Mathematics G7
Topic outline
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- Revise the following:
- o Ordering and comparing whole numbers
- o Properties of operations with whole numbers
- o Calculations using all operations with whole numbers
Calculation techniques
- • Use any strategy to perform and check written and mental calculations of whole numbers including:
- ‒ Long division
- ‒ Adding, subtracting and multiplying in columns
- ‒ Estimation
- ‒ Rounding off and compensating
- ‒ Using a calculator
N.B. Calculator is only used to check the correctness of the answer
Multiples and factors
- • List prime factors of numbers to at least 3-digit whole numbers
- • Find the LCM and HCF of whole numbers by inspection or factorisation
Solving problems
- • Solve problems involving whole numbers, including:
- ‒ Comparing of 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
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Ordering, comparing and simplifying common fractions
- • Extend to thousandths
Calculations with fractions
- • Addition and subtraction of fractions including mixed numbers where one denominator is not a multiple of the other
- • Multiplication common fractions, including mixed numbers, not limited to fractions 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
Percentages
- • Calculate the percentage of part of a whole
- • Calculate percentage increase or decrease of whole numbers
Solving problems
- • Solve problems in contexts involving common fractions and mixed numbers, including grouping and sharing; and finding fractions of whole numbers
- • Solve problems in contexts
- • involving percentages
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Ordering and comparing decimal fractions
- • Count forwards and backwards in decimal fractions to at least 3 decimal places
- • Place value of decimals to at least 3 decimal places
- • Order and compare decimal fractions to at least 3 decimals
- • Rounding off decimal fractions to at least 2 decimal places
Calculations with decimal fractions
- • 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
- • 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
- • Use rounding off and a calculator to check results where appropriate
Solving problems
- • Solve problems in context involving decimal fractions
Equivalent forms
- • Recognise equivalence between common fraction and decimal fraction forms of the same number
- • Recognise equivalence between common fraction, decimal fraction and percentage forms of the same number
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Mental calculations
- • Determine squares to at least 12² and their square roots
- • Determine cubes to at least 6³ and their cube roots
Comparing and representing numbers in exponential form
- • Compare and represent whole numbers in exponential form: 𝑎𝑏 = a ×𝑎 ×𝑎 ×… for b number of factors
Calculations using numbers in exponential form
- • Recognise and use the appropriate laws of operations with numbers involving exponents and square and cube roots
- • Calculations involving all four operations using numbers in exponential form, limited exponents up to 5, and square and cube roots
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Counting, ordering and comparing integers • Count forwards and backwards in integers for any interval • Recognise, order and compare integers Calculations with integers • Add and subtract with integers Properties of integers • Recognise and use commutative and associative properties of addition for integers
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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
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- 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
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Measuring angles
- • Accurately use a protractor to measure and classify angles:
- ‒ < 90o (acute angles)
- ‒ Right-angles
- ‒ >90o (obtuse angles)
- ‒ Straight angles
- ‒ >180o but less than 360 o (reflex angles)
Constructions
- • Accurately construct the following using a compass, ruler and protractor, limited to:
- ‒ Angles, to one degree of accuracy
- ‒ Parallel lines
- ‒ Perpendicular lines
- • Describe and name parts of a circle
GEOMETRY OF STRAIGHT LINES
Define
- • Line segment
- • Ray
- • Straight line
- • Parallel lines
- • Perpendicular lines
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Classifying 2D shapes
- • Describe, sort, name and compare triangles according to their sides and angles, focussing 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)
Similar and congruent 2D shapes
- • Recognise 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
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Transformations
- • Recognise, describe and perform translations, reflections and rotations 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
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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:
- ‒ mm2 ↔ cm2
- ‒ cm2 ↔ m2
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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:
- ‒ mm2 ↔ cm2
- ‒ cm2 ↔ m2
- ‒ mm3 ↔ cm3
- ‒ cm3 ↔ m3
- • Use equivalence between units when solving problems:
- ‒ 1 cm3 ↔ 1 ml
- ‒ 1 m3 ↔ 1 kl
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PROVIDE LEARNERS WITH DATA TO SAVE TIME
- • 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 and suggest appropriate samples for investigation
- • Design and use simple questionnaires to answer questions with:
- ‒ yes/no type responses
- ‒ multiple choice responses
Organise and summarise data
- • Organise (including grouping where appropriate) and record data using
- ‒ Tally marks
- ‒ Tables
- ‒ Stem-and-leaf displays
- • Group data into intervals
- • Summarise and distinguishing between ungrouped numerical data by determining:
- ‒ Mean
- ‒ Median
- ‒ Mode
- • 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 charts
Interpret data
- • Critically read and interpret data represented in:
- ‒ Words
- ‒ Bar graphs
- ‒ Double bar graphs
- ‒ Pie charts
- ‒ Histograms
Analyse data
- • Critically analyse data by answering questions related to:
- ‒ Data categories, including data intervals
- ‒ Data sources and contexts
- ‒ Central tendencies (mean, mode, median)
- ‒ Scales used on graphs
Report data
- • Summarise 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)
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