DIOCESAN COLLEGE PREPARATORY SCHOOL Mathematics Syllabus: Grade 7 For convenience the syllabus has been divided into sections. It is important to integrate work and set relevant problem solving tasks. Some sections will be suitable for practical assignments. BASIC NUMBER WORK A. Basic number work 1. Using short methods: multiplying and dividing by 25, 125 and multiples of 10 2. Estimating values. This should become a habit to check validity of answers 3. Rounding off 4. Writing numbers in exponential form B. Order of mixed operations 1. Determine the value of mathematical terms first 2. Using effective mental strategies e.g. compensation techniques 346 + 47 = ( 346 + 4 ) + ( 47-4 ) This should not be laboured but shown as a mental strategy 3. Re-arranging and grouping when adding- the associative rule 8 + 6 + 4 + 2 = 8 + 2 + 6 + 4 4. Commutative properties of addition and subtraction: 3 X 6 = 6 X 3 5. Distributive rule of multiplication: 3 X ( 5 + 7 ) = 3 X 5 + 3 X 7 C. The use of of 0,9 of 7,3 = 0,9 X 7,3 D. Zero and one and the operations Understanding and applying the properties of 1 and 0 E. Integer arithmetic. 1. Extension to negative numbers, crossing zero 2. Negative numbers in practice 3. Representation of integers on the number line 4. Ascending and descending order of integers 5. Addition of integers: ( +5 ) + ( +2 ) = 5 + 2 + 7 ( -2 ) + ( -4 ) = -2-4 = -6
F. Number patterns and relationships 1. Recognizing number patterns: Investigate square numbers and square roots, cube numbers and cube roots, triangular numbers, Fibonacci numbers, prime and composite numbers, multiples and factors. Factors must include prime factors of 3 digit whole numbers 2. Investigating the rules of patterns- formulating the rule e.g. the sum of the first n odd numbers = n 2 3. Ways of writing number sequences: Tabulating Spidergram Flow diagrams By equations or expressions in order to select the most useful representation for a given situation 4. Powers and indices CALCULATOR SKILLS Calculator skills should be developed and used throughout the year where applicable. 1. Use as a computational tool: using with problem solving involving large numbers using to check answers 2. Use as an investigational aid- number patterns etc 3. Number searches to solve equations 4. Planning complex calculations- using the memory button 5. Use with order of operations- computing instructions with of 6. Use with negative numbers 7. Calculating square roots on the calculator 8. Calculating percentages on the calculator 9. Interpreting results of division COMMON FRACTIONS 1. Revision of concept of fractions- extend to factors, multiples, common factors and multiples 2. Equivalent fractions- conversion of common fractions and decimal fractions 3. Consolidate the addition and subtraction of mixed numbers, including estimation 4. Multiplication; of ; fractions of fractions 5. Division: meaning and algorithm use of reciprocal expressing one quantity as a fraction of another 6. Using fractions in relevant problem solving
DECIMAL FRACTIONS 1. Consolidate place value of decimals: 7,639 = 7 + 6 / 10 + 3 / 100 + 9 / 1000 2. Decimals on the number line: ascending order, descending order, biggest, smallest 3. Converting common fractions to decimal fractions 4. Approximating and rounding off 5. Consolidating addition and subtraction 6. Multiplication: using powers and multiples of 10, 100, 1000 multiplication of a decimal by a decimal 7. Division: division by a whole number division by powers of 10, division by multiples of 10, 100 1000 division of a decimal by a decimal 8. Relevant problem solving PERCENTAGES 1. Concept of percentage as a fraction with a denominator 100 percentages of more than 100% 2. Conversion from common fractions and decimal fractions 3. Conversion by using X 100/ 1 % 4. Writing one quantity as a fraction of another e.g 15 out of 20 5. Calculating a percentage of a number e.g. 12,5 % of 80 6. Calculating a number if a percentage of it is known 7. Increasing a number by a certain percentage 8. Decreasing a number by a certain percentage 9. Percentages used for comparisons 10. Concept of profit, loss, cost price, selling price, discount 11.. Graphic representation e.g. pie charts 12 Relevant problem solving RATIO AND RATE 1. Concept of ratio 2. Writing in simplest 3. Dividing a quantity in a given ratio 4. Using a ratio for comparison 5. Using ratio for enlargement on maps and plans- using scales 6. Using rate- e.g. km/h c/kg 7. Relevant problem solving
MEASUREMENT A. Perimeter 1. Calculating the perimeter of a variety of polygons 2. Finding and using the algorithm 3. Finding a missing dimension if the perimeter is known B. Area 1. Concept of area 2. Units used- introduce hectare = 10000m 2 3. Conversion between units 4. Calculating area of squares, rectangles using the algorithm 5. Calculating area of a triangle 6. Surface area of cuboids 7. Finding the missing dimension if the area is known 8. Investigate the relationship between perimeter and area C. Volume 1. Concept of volume- counting cubes 2. Units used in calculating volume 3. Calculating volume by displacement 4. Calculating volume of prisms 5. Equivalence with fluid capacity: 1 cm 3 = 1 ml 1 m 3 = 1000 litres SHAPE AND SPACE A. Lines 1. Concepts of plane, point, line, line segment, vertical, horizontal perpendicular and parallel lines 2. using a set square to construct perpendicular and parallel lines B. Angles 1. Types of angles 2. Drawing angles 3. Measuring angles
3. Calculating angles; X angles complementary angles supplementary angles angles in parallel lines--- Z and F angles 4. Angle properties of triangles interior angles= 180 0 angles in isosceles triangle - exterior angle = sum of opp. int. angles C. Bearings and navigation Locating positions on co-ordinate systems and maps using: - horizontal and vertical change - compass directions D. 2D Figures 1. concept of polygons 2. rigidity of polygons 3. concave and concave polygons 4. classification of polygons 5. polygons and symmetry 6. using transformations and symmetry to investigate properties of geometric figures 6. tessellation 7. Triangles classification construction of triangles 8. Quadrilaterals: properties of square, rhombus, rectangle, parallelogram, trapezium and kite (refer to angles, sides, diagonals symmetry) 9. Circles terms - construction 10. recognising and describing the properties of similar and congruent figures E. Construction work 1. familiarity in using compasses, protractors, set squares 2. scale drawing from given data 3. enlargements 4. using a pair of compasses, ruler, protractor to accurately construct geometric figures for design of nets 5. designing and using nets of solids
F. 3D Figures 1. concept of polyhedron 2. prisms- face, edge, vertex 3. nets of prisms 4. recognition of different prisms, pyramids, cones 5. drawing and interpreting sketches of solids from different perspectives DATA HANDLING This should be integrated with all areas of work where possible. 1. selecting appropriate sources for the collection of data ( including peers, family, newspapers, books, magazines) 2. designing and using simple questionnaires in order to collect data 3. organising and recording data using tallies, tables and stem-and-leaf displays 4. summarising ungrouped numerical data by determining mean, median and mode as measures of central tendencies 5. identifies the largest and smallest scores in a data set and determines the difference between them in order to determine the spread of the data (range) 6. drawing a variety of graphs by hand and technology to display and interpret data including: bar graphs and double bar graphs histograms with given intervals pie charts line and broken line graphs 7. critically reading and interpreting data represented in a variety of ways to draw conclusions and make predictions sensitive to the role of: context (rural or urban; national or provincial) categories within the data ( age, gender, race) scales used in graphs as a source of error and bias choice of summary statistics ( mean; median or mode) any other human rights and inclusively issues 8. discerning the suitability of the graphs used
USING AND APPLYING MATHS IN PROBLEM SOLVING It is essential to build up problem solving strategies throughout the year. Make use of relevant problem solving tasks in all areas. 1. Make a drawing 2. Substitute easier numbers 3. Look for patterns 4. Guess and check method 5. Using tables, grids and carroll diagrams 6. Estimating and checking 7. Writing number sentences algebra use x as the unknown or variable solving equations by using balance method: 1 / 2 x + 7 = 15 1 / 2 x = 15-7 x = 8x2 = 16 PROBABILTY INVESTIGATIONS 1. Performing simple experiments or trials to investigate the probability or frequency of an event happening 2. Determining the relative frequency ( the number of times an event happens ins a statistical experiment divided by the number of trials conducted