Year 7 Mathematics

Year 7 Mathematics

Semester 1 Overview

Students will solve problems involving the order, addition and subtraction of integers and make connections between whole numbers and index notation and the relationship between perfect squares and square roots. They will apply correct procedures to problems involving all four operations with fractions and percentages and their equivalences, and express fractions in the simplest form. They will assign ordered pairs to given points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students will investigate the different types of angles formed by a transversal crossing parallel lines and apply their knowledge to solve simple numerical problems involving these lines and angles. 

Number and Algebra

Students will:

• Investigate the associative, commutative and distributive laws as powerful ways of describing and simplifying calculations
• Define and compare prime and composite numbers and discover the differences between them.
• Apply knowledge of factors as strategies for expressing whole numbers as products of powers of prime factors
• Solve problems involving lowest common multiples and highest common factors for pairs of whole numbers
• Investigate square numbers and develop square-root notation
• Plot points on the Cartesian plane from tables of integer values and investigate simple patterns
• Interpret features of graphs from authentic data, such as slope, to real life scenarios and situations
• Explore equivalence among families of fractions and develop efficient strategies to solve additive problems involving fractions.
• Investigate multiplication of fractions using a range of strategies including patterning and repeated addiction and identifying the processes for division as the inverse of multiplication
• Understand quantities can be represented by different number types and calculated using various operations as well as understanding that rate and ratio problems can be solved using fractions or percentages.
• Use their knowledge of percentages to express quantities as percentages of other amounts
• Design and implement mathematical algorithms

Measurement and Geometry

Students will:

• Define and classify pairs of angles as complementary, supplementary, adjacent and vertically opposite
• Construct parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
• Define and identify the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

Semester 2 Overview

Students will solve problems involving all four operations with decimals and compare the cost of items to make financial decisions, with and without the use of digital technology. They will also make simple estimates to judge the reasonableness of results they obtain after applying correct procedures for the solution. Students will investigate the use of variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. The development of simple linear models for situations will be discussed and used to make predictions and solve related equations. Formulas for the area and perimeter of rectangles, triangles and parallelograms are established and used in problem solving. They will classify triangles and quadrilaterals and represent transformations of these shapes on the Cartesian plane, with and without the use of digital technology. Students will investigate how to describe and produce different views of three-dimensional objects. Issues involving the collection of discrete and continuous data will be discussed in the topic of statistics as well as using data to identify and calculate the mean, mode, median and range for these data sets. 

Number and Algebra

Students will:

• Connect fractions, decimals and percentages and carry out conversions when necessary for the correct solution
• Investigate and calculate best buys with and without digital technologies
• Create algebraic expressions and evaluate them by substituting a given value for each variable
• Identify the connections between algebraic and word representations as being descriptions of the same situation
• Solve equations and investigate strategies that can be applied for the correct solution 

Measurement and Geometry

Students will:

• Build on their understanding of area of rectangles to develop formulas for the area of triangles and use these formulas to solving problems involving areas of surfaces
• Investigate volumes of cubes and rectangular prisms
• Describe patterns and experiment with different ways to produce transformations using digital technologies
• Identify properties of scalene, isosceles, right-angled and obtuse-angled triangles
• Investigate the angle sum of triangles and quadrilaterals

Statistics and Probability

Students will:

• Collect data and construct a range of data displays, such as ordered stem-and-leaf plots, to record and display data. They will also understand that some data representations are more appropriate than others for particular data sets
• Understand that summarising data by calculating measures of center and spread can help make sense of the data as well as help answer questions and make real life connections about the data set.

Year 7 Accelerated and Enhanced Mathematics

Semester 1 Overview

Students will use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. Rational and irrational numbers will be investigated, identified and described in context and problems involving rates and ratios will be discussed. Procedures for solving everyday problems involving profit, loss, rates and percentages will be discussed, with and without the use of digital technology. They will simplify a variety of algebraic expressions and connect the expansion and factorisation of linear expressions. Students will investigate angle properties, and solve related numerical problems using reasoning. The solutions of linear equations will be investigated using algebraic and graphical techniques. 

Number and Algebra

Students will:

• Evaluate numbers expressed as powers of positive integers and use patterns to assist in finding rules for the multiplication and division of integers.
• Use the number line to develop strategies for adding and subtracting rational numbers.
• Recognise terminating, recurring and non-terminating decimals and choose their appropriate representations as well as extend their knowledge of the real number system to include irrational numbers.
• Use percentages to solve problems, including those involving mark-ups, discounts and population increases and decreases.
• Investigate the methods used in retail stores to express discounts and express profit and loss as a percentage of the cost or selling price.
• Understand that rate and ratio problems can be solved using fractions or percentages and will choose the most efficient form to solve a particular problem
• Apply the distributive law to the expansion of algebraic expressions using strategies such as the area model
• Recognise the relationship between factorising and expanding. They will also identify the highest common factor of numeric and algebraic expressions and use a range of strategies to factorise algebraic expressions.

Measurement and Geometry

Students will:

• Identify properties related to side lengths, parallel sides, angles, diagonals and symmetry.
• Investigate properties of triangles and quadrilaterals
• Explore angles present at a point and those found within parallel lines and transversals

Semester 2 Overview

Students will solve linear equations using algebraic and graphical techniques. They will apply correct procedures to solve linear equations and plot linear relationships on the Cartesian plane with and without the use of digital technologies. Students will find the perimeter and area of parallelograms, rhombuses and kites. They will investigate the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms. Students will use tools, including digital technology, to construct congruent shapes leading to the establishment and the use of the conditions for congruence for solving problems. Students will model situations with Venn diagrams and two-way tables and explain the use of ‘not’, ‘and’ and ‘or’. They will choose appropriate language to describe events and experiments and determine complementary events and calculate the sum of probabilities. Problems involving rates and ratios will be discussed, as well as the process of finding solutions with and without technology. Transformations of plane shapes and the properties that determine congruence of triangles will be investigated.

Number and Algebra

Students will:

• Solve real life problems by using variables to represent unknowns.
• Use algorithms and related testing procedures
• Complete a table of values, plotting the resulting points and determine whether the relationship is linear. They will also investigate procedures for finding the rule for a linear relationship.

Measurement and Geometry

Students will:

• Establish and use formulas for areas such as trapeziums, rhombuses and kites
• Investigate the circumference and area of circles to establish an understanding of formulas
• Understand the properties that determine congruence of triangles and recgonise which transformations create congruent figures.
• Establish that two figures are congruent after one or more transformations and recognise that the matching sides and the matching angles are equal.
• Solve problems using the properties of congruent figures

Statistics and Probability

Students will:

• Understand that probabilities range between 0 and 1 and that calculating the probability of an event allows the probability of its complement to be found.
• Pose ‘and’, ‘or’ and ‘not’ probability questions about objects or people.
• Use Venn diagrams and two-way tables to calculate probabilities for events, satisfying ‘and’, ‘or’ and ‘not’ conditions as well as understanding that represent data in this way facilitates the calculation of probabilities.
• Collect data to answer the questions using Venn diagrams or two-way tables.