Download Year 5 Maths Term 1 (Word, 64 KB)

Mathematics Unit – Term 1 - Year 5
Unit Outline
In this unit students apply a variety of mathematical concepts in real-life, lifelike and purely mathematical situations.
Unit 1:
Students develop understandings of:
Number and place value — make connections between factors and multiples, identify numbers that have 2, 3, 5 or 10 as factors, round & estimate whole numbers, represent multiplication using the split &
compensate strategy, choose appropriate procedures to represent the split & compensate strategy of multiplication, use a written strategy to add & subtract, round & estimate to check the reasonableness of
answers, explore mental computation strategies for division, solve problems using mental computation strategies & informal recording methods, compare & evaluate strategies that are appropriate to different
problems, make generalisations.
Fractions and decimals — use models to represent fractions, count on & count back using unit fractions, identify & compare unit fractions using a range of representations & solve problems using unit fractions, add &
subtract simple fractions with the same denominator.
Using units of measurement — investigate time, read & represent 24-hour time, measure dimensions, estimate & measure the perimeters of rectangles, investigate metric units of area measurement, estimate &
calculate area of rectangles.
Data representation & interpretation — define numerical & categorical data, generate sample questions, explain why data is either numerical or categorical, explore why data is collected, choose appropriate methods
to record data, interpret data, generalise by composing summary statements about data.
Chance — identify & describe possible outcomes, describe equally likely outcomes, represent probabilities of outcomes using fractions, conduct a chance experiment & investigate the fairness of a game.
Year 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.
At this year level:
Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making
reasonable estimations
Fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric
units, and interpreting timetables
Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles
Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance experiments may
differ from expected results
Content Descriptors
Measurement and Geometry
Number and Algebra
Statistics and Probability
Using units of measurement
• Choose appropriate units of measurement for length, area, volume,
capacity and mass (ACMMG108)
• Calculate the perimeter and area of rectangles using familiar metric units
(ACMMG109)
• Compare 12- and 24-hour time systems and convert between them
(ACMMG110)
Number and place value
• Identify and describe factors and multiples of whole numbers and use
them to solve problems (ACMNA098)
• Use estimation and rounding to check the reasonableness of answers
to calculations (ACMNA099)
• Solve problems involving multiplication of large numbers by one- or
two-digit numbers using efficient mental, written strategies and
appropriate digital technologies (ACMNA100)
• Solve problems involving division by a one digit number, including
those that result in a remainder (ACMNA101)
• Use efficient mental and written strategies and apply appropriate
digital technologies to solve problems (ACMNA291)
Chance
• List outcomes of chance experiments involving equally likely outcomes
and represent probabilities of those outcomes using fractions
(ACMSP116)
Fractions and decimals
• Compare and order common unit fractions and locate and represent
them on a number line (ACMNA102)
• Investigate strategies to solve problems involving addition and
subtraction of fractions with the same denominator (ACMNA103)
Data Representation and Interpretation
• Pose questions and collect categorical or numerical data by
observation or survey (ACMSP118)
• Construct displays, including column graphs, dot plots and tables,
appropriate for data type, with and without the use of digital
technologies (ACMSP119)
• Describe and interpret different data sets in context (ACMSP120)
Achievement Standard
Year 4
In these units, assessment of student learning aligns to the following
components of the Achievement Standard.
Year 5
In these units, assessment of student learning aligns to the following
components of the Achievement Standard.
Year 6
In these units, assessment of student learning aligns to the following
components of the Achievement Standard.
By the end of Year 4, students choose appropriate strategies for calculations
involving multiplication and division.
They recognise common equivalent fractions in familiar contexts and make
connections between fraction and decimal notations up to two decimal places.
Students solve simple purchasing problems.
They identify unknown quantities in number sentences.
They describe number patterns resulting from multiplication.
Students compare areas of regular and irregular shapes using informal units.
They solve problems involving time duration.
They interpret information contained in maps.
Students identify dependent and independent events.
They describe different methods for data collection and representation, and
evaluate their effectiveness.
Students use the properties of odd and even numbers.
They recall multiplication facts to 10 x 10 and related division facts.
Students locate familiar fractions on a number line.
They continue number sequences involving multiples of single digit numbers.
Students use scaled instruments to measure temperatures, lengths, shapes and
objects.
They convert between units of time.
Students create symmetrical shapes and patterns.
They classify angles in relation to a right angle.
Students list the probabilities of everyday events.
They construct data displays from given or collected data.
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 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 compare and 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 find unknown quantities in number sentences.
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.
By the end of Year 6, students recognise the properties of prime, composite,
square and triangular numbers.
They describe the use of integers in everyday contexts.
They solve problems involving all four operations with whole numbers.
Students connect fractions, decimals and percentages as different
representations of the same number.
They solve problems involving the addition and subtraction of related fractions.
Students make connections between the powers of 10 and the multiplication
and division of decimals.
They describe rules used in sequences involving whole numbers, fractions and
decimals.
Students connect decimal representations to the metric system and choose
appropriate units of measurement to perform a calculation.
They make connections between capacity and volume.
They solve problems involving length and area.
They interpret timetables. Students describe combinations of transformations.
They solve problems using the properties of angles.
Students compare observed and expected frequencies.
They interpret and compare a variety of data displays including those displays
for two categorical variables.
They evaluate secondary data displayed in the media.
Students locate fractions and integers on a number line.
They calculate a simple fraction of a quantity.
They add, subtract and multiply decimals and divide decimals where the result is
rational.
Students calculate common percentage discounts on sale items.
They write correct number sentences using brackets and order of operations.
Students locate an ordered pair in any one of the four quadrants on the
Cartesian plane.
They construct simple prisms and pyramids.
Students list and communicate probabilities using simple fractions, decimals and
percentages.
Assessment
Students will complete THREE assessment pieces throughout the units.
Digging into data (Short answer questions) Students classify and interpret data and pose questions to gather data.
Multiplicative reasoning and fractions (Short answer questions) Students solve multiplication and division problems by efficiently and accurately applying a range of strategies, checking the reasonableness of answers using estimation and
rounding. They locate, represent, compare and order fractions and add and subtract fractions with the same denominator.
Chance mathematical guided inquiry (optional) (Assignment/Project) Students use simple strategies to reason and solve a chance inquiry question.
Additional Comments and Adjustments
In addition to completing the concepts covered throughout the term, it is important that NUMBER CONCEPTS eg number facts, algorithms and place value, rounding and terminology; are covered on a weekly basis to consolidate skills and
understanding.
Teaching Sequence
WALT
WILF
1

Investigate
multiples of 2, 3, 5 and
10.

Develop
understanding of the
relationship between
factors and multiples.

Identify
numbers that have 2, 3, 5
or 10 as factors.

Recall
multiplication and
division facts.

Use rounding to
estimate answers to
calculations.

Estimate
answers to calculations
to check for
reasonableness

Practice using
the split strategy for
calculating answers to
multiplication problems.

Record
multiples of 2, 3, 5 and
10?

Identify
common multiples?

Explain the
relationship between a
number and its multiples?

Use a range of
strategies to identify all
the factors of given
numbers?

Identify
common factors?

Round numbers
to the nearest ten or
hundred?

Apply rounding
to estimate answers to
calculations?

Recall
multiplication and
division facts?

communicate
how to apply the Split
strategy to solve
multiplication problems?
Vocabulary
2
Vocabulary

estimate
answers to calculations
to check for
reasonableness of
answers

practise using
the compensate strategy
for calculating answers to
multiplication

choose an
efficient and effective
strategy to solve
multiplication problems.

apply rounding
and estimation to check
for reasonableness of
answers

apply the left to
right written method to
calculate addition

apply the left to
right written method to
calculate subtraction

Observe region
models before making
mathematical statements
about the size of the unit
fractions.

Use models and
benchmark fractions to
compare and order
fractions.

communicate
how to apply the
compensate strategy to
solve multiplication and
division problems?

reflect on
strategies used to select
the more efficient and
effective method?

apply the left to
right method to solve
problems?

Identify the
larger or smaller of a pair
of fractions, justifying
their selection?

Compare region
models and reasons why
one model represents a
fraction that is greater
than or less than another
fraction?

Determine a
unit fraction of a
collection?

Recognise that
by determining a unit
fraction of a collection
other fractional amounts
can be calculated?

identify the
larger or smaller of a pair
TIB
LOCATION & TRANSFORMATION
LESSON FOCUS
Unit 1: Lesson 1 — Exploring multiples of whole numbers
Example learning sequence
Establish learning context
Investigate multiples of 2, 3, 5 and 10
Explore common multiples
Unit 1: Lesson 2 — Exploring factors of whole numbers
Example learning sequence
Establish learning context
Investigate factors of numbers to 100
Explore divisibility rules for 2, 3, 5 and 10
Unit 1: Lesson 3 — Using rounding and estimating of whole numbers
Example learning sequence
Establish learning context
Practise multiplication and division facts
Explore estimation and rounding of whole numbers
Apply rounding to estimate answers
Unit 1: Lesson 4 — Using the split strategy to multiply
Example learning sequence
Establish learning sequence
Apply a specific strategy to solve multiplication
Unit 1: Lessons 6 and 7 — Using the compensate strategy to multiply
Example learning sequence
Establish learning context
Apply a specific strategy to solve multiplication
Apply a strategy to solve multiplication problems.
Unit 1: Lesson 8 — Using a written strategy for addition and subtraction
Example learning sequence
Establish learning context
Apply the left to right place value method to solve addition
Apply the left to right place value method to solve subtraction.
Unit 1: Lesson 9 — Using region models to problem solve
Example learning sequence
Establish learning context
Compare unit fractions using region models
Order sets of unit fractions
Unit 1: Lesson 11 — Investigating fractions of a collection
Example learning sequence
Establish learning context
Unit fractions of collections
Compare unit fractions of a collection
Solve word problems involving unit fractions
Lower Adjustments
Higher Adjustments
RESOURCES
3
Vocabulary

Use models to
solve problems involving
unit fractions.

Partition
collections into equal
parts to identify a unit
fraction of a quantity.

Develop
strategies to find a
fraction of a quantity by
determining the unit
fraction.

compare and
order unit fractions.
of fractions, justifying
their selection?

order unit
fractions and place on a
number line?

Develop
strategies to locate
proper fractions on a
number line.

Compare and
order fractions using
benchmarks on a number
line.

Solve
comparison problems
using understanding of
unit fractions.

Name and
locate fractions on a
number line by using only
number line divisions to
determine a fraction
name.

Name fractions
and locate fractions that
are a unit fraction greater
than one on number
lines.

establish an
understanding of the
purpose and definition of
‘data’

Distinguish
between numerical and
categorical types of data.

read, interpret
and answer questions
about data presented in
column graphs

Present data as
a column graph.

read, interpret
and answer questions
about data presented in
dot plots

present data as
a dot plot

Recognise the
distance between zero
and one as a unit?

Identify that a
unit can be subdivided
into fractional parts?

Identify unit
fractions on a number
line?

Describe the
relationship between
benchmark fractions such
as 1-half and other unit
fractions?

Locate and
describe a whole as 2halves, 3-thirds, 4-fourths
and so on?

Count on by a
unit fraction beyond one?

Identify and
name fractions that are a
unit fraction greater than
one?

Explain the
intent of data?

Classify data as
categorical or numerical?

identify and
organise data

Locate data
within column graphs to
answer questions?

Present data as
a column graph and draw
conclusions from the
data?

Locate data
within dot plots?

Present data as
a dot plot according to
recognised conventions
and draw conclusions
form the presented data?

Pose questions
to clarify and interpret
information?
Unit 1: Lesson 12 — Comparing and ordering unit fractions using a
number line
Example learning sequence
Establish learning sequence
Compare pairs of fractions
Order sets of unit fractions
Unit 1: Lessons 13 and 14 — Comparing and ordering unit fractions to
solve problems
Example learning sequence
Establish learning context
Identify and order fractions on a number line
Apply benchmarks 0, 1-tenth, 1-half and 1 to compare and order a
fraction
Counting unit fractions
Represent, compare and reason about fractions on a number line
Unit 1: Lesson 16 — Investigating fractions greater than one
Example learning sequence
Establish learning context
Order and compare fractions on a number line
Identify and model numbers greater than one but less than two
Unit 1: Lesson 17 — Defining data
Example learning sequence
Establish learning sequence
Investigate different types of data
Distinguish between numerical and categorical data
Collect data.
Unit 1: Lesson 19 — Interpreting and creating column graphs
Example learning sequence
Establish learning context
Link questions posed to data types
Interpret column graphs
Present data in column graphs
Unit 1: Lesson 21 — Interpreting and creating dot plots
Example learning sequence
Establish learning context
Interpret dot plots
Present data in dot plots
4

Vocabulary
apply digital
technologies to
manipulate,
organise and
present data as
tables, column
graphs and dot
plots.


organise data
using digital
technologies to
create tables,
column graphs and
dot plots?
generate
statements about
data presented in
dot plots and
column graphs?
manage and
operate ICT to
present data?
Example assessment
sequence



5
Vocabulary







use fractions to
represent the
likelihood of an event
occurring.
Apply understandings
of probability and
data collection to
conduct a
Mathematical guided
inquiry to investigate
the fairness of a
game.
recall multiplication
and division facts
use rounding to
estimate answers to
calculations.
apply rounding to
estimate answers to
division apply
rounding to estimate
answers to
calculations.
consolidate skills
required for recall of
division fact families
apply rounding to
estimate answers to
division calculations.








Unit 1: Lessons 22 and 23 — Presenting data using digital
technologies
Example learning sequence



Establish learning context
Create column graphs using digital technology
Create dot plots using digital technology
Unit 1: Lesson 24 — Assessing learning – Digging into data
Example assessment sequence



Introduce and review the assessment
Review the Guide to making judgments and understand the
standards A–E
Conduct the assessment
Introduce and
review the
assessment
Review the Guide
to making
judgments and
understand the
standards A–E
Conduct the
assessment
identify all possible
outcomes in chance
experiments?
describe the
probability of
outcomes occurring
using fractions?
describe chance
experiments using
the language of
chance?
Discuss and
demonstrate
understanding of and
reason for chance
applications and
values in
mathematical and
authentic contexts?
round numbers to the
nearest ten or
hundred?
apply rounding to
estimate answers to
calculations?
recall the answers to
multiplication and
division facts families
articulate how to
apply a strategy to
solve division
problems?
Unit 2: Lesson 1 — Identifying outcomes using fractions
Example learning sequence


Establish learning context
Describe the probability of outcomes occurring
Represent probabilities of outcomes using fractions
Unit 2: Lessons 2-4 — Conducting a chance experiment
Example learning sequence

Establish learning context

Consider the game (DISCOVER)

Review the Mathematical guided inquiry process (DISCOVER)

Prepare to implement (DEVISE)

Develop responses (DEVELOP)

Present inquiry responses (DEFEND)
Explore further learning opportunities (DIVERGE)
Unit 2: Lesson 6 — Exploring rounding and estimating with
whole numbers
Example learning sequence

Establish learning context

Practise multiplication and division facts

Explore estimation and rounding.
Apply rounding to estimate answers.
Unit 2: Lesson 7 — Using the Split strategy to divide
Example learning sequence

Establish learning context
Apply a specific strategy to solve division
6

Vocabulary





7
Vocabulary
Apply rounding to
estimate answers
to calculations to
check for
reasonableness of
answers.
Practise using a
strategy for
calculating
answers to division
problems.
Compare, count,
order and add
proper fractions.
Represent unit
fractions using
materials and
diagrams.
Solve subtraction
of fractions with
the same
denominators.
solve problems
involving
multiplication by
one- digit number
and division by
one- digit numbers,
using efficient
mental and written
strategies and
checking for
reasonableness of
answers; to
compare and order
common unit
fractions and
locate and
represent them on
a number line

read and show
analogue and digital
times

Identify am and
pm times.

Make
connections between 12and 24-hour time.

Relate 24-hour
time to everyday events.

Read and
represent 24-hour times.

Convert
between 12- and 24-hour
times.







Articulate how to
apply a strategy to
solve division
problems?
Identify larger or
smaller fractions
using benchmark
fractions?
Solve addition
problems that
involve concepts
relating to unit
fractions?
Model adding
fractions using
models and/or
number lines?
Identify larger or
smaller fractions
using benchmark
fractions?
Solve subtraction
problems that
involve concepts
relating to unit
fractions?
Model subtracting
fractions using
models and/or
number lines?
Unit 2: Lesson 8 — Using the Compensate strategy to divide
(Include parts of Lesson 9)
Example learning sequence



Establish learning context
Explore strategies for solving division problems
Apply strategies to solve problems
Unit 2: Lesson 11 —Adding fractions (Include parts of Lesson
13)
Example learning sequence




Establish learning context
Compare and order common unit fractions
Count on and count back using fractions
Add fractions with the same denominator
Add fractions in problem situations
Unit 2: Lesson 12 —Subtracting fractions (Include parts of
Lesson 13)
Example learning sequence





Establish learning context
Compare and order common unit fractions
Count on and count back using fractions
Subtracting fractions with the same denominator
Adding and subtracting fractions in problem situations
Subtract fractions in problem situations
Unit 2: Lesson 14 — Assessing learning — Multiplicative reasoning and
fractions
Example assessment sequence
•
Introduce and review the assessment
•
Review the Guide to making judgments and understand the
standards A–E
•
Conduct the assessment

Read and show
times on analogue and
digital clocks?

Convert
between digital and
analogue times?

Distinguish
between am and pm
times?

Relate whole
hours in 24-hour time to
am or pm times?

Read and
represent 24-hour times?

Convert am and
pm times to 24-hour
time?
Unit 2: Lessons 16 and 17 — Measuring time
Example learning sequence
Establish learning context
Investigate measuring time
Identify am and pm times
Convert between analogue and digital time
Unit 2: Lesson 18 — Investigating 24-hour time
Example learning sequence
Establish learning context
Investigate the concept of 24-hour time
Convert simple 24-hour time
Compare 24-hour time to times of day
Unit 2: Lesson 19 — Reading and representing 24-hour time
Example learning sequence
Establish learning context
Explore minutes in 24-hour time
Convert between 12- and 24-hour time
Measure time
8
Vocabulary
9
Vocabulary
10
Vocabulary

Make
connections between the
boundary of a shape and
the term ‘perimeter’

Estimate and
measure the perimeters
of rectangles using
informal units.

Measure the
dimensions of rectangles
(including squares) in the
environment.

Estimate and
measure the perimeters
of rectangles (including
squares) using metric
units.

Identify the
perimeter of closed
shapes?

Calculate the
perimeter of squares and
rectangles using informal
units?

Calculate the
perimeter of rectangles
(including squares) using
metric units?

Explain
method/s for calculating
perimeter?
Unit 2: Lesson 21 — Exploring perimeter
Example learning sequence
Establish learning context
Investigate perimeters of rectangles using informal units

Estimate and
measure the areas of
rectangles (including
squares) using informal
units.

Investigate the
metric units used for
measuring area.

Estimate and
measure the areas of
rectangles (including
squares) using metric
units.

Identify area as
the space inside a closed
shape?

Calculate the
area of rectangles
(including squares) using
informal units?

Identify the
metric units used to
measure area?

Calculate the
area of rectangles
(including squares) using
metric units?

Explain
method/s for calculating
area?
Unit 2: Lesson 23 — Exploring area
Example learning sequence
Establish learning context
Investigate areas of rectangles
Unit 2: Lesson 22 — Calculating perimeter
Example learning sequence
Establish learning context
Calculate perimeters of rectangles
Unit 2: Lesson 24 — Calculating area
Example learning sequence
Establish learning context
Calculate areas of rectangles
Calculate areas of rectangles (monitoring task)