# Level Description

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 making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry**Fluency**includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles**Problem-solving**includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans**Reasoning**includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets.

## Number and Algebra

### Number and place value

- exploring factors and multiples using number sequences

Tutorials

- Arithmetic, Geometric and Special Sequences. Also covers square numbers, cube numbers, fibonacci numbers

Worksheets

- Interactive online geometric worksheet at IXL.
- Various computer generated worksheets on factors and multiples.

Videos

- Finding factor pairs using the number line by Icon Math
- Find all factors of a number – video lesson – Khan Academy (10 mins)
- Find all factors of a number using the tree method – video lesson – MathsSmart

- using simple divisibility tests

Tutorials

- Divisibility rules. Whether a number is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12.

Worksheets

- Scroll towards the bottom to find divisibility rules worksheets.

Videos

- Video lesson on how to test if a number is divisible by 2, 3, 4, 5, 6, 9 or 10. Khan Academy (6.5 mins)

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

- recognising the usefulness of estimation to check calculations

Tutorials

- A simple overview of why estimation is useful and how to do simple estimation.

Worksheets

- Interactive multiple choice worksheet on estimating answers to calculations. BBC.co.uk.
- Basic worksheet on estimating simple maths mental answers. BBC.co.uk.

Videos

- Video lesson on how to use rounded numbers to estimate an answer. Larry Schmidt. (2.12 mins)

- applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load

Tutorials

- A simple overview of why estimation is useful and how to do simple estimation.

Worksheets

- Interactive multiple choice worksheet on estimating answers to calculations. BBC.co.uk.
- Basic worksheet on estimating simple maths mental answers. BBC.co.uk.

Videos

- Video lesson on how to use rounded numbers to estimate an answer. Larry Schmidt. (2.12 mins)

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

- exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers

Tutorials

- The Lattice Method. Coolmath4kids.
- The Partitioning or Splitting Method. BBC.co.uk

Worksheets

- Worksheets that cover various multiplication methods including: partitioning, multiplying by 19 or 21, doubling and halving, another type of partitioning and the box method, the standard vertical algorithm method plus bonus worksheets on decimals, division, etc.

Videos

- Video lesson that explains how to use the partitioning strategy for multiplication. P Firth (14 mins)
- Video lesson that explains lattice multiplication which is a multiplication method that allows you multiply any two numbers quickly using a table.

It is especially useful in multiplying large numbers, with less mess and confusion than the traditional vertical method.

- applying the distributive law and using arrays to model multiplication and explain calculation strategies

Tutorials

Worksheets

- Create various different worksheets around commutative, associative and distributive laws.

Videos

- Video lesson on the distributive law of multiplication. Mathematics is Fun. (2 mins)

Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

- using the fact that equivalent division calculations result if both numbers are divided by the same factor
- interpreting and representing the remainder in division calculations sensibly for the context

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

- using calculators to check the reasonableness of answers

**Fractions and decimals**

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)

- recognising the connection between the order of unit fractions and their denominators

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

- modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes

Recognise that the place value system can be extended beyond hundredths (ACMNA104)

- using knowledge of place value and division by 10 to extend the number system to thousandths and beyond
- recognising the equivalence of one thousandths and 0.001

Compare, order and represent decimals (ACMNA105)

- locating decimals on a number line

**Money and financial mathematics**

Create simple financial plans (ACMNA106)

- creating a simple budget for a class fundraising event
- identifying the GST component of invoices and receipts

** **

**Patterns and algebra**

Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)

- using the number line or diagrams to create patterns involving fractions or decimals

Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121)

- using relevant problems to develop number sentences

## Measurement and Geometry

### Using units of measurement

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

- recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns
- investigating alternative measures of scale to demonstrate that these vary between countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA

Calculate perimeter and area of rectangles using familiar metric units (ACMMG109)

- exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result
- exploring efficient ways of finding the areas of rectangles

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

- investigating the ways time was and is measured in different Aboriginal Country, such as using tidal change
- using units hours, minutes and seconds

**Shape**

Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)

- identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of prisms and pyramids
- representing two-dimensional shapes such as photographs, sketches and images created by digital technologies
- Location and transformation

Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

- comparing aerial views of Country, desert paintings and maps with grid references
- creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another

Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114)

- identifying and describing the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies
- identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

- using digital technologies to enlarge shapes
- using a grid system to enlarge a favourite image or cartoon

**Geometric reasoning**

Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

- measuring and constructing angles using both 180° and 360° protractors
- recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other

### Statistics and Probability

#### Chance

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

- commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rock-paper-scissors)

Recognise that probabilities range from 0 to 1 (ACMSP117)

- investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1

** Data representation and interpretation**

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

- posing questions about insect diversity in the playground, collecting data by taping a one-metre-square piece of paper to the playground and observing the type and number of insects on it over time

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

- identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations

Describe and interpret different data sets in context (ACMSP120)

- using and comparing data representations for different data sets to help decision making

## Mathematics Achievement Standard

By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They identify and explain strategies for finding unknown quantities in number sentences involving the four operations. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students interpret different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12- and 24-hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.

## If You Need To Contact Us