GREAT LAKES COLLEGE
FORSTER CAMPUS
MATHEMATICS FACULTY
Program & Register
Year 7
2004
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
1. Syllabus - pg. 147
4.
Common Course
Properties of Solids
2 weeks
Suggested time:
SGS4.1 pg. 147/148
Identifies parallel and perpendicular lines and describes plane shapes and solids.
2.
5.
3.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Identification of common plane figures (revision of previous work)
 Describing solids in terms of vertices, edges, faces and the shapes involved
 Testing Euler’s Formula (F+V=E+2) for a variety of solids
 Identifying parallel and perpendicular lines and planes, and skew lines
 Identifying and comparing right and oblique solids
WORKING MATHEMATICALLY
Students learn to:
 Construct models of solids and describe their properties
 Illustrate solids using freehand sketches, drawings on grid paper (isometric & square), and using perspective drawing
 Name and describe the Platonic solids and explore their history
LANGUAGE
TECHNOLOGY
Terminology: concave, convex, congruent, vertex, vertices,
Poly (TILT Plus program)
edge, face, parallel, perpendicular, skew, cross-section,
polygon, polyhedron, polyhedra, apex, sphere, cone, base,
surface, right, oblique, pyramid, prism, Platonic, net.
Poster outlining how Euler’s Formula works with examples.
TEACHING STRATEGIES
 Use the modelling phase as an opportunity for substantive conversation about shapes, views, symmetry, cross-sections,
etc. not merely as a play session.
 Modelling ideas include drinking straws, cardboard cut-outs, Polydrons, commercially available solid nets.
 Try “Who am I”, or “celebrity heads” activities as consolidation.
 Matching tasks: name, description, and diagram.
EXTENSION IDEAS
REMEDIATION IDEAS
 Identification of common plane figures (revision of
 Matching tasks for names and diagrams of common
previous work)
plane figures (revision) or solids
 Describing solids in terms of vertices, edges, faces and
the shapes involved
 Testing building models of huge or complicated solids
 Creating a dodecahedron desk calendar for next year
 Narrative: “Who was Plato anyway”
Great Lakes College Forster Campus
Year 7 program
2
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
1. Syllabus – pg. 49
4.
Common Course
Investigating Whole Numbers
3 weeks
Suggested time:
Number NS4.1: recognises the properties of special groups of whole numbers and applies a range of strategies
to aid computation, (pg. 56): Operations with whole numbers (pg. 49).
Understands the history of number systems and uses the four operations with whole numbers.
2. Syllabus – pg. 56
5.
3. New Century Maths 3rd edition
6.
KNOWLEDGE & SKILLS
Students learn about:
 Compare the Hindu–Arabic number system with number systems from different societies, past and present
 Recognise, read and convert Roman numerals
 Given the appropriate symbols, convert between numerals from other number systems and Hindu–Arabic numerals
 State the place value of any digit in large numbers
 Read and write numbers of any size
 Order numbers of any size, in ascending and descending order
 Record large numbers in expanded notation using powers of 10
 Revise the four operations on whole numbers, apply mental strategies to aid computation
 Divide two-digit and three-digit numbers by a two-digit number
 Apply order of operations to simplify expressions

Use mathematical symbols, including
and
3
WORKING MATHEMATICALLY
Students learn to:
 Question whether it is more appropriate to use mental strategies or a calculator to find the square root of a given number.
(Questioning)
 Discuss the strengths and weaknesses of different number systems. (Communicating, Reasoning)
 Describe and recognise the advantages of the Hindu-Arabic number system. (Communicating, Reasoning)
LANGUAGE
TECHNOLOGY
Number = quantity, amount numeral = symbol representing
Cheaper, non-scientific calculators do not follow order of
that quantity.
operations rules.
A billion is a thousand million in the US, but a million
million in the UK. However, most countries are adopting the
US meaning for world finance purposes.
The abbreviation ‘K’ is sometimes used for a thousand: for
example, a salary of $450K, 10K (kilobytes) of computer
memory. This comes from the Greek khiloi, meaning
thousand.
There are three types of grouping symbols:
( ) = parentheses or round brackets (Parentheses is the plural
of parenthesis) [ ] = (square) brackets
{ } = braces.
TEACHING STRATEGIES
 Resources: spike abacus, counting beads, base 10 blocks, the library and Internet, Video: History of Number (game show).
 Research the history of the Hindu–Arabic numerals and other numerals: Greek, Mayan, Sumerian, Chinese, Papua New
Guinean. How were fractions written in each one?
 Roman numerals are often used in film and TV credits to hide their age.
 Research the invention and history of zero.
 Make a calendar or write phone numbers using different number systems. Demonstrate how our decimal place value
system makes calculations much easier.
 Place value is a key mathematical concept. It cannot be assumed that all students will have a clear understanding of it.
 Four-digit numbers may be written without the space after the thousands place, for example, 8452.
 This is the first time students learn dividing by a two-digit number (long division). Reinforce estimation skills and the idea
that division is the inverse of multiplication. See page 57 of the syllabus for ideas.
 Common mistake:
syllabus.
EXTENSION IDEAS
9 = ±3. The square root of a number is a single positive value, so
Great Lakes College Forster Campus
9 = 3 only. See page 57 of
REMEDIATION IDEAS
Year 7 program
3
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
1. Connections
4.
Common Course
Introductory Algebra
Suggested time:
PAS 4.1 pg. 82
Is able to interchange numbers, words and algebraic symbols.
2. Signpost
5.
1 week
3.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Using letters to represent numbers an developing the notion that a letter is used to represent a variable
 Using concrete materials such as cups and counters to model:
 Expressions that involve a variable and a variable plus a constant eg. a, a  1
 Expressions that involve a variable multiplied by a constant eg. 2a, 3a
 Sums and products eg. 2a  1,2(a  1)





Equivalent expressions such as: x  x  y  y  y  2 x  2 y  y  2( x  y)  y
 And to assist with simplifying expressions, such as: (a  2)  (2a  3)  (a  2a)  (2  3)  3a  5
Recognising and using simple equivalent algebraic expressions based on modelling above
a
 Eg. y  y  y  y  4 y, w  w  w 2 , a  b  ab, a  b 
b
Translating between simple words and algebraic symbols and vice versa
Performing simple substitution eg. Find the value of x  7 if x  5
Solving one step equations by inspection
WORKING MATHEMATICALLY
Students learn to:
 Determine the equivalence of expressions by substituting a number for a numeral
LANGUAGE
Algebra, equation, pronumeral, substitute, term.
TECHNOLOGY
TEACHING STRATEGIES
 Emphasis should be on understanding that a pronumeral stands in place of a numeral.
EXTENSION IDEAS
 Use non-letter pronumerals in tasks such as   5  7 ,
what is the value of   5 if   3 .
Great Lakes College Forster Campus
REMEDIATION IDEAS
Year 7 program
4
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
1. Syllabus – pg. 114
4.
Common Course
Data Representation
3 weeks
Suggested time:
DS4.1 pg. 114: Constructs, reads and interprets graphs, tables, charts and statistical information.
Constructs, reads and interprets graphs, tables, charts and statistical information.
2.
5.
3.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Drawing and interpreting graphs such as: sector, conversion, divided bar, line, step graphs
 Choosing appropriate scales on the horizontal and vertical axes when drawing graphs
 Drawing and interpreting travel graphs, recognising concepts such as change of speed and change of direction
 Using line graphs for continuous data only
 Reading and interpreting tables, charts and graphs
 Recognising data as quantitative (either discrete or continuous) or categorical
 Using a tally to organise data into a frequency distribution table (class intervals to be given for grouped data)
 Drawing frequency histograms and polygons
 Drawing and using dot plots
 Drawing and using stem-and-leaf plots
 Using the terms ‘cluster’ and ‘outlier’ when describing data
WORKING MATHEMATICALLY
Students learn to:
 Choose appropriate forms to display data (Communicating)
 Write a story which matches a given travel graph (Communicating)
 Read and comprehend a variety of data displays used in the media and in other school subject areas (Communicating)
 Interpret back-to-back stem-and-leaf plots when comparing data sets (Communicating)
 Analyse graphical displays to recognise features that may cause a misleading interpretation eg displaced zero, irregular
scales (Communicating, Reasoning)
 Compare the strengths and weaknesses of different forms of data display (Reasoning, Communicating)
 Interpret data displayed in a spreadsheet (Communicating)
 Identify when a line graph is appropriate (Communicating)
 Interpret the findings displayed in a graph eg the graph shows that the heights of all children in the class are between 140
cm and 175 cm and that most are in the group 151–155 cm (Communicating)

Generate questions from information displayed in graphs (Questioning)
LANGUAGE
Variable, categorical, quantitative, discrete, continuous,
graph, picture, divided, classify, data, column, bar, line,
sector, axes, scale, horizontal, vertical, step, travel, slope,
speed, distance, time, linear, clusters, correlation, frequency,
distribution, histogram, polygon, outliers, stem-and-leaf-plot,
classes, misuse.
TEACHING STRATEGIES
TECHNOLOGY
Spreadsheet program using a table and Chart Wizard.

Draw, read and interpret graphs (line, sector, travel, step, conversion, divided bar, dot plots and stem-and-leaf plots),
tables and charts.

Distinguish between types of variables used in graphs.

Identify misrepresentation of data in graphs.

Construct frequency tables.
 Draw frequency histograms and polygons.
EXTENSION IDEAS
Inserting terms (from language list) in blank spaces in
sentences.
Collecting tables, graphs etc. from newspapers and
categorising the data and writing stories about the data.
Great Lakes College Forster Campus
REMEDIATION IDEAS
Year 7 program
5
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
Common Course
Operations with Whole Numbers
2 weeks
Suggested time:
Number NS4.1: recognises the properties of special groups of whole numbers and applies a range of strategies
to aid computation (p. 56); Operations with whole numbers.
Recognises the properties of special groups of numbers, determines the tests for divisibility, finds square and
cubes of numbers, and uses factors trees.
References & Resources
1. Syllabus – pg 56
4.
2. New Century Maths 3rd Edition
5.
3.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Identify special groups of numbers: triangular, square, Fibonacci, Pascal’s triangle and palindromes, and their properties
 Determine and apply tests for divisibility
 Identify the factors of a number and distinguish between prime and composite numbers
 Use a factor tree and index notation to express a number as a product of its prime factors
 Calculate squares and cubes
 Estimate and calculate square roots and cube roots
 Find square roots and cube roots of numbers expressed as a product of their prime factors
WORKING MATHEMATICALLY
Students learn to:
 Question whether it is more appropriate to use mental strategies or a calculator to find the square root of a given number.
(Questioning)
 Discuss the strengths and weaknesses of different number systems. (Communicating, Reasoning)
 Describe and recognise the advantages of the Hindu-Arabic number system. (Communicating, Reasoning)
 Apply tests of divisibility mentally as an aid to calculation. (Applying Strategies)
 Verify the various tests of divisibility. (Reasoning)
LANGUAGE
TECHNOLOGY
There is a lot of mathematical jargon in this topic, especially
Investigate powers and roots on scientific calculators,
with words that have other everyday meanings, such as
graphics calculators and spreadsheets.
prime, composite, factor and index. How are the words
square and cube used here related to their geometrical
meanings?
TEACHING STRATEGIES
 Resources: counters for building square and triangular numbers, the library and the Internet, books on special numbers.
 RIME lessons: Sieve of Eratosthenes, Palindromes, Odds and Evens, Happy Numbers, Check Math. MCTP Lesson:
Bingo Bodies for factors. Videos: Follow that number! , Factor Fiction.
 There also exist pentagonal and hexagonal numbers. The general name for these is figurate numbers.
 The difference between consecutive square numbers is an odd number. Adding consecutive triangular numbers gives a
square number. Use diagrams to see why.
 Investigate other types of numbers: amicable numbers, perfect numbers, golden ratio/rectangle, figurate numbers and
factorials. Examine Fibonacci numbers in nature.
 Research the history and achievements of Eratosthenes. The sieve works best when numbers are grouped in rows of six.
 As an alternative to factor trees, repeated division can also extract prime factors. See Skillsheet 3-03 on the CD-ROM
(New Century Maths).

Common mistake:
9 = ±3. The square root of a number is a single positive value, so 9 = 3 only.
However, - 9 = -3.
 For advanced students, introduce the concept of irrational numbers and surds.
 How did mathematicians find square roots before calculators and computers? Investigate Newton’s method.
EXTENSION IDEAS
REMEDIATION IDEAS
Great Lakes College Forster Campus
Year 7 program
6
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
Common Course
Perimeter
Suggested time:
2 weeks
MS4.1 a) (p124)
Use formulae in calculating perimeter of squares and rectangles and the circumference of circles.
Estimation and measurement of lengths and converting between units of length.
References & Resources
1. New Signpost Ex 9:01 p 238
4. Syllabus – pg. 124
2. Connections 7 Ex 14A p423
5.
3. New Insight Ex 8A – F p203
6.
KNOWLEDGE & SKILLS
Students learn about:
 Estimating lengths and distances using visualisation strategies
 Recognising that all measurements are approximate
 Describing the limits of accuracy of measuring instruments (  0.5 unit of measurement)
 Interpreting the meaning of the prefixes ‘milli’, ‘centi’ and ‘kilo’
 Converting between metric units of length
 Finding the perimeter of simple composite figures
WORKING MATHEMATICALLY
Students learn to:
 Consider the degree of accuracy needed when making measurements in practical situations
 Choose appropriate units of measurement based on the required degree of accuracy
 Make reasonable estimates for length and area and check by measuring
 Select and use appropriate devices to measure lengths and distances
 Find the dimensions of a square given its perimeter, and of a rectangle given its perimeter and one side length
 Solve problems relating to perimeter
 Compare rectangles with the same area and ask questions related to their perimeter such as whether they have the same
perimeter
LANGUAGE
Perimeter, length, measurement, circles, rectangles,
triangles, estimation, metre, centimetre.
TECHNOLOGY
Calculator for variations in .
TEACHING STRATEGIES
EXTENSION IDEAS
Great Lakes College Forster Campus
REMEDIATION IDEAS
Year 7 program
7
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
Common Course
Number Patterns
Suggested time:
2 weeks
PAS 4.2 pg. 83
Describe number patterns using words and algebraic symbols.
1. Connections Chapter 8
2. Signpost Chapter 4
4.
5.
KNOWLEDGE & SKILLS
Students learn about:
 Completing number patterns.
 Describing number patterns in words, progressing towards algebraic usage.
 Modelling patterns in tables, usually pattern will be linear and increasing.
 Using algebraic symbols to create an equation, which describes the pattern.
 Completing table of values from the algebraic rule.
3. Syllabus – pg. 83
6.
WORKING MATHEMATICALLY
Students learn to:
 Engage in substantive conversations about the descriptions of the patterns.
 Test a variety of solutions in the pursuit of a correct algebraic description of the pattern.
 Determine whether a particular number pattern can be described using algebraic symbols.
LANGUAGE
Pattern, symbol.
TECHNOLOGY
Spreadsheet Activities
TEACHING STRATEGIES
 Use top and bottom row notation to develop function rule.
EXTENSION IDEAS
Decreasing functions.
Harder functions not necessarily linear.
Great Lakes College Forster Campus
REMEDIATION IDEAS
Revisit ideas of introductory algebra.
Year 7 program
8
Common Course
Year 7 Mathematics
Topic:
Syllabus ref:
Fractions
3 weeks
Suggested time:
Number NS4.3: operates with fractions, decimals, percentages, ratios and rates (p. 63); 3.4:
Fractions, Decimals and Percentages (p. 61).
Performs operations with fractions.
Report Outcome(s)
References & Resources
1. Syllabus – pg 61
2. Syllabus – pg 63
3. New Century 3rd Edition
4.
5.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Find highest common factors and lowest common multiples
 Name the different parts of fractions and the different types of fractions
 Express improper fractions as mixed numerals and vice-versa
 Find equivalent fractions
 Reduce a fraction to its lowest equivalent form
 Order fractions by expressing them with the same denominator
 Add and subtract fractions and mixed numerals using written methods
 Subtract a fraction from a whole number
 Find a fraction of a number or metric quantity
 Multiply and divide fractions and mixed numerals
WORKING MATHEMATICALLY
Students learn to:

Explain multiplication of a fraction by a fraction using a diagram to illustrate the process (Reasoning, Communicating)

Explain why division by a fraction is equivalent to multiplication by its reciprocal (Reasoning, Communicating)
1

Choose the appropriate equivalent form for mental computation, e.g. 10% of $40 is 10
of $40 (Applying Strategies)

Recognise and explain incorrect operations with fractions, e.g. explain why
2
3
 14 
3
7
(Applying Strategies, Reasoning,
Communicating)
LANGUAGE
TECHNOLOGY
Strictly speaking, what we call ‘fractions’, written of the
The CD-ROM (New Century Maths) contains
form, are actually common fractions. Decimals, percentages
demonstrations of operations with fractions using pictures.
and ratios are other types of fractions.
The reciprocal of a number is that value which if multiplied
by that number gives the product of 1.
TEACHING STRATEGIES

Resources: Cuisenaire rods, pattern blocks, RIME lesson: Fractions, MCTP lesson: Estimating with Fractions.

In music, reading and interpreting note values links with fraction work. Semiquavers, quavers, crotchets, minims and
semibreves can be compared using fractions e.g. a quaver is 12 of a crotchet, and 14 of a minim. Musicians indicate



fraction values by tails on the stems of notes or by contrasting open and closed notes. Time signatures in music appear
similar to fractions
A mixed numeral can be seen as a way of expressing the remainder in division.
See Worksheet 10-07 on the CD-ROM (New Century Maths) for making ‘paddle-pop stick’ calculators.
Some students may have trouble seeing why, for example, 13  15 , since 3 < 5.

The word fraction comes from the Latin frangere meaning ‘to break’. The earliest evidence of fractions can be traced
back to the Egyptian papyrus of Ahmes (about 1650 BC). In the seventh century AD the method of writing fractions as
we write them now was invented in India, but without the fraction bar (vinculum), which was introduced by the Arabs.
Fractions were widely in use by the 12th century.

Applications of fractions: adding fractions of an hour for payroll calculations, multiplying for overtime, fractions of
ingredients in a cooking recipe, converting recipes for different serves.

With fractions of a metric quantity, include examples with length, time, mass, volume and money.

Show that multiplication of fractions is simpler if cancellation occurs first.

Why is division by a fraction equivalent to multiplication by its reciprocal?
EXTENSION IDEAS
REMEDIATION IDEAS
Great Lakes College Forster Campus
Year 7 program
9
Year 7 Mathematics
Common Course
Algebraic Techniques 1
3 weeks
Topic:
Suggested time:
PAS4.3 pg. 85
Syllabus ref:
Manage simple algebraic techniques.
Report Outcome(s)
References & Resources
1. Text: Connections Chapter 12
2. Text: Signpost Chapter 10
3. Syllabus – pg. 85
4.
5.
6.
KNOWLEDGE & SKILLS
Students learn about:

Simplifying algebraic expressions involving multiplication and division

Simplifying algebraic expressions involving like terms

Expanding simple expressions, which involve grouping symbols

Substituting into more complex expressions, such as 17  3k when k = 2

Solving one and two step equations, using a more formal process
WORKING MATHEMATICALLY
Students learn to:

Distinguish between like and unlike terms.

Apply opposite operations to solve equations.
LANGUAGE
Equation, evaluate, expression, like, simplify, solve, unlike.
TECHNOLOGY
TEACHING STRATEGIES
 Stress the difference between terms like ‘equation’ and ‘expression’
EXTENSION IDEAS
REMEDIATION IDEAS
Depth of study.
Review number combinations.
Index Laws.
Calculator usage .
Great Lakes College Forster Campus
Year 7 program
10
Year 7 Mathematics
Common Course
Area
2 weeks
Topic:
Suggested time:
Syllabus ref:
MS4.1 b) (p124)
Report Outcome(s)
Develops and applies appropriate formula for plane and composite plane shapes.
References & Resources
1. New Signpost Ex 12:01 p359
2. Connections 7 Ex 14G p445
3. New Insight Ex. 8G p229
4. Syllabus – pg. 124
5.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Developing and using formulae for the area of a square and rectangle
 Developing (by forming a rectangle) and using the formula for the area of a triangle
 Finding the areas of simple composite figures that may be dissected into rectangles and triangles
 Developing the formula by practical means for finding the area of a parallelogram eg by forming a rectangle using
cutting and folding techniques
 Converting between metric units of area 1 cm2 = 100 mm2 , 1 m2 = 1 000 000 mm2 , 1 ha = 10 000 m2,
 1 km2 = 1 000 000 m2 = 100 ha
WORKING MATHEMATICALLY
Students learn to:
 Solve problems relating to area
 Compare rectangles with the same area and ask questions related to their perimeter such as whether they have the same
perimeter
 Compare various shapes with the same perimeter and ask questions related to their area such as whether they have the
same area
 Explain the relationship that multiplying, dividing, squaring and factoring have with the areas of squares and rectangles
with integer side lengths
LANGUAGE
Area, square units, rectangle, triangle, composite,
parallelogram, centimetres, millimetres.
TECHNOLOGY
Spreadsheets or graphics calculator table function to draw up
comparison lists.
TEACHING STRATEGIES
 Using SNAP handouts with the clear grid to do measuring exercises
EXTENSION IDEAS
Great Lakes College Forster Campus
REMEDIATION IDEAS
Year 7 program
11
Year 7 Mathematics
Topic:
Syllabus ref:
Report Outcome(s)
Common Course
Integers
3 weeks
Suggested time:
Number NS4.2: compares, orders and calculates with integers (p. 58); Integers; Space and
Geometry SGS3.3: uses a variety of mapping skills (p. 166); Position; Patterns and Algebra
PAS4.5 (p. 96): Linear Relationships.
Performs operations with directed numbers and the number plane, and simplifies expressions
involving grouping symbols and applies order of operations.
References & Resources
1. Syllabus – pg 58
2. Syllabus – pg 166
3. Syllabus – pg 96
4. New Century Maths 3rd Edition
5.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Place positive numbers on a number line
 Interpret different meanings (direction or operation) for the + and – signs depending on the context
 Recognise the direction and magnitude of an integer
 Place directed numbers on a number line
 Order directed numbers
 Add and subtract directed numbers, multiply and divide directed numbers
 Apply order of operations to simplify expressions
 Using grouping symbols as an operator
 Use the calculator to perform operations with integers, keying integers into a calculator using the +/- key
 Find a place on a map or in a directory, given its coordinates
 Locate and plot points on a number plane
 Identify the origin and the four quadrants of the number plane
WORKING MATHEMATICALLY
Students learn to:

Interpret the use of directed numbers in the real world context e.g. rise and fall of temperature (Communicating)

Construct a directed number sentence to represent a real situation (Communicating)

Apply directed numbers to calculations involving money and temperature (Applying Strategies, Reflecting)

Use number lines in applications such as time lines and thermometer scales (Applying Strategies, Reflecting)

Verify, using a calculator or other means, directed number operations e.g. subtracting a negative number is the same as
adding a positive number (Reasoning)

Question whether it is more appropriate to use mental strategies or a calculator when performing operations with integers
(Questioning)
LANGUAGE
TECHNOLOGY
-3 is read negative 3, not minus 3. Students shouldn’t confuse Spreadsheet applications are available on playing
the negative sign with the minus operation. It is important to
‘Battleships’
note that negative numbers were once written with the ‘-’
sign superscripted.
TEACHING STRATEGIES
 Resources: number line, number plane or grid paper, street map and grids, battleship games, number plane picture
puzzles.
 Introduce directed numbers using the idea of opposites, e.g. North/South, profit/loss, temperature, AD/BC, before/after
take-off. Extend the number line backwards in order to answer questions such as 4 – 9 = ?
 Syllabus, p. 58: ‘Brahmagupta, an Indian mathematician and astronomer (c 598–c 665 AD) is noted for the introduction
of zero and negative numbers in arithmetic.’
 Applications of negative numbers: bank balance, temperature, profit and loss, indoor cricket, T-minus-5 seconds (before
take-off).
 An integer is a positive or negative whole number, or zero. The set of integers J may be examined as an extension.
 In addition and subtraction, a negative number implies the opposite operation, that is + (-b) = – b, – (-b) = + b. Adding a
‘drop’ of 8 means subtracting 8. Another way of thinking about 3 – (-4) is to count how many places between -4 and 3.
 Discover the rules for multiplication through repeated addition.
 Convert the classroom into a coordinate system of rows and columns.
 Stress that order is important with coordinates, e.g. (2,5) is not (5,2). Hence the term ordered pair.
 Syllabus, p. 96: ‘Investigate the use of coordinates by Descartes and Fermat to identify points in terms of positive or zero
distances from axes. Isaac Newton introduced negative values.’
 Note that the coordinates on a number plane describe a point, not a rectangular region as in a road map or battleships
game.
EXTENSION IDEAS
REMEDIATION IDEAS
Great Lakes College Forster Campus
Year 7 program
12
Year 7 Mathematics
Topic:
Syllabus ref:
Common Course
Number Plane
2 weeks
Suggested time:
PAS4.2; Creates, records, analyses and generalises number patterns using words and algebraic
symbols in a variety of ways.
Represent number pattern relationships as points on a grid.
Report Outcome(s)
References & Resources
1. Text: Connections Chapter 8.
2. Text: Signpost Chapters 4 & 10.
3. Syllabus – pg. 83.
4.
5.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Locating positions on 2dimensional diagrams such as maps, seating arrangements and chess boards
 Positioning points on the Cartesian plane, including notions of x and yaxes and ordered pairs
 Graphing the points on the Cartesian plane that describes the pattern
 Completing the table from the graph of the function
 Graphing linear relationships
WORKING MATHEMATICALLY
Students learn to:
 Distinguish between increasing and decreasing number patterns from their graphs
 Understand why a function can be drawn linking the points plotted from the table
LANGUAGE
Axis, axes, Cartesian plane, coordinate, grid, linear, ordered
pairs, plot.
TECHNOLOGY
Graph packages  software and graphical calculators.
TEACHING STRATEGIES
 Cartoon characters on number plane.
EXTENSION IDEAS
Nonlinear graphs.
4 quadrant coordinate plane.
Great Lakes College Forster Campus
REMEDIATION IDEAS
Review Number Pattern Unit.
Year 7 program
13
Year 7 Mathematics
Topic:
Syllabus ref:
Common Course
Decimals
3 weeks
Suggested time:
Number NS4.3: operates with fractions, decimals, percentages, ratios and rates (p. 63), 3.4:
Fractions, Decimals and Percentages (p. 61).
Performs operations with decimals.
Report Outcome(s)
References & Resources
1. Syllabus – pg 61
2. Syllabus – pg 63
3. New Century Maths 3rd Edition
4.
5.
6.
KNOWLEDGE & SKILLS
Students learn about:
 Revise place value in a decimal
 Understand the role of the decimal point in determining place value
 Compare and order decimals and place them on a number line
 Convert a fraction with a power-of-10 denominator to a decimal and vice-versa
 Add and subtract decimals
 Multiply and divide decimals (limit operators to two-digits)
 Round decimals to a given number of decimal places
 Calculate decimals of quantities
 Convert fractions to terminating decimals
 Use the notation for recurring decimals
WORKING MATHEMATICALLY
Students learn to:
 Question the reasonableness of statements in the media that quote fractions, decimals or percentages, e.g. ‘the number of
children in the average family is 2.3’ (Questioning)
 Interpret a calculator display in formulating a solution to a problem, by appropriately rounding a decimal
(Communicating, Applying Strategies)
 Recognise equivalences when calculating, e.g. multiplication by 1.05 will increase number/quantity by 5%, multiplication
by 0.87 will decrease a number/quantity by 13% (Applying Strategies)
 Solve a variety of real-life problems involving fractions, decimals and percentages (Applying Strategies)
 Use a number of strategies to solve unfamiliar problems, including: using a table, looking for patterns, simplifying the
problem, drawing a diagram, working backwards, guess and refine (Applying Strategies, Communicating)
LANGUAGE
TECHNOLOGY
Deci = tenth, e.g. decade, decathlon, decimetre, December.
Students may investigate the FIX mode on a calculator (or
The word decimal is actually short for ‘decimal fraction.’
the Format cell function on a spreadsheet) for rounding
Syllabus, p. 60: ‘The decimal 1.12 is read ‘one point one
decimals.
two’ and not ‘one point twelve’.’
Terminate = stop, recurring = repeating.
Note the different names for rounding: ‘Approximate’,
‘Write correct to’, ‘to 2 decimal places’, ‘to the nearest
hundredth’.
As with larger numbers, when writing long decimals leave a
space after every three digits, for example, 3.141 592 65.
TEACHING STRATEGIES
 At Stage 3, students learn to write, compare, add and subtract decimals up to thousandths (three decimal places), as well
as multiply decimals by single-digit numbers.
 Investigate the Dewey classification system for classifying books, as an application of ordering decimals. See Worksheet
7-02 on the CD-ROM. (New Century Maths)
 The syllabus says multiplication and division may be limited to operators with two digits.
 Applications of decimals: shopping, buying fruit, meat, petrol, calculating wages, car odometers (tenth of a km), stop
watches.
 Rounding may be introduced by examining examples in rounding to the nearest dollar, cent, 5 cents, centimetre or whole
number. One and two cent coins were phased out in Australia in 1990.
 When teaching rounding, include harder examples such as 4.897 1 to two decimal places.
EXTENSION IDEAS
REMEDIATION IDEAS
Great Lakes College Forster Campus
Year 7 program
14
Year 7 Mathematics
Common Course
Topic:
Syllabus ref:
Surface Geometry
Spacial
Area
and Angles.
23 weeks
Suggested time:
SGS4.3 pg. 154,
pg. 153;
Classifies,
constructs,
and and
determines
the properties
of volume
triangles of
andright
MS4.2
131;SGS4.2
Calculates
surface
area of
rectangular
triangular
prisms and
quadrilaterals.
prisms
and cylinders.
Report Outcome(s)
Outcome(s)
Report
References &
& Resources
Resources
References
1.
1. Syllabus
Syllabus –– pg.
pg. 153/154.
131
4.
4.
Classifies, constructs
and
properties
of triangles
and quadrilaterals.
Calculates
surface area
of determines
prisms and the
volumes
of prisms
and cylinders.
2.
2.
5.
5.
3.
3.
6.
6.
KNOWLEDGE
KNOWLEDGE &
& SKILLS
SKILLS
Students
learn
about:
Students learn about:

 Notation
Identifying the surface area and edge lengths of rectangular and triangular prisms.
 Labelling
and naming
intervals
lines, triangles
 Finding
the surface
area of points,
rectangular
andand
triangular
prismsand
byquadrilaterals
practical means eg from a net.
 Calculating
the
surface
area
of
rectangular
and
triangular
prisms.
 Marking equal intervals and angles on diagrams

 Labelling sides of triangles and quadrilaterals
Triangles
 Recognising and naming types of triangles
 Constructing triangles using geometrical instruments
 Constructing triangles given different information
WORKING
 TheMATHEMATICALLY
sum of the angles of a triangle is 180
Students learn to:
 The exterior angle of a triangle is equal to the sum of the two interior opposite angles
 Solve problems involving surface area of rectangular and triangular prisms.

Quadrilaterals
 Recognise that shapes with the same surface area may have different volumes.
 Recognising and naming special quadrilaterals using their properties
 Constructing various types of quadrilaterals
 The angle sum of a quadrilateral is 360
 Investigating the properties of special quadrilaterals
Angles
 Revising basic angle types (acute, obtuse, etc. see SGS3.2b)
LANGUAGE
TECHNOLOGY
 Labelling and naming points, lines, intervals and angles using appropriate conventions
Surface area, cross-section, right prisms, rectangular,
Surface area calculations in spreadsheets.
 Using mathematical conventions, abbreviations and symbols for equal angles & sides and perpendicular & parallel

triangular, perpendicular, composite.
lines
 Defining and identifying adjacent, complementary and supplementary angles
WORKING MATHEMATICALLY
Students learn to:
 Sketch and label triangles and quadrilaterals from a given verbal description
 Describe a sketch in sufficient detail for it to be drawn
TEACHING

Recognise STRATEGIES
that a given triangle may belong to more than one class
 Students
able side
to sketch
right prisms
in opposite
differentthe
orientations.
Recogniseshould
that thebe
longest
of a triangle
is always
largest angle

that the sumtoofdevelop,
any two sides
a triangle
is greater
the third
 Recognise
Use of spreadsheets
trial,ofevaluate
and
refine than
formulae
forside
surface area.
 Recognise special types of triangles and quadrilaterals embedded in composite figures or drawn in various orientations
 Determine if particular triangles and quadrilaterals have line and/or rotational symmetry
 Apply geometrical facts, properties and relationships to solve numerical problems such as finding unknown sides and angles in
diagrams
EXTENSION
REMEDIATION
IDEAS
 Justify their IDEAS
solutions to problems by giving reasons using their own
words
Finding
surface
area
of
other
right
prisms
5.2.2
Constructing
rectangular
prisms with cm3 blocks 3.3
 Bisect an angle by applying geometrical properties of figures eg constructing a rhombus
Surface
area
cylinders
5.2.2 geometrical properties eg constructing a rhombus

Bisect
an of
interval
by applying
Practical

Drawproblems
a perpendicular
related
to to
a line
surface
from area
a point
5.2.2
on the line by applying geometrical properties. eg constructing an isosceles triangle



Draw a perpendicular to a line from a point off the line by applying geometrical properties. eg constructing a rhombus
Use angle relationships to find unknown angles in diagrams
Apply angle knowledge to problems involving angles
LANGUAGE
TECHNOLOGY
Acute-angled, right-angled, obtuse-angled, scalene,
Mathematical templates and software such as dynamic
isosceles, equilateral, vertex, angle, interval, arm,
geometry, and draw and paint packages are additional tools
complementary, supplementary, revolution
that are useful in drawing and investigating geometrical
figures. Computer drawing programs enable students to
prepare tessellation designs and to compare these with other
designs such as those of Escher.
TEACHING STRATEGIES
 Paper folding, tessellations, wanted posters for each type of triangle or quadrilateral, giving description as properties of
the shape.
 Informal ideas can be established through superimposing angles following translation, rotation, etc.
 This topic is pretty “language heavy”, so language based activities are appropriate.
 Matching tasks (name, definition and diagram) are great for reinforcing the concepts met.
EXTENSION IDEAS
REMEDIATION IDEAS
Research the origin of some terms: eg: isosceles, equilateral,
Activities on recognising triangles and quadrilaterals in
rhombus.
Research
Euclid
on
the
library
or
internet
Great Lakes College Forster Campus
Year 7buildings
programand constructions and identifying triangle types15and
‘Securing Their Future’ folder activity on Quadrilaterals and quadrilateral types. Transformation geometry; flip, slide and
What shape was that?
turn. More work on estimating and measuring angles.
Great Lakes College Forster Campus
Year 7 program
16
Year 7 Mathematics
Common Course
Time
Suggested time:
MS4.3 pg. 138; Performs calculations of time that involve mixed units.
Performs operations involving time.
Topic:
Syllabus ref:
Report Outcome(s)
References & Resources
1. New Signpost Ex 9:07 p 259
4.
2. Connections 7 Ex7A – 7D p167
5.
1 week
3. New Insight Ch 3 p43
6.
KNOWLEDGE & SKILLS
Students learn about:
 Adding and subtracting time with a calculator using the ‘degrees, minutes, seconds’ button
 Rounding calculator answers to the nearest minute or hour
 Interpreting calculator displays for time calculations
 Comparing times and calculating time differences between major cities of the world
 Interpreting and using tables relating to time eg. Tide charts, bus, and airline timetables, standard time zones
WORKING MATHEMATICALLY
Students learn to:
 Plan the most efficient journey to a given destination involving a number of connections and modes of transport
 Ask questions about international time relating to everyday life eg whether a particular soccer game can be watched live
on television during normal waking hours
 Solve problems involving calculations with mixed time units eg ‘How old is a person today if he/she was born on
30/6/1989?’
LANGUAGE
Spelling, terminology and literacy strategies.
TECHNOLOGY
Use of calculator to do sexagesimal calculations.
TEACHING STRATEGIES
EXTENSION IDEAS
Great Lakes College Forster Campus
REMEDIATION IDEAS
Year 7 program
17