e.g.100 ● km/h, 70 beats/min, $1.69/100 g, $9.50/kg) ● Suggested Online Resources: http://mathsnacks.com/ratio-rumble.html (for developing the concept of ratios) ● Use letter symbols to ● Introduce students to a ● 2 weeks Algebra Algebraic ● Expressions and represent unknown relations game e.g. Factorization numbers. Amanda puts a 3 into the ● ● Develop an understanding function machine and gets ● ● of the algebraic terms out a 7. The function including like term, machine continues to use ● ● variable, constant, the same rule, but this expression and equation time, Amanda puts in a 6 ● ● and inequality and gets out a 13. Now ● Multiply simple algebraic ● predict what the output ● expressions by positive and will be if the input is 5. ● negative constants and a Explain how you know ● variable this. Use symbols or ● Simplify linear algebraic ● words to show three expressions by collecting different rules the function ● ● like terms (addition and machine could be ● subtraction) following at each step. ● Use knowledge of Later introduce the concept ● BODMAS to simplify of changing number to be a ● algebraic expressions variable and fixed number ● ● involving brackets to be a constant for Constant Variables Coefficient Term Like term Reciprocal Power Numerical expression Algebraic expression Operation Monomial Binomial Polynomial Linear expression Equation Linear equation formula Inequality Linear Inequality Simplify Expand ● Variable and number cards ● Algebra Tiles ● Function machines ● Online games ● ● Factorize simple algebraic students to be able to expressions with numeric define the simple algebraic ● ● and algebraic common expression. ● Recall the concept of ● factors(by taking out ● common terms and by factors of a numeral to regrouping) make students understand ● the concept of factorization ● ● in algebra. Also, take factorization as the inverse ● process of multiplication ● of an algebraic expression ● with a number or a variable or both. ● Online games on factorization and simplifications of algebraic expressions Suggested online resources: https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1inequalities/e/inequalities_on_a_number_line (Tutorial --- Use of number lines for algebraic inequalities) ● Use the example of 2 weeks Equations and ● Solve basic linear Inequalities equations in single function machines once variable (using balancing again to help students and inverse operation understand how to form an methods) equation e.g. a girl owns ● Begin to use conventional three horses. She purchases linear algebra to construct more horses at an auction; and solve simple linear consequently, she now has equations in given more horses. Look for situations (single variable some quantity that acts like only) a term number, in that it ● Change the subject of a can change in a step-byformula and use step fashion. That number substitution method to will be represented by the calculate values of x-variable. The girl may unknown variables (simple buy 1, or 2, or 3, or 4, or . . cases) . horses. In this case, the x- Evaluate Factorize Common factor Numeric Algebraic Regrouping BODMAS Inverse operation Subject of a formula Substitute Number line ● Develop an understanding of the use of <,> and = signs in algebraic numbers ● Use number line to illustrate basic algebraic inequalities in single variable (without solution e.g. x=3, x= -4.5, x= ½) variable will be the number of horses she buys. Next, identify what is the term value. The term value depends on the term number. The number of horses she ends up with depends on how many she buys, so the term value will be the number of horses she ends up with. Then, consider the presence of a constant or a numerical coefficient. If there is a quantity to start with, or one to remove at the end, there will be a constant to add or subtract. If a variable is being multiplied or divided, there will be a numerical coefficient to connect to the variable. In this example, the girl starts with three horses. She has three horses no matter how many she buys. These three horses are represented by the constant + 3. Hence Put the pieces together in the relation to form an equation. ● Ask the class to list all the values of x that make x>3 true to make them understand the importance of number line to illustrate inequalities and intervals ● Online games on linear equations and linear inequalities in one variable Suggested Online Resources: http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html (linear equation) http://www.mathplayground.com/AlgebraEquations.html (solving a linear equation) ● 1 week Sequence and ● Recognise simple patterns ● Ask students to share Patterns in different number patterns they have seen, or ● sequences (both increasing present them with samples ● ● and decreasing) of patterns. Ask them to ● Generate sequences from describe the patterns. Ask ● ● practical contexts and whether there are other describe the nth term in ways to represent the same simple cases. pattern. Review pattern● Use the nth term to related vocabulary as generate a sequence. opportunity arises during the discussion. ● Introduce students to a relations game e.g. Amanda puts a 3 into the function machine and gets out a 7. The function machine continues to use the same rule, but this time, Amanda puts in a 6 and gets out a 13. Now predict what the output will be if the input is 5. Explain how you know this. Use symbols or words to show three different rules the function machine could be following at each step. Later introduce the concept of changing number to be a variable and fixed number Pattern Sequence Rule Increasing sequences Decreasing sequences Formula to be a constant for students to be able to define the nth (algebraic expression) term. ● Online games on Sequences, patterns and nth term Suggested Online Resources: http://www.scootle.edu.au/ec/viewing/L1922/index.html (to generate sequences from practical context) https://mathsframe.co.uk/en/resources/resource/42/sequences (for sequences) https://www.funbrain.com/games/number-cracker-game (to find a missing number in given sequence) http://www.kidport.com/Grade7/TAL/Patterns.htm (Higher order number pattern) 1.5 weeks Space, 2-D and 3D ● Classify different types of ● Provide students with or Shape and shapes polygons and polyhedra have them bring in a Measure (pyramids, cubes and multitude of 2-D shapes prisms) and classify them ● Differentiate between according to the number of regular and irregular lines of symmetry, and polygons rotational symmetry with ● Differentiate between the angle and order of convex and concave rotation. ● Use graph paper and ask polygons ● Identify and illustrate all students to draw a shape lines of symmetry in a wide and to cut it along a line of range of 2D shapes and symmetry. Students applies this understanding exchange their drawing to complete a range of with another student who symmetrical patterns will complete the 2-D ● Rotate objects using shape. Students should rotational symmetry and approach this by counting describe order of rotational the spaces from the symmetry of different 2D vertices to the line of shapes symmetry in order to place ● Identify and recognize each of the mirrored planes of symmetry of 3D vertices and complete the shapes shape. ● Uses mathematical ● Identify different 2D ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2-dimensional figure 3-dimensional solid Polygon Ployhedra Regular polygon Irregular polygons Concave polygons Convex polygons Equilateral polygons Equiangular polygons Triangles Quadrilateral Equilateral triangle Isosceles Triangle Scalene triangle Right triangle Obtuse angled triangle Square Parallelogram Rectangle Rhombus Kite trapezium Pentagon Hexagon ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ruler set square protractor pencils pair of compasses squared paper nets of shapes 2-D shape cutouts 3-D Solids set square pair of compasses protractor ruler tracing paper scissors empty cardboard boxed and tins ● Calculator where necessary ● Unit cards ● Calculator where necessary ● ● ● ● ● language to describe the properties of a range of common 2D shapes and 3D ● objects including side, face, edge, corner, base and ● angle. Identify 2D shapes within 3D objects and recognises 3D objects from 2D drawings. Describes 2D shapes and 3D objects using specific vocabulary including face, edge, vertex, angle, diagonal, radius, diameter and circumference Demonstrate understanding of the relationship between 3D objects and their nets. Identify similar and congruent 2D shapes and 3D objects Use mathematical language to describe the properties of regular and irregular, convex and concave 2D shapes and 3D objects. shapes and 3D objects in ● ● their environment ● Online games on recognition of congruent ● ● and similar shapes Online games on linear and ● rotational symmetry in 2D ● ● shapes and planes of ● symmetry in 3D objects Suggested Online Resources: https://www.youtube.com/watch?v=sWgHtiTSywc (differentiation between convex and concave polygons) http://study.com/academy/lesson/concave-convex-polygons-definition-examples.html (Tutorial on differentiation between convex and concave polygons) https://illuminations.nctm.org/activity.aspx?id=3544 (relationship between 3D objects and their nets) http://www.hbschool.com/activity/elab2004/gr3/21.html (lines of symmetry) ● Know use and convert ● Provide pictures of many 1.5 weeks Area and Volume among km, m, cm and mm, regular triangles, squares kg and g, liters and mili and rectangles, with the ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Heptagon Octagon Nonagon decagon solid faces vertices edges Cube/cuboid prism pyramid cylinder circle circumference diameter radius/radii sector chord arc concentric eccentric pi (p) polyhedra Angle diagonal Area Surface Area Perimeter Squared units Net Volume Cubic units Space Capacity Mass Length Altitude Right Prism ● ● ● ● ● ● ● liters, and vice versa Use mathematical language to describe the properties of regular and irregular 2D shapes and 3D objects. Illustrate and name parts of circles, including radius, diameter and circumference, semi circle, quadrant and know that the diameter is twice the radius of a circle. ● Identify chord, arc and sector in a circle By applying appropriate formulae, calculate the areas and perimeters of triangles, squares, rectangles, and circles. Calculate the perimeter and area of simple compound shapes made with the above ● mentioned 2D shapes only (only whole shape). Understand the meaning of prisms and right prisms. Describe 2D shapes and 3D ● objects using specific vocabulary including face, edge, angle, diagonal, radius, diameter and ● circumference and apply this knowledge to demonstrate understanding of the relationship between 3D objects and their nets (including triangular prisms, cube, cuboids and ● measure of one side provided for each. Have ● students explore to find the ● most efficient method for ● finding the perimeters of ● ● each. Lead students to discover that “side + side + ● side + side…” is inefficient ● when multiplication can be ● used instead. Repeat the ● activity with rectangles and ● ● squares. Use exploratory activities ● to find the value of p. Give ● students circles of different ● sizes and thread/string to ● ● calculate the perimeter. Compare the answer with ● the answers calculated by ● the formula and discuss the ● ● error in the answer ● Provide paper copies of nets for students who are ● having difficulty visualizing the parts of a 3- ● D object, for them to cut ● and fold or use Polydrons. ● Use a variety of different ● ● shapes of boxes and containers for cutting and ● calculating surface area. ● Generate a discussions on ● ● volume, using informal ● measurement methods, ● such as linking cubes. ● Show and discuss the centimetre cube. Explain ● that just as square units are ● Polydron Triangular prism Rectangular prism Right cylinder Pipe Right Pyramid Cone sphere lines segments rays parallel perpendicular intersecting lines angles set square measure acute obtuse reflex opposite angles alternate angles vertically opposite angles adjacent angles corresponding angles Triangles Quadrilateral Protractor Standard ruler Compass Angle bisector Line bisector SSS SAS AAS Symmetry Rotation ● ● ● ● ● ● ● cylinders) Calculate the surface area and volume of simple right prisms with basic 2D shaped bases (including triangular, square, rectangular bases) Calculate the surface area and volume of a right Cylinder Calculate volume of fluid in the aforementioned 3D ● solids Calculate the missing dimension from the given area/perimeter/surface area/volume of aforementioned shapes and solids. (simple cases) Use concepts of area, perimeter, surface area and volume in problem solving (simple cases) Approximate areas and perimeters, surface areas and volumes of shapes and objects with non-integer dimensions Use metric units length, mass, capacity for estimation and calculations. used to measure area and surface area, cubic units are used to measure volume. Have students bring in small boxes of various shapes and sizes and use centimetre cubes to determine the volume of each box and provide students with relevant contexts for determining volume Use online games on calculation of perimeters, areas and volumes Suggested online resources: https://mathsframe.co.uk/en/resources/resource/86/convert_g_to_kg (Online Games & Activities) https://www.studyladder.com/games/activity/converting-between-units-of-mass-grams-and-kilograms27995 (Problems & Activities) http://www.onlinemathlearning.com/parts-of-circle.html (Parts of a circle) http://www.hoodamath.com/mobile/games/tronix.html (Online Games & Activities) ● ● ● ● ● ● ● ● ● ● ● ● Similar Congruent Plane Planes of symmetry Kilometer Meter Centimeter Millimeter Kilograms Grams Liters Mili-liters 1.5 weeks Lines and Angles Properties ● ● ● ● ● ● ● ● Estimate angles to the nearest 10 and 100 degrees Differentiate among lines, rays and line segments Differentiate between Parallel and Perpendicular lines Identify, construct acute, obtuse and reflex angles using a protractor and use the vocabulary to describe and classify a range of angles within shapes in the environment Uses informal methods to estimate, measure and describe the size of angles in relation to a right angle. Understand identify between interior and exterior angles of polygons Knows that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees and uses this knowledge to calculate missing angles Understand and use the angle properties of angles on a point, adjacent angles on a line, vertically opposite angles, alternate angles, corresponding angles and interior angles between parallel lines to calculate unknown angles in simple problems. ● Have students investigate angles in various shapes, using the corner of a piece of paper as a reference for right angle. Does it fit the angle of the shape or is the angle greater/less than the corner of the paper? ● Have students identify angles in a variety of real life contexts (e.g., angles formed by the two hands of a clock, by the intersection of two roads, and by the blades of scissors or hedge clippers etc.) ● Have students represent parallel or perpendicular lines, or to make a variety of angles, including a right angle, vertically opposite angles on a straight line etc., concretely using items like toothpicks or straws ● Online games on angle properties of parallel and perpendicular lines Suggested Online Resources: https://www.khanacademy.org/math/basic-geo/basic-geo-lines/linesrays/e/recognizing_rays_lines_and_line_segments (for practice) http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/68848 (Questions Eliciting Thinking) http://www.transum.org/Software/SW/Starter_of_the_day/Similar.asp?ID_Topic=3 (A complete resource including activities, videos and worksheets for teaching Angles& Lines and Angles) http://study.com/academy/lesson/interior-and-exterior-angles-of-triangles.html (Video for teachers) ● Know how to name ● Use paper folding activity 1.5 weeks Angle properties, polygons and their angles to explain the concept of bisectors and mathematically (e.g using perpendicular and line construction of different notation such as bisectors ● Have students arrange two Polygons <ABC or <A etc.) ● Using a standard ruler and straws, or two toothpicks: compass, draw angle and ● parallel to one another; ● intersecting; line bisectors to divide ● perpendicular at an end angles and lines ● Understand the terms SSS, point of one straw; SAS and ASA in triangles ● perpendicular at endpoints ● Use a ruler and protractor to of each straw; ● construct a triangle given one straw perpendicular to two sides and the included the other straw and angle (SAS) or two angles bisecting; ● one straw perpendicular to and the included side (ASA) or three sides (SSS) the other straw, but not at ● Draw angle and line its end points and not bisectors to divide angles bisecting; ● one straw bisecting the and sides of triangles ● Understand and use the sum other straw but not of all angles properties of perpendicular; triangles and quadrilaterals ● each straw bisecting the to calculate missing other straw but not angle(s) in triangles and perpendicular; ● one straw bisected by the quadrilateral (simple questions only) other straw and perpendicular; ● each straw bisecting the other straw and perpendicular. ● Have students write the upper case letters of the alphabet that only use line segments. Have them find examples of bisectors of segments, perpendicular segments, and perpendicular bisectors ● Have the student draw a triangle of any type and label its angles 1, 2, 3. Cut it out. Then have the student tear off the three angles and place the three vertices together to form a 180° angle. Have students measure and record the three angles and investigate the sum of the angles. Use the same activity for investigation on sum of the interior angles of a quadrilateral. Suggested online resources: https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-interior-angles-of-a-polygon (for teachers’ exposition) http://www.onlinemathlearning.com/congruent-triangles.html (Resource to explain SSS, SAS and ASA in triangles including explanations, practice sheets & activities) http://www.helpingwithmath.com/by_subject/geometry/geo_missing_angles_8g5.htm (worksheets ) ● Convert between 12 hour ● Online game on ● second ● Analog Wall 1 week Time and ● minute Average Speed clock and 24 hour clock conversion of times Clock ● Use real life situations to ● hour ● Digital Clock and vice versa ● With a degree of ● analogue ● Calculator calculate arrival time, ● digital complexity, give the time journey time and where ● that is earlier than or later departure time. 12- hour necessary ● 24 – hour than a particular point in ● ● ● ● time, calculate the difference between two times and find start or end times for a given time interval on the same day Know and calculate arrival time, departure time and journey time in a given situation on the same day Differentiate between uniform and average speed Understand the relationship between speed, distance and time. Solve simple problems involving time and average speed Suggested Online Resources: http://www.onlinemathlearning.com/average-speed-problems.html (average speed word problems) http://www.homeschoolmath.net/worksheets/speed_time_distance.php (lessons, activities & worksheets) https://www.texasgateway.org/resource/average-speed (practice sheets) 1 weeks Introduction to ● Understand in a coordinate ● Play the game of Coordinate point (a,b), “a” is the xBattleships in four Geometry coordinate and “b” is the yquadrants by placing coordinate submarines carriers and ● Plot and Locate points in destroyers in different the four quadrants quadrants on different ● Use knowledge of function points and then take turns machines to understand and in asking the destroyers to formulate basic linear destroy a particular ship functions by calling out the point at ● Plot and compare the which the ship is located graphs of linear functions in that moment. or play (e.g. Y = c, x =a and y = mx Treasure Hunt to find a + c) and observe the pattern selected coordinate from in the coordinate points that "closer" or "further away" form these linear responses. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Arrival time Departure time Journey time Distance Speed Uniform speed Average speed Ordinate Abscissa Point Coordinates Location Quadrant Function machine Rule Formula Linear Origin Horizontal Vertical X-axis Y-axis translation ● ● ● ● Graph papers Rulers Pencils Protractor functions ● Use the knowledge of function machines to remind students the concept of input and output numbers and develop the concept of input as the x-coordinate and output as the ycoordinate. ● Use online resources to draw lines and observe the changes in them as the points are changed and vice versa Suggested Online Resources: https://www.engageny.org/sites/default/files/downloadable-resources/math-g6-m3-topic-c-lesson-15-teacher.pdf (lesson plan with complete resources) https://www.khanacademy.org/math/basic-geo/basic-geo-coord-plane/coordinate-plane-4-quad/v/the-coordinate-plane (Teachers’ exposition) https://www.mathplayground.com/functionmachine.html (Games & Videos can be used as starter activity) ● Demonstrate ● Distribute to each student 0.5 week Transformation (2D shapes) understanding of a sheet of graph paper, a transformation by pair of scissors. Have reflecting 2D shapes in students cut out a 2-D a given line on four shape and draw a quadrant grid (simple vertical/horizontal line on cases) the graph paper. To model a set of successive reflections, have students do a few reflections downward or upward and a few to the left or right. After each reflection, students will be asked the following questions: a) In which direction did the 2D shape move? b) What changed? c) What remained the same? ● Online games on reflection of 2D shapes in different lines of reflection Suggested Online Resources: https://www.khanacademy.org/math/geometry-home/transformations ( for understanding transformation by reflecting) https://mathsframe.co.uk/en/resources/resource/153/coordinates--reasoning-about-position-and-shapes ( transformation) ● Collect and record data, ● coordinates 1.5 Handling Frequency 1. Have a class discussion ● quadrant weeks Data Distribution choosing an appropriate about first-hand and ● x-axis and Statistical method (by surveys, second-hand data, the ● y-axis Graphs interviews, differences between ● vertices measurement and continuous and discrete ● positive electronic means) data and when to use ● Differentiate between ● negative each type. ● horizontal discrete and continuous 2. Ask students to look up ● vertical data the ● Construct and interpret ● origin hockey/cricket/football ● data frequency tables for scores for a favourite ● ungrouped data discrete data only team over the course of ● Construct, compare and ● grouped data 10 games and then ● sector interpret of bar create a line graph with ● Fraction graphs(vertical, the ordered pairs (game ● proportion horizontal, multiple number, number of ● angle (upto 3 bars), line goals scored by ● data graphs and pictogram favourite team). Have ● degrees for discrete data only them create a second ● Calculate sector angles ● survey graph with the ordered ● interview from a given data set pairs (game number, ● discrete data and construct and goals scored by ● continuous data interpret pie charts opposing team) and ● Selects and justify most ● frequency then compare the two ● frequency table appropriate graph(s) for graphs. ● bar graph a given data set and 3. Set up groups that ● multiple bar graph draw simple collect, arrange and ● sectional bar graph conclusions based on display different kinds ● histogram the shape of graphs. of data through ● line graph different methods ● ● ● ● ● Ruler Protractor compass Graph paper Calculator where necessary including questionnaires, experiments, databases, electronic media. Ask students to construct frequency tables from that data and choose the most appropriate graph to represent it.The groups may give a presentation at the end of their data collection. 4. Examine many realworld pictographs, bar, double bar, and line graphs gathered from newspapers, magazines, and other print media. Discuss why the choice of format is appropriate in each case. Ask students questions that can be answered through careful analysis of the graph. 5. Link the concept of fraction and ratio with the calculation of area of sectors for a pie charts ● ● ● ● pictogram pie chart questionnaire tally bars Suggested Online Resources http://shodor.org/interactivate/activities/CircleGraph/ ( for Pie chart) http://study.com/academy/lesson/interpreting-pie-charts-and-bar-graphs.html ( for bar and pie chart along with quiz) http://www.scholastic.com/browse/unitplan.jsp?id=273 ( for bar graph) ● Calculate mean, ● For quantitative data ● data 1 week Measure of Central Tendency median, mode and range for any ungrouped data. ● Compare, choose and justify the appropriate measures of central tendency (mean, mode, median) for a given set of data collected in the previous unit, Ask students to choose and calculate appropriate measure of central tendency and explain why it is the most suitable average for the given data. ● Data collected on heights and weights of various students in the school could be used to show average height of students in class, even give information on height by gender. ● Use online games on measures of central tendency ● ● ● ● ● ● ● ● ● Grouped data Ungrouped data Discrete data Continuous data median mode mean range average Suggested Online Resources: https://www.pbslearningmedia.org/resource/ea4d290e-7d88-43b6-b50f-5f3355df5e49/ea4d290e-7d88-43b6-b50f-5f3355df5e49/#.WSaPqNwlHIU (mean, median and mode) https://www.brainpop.com/math/probability/meanmedianmodeandrange/ ( mean, mode and median) http://www.shodor.org/interactivate/lessons/IntroStatistics/ (introduction to statistics) ● Understand the meaning ● Use the example of ● Set 1.5 weeks Introduction to ● Element Set Theory of the terms “set” and collective nouns (e.g. a ● Equal sets “elements of a set” flock of birds, a fish of ● Describe and write ● Finite sets school, a pack of ● Infinite sets mathematically if an wolves, a hive of bees) ● Natural numbers object/number is an to develop the basic ● Whole numbers element of a set understanding of a set ● Differentiate between ● Integers (i.e. it is a ● Rational numbers finite and infinite set collection/group of like ● Describe and list ● Irrational numbers items) ● ● Proper set elements of a set from a Use the knowledge of ● Improper set simple descriptive infinite and finite ● ● ● ● set(e.g. set of first 5 positive even numbers) Understand, describe and write the universal set, subsets ( both proper and improper), an empty set, equal sets, disjoint sets and overlapping sets Describe in words and write number of elements in a set mathematically Find union and intersection between two sets Show relationships between sets using Venn diagram (with 1 universal set and two subsets) sequences to introduce infinite/finite sets ● Generate a discussion on numbers system to deepen the knowledge of basic set theory ● Online games on set theory and Venn diagram Suggested Online Resources: http://www.math-only-math.com/types-of-sets.html (for sets) https://www.youtube.com/watch?v=LOcHPWi3X2I&feature=youtu.be (sets game) http://www.math-only-math.com/disjoint-of-sets-using-Venn-diagram.html (all type of sets) ● Understand the meaning ● Ask students to roll a 1 week Probability of the terms outcome, die, toss a coin and event, sample space, spin a spinner to list all mutually exclusive possible outcomes of events, equally likely the experiment ● Make a connection events, impossible outcomes, favorable with set theory to make outcome. sample space set of all ● Use the knowledge of possible outcomes of sets theory to list all different experiments ● element of sample space Use two spinners (one and its subsets of a divided in equal sectors ● ● ● ● Empty set Universal set Overlapping sets Venn diagram ● ● ● ● Event outcome Experiment Mutually exclusive event Equally likely events Impossible events Favorable outcomes Sample space probability probability scale ● ● ● ● ● ● ● ● ● ● ● ● ● Dice Coins Bag of colored balls A pack of 52 cards Numbered spinners Numbered cards Calculator where ● ● ● ● ● single event experiment ( a die, a coin, numbered cards, a bag of balls, a spinner , a pack of 52 cards etc.) Understand what it means for an event to be “mutually exclusive event” Use the knowledge of set theory to write number of elements in sample space and its subsets mathematically Find and justify probabilities in single event experiments Calculate and check that the total probability of all the mutually exclusive outcomes of an experiment is 1. Use the knowledge of probability in simple problem solving. and the other divided in unequal sectors) to develop the concept of equally likely events. Have students explore situations for which outcomes are equally likely (e.g equal numbers of different coloured balls in a bag etc.) ● Link the concept of fractions to explain students the idea of probability of an event. Also, sum of all parts of a fraction makes a whole = sum of all probabilities of an experiment is 1 ● Ensure students acquire an understanding that probability can be represented in multiple forms (e.g. fraction, decimal, ratio, and percentage. One means of accomplishing this understanding is by specifying a particular form for the answer. ● Give questions, occasionally, for which different groups are given the same problem but each group is asked to present the answer in a different ● ● ● ● poor chance even chance certain impossible necessary form. When the class discusses the results in a large group, students should observe the variation in the answers and discuss or account for the differences. Through such experiences, students should come to the realization that the various forms are alternative representations of the same value. ● Online games on probability Suggested Online Resources: http://www.mathgoodies.com/lessons/vol6/sample_spaces.html (probability) https://www.youtube.com/watch?v=4IQpe3J-2AU (teacher’s resource) https://www.youtube.com/watch?v=mhlc7peGlGg (teacher’s resource)