# CAMI Education linked to CAPS: Mathematics

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1 - 1 - TOPIC 1.1 Whole numbers Grade 7_CAPS Curriculum TERM 1 CONTENT Mental calculations Revise the following done in Grade 6: Multiplication of whole numbers to at least 12 x 12. Multiplication facts for: units and tens by multiples of 10 units and tens by multiples of 100 units and tens by multiples of units and tens by multiples of Inverse operation between multipli - cation and division. Ordering and comparing whole numbers Revise the following done in Grade 6: order, compare and represent numbers to at least 9-digit numbers recognize and represent prime numbers to at least 100 round off numbers to the nearest 5, 10, 100 or Properties of whole numbers Revise the following done in Grade 6: recognize and use the commutative, associative, distributive properties of whole numbers recognize and use 0 in terms of its additive property (identify element for addition) recognize and use 1 in terms of its multiplicative property (identify element for multiplication) Calculations using whole numbers Revise the following done in Grade 6, without use of calculators: CAMI Keys

2 - 2 - additions and subtraction of whole numbers to at least 6- digit numbers multiplication of at least whole 4-digit by 2-digit numbers division of at least 4-digit by 2- digit numbers Perform calculations using all four operations on whole numbers, estimating and using calculators where appropriate Calculation techniques Use a range of techniques to perform and check written and mental calculations of whole numbers including: Estimation Adding, subtracting and multiplying in columns Long division Rounding off and compensating Using a calculator Multiples and factors Revise the following done in Grade 6: Multiples of 2-digit and 3-digit whole numbers Factors of 2-digit and 3-digit whole numbers Prime factors of numbers to at least 100 List prime factors of numbers to at least 3-digit whole number Find the LCM and HCF of numbers to

3 Exponents at least 3-digit whole numbers, by inspection or factorization Solving problems Solve problems involving whole numbers, including: Compare two or more quantities of the same kind (ratio) Comparing two quantities of different kinds (rate) Sharing in a given ratio where the whole is given Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as: Profit, loss and discount Budgets Accounts Loans Simple interest Mental calculations Determine squares to at least 12 2 and their square roots Determine cubes to at least 6 3 and their cube roots Comparing and representing numbers in exponential form Compare and represent whole numbers in exponential form: a b = a a a... for b numbers of factors Calculations using numbers in exponential form Recognize and use the appropriate laws of operations with numbers involving exponents and square and cube roots

4 - 4 - Perform calculations involving all four operations using numbers in exponential form, limited to exponents up to 5. and square and cube roots Solving problems Solve problems in contexts involving numbers in exponential form 3.5 Construction of geometric figures Measuring angles Accurately use a protractor to measure and classify angles: < 90 (acute angles) Right-angles >90 (obtuse angles) Straight angles >180 (reflex angle) Constructions Accurately construct geometric figures appropriately using compass, ruler and protractor, including: Angles, to one degree of accuracy Circles Parallel lines Perpendicular lines Geometry of 2D shapes Classifying 2D shapes Describe, sort, name and compare triangles according to their sides and angles, focusing on: Equilateral triangles Isosceles triangles Right-angled triangles Describe, sort, name and compare quadrilaterals in terms of: Length of sides Parallel and perpendicular sides Size of angles (right-angles or not)

5 Geometry of 2D shapes Describe and name parts of a circle Similar and congruent 2D shapes Recognize and describe similar and congruent figures by comparing: Shape Size Solving problems Solve simple geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties Geometry of straight lines 1.4 Common fractions Define Line segment Ray Straight line Parallel lines Perpendicular lines Term 2 Ordering, comparing and simplifying fractions Revise the following done in Grade 6: Compare and order common fractions, including specifically tenths and hundredths Extend to thousandths Calculations using fractions Revise the following done in Grade 6: Addition and subtraction of common fractions, including mixed numbers, limited to fractions with the same denominator or where one denominator is a multiple of another Finding fractions of whole numbers Extend addition and subtraction to

6 Common fractions fractions where one denominator is not a multiple of the other Multiplication of common fractions, including mixed numbers, not limited to fraction where one denominator is a multiple of another Calculation techniques Convert mixed numbers to common fractions in order to perform calculations with them Use knowledge of multiples and factors to write fractions in the simplest form before or after calculations Use knowledge of equivalent fractions to add and subtract common fractions Solving problems Solve problems in contexts involving common fractions and mixed numbers, including grouping, sharing and finding fractions of whole numbers Percentages Revise the following done in Grade 6: Percentages of whole numbers Calculate the percentage of part of a whole Calculate percentage increase or decrease of whole numbers Solve problems in contexts involving percentages Equivalent forms Revise the following done in Grade 6: Recognize and use equivalent forms of common fractions with 1-digit or 2- digit denominators (fractions where one denominator is a multiple of the

7 Decimal fractions other) Recognize equivalence between common fraction and decimal fraction forms of the same number Recognize equivalence between common fraction, decimal fraction and percentage forms of the same number Ordering and comparing decimal fractions Revise the following done in Grade 6: Count forwards and backwards in decimal fractions to at least two decimal places Compare and order decimal fractions to at least two decimal places Place value of digits to at least two decimal places Rounding off decimal fractions to at least 1 decimal place Extend all of the above to decimal fractions of at least three decimal places and rounding off to at least 2 decimal places Calculations using decimal fractions Revise the following done in Grade 6: Addition and subtraction of decimal fractions of at least two decimal places Multiplication of decimal fractions by 10 and 100 Extend addition and subtraction to decimal fractions of at least three decimal places Multiply decimal fractions to include: Decimal fractions to at least 3 decimal places by whole numbers Decimal fractions to at least 2 decimal places by decimal fractions to at least 1 decimal place

8 Decimal fractions 2.2 Functions and relationships Divide decimal fractions to include decimal fractions to at least 3 decimal places by whole numbers Calculation techniques Use knowledge of place value to estimate the number of decimal places in the result before performing calculations Use rounding off and a calculator to check results where appropriate Solving problems Solve problems in context involving decimal fractions Equivalent forms Revise the following done in Grade 6: Recognize equivalence between common fraction and decimal fraction forms of the same number Recognize equivalence between common fraction, decimal fraction and percentage forms of the same number Input and output values Determine input values, output values or rules for patterns and relationships using: Flow diagrams Tables Formulae Equivalent forms Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented: Verbally In flow diagrams In tables

9 - 9 - By formulae By number sentences 4.1 Area, perimeter of 2D shapes Area and perimeter Calculate the perimeter of regular and irregular polygons Use appropriate formulae to calculate perimeter and area of: Squares Rectangles Triangles Calculations and solving problems Solve problems involving perimeter and area of polygons Calculate to at least 1 decimal place Use and convert between appropriate SI units, including: mm 2 cm 2 cm 2 m Surface area and volume of 3D objects Surface area and volume use appropriate formulae to calculate the surface area, volume and capacity of: cubes rectangular prisms Describe the interrelationship between surface area and volume of the objects mentioned above Calculations and solving problems Solve problems involving surface area, volume and capacity Use and convert between appropriate SI units, including: mm 2 cm 2 cm 2 m 2 mm 3 cm 3 cm 3 mm

10 Use equivalence between units when solving problems: 1cm 3 1ml 1m 3 1 kl 2.1 Numeric and geometric patterns 2.2 Functions and relationships TERM 3 Investigate and extend patterns Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns: Represented in physical or diagram form Not limited to sequences involving a constant difference or ratio Of learner s own creation Represented in tables Describe and justify the general rules for observed relationships between numbers in own words Input and output values Determine input values, output values or rules for patterns and relationships using: Flow diagrams Tables Formulae Equivalent forms Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented: Verbally In flow diagrams In tables By formulae By number sentences

11 Algebraic expressions 2.4 Algebraic equations 2.5 Graphs 3.4 Transformation Geometry Algebraic language Recognize and interpret rules or relationships represented in symbolic form Identify variables and constants in given formulae and equations Number sentences Write number sentences to describe problem situations Analyze and interpret number sentences that describe a given situation Solve and complete number sentences by: - inspection - trial and improvement identify variables and constants in given formulae or equations determine the numerical value of an expression by substitution Interpreting graphs analyze and interpret global graphs of problem situations, with special focus on the following trends and features: linear or non-linear constant, increasing or decreasing Drawing graphs Draw global graphs form given descriptions of a problem situation, identifying features listed above Transformation Recognize, describe and perform translations, reflections and rotations

12 Geometry of 3D objects 1.3 Integers with geometric figures and shapes on squared paper Identify and draw lines of symmetry in geometric figures Enlargements and reductions Draw enlargements and reductions of geometric figures on squared paper and compare them in terms of shape and size Classifying 3D objects Describe, sort and compare polyhedra in terms of: Shape and number of faces Number of vertices Number of edges Building 3D model Revise using nets to create models of geometric solids, including: Cubes Prisms TERM 4 Counting, ordering and comparing integers Count forwards and backwards in integers for any interval Recognize, order and compare integers Calculations with integers Add and subtract with integers Properties of integers Recognize and use commutative and associative properties of addition and multiplication for integers Solve problems Solve problems in contexts involving addition and subtraction of integers

13 Numeric and geometric patterns 2.2 Functions and relationships 2.3 Algebraic expressions Investigate and extend patterns Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns: Represented in physical or diagram form Not limited to sequences involving a constant difference or ratio Of learner s own creation Represented in tables Describe and justify the general rules for observed relationships between numbers in own words Input and output values Determine input values, output values or rules for patterns and relationships using: Flow diagrams Tables Formulae Equivalent forms Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented: Verbally In flow diagrams In tables By formulae By number sentences Algebraic language Recognize and interpret rules or relationships represented in symbolic form Identify variables and constants in given formulae and equations

14 Algebraic equations 5.1 Collect, organize and summarize data Number sentences Write number sentences to describe problem situations Analyze and interpret number sentences that describe a given situation Solve and complete number sentences by: - inspection - trial and improvement Identify variables and constants in given formulae or equations Determine the numerical value of an expression by substitution Collect data Pose questions relating to social, economic and environmental issues in own environment Select appropriate sources for the collection of data (including peers, family, newspapers, books, magazines) Distinguish between samples and populations Design and use simple questionnaires to answer questions: With yes/no type questions With multiple choice responses Organize and summarize data Organize (including grouping where appropriate) and record data using: Tally marks Tables Stem-and-leaf display Group data into intervals

15 Summarize and distinguish between ungrouped numerical data by determining: Mean Median Mode Representing data 5.3 Interpret, analyze and report data Identify the largest and smallest scores in a data set and determine the difference between them in order to determine the spread of the data (range) Represent data Draw a variety of graphs by hand / technology to display and interpret data (grouped and ungrouped) including: Bar graphs and double bar graphs Histograms with given intervals Pie graphs Interpret data Critically read and interpret data represented in: Words Bar graphs Double graphs Pie charts Histograms Analyze data Critically analyze data by answering questions related to: Data categories, including data intervals Data sources and contexts Central tendencies (mean, median, mode) Scales used on graphs

16 Probability Report data Summarize data in short paragraphs that include: Drawing conclusions about the data Making predictions based on the data Identifying sources of error and bias in the data Choosing appropriate summary statistics for the data (mean, median, mode) Probability Perform simple experiments where the possible outcomes are equally likely and List the possible outcomes based on the conditions of the activity Determine the probability of each possible outcome, using the definition of probability

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- 1 - TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Mental calculations Revise the following done in Grade 6: Multiplication of whole numbers to at least 12 x 12. Multiplication facts for: units

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