MathsBites is your go-to guide for
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MathsBites is based on the NSW syllabus, but it also aligns with every concept your child learns in the Australian Curriculum. Each topic is matched to its NSW equivalent and brought to life through engaging MathsBites videos.
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Stage 3, Part A - Year 5
Whole numbers: Recognise, represent and order numbers in the millions
Name millions using the place value grouping of ones, tens and hundreds
Arrange numbers in the millions in ascending and descending order using place value
Round numbers to a specified place value
Represents Numbers
Number
No associated ACARA code
Whole numbers: Apply place value to partition, regroup and rename numbers to 1 billion
Recognise 1000 thousands is 1 million and 1000 millions is 1 billion
Regroup numbers in different forms
Partition numbers to 1 billion in non-standard forms
No associated ACARA code
Decimals and percentages: Recognise that the place value system can be extended beyond hundredths
Express thousandths as decimals
Interpret decimal notation for thousandths
Indicate the place value of digits in decimal numbers of up to 3 decimal places
Use place value to partition decimals
AC9M5N01
interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line.
Decimals and percentages: Compare, order and represent decimals
Compare and order decimal numbers of up to 3 decimal places
Interpret zero digit(s) at the end of a decimal
Compare the place value of digits by determining numbers that are 10 or 100 times the original decimal number as well as or times the original decimal numbers
Approximate the size of decimals
Place decimal numbers of up to 3 decimal places on a number line
AC9M5N01
interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line.
AC9M6N06 (Year 6 concept)
multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers.
Additive relations
Apply efficient mental and written strategies to solve addition and subtraction problems
Solve word problems, including multistep problems
Apply known strategies such as levelling, addition for subtraction, using constant difference, and bridging (Reasons about relations)
Use place value to add or subtract 3 or more numbers with different numbers of digits
Determine when it would be more efficient to use a calculator to add numbers
Identify efficient and inefficient multidigit subtraction strategies
Number
AC9M5N08
check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context
Use estimation and place value understanding to determine the reasonableness of solutions
Round numbers appropriately when obtaining estimates to numerical calculations
Use place value understanding to check for errors in calculations
Use estimation to check the reasonableness of solutions to addition and subtraction calculations
AC9M5N08
check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context
Determine products and factors
Use the term product to describe the result of multiplying 2 or more numbers
Model different ways to show a whole number as a product
Determine factors for a given whole number
Determine whether a number is prime, composite or neither (0 or 1)
Multiplicative relations
Number & Algebra
AC9M5N02
express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
AC9M6N02 (Year 6 concept)
identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations
Use partitioning and place value to multiply 2-, 3- and 4-digit numbers by one-digit numbers
Use mental strategies to multiply one-digit numbers by 10, 100, 1000 and their multiples
Estimate the product of 2 numbers (one-digit by 2- or 3-digit numbers) using multiples of 10 or 100
Use informal written strategies such as the area model to solve multiplication and division problems
Use the distributive property with the area model to partition numbers in representing multiplication problems
Use the distributive property with partial products to solve problems by multiplying the hundreds, then the tens and then the ones
Record the product of multiplying by a one-digit number using a formal algorithm
AC9M5N06
solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
AC9M5A02
find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
Select and apply mental and written strategies to multiply 2- and 3-digit numbers by 2-digit numbers
Factorise numbers to aid mental multiplication
Extend the area model to represent 2-digit by 2-digit multiplication
Use a multiplication algorithm with understanding (Reasons about relations)
Solve multiplication word problems
AC9M5N02
express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
AC9M5N06
solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
Represent and solve division problems with whole number remainders
Model division, including where the answer involves a remainder, using materials or diagrams
Record remainders in words to division problems
Use known multiplication fact families to solve division problems for which answers may include a remainder
Use the term quotient to describe the result of a division calculation
Show the connection between division and multiplication involving the divisor and quotient
AC9M5N07
solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
AC9M5A01
recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts
Select and apply strategies to divide a number with 3 or more digits by a one-digit divisor
Estimate the result of dividing by a one-digit divisor
Use knowledge of multiples to partition as appropriate and divide
Apply and record appropriate strategies to solve division word problems
Use and interpret remainders in solutions to division problems
Use digital technologies to divide whole numbers by one- and 2-digit divisors
AC9M5N07
solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction
AC9M5A01
recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts
Use estimation and rounding to check the reasonableness of answers to calculations
Use estimation to check the reasonableness of answers to multiplication and division calculations
AC9M5N08
check and explain the reasonableness of solutions to problems including financial contexts using estimation strategies appropriate to the context
Covered in Stage 3, Part B topics
AC9M5N09
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
AC9M5N010
create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns
Recognise the role of the number 1 as representing the whole
Compare halves and quarters of different sized wholes
Justify the need for fractions to refer to the number 1 as the common whole
Representing Quantity Fractions
AC9M5N03
compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
AC9M5N04
recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents
Number
Compare and order common unit fractions
Compare unit fractions as numbers to the benchmark value
Compare and order unit fractions with denominators of 2, 3, 4, 5, 6, 8 and 10 by placing them on a number line
AC9M6N03 (Year 6 concept)
apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Solve problems involving addition and subtraction of fractions with the same denominator
Represent the sum of fractions with the same denominator, recreating the whole, where the result may exceed one
Find the difference between fractions with the same denominator and interpret the answer
Solve word problems that involve fractions with the same denominator
Use diagrams, objects and mental strategies to subtract a unit fraction from any whole number including 1 (the complement principle)
AC9M5N05
solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
AC9M6N05 (Year 6 concept)
solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
Geometric Measure
Position: Explore the Cartesian coordinate system
Recognise that the grid-map reference system gives the area of a location and the number plane identifies a specific point
Identify that in the coordinate system the lines are numbered, not the spaces
Identify the point of intersection of the 2 axes as the origin, having coordinates (0, 0)
Plot and label points, given coordinates, on the number plane in the first quadrant, describing the horizontal position first, followed by the vertical position
Identify and record the coordinates of given points on the number plane in the first quadrant
Measurement & Space
AC9M5M01
choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
AC9M6M01 (Year 6 concept)
convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem
AC9M5SP02
construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement
Length: Use metres and kilometres for length and distances
Recognise the need for a formal unit longer than the metre for measuring distance
Measure 100 metres and recognise that 10 times 100 metres is one kilometre, ie 1000 metres 1 kilometre
Estimate lengths and distances using an appropriate unit
Record distances using the abbreviation for kilometres (km)
Use a variety of measuring devices to measure lengths and distances in different contexts
AC9M5M01
choose appropriate metric units when measuring the length, mass and capacity of objects; use smaller units or a combination of units to obtain a more accurate measure
AC9M5M02
solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
Length: Measure lengths to find perimeters
Use efficient strategies to calculate the perimeter of a large rectangular area in metres
Calculate perimeters of common two-dimensional shapes, including squares, rectangles and triangles
Determine which side lengths are needed to find the perimeter of a shape
Recognise that rectangles with the same perimeter may have different dimensions
AC9M5M02
solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
Angles: Estimate, measure and compare angles using degrees
Identify the arms and vertex of an angle where both arms are invisible, such as for rotations
Explain how a protractor is formed and used to measure an angle
Estimate and describe the size of angles using known angles as benchmarks
Record angle measurements using the symbol for degrees (°)
Measure angles of up to 360° using a protractor
AC9M5M04
estimate, construct and measure angles in degrees, using appropriate tools including a protractor, and relate these measures to angle names.
Angles: Use a protractor to measure and identify types of angles
Create angles of up to 360° using a protractor
Recognise that a right angle is 90°, a straight angle is 180° and an angle of revolution is 360°
Identify and describe angle size in degrees for the classifications acute, obtuse and reflex
AC9M5M04
estimate, construct and measure angles in degrees, using appropriate tools including a protractor, and relate these measures to angle names.
2D shapes: Classify two-dimensional shapes and describe their properties
Identify and classify triangles as equilateral, isosceles or scalene triangles
Recognise that triangles and quadrilaterals can be classified in more than one way
Compare side and angle properties of triangles and quadrilaterals using measurement and symmetry
Investigate the symmetry properties (line and rotational) of quadrilaterals
Identify regular and irregular polygons
Two-dimensional spatial structure
AC9M5M02
solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
AC9M5SP03
describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries
AC9M6SP03 (Year 6 concept)
recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate
Measurement & Space
Area: Use hectares and square kilometres as units of measurement for area
Recognise the need for formal units larger than the square metre
Identify situations where square kilometres and hectares are used for measuring area
Equate one hectare to the area of a square with side lengths of 100 m,
ie 10 000 square metres 1 hectare (ha)
Record areas using square kilometres and hectares
Area: Calculate the areas of rectangles using familiar metric units
Recognise the importance of using the same units of length on the sides of rectangles to create ‘square units’
Establish the relationship between the lengths, widths and areas of rectangles
Record, using words, the method for finding the area of any rectangle
Calculate areas of rectangles in square centimetres (cm2), square metres (m2) and square kilometres (km2)
Recognise that rectangles with the same area may have different dimensions
Investigate and compare the areas of rectangles that have the same perimeter
No associated ACARA code
AC9M6M02 (Year 6 concept)
establish the formula for the area of a rectangle and use it to solve practical problems.
3D objects: Compare, describe and name prisms and pyramids
Compare properties of prisms and pyramids
Name prisms and pyramids according to the shape of their base
Three-dimensional spatial structure
Space & Measurement
AC9M6SP01 (Year 6 concept)
compare the parallel cross-sections of objects and recognise their relationships to right prisms
3D objects: Connect three-dimensional objects with two-dimensional representations
Visualise and sketch three-dimensional objects from different views, including top, front and side views
Examine a diagram to determine whether it is or is not the net of a closed 3-dimensional object
Visualise and sketch nets for given three-dimensional objects
Visualise and name prisms and pyramids, given representations of their nets
AC9M5SP01
connect objects to their nets and build objects from their nets using spatial and geometric reasoning
Volume: Choose appropriate units of measurement for capacity
Select and use appropriate units to measure the capacities of a variety of containers
AC9M5SP01
connect objects to their nets and build objects from their nets using spatial and geometric reasoning
Volume: Use displacement to investigate volumes of irregular solids
Recognise that an object’s volume takes up space by observing the change in water level when an object is placed in a container of water
Compare the volumes of 2 or more objects by marking the change in water level when each is submerged in a container
AC9M5SP01
connect objects to their nets and build objects from their nets using spatial and geometric reasoning
Volume: Connect decimal representations to the metric system
Recognise the equivalence of whole-number and decimal representations of measurements of capacities
Interpret decimal notation for capacities
Record measurements to 3 decimal places
AC9M5SP01
connect objects to their nets and build objects from their nets using spatial and geometric reasoning
Mass: Choose appropriate units of measurement for mass
Identify the appropriate unit and device to measure mass
Recognise situations where mass would be measured in thousands of kilograms or tonnes (t)
Non-spatial Measure
AC9M6M01 (Year 6 concept)
convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem
Measurement
Mass: Connect decimal representations to the metric system
Recognise the equivalence of whole-number and decimal representations of measurements of mass
Interpret decimal notation for masses
Measure mass using scales and record using decimal notation of up to 3 decimal places
AC9M6M01 (Year 6 concept)
convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem
Time: Compare 12- and 24-hour time systems and convert between them
Recognise that 24-hour time is used to avoid confusion between am and pm
Read time using appropriate 24-hour time language
Convert between 24-hour time and 12-hour time using am or pm notation
Read, interpret and use timetables from real-life situations, involving 12- and 24-hour time
AC9M5M03
compare 12- and 24-hour time systems and solve practical problems involving the conversion between them
Collect categorical and discrete numerical data by observation or survey
Pose and refine questions to construct a survey to obtain categorical or discrete numerical data about a matter of interest
Collect ordinal or nominal categorical data, and discrete numerical data through observation or by conducting surveys
Data
AC9M5ST01
acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables, to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data
AC9M5ST02
interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made
AC9M5ST03
plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation
Choose and use appropriate tables and graphs
Tabulate collected data with and without the use of digital technologies such as spreadsheets
Recognise which types of data display are appropriate to represent data (Statistical reasoning)
Determine an appropriate scale (horizontal and vertical) to represent the data
Construct column graphs using a many-to-one scale, with and without the use of digital technologies
Draw an accurate timeline using an appropriate scale
AC9M5ST01
acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables, to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data
AC9M5ST03
plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation
Statistics
Describe and interpret different datasets in context
Interpret line graphs using the scales on the axes
Describe and interpret data presented in tables, column graphs and line graphs
Determine the total number of data values represented in column graphs
AC9M5ST01
acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables, to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data
AC9M5ST02
interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made
AC9M5ST03
plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation
List outcomes of chance experiments involving equally likely outcomes and represent probabilities
Use the term probability to describe the numerical value that represents the likelihood of an outcome of a chance experiment
Recognise that outcomes are described as equally likely when any one outcome has the same chance of occurring as any other outcome
Record all outcomes in chance experiments where each outcome is equally likely to occur
Represent probabilities of outcomes of chance experiments using fractions
Establish that the total of the probabilities of the outcomes of a chance experiment equals one
Discuss the imprecise meaning of commonly used chance words including possible, likely and unlikely
Chance
AC9M5P01
list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely
AC9M5P02
conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results; use frequency to compare outcomes and estimate their likelihoods
Probability
It’s a lot, right?
Don’t worry … MathsBites walks you through every single one, so that you are:
clear on exactly what your child is learning and how to help using the language and strategies they’ll use in class
ready to help them work with the maths concepts that are a part of their everyday lives
prepared, so when they get ‘stuck’, you can help them through
proactive rather than reactive.
