The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.
At this year level:
- understanding includes describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions
- fluency includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms
- problem-solving includes formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments
- reasoning includes applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.
By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays.
Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.
Adding and Subtracting Fractions Worksheets
Three worksheets to use when teaching your students how to add and subtract fractions.
Equivalent Fractions Chart – Differentiated Worksheets
Use a fraction wall to practise finding equivalent fractions and comparing fractions with this set of differentiated worksheets.
Capacity Vs Volume Poster
A poster explaining the difference between capacity and volume.
Shopping Catalogue with Worksheet
A shopping catalogue and worksheet to use when working on financial mathematics.
2D Shapes with Information – Poster
A 2D shapes poster with 16 common shapes, as well as information characterising each shape.
Operations With Decimals PowerPoint
A 26 slide editable PowerPoint Template to use when teaching your students how to add, subtract, multiply and divide using decimal numbers.
Adding Fractions with Common Denominators Worksheet
A worksheet using fractions with common denominators.
Multiplication Strategies Posters
A set of nine posters with clear examples of multiplication strategies.
3 volume worksheets.
2D Symmetry Poster - Reflection and Rotational
This 2D symmetry poster explores both reflection and rotational symmetry.
Fractions Number Line - Halves, Quarters and Eighths
Demonstrate the concept of fractions on a number line with a printable number line display and student reference sheets.
Adding and Subtracting Fractions PowerPoint
A 17 slide editable PowerPoint Template to use when teaching your students how to add and subtract fractions.
Adding, Subtracting, Multiplying and Dividing Fractions Posters
Posters outlining the processes involved when adding, subtracting, multiplying and dividing fractions.
Missing Angles Worksheet
A worksheet to use when learning about angles.
Decimals and Percentages Maths Investigation – Prepare to Party!
A mathematics investigation about decimals and percentages, embedded in a real-world context.
Comparing Fractions Mini-Book
Use this mini-book to help your students learn how to compare fractions with visual models, number lines and mathematical reasoning.
Interactive Maths Review – Activities for Years 5, 6 & 7
Review important maths concepts covered in years 5, 6 and 7 with a student-led interactive activity.
Equivalent Fractions on a Number Line – Differentiated Worksheets
Practise placing equivalent fractions on a number line with this cut-and-paste worksheet.
Calculating Discounts PowerPoint
A 21 slide editable PowerPoint template to use when teaching discounts to your students.
Factor Trees – Worksheet
A worksheet with factor trees that are used to find the prime factors of numbers.
Describe That Decimal Worksheet
A worksheet to deepen students' understanding of decimals.
Maths Mazes (Factors)
A set of maths mazes that allow students to demonstrate their knowledge of factors.
Equations, Tables, and Graphs, Oh My! – Differentiated Worksheets
Use these differentiated worksheets to practise using equations to create patterns within input-output tables and graphs.
Improper Fractions Cards
A set of 30 cards displaying various improper fractions.
Decimals Worksheet - Operations
Two worksheets that focus on operations using decimals.
Complementary Angles Worksheet
A worksheet to use when learning about complementary angles.
Finding the Angle Sum of a Triangle Worksheet
A worksheet to consolidate your students' understanding of the angle sum of a triangle.
Area of 2D Shapes Posters
Area of 2D Shapes - so many rules and formulas to remember!
Pandora's Party Palace Maths Activity – Upper Years
Sixteen mathematics problem-solving task cards involving money in a real-world context.
Number and Algebra Mathematics Investigation - The Solar System in Our Space
A mathematics investigation about number and the scale of the solar system, embedded in a real-world context.
Supplementary Angles Worksheet
A worksheet to use when learning about supplementary angles.
Working with Angles PowerPoint
A 12 slide editable PowerPoint template to use when introducing more complex angles to older students.