Year 8 Teaching Programme TERM 1 # of weeks 1. Integers and Whole Numbers 3 2. Geometry of Polygons 2 3. Fractions and Decimals 3 4. Percentage 2 TERM 2 5. Algebra 2 6. Expansion and Factorisation 2.5 Revision and Semester 1 Exam 1.5 7. Perimeter and Area 2 8. Volume, Capacity and Time 2 TERM 3 9. Ratios and Rates 3 10. Equations 3 11. Sets and Probability 4 TERM 4 12. Statistics 2.5 13. Straight Lines 2.5 14. Transformation and Congruence 2 Revision and Semester 2 Exam 1.5 Page 1
1. Integers and Whole Numbers a. Whole Numbers add / subtract (E1.1, G1.1, H1B) Using mental arithmetic Using an algorithm b. Whole Numbers multiply / divide (E1.2, G1.2, H1B) Using mental strategies for multiplication Using mental strategies for division Using multiplication and division setting out c. Order of Operations ( +,-,, and brackets) (G1.3, H1D) Two operations Several steps Using a calculator d. Squares, Cubes, Square Roots and Cube Roots (E1.3, G1.4, H1C, H1F) Using index notation Expanded notation and evaluating index notation Finding squares, cubes, square roots and cube roots e. Index laws (using numbers) (G1.5, H6A, H6B, H6C) The first 2 index laws Raising powers (expansion laws for positive indices) The power of zero f. Number properties (E1.3, G1.6, H1A, H1E) Primes and composites Finding the LCM Finding the HCF g. Divisibility and Prime Factorisation (E1.4, G1.7) Finding prime factor form Testing for divisibility Finding the LCM and HCF h. Negative Numbers (E1.5, G1.8) Adding a positive integer Subtracting a positive integer i. Add/Subtract negative numbers (E1.6, G1.9) Adding negative numbers Subtracting negative numbers j. Multiply/Divide negative numbers (E1.7, G1.10) Finding products Finding quotients Combining multiplication and division k. BIMDAS (E1.8) Using order of operations including brackets and indices Substituting integers Using a calculator Page 2
Investigations 1. Aboriginal counting systems (H10) 2. The 3-digit problem (H21) 3. Sums of square numbers (H23) 4. Discovering index laws (H106) 5. Discovering expansion laws (H110) needs changing to integers 6. The zero index law (H112) 7. Euclidean division algorithm (E39) Page 3
(ACMNA182) Use index notation with numbers to establish the index laws with positive integral indices and the zero index evaluating numbers expressed as powers of positive integers (ACMNA183) Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies using patterns to assist in finding rules for the multiplication and division of integers using the number line to develop strategies for adding and subtracting rational numbers A B C D E Substitutes integers and rational numbers to find the value of complex algebraic expressions involving powers. Substitutes integers and rational numbers to find the value of algebraic expressions involving the four operations. Substitutes integers to find the value of algebraic expressions involving the four operations. Calculates numerical values with the use of technology. Calculates numerical values with the use of technology. Explains and justifies statements, shows working, and uses correct mathematical procedures and language. Explains mental strategies. Explains mental strategies and shows written strategies. Checks that values are reasonable. Page 4
2. Geometry of Polygons a. Angles and lines (E2.1, G2.1, H8A) Naming angles Line terminology Finding angles at a point Finding angles on a straight line b. Parallel Lines (E2.2, G2.2, H8A) Finding angles on parallel lines Using parallel lines in shapes c. Triangles classification and properties (E2.3, G2.3, H8B) Classification by sides Classification by angles Properties of triangles Using the angle sum of a triangle Using the exterior angle theorem d. Isosceles Triangle Theorem (H8C) Working with isosceles triangles Converses e. Quadrilaterals properties (E2.5, G2.4, H8D) Angles of a quadrilateral Properties of special quadrilaterals Working with parallelograms Investigations 1. The midpoints of a quadrilateral (H163) 2. Angles of an n-sided polygon (H163) Page 5
(ACMMG202) Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning establish the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry A B C D E Page 6
3. Fractions and Decimals a. Equivalent Fractions (E3.1, G3.1, H3A) Types of fractions Negative fractions Placing fractions on a number line Generating equivalent fractions Converting to simplest form b. Operations with Fractions (E3.2, G3.2, H3B) Adding and subtracting fractions Adding and subtracting mixed numbers Multiply fractions Dividing fractions c. Operations with Negative Fractions (E3.3, H3B) Adding and subtracting negative fractions Multiplying with negative fractions Dividing with negative fractions d. Understanding Decimals (E3.4, G3.3, H3C) Comparing decimals Converting decimals to fractions Converting fractions to decimals e. Operations with decimals (E3.5, G3.4, H3D) Adding and subtracting decimals Multiplying and dividing by powers of 10 Multiplying decimals Dividing decimals f. Terminating, recurring and rounding decimals (E3.6, G3.5, H3C, H3E) Rational numbers Writing terminating decimals Writing recurring decimals Rounding decimals Roundng recurring decimals g. Irrational numbers (H3F) Decimal representation of irrational numbers Investigation 1. Division by zero (H59) 2. Terminating decimals (H62) 3. Decimal representation of 20 (H64) Page 7
(ACMNA184) Investigate terminating and recurring decimals recognising terminating, recurring and non-terminating decimals and choosing their appropriate representations (ACMNA186) Investigate the concept of irrational numbers, including p understanding that the real number system includes irrational numbers A B C D E Substitutes integers and rational numbers to find the value of complex algebraic expressions involving powers. Substitutes integers and rational numbers to find the value of algebraic expressions involving the four operations. Substitutes integers to find the value of algebraic expressions involving the four operations. Calculates numerical values with the use of technology. Calculates numerical values with the use of technology. Explains and justifies statements, shows working, and uses correct mathematical procedures and language. Explains mental strategies. Explains mental strategies and shows written strategies. Checks that values are reasonable. Identifies equivalent forms of irrational numbers. Identifies forms of numbers and classifies numbers as rational or irrational. Identifies forms of numbers and classifies numbers as rational or irrational. Page 8
4. Percentage and Finance a. Converting Percentages (E3.7, G3.6, H5A) Converting percentages to fractions Converting fractions to percentages Converting percentges to decimals Converting decimals to percentages b. Expressing one quantity as a percentage of another (E3.8, G3.7, H5B, H5C) Expressing one quantity as a percentage of another Converting units before expressing as a percentage Finding a certain percentage of a quantity c. Percentage increase/decrease (2 steps - without multiplier) (E3.9, G3.8, H5D) Finding new values: increasing Finding new values: decreasing Calculating discounts and mark-ups d. % change, % profit, % loss (E3.10, G3.9, H5E, H5F) Profit and Loss Calculating percentage profit Calculating percentage loss Calculating percentage change Solving word problems e. Unitary method (with multiplier) (E3.11, G3.10, H5F) Using the unitary method to find the full amount Using the unitary method to find a new percentage Using the unitary method to find the original price f. GST (E3.11, G3.8, G3.10) Finding the GST to be paid Finding the selling price Finding the GST that has been paid Finding the cost price Activity 1. Currency exchange (H101) Page 9
(ACMNA187) Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies using percentages to solve problems, incuding those involving markups, discount and GST using percentages to caculate population increase and decreases (ACMNA189) Solve problems involving profit and loss, with and without digital technologies expressing profit and loss as a percentage of cost or selling price, comparing the difference investigating the methods used in retail stores to express discounts A B C D E Applies percentages in complex worded problems requiring at least three calculations, including inverse, with and without technology. Applies percentages in complex worded problems requiring at most two calculations, including inverse, with and without technology. Applies percentages in simple worded problems requiring at most two calculations, with and without technology. Calculates using percentages in simple one-step problems, with and without technology. Calculates using percentages in simple one-step problems with technology. Solves complex multi-step worded problems involving profit and loss, including inverse calculations, with and without technology. Solves multi-step worded problems involving profit and loss, with and without technology. Solves simple worded problems involving profit and loss, with and without technology. Solves profit and loss, with and without technology. Solves profit and loss, with technology. Page 10
5. Algebra a. The language of algebra (E5.1, G5.1, H4A, H4B) Writing sums as products (expanded form) Index notation (index form) Using the language of algebra Creating expressions from a description b. Substitution and equivalence (E5.2, G5.2, H4F) Substituting a variable Substituting multiple variables Deciding if expressions are equivalent c. Collecting like terms (E5.3, G5.3, H4C) Identifying like terms Identifying like terms with multiple variables Simplifying by combining like terms d. Product and quotient simplification (E5.4, G5.4, H4D) Multiplying terms Multiplying terms with squares Dividing terms e. Generalising arithmetic (H4E) Finding expressions for real world situations f. Algebraic fractions + / - (numerical denominators) (E5.5) Working with denominators Adding and subtracting algebraic fractions g. Algebraic fractions / (E5.6) Multiplying algebraic fractions Dividing algebraic fractions Investigations 1. Equal expressions (H81) Page 11
(ACMNA192) Simplify algebraic expressions involving the four operations understanding that the laws used with numbers can also be used with algebra A B C D E Simplifies algebraic expressions, including fractions with numerical denominators, the four operations and multiple uses of the distributive law. Simplifies algebraic expressions involving the four operations and the use of the distributive law twice. Simplifies algebraic expressions with at most three operations and the use of the distributive law once. Simplifies algebraic expressions with like terms only. Attempts to simplify algebraic expressions, but frequently mixes all terms together. Page 12
6. Expansion and Factorisation a. Distributive law (E5.7, G5.5, H6D, H6E, H6F) Expanding brackets by simplifying repeated terms Expanding brackets using rectangle areas Expanding using the distributive law Brackets with negative coefficients Expanding and combining like terms b. Factorising expressions (only factor numbers) (E5.8, G5.6, H6G) Finding the HCF Factorising expressions c. Applying algebra (E5.9, G5.7) Writing expressions from descriptions Page 13
(ACMNA190) Extend and apply the distributive law to the expansion of algebraic expressions applying the distributive law to the expansion of algebraic expressions using strategies such as the area model (ACMNA191) Factorise algebraic expressions by identifying numerical factors applying the distributive law to the expansion of algebraic expressions using strategies such as the area model A B C D E Simplifies algebraic expressions, including fractions with numerical denominators, the four operations and multiple uses of the distributive law. Simplifies algebraic expressions involving the four operations and the use of the distributive law twice. Simplifies algebraic expressions with at most three operations and the use of the distributive law once. Simplifies algebraic expressions with like terms only. Attempts to simplify algebraic expressions, but frequently mixes all terms together. Uses factorisation to help solve word problems. Uses factorisation to help solve word problems with diagrams. Factors algebraic expressions using the HCF. Identifies HCF. Does not identify HCF. *** NEED TO FIX FACTORISATION Page 14
7. Perimeter and Area a. Length and perimeter (E4.1, G4.1, H9A, H9B) Converting length measurements Finding perimeters Formulae for perimeters of common quadrilaterals Finding perimeters of composite rectangular shapes Finding an unknown length b. Circumference (E4.2, G4.2, H9C) Finding the circumference using the radius Finding the circumference using the diameter Finding the circumference with and without a calculator c. Area (E4.3, G4.3, H9D, H9E) Converting units of area Finding areas of rectangles and squares Finding the area of triangles Finding areas of composite shapes (rectangles and triangles) d. Area of special quadrilaterals (E4.4, G4.4, H9E) Finding areas of parallelograms Finding areas of rhombuses and kites Finding areas of trapeziums e. Area of a circle (E4.5, G4.5, H9F) Finding circle areas using a radius Finding circle areas using a diameter Finding circle area with and without a calculator f. Sectors (E4.2, E4.6) Finding the perimeter of quadrants and semicircles Finding area of quadrants and semicircles g. Composite shapes(e4.6) Finding the area of composite shapes h. Rearrange circle formulae Rearrange formulas for the circumference of a circle Rearrange formulas for the area of a circle Investigation 1. Circumference (H179) 2. Area of a triangle (H187) Activity 1. Court lines (H178) 2. Shikaku puzzle (H193) Page 15
(ACMMG195) Choose appropriate units of measurement for area and volume and convert from one unit to another choosing units for area including mm 2, cm 2, m 2, hectares and km 2 recognising that the conversion factors for area units are the squares of those for the corresponding linear units (ACMMG196) Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites establishing and using formulas for areas such as trapeziums, rhombuses and kites (ACMMG197) Investigate the relationship between features of circles such as circumferences, area, radius and diameter. Use formulas to solve problems involving volume investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas investigating the area of circles using a square grid or by rearranging a circle divided into sectors A B C D E Uses the correct relationship to solve multi-step problems, including the inverse use of formulas, involving the circumference and area of circles and uses numbers expressed in exact form. Uses the correct relationship to solve problems involving the circumference and area of circles, e.g. perimeter of a sector. Names features of circles and calculates their circumference and area. Converts between units of area. Uses formulas incorrectly in calculations for circumference and area. Uses the conversion number only once in the conversion of units of area. Does not distinguish between perimeter and area and consequently uses formulas indiscriminately. Page 16
8. Volume, Capacity and Time a. Volume and Capacity (E4.8, G4.6, H11A, H11B, H11C, H11D) Converting units Finding the volume of a rectangular prism Finding capacity b. Prisms with uniform cross-section (E4.9, G4.7, H11B) Finding the volumes of prisms given the cross-section Finding the volumes of prisms c. Cylinders (E4.9) Finding the volume of a cylinder d. Time (E4.10, G4.8, H11G, H11H, H11I, 9H11E) Converting units of time Calculations with time 24 hour time Time zones Investigation Activity 1. Fly-by-Night Airlines (H224) 2. Time Zones (H239) Research 1. Time in Aboriginal Culture (9H239) Page 17
(ACMMG195) Choose appropriate units of measurement for area and volume and convert from one unit to another choosing units for volume including mm 3, cm 3 and m 3 recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units (ACMMG198) Develop the formulas of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involviing volume investigate the relationship between volumes of rectangular and triangular prisms (ACMMG199) Solve problems involving duration, including using 12- and 24-hour time within a single time zone identifying regions in Australia and countries in Asia that are in the same time zone A B C D E Selects and uses formulas for the volume of prisms and performs inverse calculations in worded problems with multiple steps. Selects and uses formulas for the volume of prisms and performs inverse calculations. Uses formulas for the volume of prisms, identifying the need to use consistent units. Finds the volume of rectangular prisms. Does not discern between perimeter, area and volume. Finds capacity of prisms with uniform cross-section. Finds capacity of prisms given the cross-section. Finds capacity of rectangular prisms. Finds capacity of rectangular prisms using formula. Does not discern between volume and capacity. Converts between units of volume and capacity. Converts between units of volume and capacity. Converts between units of volume and capacity. Uses the conversion number only once in the conversion of units of volume. Does not convert units of volume. Solves word problems and explains time differences. Solves word problems. Uses time zone map to calculate time differences between places. Uses time zone map to find the time of places. Uses time zone map incorrectly. Page 18
9. Ratio & Rates a. Ratios (H13A, H13C) Understanding the order of numbers in a ratio Writing ratios Producing equivalent ratios b. Simplifying ratios and proportions (H13B Simplifying ratios Simplifying ratios involving fractions Simplifying ratios that have different units c. Dividing quantities (H13D) Dividing a quantity in a particular ratio Dividing a quantity in a ratio with three numbers Finding a total quantity from a given ratio o Unitary method o Equivalent ratios method d. Scale diagarams real and actual distance (H13E) Writing the scale ratio and scale factor Comparing scale distance to real distance Calculating the real distance Converting scale distance to actual distance Converting actual distance to scaled distance Determining the scale factor e. Rates (E6.5, G6.5, H14A) Writing simplified rates Finding average rates f. Unitary method (E6.6) Reviewing the unitary method Solving ratio problems using the unitary method Solving rate problems using the unitray method Converting uits using the unitary method g. Rate problems (E6.7, G6.6) Solving rate problems Solving combination rate problems h. Speed (E6.8, G6.6, H14B, H14C) Finding average speed Finding the distance travelled Finding the time taken Travel graph i. Rate conversions (H14E) Converting units of speed Page 19
Investigation 1. Equal ratios by spreadsheet (H275) 2. Calculating areas from scale diagrams (H285) 3. Population density (H293) 4. Travel graphs (H295) 5. Not all that glitters is gold (H299) Activity 1. Scale diagrams (H284) 2. Measuring your heart rate (H290) Page 20
(ACMNA188) Solve a range of problems involving rates and ratios, with and without digital technologies understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem calculating population growth rates in Australia and Asia and explaining their difference A B C D E Applies rates and ratios in complex worded problems requiring at least three calculations, including inverse, with and without technology. Applies rates and ratios in complex worded problems requiring at most two calculations, including inverse, with and without technology. Applies rates and ratios in simple worded problems requiring at most two calculations, with and without technology. Calculates using rates and ratios in simple one-step problems, with and without technology. Calculates using rates and ratios in simple one-step problems with technology. Page 21
10. Linear Equations a. Review (E7.1, E7.2, G7.1, H7A) Classifying equations as true or false Classifying equations as true or false by sustitution Stating a solution to an equation Writing equations frm a description Solution by inspection Solution by guess, check and improve b. Back-tracking (flowcharts) (G7.2, H7E) Using backtracking to solve simple equations Using backtracking to solve two-step equations c. Balancing method (Inverse operations) (G7.3, H7C, H7D) Inverse operations Finding equivalent equations Solving equations using the balancing method (algebraically) d. Equations with fractions (E7.3, G7.4, H7F) Solving equations with fractions Solving more complex equations with fractions e. Variables on both sides (E7.4, H7G) Solving equations with variables on both sides f. Equations with brackets (E7.5, G7.5, H7F) Expanding brackets Solving equations with brackets g. Formulas and relationships (E7.6, G7.6) Applying a formula h. Applications (E7.7, G7.7) Writing problems as equations Solving a problem using equations Solving a harder problem using equations Solving problems with two related unknowns Investigation 1. Recurring decimals (H141) Activity 1. Arithmagons (H141) Puzzles 1. Jumping students (H144) Page 22
(ACMNA194) Solve linear equations using algebraic and graphical techniques. Verify solutons by substitution solve real life problems by using variables to represent unknowns A B C D E Solves multi-step linear equations, including the use of fractions, using algebraic techniques. Solves multi-step linear equations, using algebraic techniques. Solves two step linear equations using algebraic conventions. Solves linear equations without justification. Solves one-step linear equations. Page 23
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11. Sets and Probability a. Sets (H2A, H2B, H2C) Notation Complement of a set Intersection and union b. Probability (E8.7, E8.8, G8.6, H15A, H15B, H15C, H15D) Review Sample Space Working with probabilities Complementary events Inclusive and exclusive OR Using a table for multiple events c. Venn diagrams and probability(e8.10, G8.7, H2D, H2E, H15G) Interpreting a Venn diagram Disjoint sets Problem solving with Venn diagrams Finding probabiity using a Venn diagram d. Two way tables and probability (E8.8,E8.10, G8.8, H15F) Completing a two-way table Constructing two-way tables from Venn diagrams Using two-way tables to calculate probabilities Using two-way tables in worded problems e. Experimental probability (G8.9, H15E) Working with experimental probability Accuracy Designing and running a simulation Investigation 1. 3 circle Venn diagrams (H40) 2. Tossing a coin (H317) 3. Secret Santa (H319) 4. The cereal box problem (H325) Page 26
(ACMSP204) Identify complementary events and use the sum of probabilities to solve problems identifying the complement of familiar events understanding that probabilities range between 0 and 1 and that calculating the probability of an event allows the probability of its complement to be found (ACMSP205) Describe events using language of at least, exclusive or (A or B but not both), inclusive or (A or B or both) and and posing and, or and not probability questions about objects or people (ACMSP292) Represent events in two-way tables and Venn diagrams and solve related problems using Venn diagrams and two-way tables to calculate probabilities for events, satisfying and, or and not conditions understanding that representing data in Venn diagrams or two-way tables facilitates the calculation of probabilites collecting data to answer the questions using Venn diagrams or two-way table A B C D E Uses Venn diagrams and Constructs Venn diagrams Completes Venn diagrams two-way tables to model and two-way tables to model and two-way tables to find more than two choices, authentic situations. missing information and showing that their Indicates where events are answer simple probability probabilities sum to 1. complementary and shows questions. Interprets the sample space that probabilities sum to 1. using relevant language. Interprets the sample space using relevant language. Uses Venn diagrams and two-way tables to model more than two choices and describes each region of the sample space. Writes the associated probability in multiple number forms. Applies probability to solve problems. Interprets the sample space using relevant language, `including the distinction between inclusive and exclusive OR. Reads Venn diagrams and two-way tables to give the number satisfying a simple condition, not the probabilities. Page 27
12. Statistics a. Displaying data(e8.1, G8.1 H18A, H18B) column graphs bar charts dot plots sector graphs (pie charts) column graph stem-and-leaf plots (integer values) b. Frequency tables and tallies (E8.2, G8.2, H18C) Interpreting tallies Constructing tables from data c. Histograms (E8.3, G8.3) Constructing histograms from frequency tables with individual labels Constructing histograms from frequency tables using intervals d. Measures of centre (E8.4, G8.4, H18D) Finding the mean and the mode Finding the median Finding measures of centre from a frequency table e. Measures of spread (E8.5, G8.4, H18D) Finding the range Finding the upper and lower quartiles Finding the IQR Finding the range from a frequency table f. Data collection (E8.6, G8.5, H18E) Census or sample Bias in sampling Sample size Calculating population numbers from random sample data Interpreting survey results Investigations 1. A statistical project (H401) 2. Data in the media (H402) Page 28
(ACMSP284) Investigate techniques for collecting data, including census, sampling and observation identify situations where data can be collected by census and those where a sample is appropriate (ACMSP206) Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes investigating the areas of random sampling to collect data (ACMSP293) Explore the variation of means and proportions of random samples drawn from the same population using sample properties to predict characteristics of the population (ACMSP207) Investigate the effect of individual data values, including outliers, on the mean and median using displays of data to explore and investigate effects A B C D E Calculates the mean and the median of a data set, explaining how the relationship between the two is influenced by outliers and other values. Calculates the mean and the median of a data set and explaining their influence on the relationship between the two. Calculates the mean and the median of a data set and identifies how an outlier affects the relationship between the two. Calculates the mean and the median of data in a list. Calculates the mean and the median for given data. Describes different methods for the collection of data and explains their impact on the collected data. Describes two different methods for the collection of data. Identifies issues related to the collection of data. Page 29
13. Straight Line Graphs a. Cartesian plane (E9.1, G9.1, H12A) Writing coordinates Plotting points Quadrants b. Rules, Tables and Graphs (E9.2, G9.2, G9.3, H12B, H12C, H12D, H12E, H12F Constructing tables using positive numbers Constructing tables using negative numbers Plotting points from a table of values Plotting a linear relationship from a table of values Plotting a linear relationship from a rule Horizontal and vertical lines Points on line c. Solution to linear equations (H12G) Using a graph to solve a linear equation d. Finding the rule using tables and graphs (E9.3, G9.4, H10A) Finding rules from tables Finding rules when y is decreasing Finding rules for geometric patterns Finding a rule from a graph e. Problem solving (E9.7, G9.6, H10D) Linking distance with time Applying graphs when the rate is negative Problems using patterns Practical problems Investigations 1. Zoo prices (H262) 2. The graph of y = x 2 (H263) 3. The cubes pattern (H212) 4. Making triangles (H212) Page 30
(ACMNA193) Plot linear relationships on the Cartesian plane with and without the use of digital technologies completing a table of values, plotting the resulting points and determining whether the relationship is linear finding the rule for a linear relationship (ACMNA194) Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution solving real life problems by using variables to represent unknowns A B C D E Identifies relationships as linear or non-linear, justifying that a relationship is linear by providing reasoning for the conclusion. Compares and explains similarities and differences between different linear relationships. Plots points on the Cartesian plane, identifies and writes a linear relationship. Plots points on the Cartesian plane. Attempts to plot points on the Cartesian plane, but mixes the coordinates. Page 31
14. Transformations and Congruence a. Reflections (E10.1, G10.1, H17A) Drawing simple reflected images Drawing more complex reflected images Using coordinates in reflection b. Translations (E10.2, G10.2, H17A) Translating points Finding the translation vector Drawing images using translation c. Rotations (E10.3, G10.3, H17A) Finding the order of rotational symmetry Rotating a shape by 90 Rotating a shape by 180 Rotating a shape by angles that are multiples of 45. d. Congruent figures (E10.4, G10.4, H17B) Naming corresponding pairs Using transformations to define congruence e. Unique triangles (E2.4) Constructing unique triangles f. Congruent triangles (E10.5, G10.5, H17C) Writing a congruence statement Deciding on a test for congruence g. Proof using congruence (H17D) Statements required Importance of order h. Congruence and quadrilaterals (E10.8, G10.6) Exploring the diagonals of a parallelogram Proving that diagonals of a parallelogram bisect each other Investigations 1. Reflections (H356) 2. Congruent Triangles (H366) 3. Constructing triangles (H366) Page 32
(ACMMG200) Define congruence of plane shapes using transformations understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection rotation), and recognising that the matching sides and the matching angles are equal (ACMMG201) Develop the conditions for congruence of triangles investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA, RHS) *** there are 5 tests solving problems using the properties of congruent figures constructing triangles using the conditions for congruence (ACMMG202) Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry Page 33
A B C D E Identifies congruency in triangles of varying orientations, naming the triangles. Identifies congruency in triangles of varying orientations, naming the triangles. Identifies congruency in triangles, naming the triangles. Identifies congruency in triangles when the orientation is different. Identifies congruency in triangles only when the triangles have similar orientations. Justifies the condition of congruency with a full explanation. Justifies congruency by naming the condition. Justifies congruency by naming the condition. Extracts information and constructs a diagram from a worded description, correctly using geometric symbols. Solves numerical problems associated with congruent triangles. Uses congruency of triangles and related angle properties to prove the properties of quadrilaterals. Uses congruency of triangles to justify the properties of quadrilaterals. Identifies and correctly names quadrilaterals, and applies distinguishing properties. Identifies and correctly names quadrilaterals. Identifies and correctly names only squares and rectangles. Uses properties of quadrilaterals to solve numerical problems.. Page 34