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PIALBA STATE SCHOOL: MATHEMATICS YEAR 4 SEMESTER 1 UNIT 2 TERM 2 PLAN

Proficiency Strands

At this Year level:

• understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes

• fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data

• problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns

• reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

Pedagogical Practices Levering Digitally Learning Environments Learning PartnershipsPedagogical Practices are used to design, monitor and assess learning.

Leveraging digital accelerates access to knowledge beyond the classroom and cultivates student driven deep learning.

Learning Environments foster 24/7 interaction in trusting environments where students take responsibility for their learning.

Learning Partnerships are cultivated between and among students, teachers, families and the wider environment

Continual Feedback loop / monitoring

Deep Learning opportunities through open-ended questioning and tiered tasks using Collaboration: Elbow partners, small groups, whole class, Innovation Space, Computer lab.

Check in / Check out (thumbs up) strategies

Deep Learning Competency Focus: Collaboration Creativity Critical Thinking Citizenship Character Communication

Assessment (D – Diagnostic, M- Monitoring, S – Summative)Week D-F-S Assessment Title

Term 1 Week 10 D Show Me Term 2 Pre-Test

3 S Recall Multiplication / Division Facts

5 S Interpreting Maps, Angles.

6 M Investigation Distance on Maps

10 D Show Me Term 2 Post-TestShow Me Term 3 Pre-Test

Planning is sequenced across the Term or Semester. Timings of units are based on data and school timetabled events.

Key Learning Area: Maths

Year Level Team: Year 4 Term: 2Show Me Pre-test is to be completed, entered into Spreadsheet and

unpacked with Year Level teachers prior to the commencement of the UnitWalt / Wilf / Tib(The What)

Active learning Engagement(The How)C2C Lessons 1-11

Check for Understanding Differentiation ResourcesALL RESOURCES HAVE BEEN UPLOADED TO ONENOTE

Number and Place Value

#Warm Ups

Lesson 1#Activities – Exploring five-digit numbers

Recognise and read five-digit numbers• Consider place value and the repeated pattern.• Read five-digit numbers using place value.• Order numbers up to five digits in ascending and

descending order.• Investigate the cyclical pattern in which whole

numbers are said and written.

Make connections between representations of five-digit numbers• Represent and write five-digit numbers including those

with internal zeros on number expanders, number cards or place value charts.

• Write five-digit numbers in words.

Identify and describe the place value of digits in five-digit numbers• Recognise that five-digit numbers are made up of ten

thousands, thousands, hundreds, tens and ones, and the role of zero as a place holder in those numbers.

• Show place value understanding using models such as number expanders, place value charts and calculators.

• Describe the value of digits in large numbers:o Pose questions that prove understanding of

numbers, e.g. 82 008 — What is the value of each 8? How can I rearrange the digits to make the smallest possible number?

o How many times greater is the 5 in the thousands place than the 5 in the tens place? (e.g. 35 554.)

Monitor students’ ability to:

Represent numbers with materials

Learning alertsBe aware of:

Students representing five-digit numbers without fully understanding place value (e.g. recording fifty thousand and two as 50 000 2).

L2B

Allow 'wait time' for the student to process information

Explicitly teach the vocabulary to ensure the students have the required prior knowledge.

Plan for visual supports to instruction.

Break tasks into smaller, achievable steps.

Use small group instruction and cooperative learning strategies

Build fluency recognising, naming and partitioning place value parts of four-digit numbers before extending to five-digit numbers.

U2BReading calendars

Linking months of the year to seasons

Expose to more technical or specific Maths vocabulary.

Independent Work

Peer Instruction

Tiered tasks

Challenge students to choose any five-digit number and represent it in as many different ways as possible. Explain the connection between all representations.

Have students

C2C Maths Library:https://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-5cb2-4db6-8fd2-43d3563ffe8a/1/Mathematics_Library/index.html

ResourcesSupporting learning resource — Exploring five-digit numbers

Sheet — 5-digit number maker

Sheet — Place value chart: Hundreds of thousands

Sheet — Number expander with 10 thousands

calculators

Supporting learning resource — Mathematics tool kit Years 3–6

Supporting learning resource — Monitoring audit — by the end of Year 4

Languagethousands, hundreds, tens, ones, place value, digit, place, column

Walt: Recognise, read and represent five-digit numbers..

Wilf: Read and write five-digit numbers?Recognise the value of digits in five-digit numbers?

https://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-5cb2-4db6-8fd2-43d3563ffe8a/1/Mathematics_Library/index.html



Languagethousands, hundreds, tens, ones, place value, digit, number line, greater than, smaller than, column

Walt: Order and compare five-digit numbers.

Wilf: Identify numbers greater or less than a given number?

Use the symbols < and > to record information about numbers?

Order numbers on a number line?

Locate numbers on a number line?

Languagethousands, hundreds, tens, ones, place value, column, digit, standard, non-standard, partition

Walt: Represent five-digit numbers using partitioning.

Wilf:

Show standard five-digit place value partitioning?

Record standard place value partitions as number sentences?

Show non-standard five-digit place value partitioning?

#Warm Ups

Lesson 2#Activities – Ordering and comparing five-digit numbers

Compare numbers beyond 10 000• Write two or more five-digit numbers and identify

which is greater or smaller.• Record comparisons between 2 five-digit numbers

using the symbols < and >.• Represent and record numbers 10 000, 1 000, 100, 10,

1 greater or less than a given number, include numbers that bridge 10s, 100s, 1 000s and 10 000s.

Order five-digit numbers• Sequence numbers and create number lines to show

their order.• Locate numbers on number lines relative to zero and

relative to each other and explain reasoning. For example, identify and mark a number on the number line that is 10 more than a number or name and mark a number halfway between two numbers.

#Warm Ups

Lesson 3#Activities – Partitioning five-digit numbers

Partition five-digit numbers into standard place value parts• Record standard place value partitions as number

sentences, e.g. 12 357 = 10 000 + 2 000 + 300 + 50 + 7.• Identify numbers from expanded number sentences,

e.g. 400 + 10 + 3 000 + 8 + 20 000 = ?

Partition five-digit numbers into non-standard place value parts

Monitor students’ ability to:Know which number is larger/smaller.

Learning alertsBe aware of:Students not having a sense of the order and magnitude of numbers.


Represent numbers using non-standard partitioning.


Students having a limited understanding of partitioning larger numbers.

Provide opportunities to count and sequence numbers, include sequences that bridge the tens, hundreds, thousands and ten thousands.

Use MAB base 10 materials and a place value chart to build an understanding of non-standard partitioning (e.g. 1 356 has 1 thousand, 2 hundreds, 15 tens, 6 ones and can be illustrated with materials).

create their own number lines and mark in mystery numbers using symbols. Swap number lines with a partner and work out the mystery numbers.

Challenge students to make sets of cards showing as many different non-standard partitions for the same five-digit number as possible.

ResourcesSupporting learning resource — Ordering and comparing five-digit numbersSheet — 0 to 9 digit cardsSheet — Number goalsticky notes, marker pens and playing cards

ResourcesSupporting learning resource — Partitioning five-digit numbersSheet — Number expander with 10 thousandsSheet — 5-digit number maker

Record non-standard place value partitions as number sentences?

Languagethousands, hundreds, tens, ones, place value, MAB, digit, standard, non-standard, partition, increasing/decreasing order, greater than, less than

Walt: Compare whole numbers using place value understanding.

Wilf:

Classify numbers using the symbols < and >?

Position numbers correctly along a number line?

Represent numbers using standard and non-standard five-digit place value partitioning?

Record standard and non-standard partitions as number sentences?

• Represent non-standard place value partitioning on a number expander, place value chart, number line or calculator.

• Construct and describe alternative ways of naming numbers using non-standard partitioning, e.g. 12 357 written on a number expander demonstrates how 123 hundreds, 57 ones or 1 235 tens, 7 ones are alternative ways of naming 12 357.

• Represent different non-standard partitioning representations as number sentences, e.g. 12 357 = 11 000 + 1 300 + 40 + 17; 12 300 + 57; 10 000 + 1 000 + 1 000 + 357.

• Represent and describe numbers in alternative ways using the same tool or materials.

#Warm Ups

Lesson 4#Activities – Applying place value understanding to five-digit numbers

Demonstrate place value understandings• Find examples of numbers with five-digits within

everyday contexts.• Represent numbers in different ways using number

cards, number expanders and/or place value charts.• Compare numbers with five-digits:

o use the smaller than (<) and greater than (>) signs to write and complete number sentences.

• Make observations and explain relationships between pairs of numbers. For example, this number is 10 times larger; this number is 4 hundreds and 2 tens smaller.

• Order sets of whole numbers with five-digits in ascending and descending order.

• Partition numbers with five-digits into standard and non-standard place value parts.


Represent, order and partition numbers into place value and non-standard parts.


Students not being able to represent and partition numbers in multiple ways.

Have students use number expanders to record alternative ways four-digit numbers can be written before progressing to naming and representing five-digit number.

Build fluency in

Challenge students to solve word problems using standard and non-standard partitioning, e.g. How many $100 notes do you need to make a total of $12 500?

In problem solving contexts, challenge students to

Supporting learning resource — Mathematics tool kit Years 3-6

ResourcesSupporting learning resource — Applying place value understandings to five-digit numbersSheet — Number expander with 10 thousandsSupporting learning resource — Mathematics tool kit Years 3-6Helpful informationText — Department of Education Western Australia (2013), First Steps in Mathematics: Number – Book 1http://det.wa.edu.au/stepsr

http://det.wa.edu.au/stepsresources/redirect/?oid=com.arsdigita.cms.contenttypes.FileStorageItem-id-13683969&stream_asset=true

Languagethousands, hundreds, tens, ones, place value, digit, place, column

Walt:

Recognise, read and represent numbers to 10 000 and beyond.

Locate numbers on a number line.

Compare and order numbers.

Use the symbols > or <.

Wilf:

Read and write numbers up to 10 000 and beyond?

Represent numbers using materials?

Identify the value of digits in five-digit numbers?

Languageaddition, add, sum, total, altogether, increase, more, plus, subtraction, minus, decrease, reduce, take away, less than, difference, fewer than, part-part-whole

Walt:

Solve addition and subtraction problems including word problems.

#Warm Ups

Lesson 5#Activities – Working with five-digit numbers

Consolidate place value understanding of five-digit numbers• Demonstrate place value understanding using

materials, e.g. number expanders, number sliders or place value charts.

• Locate numbers on a number line relative to zero and each other.

• Explain the value of digits in different places, e.g. ask students to explain the value of the digit 5 in 13 527 and 15 372.

Compare and order five-digit numbers• Describe which five-digit number is larger or smaller.• Compare pairs of numbers using the symbols > or <.• Sequence and order numbers using place value

understanding.

Read, write and count five-digit numbers• Use ICT to read and write numbers.• Investigate and create counting sequence using ICT.

#Warm Ups

Lesson 6#Activities – Solving addition and subtraction problems

Recall addition and subtraction number facts• Practise addition and subtraction facts.• Develop the inverse relationship between addition and

subtraction.• Apply understanding of odd and even number

relationships when performing addition and subtraction.


Outline larger or smaller numbers and have them explain how they know this.


Students not having a sense of the order of magnitude of numbers.

Monitor students’ ability to:Use strategies to solve addition and subtraction problems of whole numbers up to four digits.


Students who lack accuracy or fluency with addition and subtraction facts.

Students with limited strategies in solving addition and subtraction problems.

recognising and naming four-digit numbers before extending to five-digit numbers.

Explore additive thinking strategies and provide opportunities to practise and build fluency.

sequence a series of five-digit numbers on a number line.

Challenge students to discuss and explain how they solve problems and to compare and evaluate the efficiency of their methods.

esources/redirect/?oid=com.arsdigita.cms.contenttypes.FileStorageItem-id-13683969&stream_asset=true

Understanding whole and decimal numbers, Key understanding 3

ResourcesSupporting learning resource — Working with five-digit numbersLearning object — Number sliderSheet — Number expander with 10 thousandsSheet — 0 to 9 digit cardsSheet — 5-digit number makerfive-digit numbers written on cardscalculatorblank cards



Wilf:

Solve addition and subtraction problems using a range of strategies?

Apply generalisations of odd and even numbers to check calculations?

Languagecommutativity, multiples, multiply, multiplication, divide, division, fact family, round, calculation, split, compensate

Walt: Solve multiplication and division problems including word problems.

Wilf: Recall multiplication facts accurately?

Apply multiplication facts to complete extended facts?

Solve multiplication and division problems?

Solve addition problems• Choose efficient strategies to add.• Apply the understanding of odd and even

combinations to check accuracy of calculations.• Solve addition word problems in context.

Solve subtraction problems• Choose efficient strategies to subtract.• Apply the understanding of odd and even

combinations to check accuracy of calculations.• Solve subtraction word problems in context.

#Warm Ups

Lesson 7#Activities – Solving multiplication and division problems

Practise recalling multiplication facts• Use efficient strategies to recall multiplication facts to

10 x 10 and related division facts.• Apply the commutative principle to known

multiplication fact families, e.g. 8 x 5 = 40, 5 x 8 = 40.• Apply recall of multiplication facts to determine

related division facts, e.g. 5 x 8 = 40, 40 ÷ 8 = 5, 40 ÷ 5 = 8.

• Consider patterns that emerge from increasing the magnitude of numbers by a factor of 10, e.g. 5 x 8 = 40, 50 x 8 = 400.

• Apply known multiplication facts to recall extension facts.

Use efficient strategies to solve multiplication problems• Apply computation strategies to solve problems.• Solve multiplication problems.

Use efficient strategies to solve division problems• Apply computation strategies to solve problems.• Solve division problems.

Monitor students’ ability to:Use strategies to recall multiplicative facts.

Learning alertsBe aware of:Students lacking accuracy or fluency when recalling multiplicative facts.

Use materials, such as counters, to illustrate the commutative property (turnaround) or establish the thinking used to recall multiplicative facts.

Students use

Challenge students to solve multiplication or division problems with larger numbers using a range of strategies, and compare the efficiency of each method.

Have students create ‘Who am I?’ number puzzles using

ResourcesSupporting learning resource — Mathematics tool kit Years 3-6Supporting learning resource — Solving addition and subtraction problemsSheet — Blot out factsSheet — 0 to 9 digit cardsSheet — Big Ron’s car emporiumLearning object — Becoming a better problem solverSheet — 'Becoming a better problem solver' posterSheet — Game card: Stealing numbersCalculators

ResourcesSupporting learning resource — Solving multiplication and division problems

Languageodd, even, value, digit, zero, patterns, consecutive numbers, properties, divisible, operations

Walt: Form generalisations about odd and even numbers.

Investigate patterns and relationships relating to odd and even numbers.

Wilf: Identify odd and even numbers and discuss their properties?

Comprehend language associated with odd and even concepts?

Languageodd, even, value, digit, zero, patterns, consecutive numbers, properties, divisible, operations, addition, subtraction

Walt: Investigate and apply understandings about the properties of odd and even numbers when performing addition and subtraction.

#Warm Ups

Lesson 8#Activities – Identifying properties of odd and even numbers

Identify odd and even numbers• Sort and classify numbers as odd or even.• Form generalisations about odd and even numbers:

o Numbers can be classified using their properties.o A number can be odd or even.o We can prove a number is odd or even by making a

pattern, e.g.

4 is even 3 is oddo An even number can be shown as pairs. That

means they can be divided evenly by 2.o An odd number is not shown as pairs.

• Prove numbers to be odd or even using materials, e.g. counters.

Investigate how odd and even numbers are used• Apply generalisations about odd and even numbers.• Investigate odd/even rationing numbers.

#Warm Ups

Lesson 9#Activities – Using the properties of odd and even numbers in addition and subtraction

Investigate the properties of odd and even numbers when adding and subtracting• Identify unknown numbers from clues about number

properties.

Monitor students’ ability to:Identify and sort numbers according to whether they are odd or even.

Learning alertsBe aware of:Students identifying odd or even numbers using visible features without considering the properties of odd or even numbers.


Use the properties of odd and even numbers when adding or subtracting.


Students misunderstanding the generalisations of adding or subtracting odd and even numbers.

materials such as counters or bundling materials to prove or disprove if a number is divisible by 2.

Use counters and ten frames to illustrate and describe the concepts, relationships and generalities of adding and subtracting odd and even numbers.

clues that incorporate number properties such as odd and even numbers.

Provide problems with three or more addends for students to apply their understandings of odd and even relationships to and to make predictions about unknown answers..

Learning object — Becoming a better problem solverLearning object — Number sliderSlideshow — Multiplication facts (5s)Slideshow — Multiplication facts (8s)Slideshow — Extension multiplication facts starring Goldie GiraffeSheet — Multiplication pathway: EightSheet — Multiply or divide?Sheet — Monsters in a row gamecalculators10-sided diceLearning object — Tren's alien pet shop

ResourcesSupporting learning resource — Identify properties of odd and even numbersLearning object — Sorting odd and even numbersLearning object — Odd and evenSheet — Investigating odd/even rationingsticky notes or flashcards of numbers 0–40, T chart, counters, 100 charts, calculator

Wilf:


Apply generalisations about the structure and properties of odd and even numbers to check the accuracy of addition and subtraction?

Languageodd, even, value, digit, zero, patterns, consecutive numbers, properties, divisible, operations, multiplication, division

Walt:

Investigate and apply understandings about the properties of odd and even numbers when performing multiplication or division

Wilf:


Apply number relationships to check the accuracy of operations?

• Pose questions to help students form conjectures about adding odd and even numbers using the generalisations formed previously.o What is the result when you add an odd and an

even number?o Is there a way to prove that your conjecture is

true?o Will it work every time?

• Extend conjectures to include what the sum will be when three odd numbers are added together.

• Investigate what happens when the operation is changed to subtraction.o Do the same results apply as in addition?

• Make predictions and investigate subtraction with combinations of odd and even numbers.

Add and subtract odd and even numbers• Solve number problems involving addition with

combinations of odd and even numbers.• Solve number problems involving subtraction with

combinations of odd and even numbers.• Use established relationships to check accuracy of

calculations.

#Warm Ups

Lesson 10

#Activities – Using the properties of odd and even numbers in multiplication and division

Investigate the properties of odd and even numbers using multiplication and division• Identify unknown numbers from clues about number

properties.• Pose questions to help students form conjectures

about multiplying odd and even numbers.o What is the result when you multiply an odd and

an even number?o Is there a way to prove that your conjecture is

true?o Will it work every time?


Use the properties of odd and even numbers when multiplying and dividing.


Students misunderstanding the generalisations of multiplying or dividing odd and even numbers.

Use bundling materials and place value charts to illustrate and describe the concepts, relationships and generalities of multiplying and dividing odd and even numbers.

Have students create a digital presentation about odd and even numbers and the generalities of multiplying and dividing odd and even numbers.

ResourcesSupporting learning resource — Using the properties of odd and even numbers in addition and subtractionLearning object — Sorting odd and even numbersSlideshow — Odd or even numbers?Sheet — 20 frame or double 10 framecounterscalculators

• Investigate what happens when the operation is changed to division.o Do the same results apply as in multiplication?

• Make predictions and investigate division with combinations of odd and even numbers.

Multiply and divide odd and even numbers• Solve number problems involving multiplication with

combinations of odd and even numbers.• Solve number problems involving division with

combinations of odd and even numbers.• Discuss and apply conjectures about the properties of

odd and even numbers to check accuracy of calculations.

Lesson 11

#Activities – Number and place value —

Assessing student learning

Understand the assessment• Review the separate sections of the assessment and

ensure students understand what they are expected to do.

Review the Guide to making judgments and understand the standards A–E• Work through the Guide to making judgments with

students and highlight the assessable elements for the assessment and discuss what responses might look like at each of the standards A–E.

• Provide students with an opportunity to clarify any components of the assessment.

Conduct the assessment• Distribute the assessment task to students and ask

them to not commence work until signalled.• Explain to students that they may work in any order.• Signal to students to commence work.

Assessment purpose

To use the relationships between the four operations and odd and even numbers.

ResourcesSupporting learning resource — Using the properties of odd and even numbers in multiplication and divisionSlideshow — Investigating the division of odd and even numberscounters, calculators, playing cards

ResourcesAssessment task — Using the properties of odd and even numbers Assessment task — Using the properties of odd and even numbers: Model response





Active learning Engagement(The How)C2C Lessons 22 - 25

Check for Understanding

Differentiation ResourcesALL RESOURCES HAVE BEEN UPLOADED TO ONENOTE

Location and transformation

#Warm Ups

Lesson 22Location and transformation — Describing location on simple maps and plans #Activities

Establish learning context• Consider the objective of the lesson.• Review the language associated with maps and plans.• Investigate words and phrases commonly used in mapping.

Investigate the features on maps and plans• Identify and describe features found on maps and plans, such as

mountains, hospitals and major landmarks.

Monitor students’ ability to:Use symbols in their legend and give reasons for their use.Use mathematical language when finding locations and describing pathways.

Learning alertsBe aware of:Students referring to symbols in legends by their everyday name rather than the

L2B



Plan for visual supports to instruction.

Break tasks into smaller, achievable steps.

U2B


Compact the curriculum where possible.

Independent Work

Peer Instruction

Tiered tasks

Students create a legend for a world


ResourcesSupporting learning resource — Describing location on simple mapsSheet — Sunny Park School evacuation plan

Languagereflect, flip, line of symmetry, diagonal, single, multiple, infinite, similar, congruent, two-dimensional shape, angle, side, translate, slide, direction, vertical, horizontal, element

Walt: Review and describe reflection symmetry in two-dimensional shapes.




Create shapes and designs containing reflection symmetry.Investigate and design patterns produced using translation symmetry.

Wilf: Identify lines of symmetry in two-dimensional shapes?

Describe reflection symmetry in two-dimensional shapes?

Create a shape that contains reflection symmetry?

Identify examples of translation symmetry?Create designs or patterns based on translation symmetry?

Languagelegends, symbols, scale, cardinal compass points, compass rose, bird’s-eye view

Walt: Use a compass to describe directions.

Give and follow directions using turns and compass points.

• Compare information found in a variety of maps and plans. This could include city maps, street directories, treasure maps, maps from an atlas and GPS.

• Match symbols with the features that they represent.

Identify the need for legends• Explore reasons for similarities and differences in symbols used

on maps and plans, e.g. people from foreign countries know what a symbol represents, or the use of a common language to find different locations.

• Draw and represent symbols tourists might find helpful on maps.• Create a legend containing symbols that would be used on a

school map and justify reasons for including particular symbols.

Find locations using turns and everyday directional language• Investigate the meaning of the terms ‘clockwise’ and

‘anticlockwise’ by using the hands on an analog clock face to show full, half and quarter turns.

• Represent combinations of directional turns by asking students to move and turn appropriately using directional language.

• Use a map to give verbal and/or written directions to find locations/objects in the classroom or on a town map.

Draw simple plans with symbols and legends• Outline the features of a simple plan.• Draw and represent the main features of a theme park on a

simple plan.

#Warm Ups

Lesson 23Location and transformation — Using cardinal compass points #Activities

Identify the cardinal points of a compass• Identify the cardinal points shown on compasses.• Use compasses outside the classroom to locate north.• Describe the position of various features using cardinal points:

north, south, east and west.

feature they are intended to represent. For example, a student refers to a wave as a wave rather than understanding that it represents the beach.Students who don’t use a reference point to establish a location.Students who don’t realise that the orientation of an object can be dependent on the position of the viewer.

Monitor students’ ability to:Interpret and respond to directions involving the cardinal points of north, south, east and west.

Learning alertsBe aware of:Students not grasping the

Students match symbols with the features that they represent and then design alternative symbols to represent the same feature.

Students work in pairs to write a set of instructions to guide each other from their own desk to another point in the classroom or school.

Use a large image of a compass on the classroom floor to support the answering of directional questions, e.g. Which direction is the whiteboard? or

map and explain reasons for including particular symbols.Students draw up identical grids with a partner. On one grid the students draw any five shapes in different cells. Students take turns to verbalise directions (e.g. draw a square in the bottom right corner). The partner will reproduce the pattern on the empty grid.

Students investigate how Aboriginal communities and Torres Strait Islander communities use the cardinal compass points in their communities.

Learning object — Clocks: Analog and digitaldifferent examples of maps or plans to explorecity map of an Asian citycity map of an Australian rural townSupporting learning resource — Mathematics tool kit Years 3–6Helpful informationWebsite — OpenStreetMap (OpenStreetMap Foundation) https://www.openstreetmap.org/

Website — Year 4 Maths: Maps of Indian cities (Scoop.it Inc., Asia Education Foundation)http://www.scoop.it/t/year-4-maths-maps-of-indian-cities

Website — Year 4 Maths: Maps of South Korean cities (Scoop.it Inc., Asia Education Foundation)http://www.scoop.it/t/year-4-maths-maps-of-south-korean-citie

Website — Year 4 Maths: Maps of Thailand’s cities (Scoop.it Inc., Asia Education Foundation)http://www.scoop.it/t/year-4-maths-maps-of-thailand-s-cities

Resources

http://www.scoop.it/t/year-4-maths-maps-of-thailand-s-cities



http://www.scoop.it/t/year-4-maths-maps-of-south-korean-citie



http://www.scoop.it/t/year-4-maths-maps-of-indian-cities



https://www.openstreetmap.org/

https://www.openstreetmap.org/

Wilf: Identify the cardinal points on a compass?

Make connections between turns and compass directions?

Use compass points to locate positions and give directions?

Languagelegends, symbols, scale, cardinal compass points, compass rose, bird’s-eye view

Walt: Use scale to interpret basic maps and plans.

Give and follow directions that include the use of scale.

Wilf: Identify the relationship between the distances on paper and the distances on the ground?

Use scale when giving and following directions?

Languagelegends, symbols, scale, cardinal

• Identify south, east and west from a compass that displays north only.

Investigate compass directions on maps• Explore the inter-cardinal points of a compass: north-west,

north-east, south-east and south-west.• Use maps to locate places that use directional words as part of

their names, such as Western Australia, South Australia or the Northern Territory.

• Use compass points to give and follow directions in order to find locations, e.g. Which city is north of Sydney? What is the ocean south of the Indian Ocean? Where is the east coast of Australia?

• Find locations on a map using the inter-cardinal points of a compass.

#Warm Ups

Lesson 24 Location and transformation — Using scale on maps#Activities

Investigate the purpose of scale• Examine a simple scale where 1 cm on a plan or map represents

1 metre on the ground.• Represent objects placed in a 4 m x 4 m grid on centimetre grids.• Interpret maps/plans with a scale of 1 cm represents 1 m.

Apply scale to maps and plans• Use scale to estimate lengths and distances from maps.• Use scale to interpret maps and plans.

#Warm Ups

Lesson 25Shape — Identifying properties of three-dimensional objects

concept that a compass will always point north.

Monitor students’ ability to:Read and interpret scale on maps.

Learning alertsBe aware of:Students who don’t realise that all lengths of a shape need to be scaled.Suggested next steps for learningProvide students with grids to reduce a shape to a specific scale.

Monitor students’ ability to:Understand directional language

Which direction is the principal’s office?

Provide students with maps of places that they are familiar with..

Students use a grid map with

Ask students to draw a scaled map of a familiar place, e.g. their classroom.

Have students use a map of their local area

Supporting learning resource — Using cardinal compass pointsSheet — Map of Australiablindfoldcompassesanalog clock

ResourcesSupporting learning resource — Using scale on mapsSupporting learning resource — Mathematics tool kit Years 3-6Sheet — Classroom planSheet — Grid paper: 1 cmset of cards with paths drawn on 4 cm x 4 cm grids

compass points, compass rose, bird’s-eye view, aerial photograph, directional language

Walt: Find locations using direction, compass points, legends and scale.

Give instructions that use direction, compass points, legends and scale.

Wilf: Read and use combinations of direction, compass points, legends and scale to find locations and give and follow instructions?

Apply directional language in real-life contexts• Explore and interpret a variety of maps using simple scale.• Identify language and phrases associated with direction.• Use directional language to find locations and describe pathways

on maps. This could include maps from atlases, evacuation plans or a school map. Example scales are: 1 cm = 1 m or 1 cm = 1 km.

• Identify the different ways scale is recorded.

Use directional language with digital mapping software• Use digital images to extend the use of directional language by

investigating unfamiliar features such as features outside the school grounds.

• Use mapping tools to draw a line on a map to show pathways as they are being described, e.g. the path students travel from home to school.

• Indicate features along a path with place markers.

and pathway representations.

Learning alertsBe aware of:Students who use ambiguous language to give instructions.

different shapes drawn, and write directions to each object from a given starting point.

to plan a route for a cross-country jog. Students write the directions down for each stage of the jog and hand it to a partner. The partner then follows those directions to draw the route on the map.

ResourcesSupporting learning resource — Using directional language to find locations and describe pathwaysSheet — Dream Islandsimple grid mapsdigital mapping software








Geometric Reasoning

#Warm Ups Monitor students’ ability to:Recognise and classify angles in relation to

L2B




C2C Maths Library:https://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-



Lesson 26Geometric reasoning — Exploring Right Angles #Activities

Establish learning context• Consider the objective of the lesson.• Revisit regular and irregular 2D shapes.

Identify angles• Investigate and identify angles in the immediate environment.• Identify the components of angles including the terms ‘ray’ and ‘vertex’.• Discuss and identify the properties of a right angle and its relationship to a

quarter turn.• Identify different orientations of right angles in different contexts.• Compare and identify angles not equal to a right angle.• Compare and order angles that are greater than or less than a right angle.

Construct and label right angles• Construct a right-angle finder to investigate right angles.• Identify objects that contain right angles and check using the finder.

#Warm Ups

right angles.

Learning alertsBe aware of:Students who classify angles based on the length of an angle’s ray rather than the amount of turn between the rays.

Monitor students’ ability to:Use a right-angle finder and classify angles as


Provide smaller number of vocabulary words and use picture clues with explanation.

Construct an angle maker using two strips of plastic or card connected at the vertex with a split pin. Use this to model and discuss the amount of turn between the rays.

Students trace around various 2D shapes on a sheet of paper


Organise students into groups and provide each group with a variety of print materials such as magazines and newspapers.Have the groups cut out images of objects or shapes that contain right angles. Label the right angles on the images and paste on charts for display.

Have students choose five shapes on the

5cb2-4db6-8fd2-43d3563ffe8a/1/Mathematics_Library/index.html

ResourcesSupporting learning resource — Exploring right anglesSheet — How to make an angle finderSheet — Tangrambell or whistlesheet of paper, scissors, hole punch, stringmaterials for making angles (e.g. straws, string, drawing pin, paper strips, matchsticks or ice-cream sticks)

Language

angle, ray, vertex, amount of turn, right angle, acute, degree, perpendicular, benchmark

Walt:

Identify the components of angles.

Identify right angles.

Compare angles and classify them in relation to right angles.

Establish benchmarks in relation to angle size.

Estimate the size of angles based on the application of benchmark angles.

Wilf:

Identify the components of angles?

Identify right angles?

Compare or classify angles in relation to right angles?

Apply knowledge of right angles to make reasonable estimates of other angle sizes?

Languageangles, turns, right angle, quarter turn, rays, arms, label



Walt: Compare and classify angles as equal to or not equal to a right angle.

Wilf: Construct angles not equal to a right angle?

Use a right-angle finder to identify angles not equal to a right angle?

Use conventions for labelling angles not equal to a right angle?

Classify angles as equal to or not equal to a right angle?

LanguageRevise vocab before assessment

Lesson 27Geometric reasoning — Comparing angles to a right angle #Activities

Identify and construct angles not equal to a right angle• Identify angles in real-life contexts that are less than, greater than or

equal to a right angle and use the right-angle finder to compare.• Use digital technologies to draw and rotate shapes a quarter turn.• Construct angles less than, greater than or equal to a right angle using a

variety of construction materials.

Mark angles not equal to a right angle• Discuss ways an angle could be marked to show it is not equal to a right

angle.• Investigate the conventions used for marking an angle not equal to a right

angle.• Mark the angles on previously drawn shapes using the correct label.

Lesson 28 (Summative Assessment)Geometric reasoning — Measuring and constructing angles #Activities

Example assessment sequence

Understand the assessment• Review the separate sections of the assessment and ensure students

understand what they are expected to do.

Review the Guide to making judgments and understand the standards A–E• Work through the Guide to making judgments with students and highlight

the assessable elements for the assessment and discuss what responses might look like at each of the standards A–E.

greater than, less than or equal to right angles.

Learning alertsBe aware of:Students who are unable to visualise internal angles in 2D shapes.

Assessment purpose

To recall multiplication and division facts, interpret information contained in simple maps and classify angles in relation to a right angle.

and identify each internal angle. Students discuss the components of each angle.

computer. Students expand, enlarge and rotate shapes before printing and handing them to a partner who then uses the correct conventions for marking all angles in the shape correctly

ResourcesSupporting learning resource — Comparing angles to a right anglecraft materials such as straws, cardboard strips, matchsticks or ice-cream sticksstringSheet — Mathema t ics tool kit Years 3-6

ResourcesAssessment task — Recalling multiplication and division facts, interpreting simple maps and classifying anglesAssessment task — Recalling multiplication and division facts,

• Provide students with an opportunity to clarify any components of the assessment.

Conduct the assessment• Distribute the assessment task to students and ask them not to commence

work until signalled.• Have students complete the assessment task.

interpreting simple maps and classifying angles: ResourceAssessment task — Multiplicative number facts assessment Term 2Assessment task — Multiplicative number facts assessment Term 2 (Answers)Assessment task — Recalling multiplication and division facts, interpreting simple maps and classifying angles: Model response

Assessment task — Recalling multiplication and division facts, interpreting simple maps and classifying angles: Teaching notes




unpacked with Year Level teachers prior to the commencement of the Unit

Walt / Wilf / Tib(The What)




Location and Transformation

Maps

#Warm Ups

Lesson 29-32 (Monitoring Task Investigation)Location and transformation — Investigating distance on maps (MGI)#Activities

Establish learning context• Consider the objective of the lesson.• Consider the Mathematical guided inquiry question, ‘What is the shortest

distance around Australia?’• Predict possible findings of the inquiry and how they may be presented.

Identify the information required (Discover)• Establish prior knowledge of the maps.• Develop vocabulary of location and transformation.• Explore mapping conventions and features (e.g. legend, orientation,

scale).• Discuss and explore possible visual tools, including simple maps, mapping

grids, pictures, diagrams and images.• Develop criteria for answering the Mathematical guided inquiry question

(e.g. Does the route have to be the shortest or the safest?).

Plan how to explore the MGI question (Devise)• Determine the information that will be represented.• Plan how the information will be presented.• Describe the plan using mathematical language.

Follow plans (Develop)• Review and finalise criteria to be met when answering the Mathematical

guided inquiry question.• Practise calculating distances using scales.• Plot the best route to collect treasure on a map, meeting established

criteria.• Carry out calculations to determine the distance to the treasure.• Review and adjust responses to the inquiry question.• Prepare a presentation of conclusion and supporting evidence.

Explain (Defend)• Draw conclusions in response to the inquiry question.

Monitor students’ ability to:Formulate and solve authentic problems involving location.

Learning alertsBe aware of:Students having difficulty calculating distances by converting information from the scales on maps to actual distances.

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Use smaller scales to assist in proportional understanding. For example, investigate how 1 mm on a map represents 1 cm so students can create the actual scale to compare to the modelled scale.




Explore calculating distances/lengths using scales along curved lines.


ResourcesSupporting learning resource — Investigating distance on maps (MGI)Supporting learning resource — Guided inquiry posterSupporting learning resource — Evidence cycleSheet — Reading a map and using scaleSheet — Treasure mapSheet — Scale drawingcollection of measuring tools for length (metre ruler, 30 cm ruler, trundle wheel, tape measure)chalk

Languagescale, legend, direction, map, plan, route, measurement, millimetre, centimetre, metre, kilometre

Walt: Use simple strategies to reason and solve location inquiry questions.

Wilf: Understand and apply mapping conventions to solve problems?Use scales on maps to calculate distances?Use appropriate units of measurement?




• Justify reasoning using appropriate units of measurement and mathematical terms for mapping conventions.

• Evaluate responses.

Explore further questions (Diverge)• Reflect on learning about mapping conventions.• Establish further questions that have arisen from the MGI.• Explore questions.








ShapeFractions

& Decimals

#Warm Ups

Lesson 12Shape — Identifying combined shapes #Activities

Establish learning context• Consider the objective of the lesson.• Review regular and irregular quadrilaterals.

Explore tangrams• Explore the origin of tangrams.• Manipulate tangrams to investigate the properties of the 2D shapes

within the tangram. (Properties are the individual features of a shape including the number of sides, number of corners and number of straight or curved edges. We can identify polygons by looking at their properties.)

Use triangles to create combined shapes• Identify triangles and develop a definition of what a triangle is.• Classify regular and irregular triangles.• Explore different ways triangles could be combined to make a regular

shape (e.g. rectangle, triangle).• Create examples of combined shapes by combining two or more triangles.• Investigate the properties of shapes made by combining triangles.• Explore other shapes made by splitting and combining using concrete

materials (e.g. attribute blocks, geoboards).

Identify shapes in the environment• Investigate two-dimensional shapes in real-life contexts, e.g. in patterns in

walls and ceilings.• Identify how shapes could be split into two or more common shapes, e.g.

a rectangle could be split into two triangles.)• Show how the shape could be split into common shapes. (For example,

draw and label each new shape that has been created.)

Warm Ups

Monitor students’ ability to:Make shapes by combining other shapes.Describe findings when examining the shapes.

Learning alertsBe aware of:Students believing that combining two triangles together always makes a square.Students believing that larger rectangles are always enlargements of smaller ones.

Monitor students’

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Construct combined or irregular shapes using attribute blocks and describe attributes of the newly created shapes (e.g. number of sides).Ask students to select a piece within the tangram set and see if it can be made with two of the other pieces, then try making it with three of the other pieces.

Complete




Students investigate composite shapes by deconstructing irregular shapes found in the natural and built environment.

Investigate


ResourcesSupporting learning resource — Identifying combined shapesLearning object — GeoboardSheet — Square dot paperLearning object — Tangram shapesSupporting learning resource — Mathematics tool kit Years 3-6concrete geoboard and/or geostripsdigital cameraLearning object — Tangrams (1)Learning object — Tangrams (2)Sheet — Tangram pieces

Languageshape, two-dimensional, polygon, quadrilateral, side, edge, straight, curved, corner, closed, open, irregular, regular, square, triangle, rectangle, rhombus, kite, parallelogram, angle, tangram, flip, turn

Walt: Review the properties of 2D shapes using tangrams.

Create and describe two-dimensional shapes made by combining common shapes.

Wilf: Identify the properties of 2D shapes?

Create and record composite shapes?Identify combined shapes in the environment?

Language




shape, two-dimensional, polygon, quadrilateral, side, edge, straight, curved, corner, closed, open, irregular, regular, square, triangle, rectangle, rhombus, kite, tangram, parallelogram, flip, turn, angle

Walt: Manipulate tangram pieces to investigate and construct combined shapes.

Wilf: Combine tangram pieces to make new shapes?

Languagepartition, halve, half, third, sixth, ninth, unit fraction, numerator, denominator, vinculum, equivalent fraction, one whole, equal parts

Walt: Develop an understanding of the proportion and relationships between fractions in the third, sixth and ninth families.Represent fractions using linear models

Lesson 13Number and place value — Calculating multiplication problems using the area model #Activities

Establish learning context• Consider the objective of the lesson.• Review the properties of tangram pieces.

Create shapes using tangram pieces• Combine tangram pieces to create different polygons.• Describe polygons being created using mathematical terms.• Create different shapes (e.g. regular and irregular) by rearranging tangram

pieces.• Record and describe the shapes made.

Warm Ups

Lesson 14Fractions and decimals — Partitioning to investigate thirds, sixths and ninths #Activities

Establish learning context• Consider the objectives of the lesson.

Investigate thirds, sixths and ninths• Fold linear materials of various lengths to create and compare thirds of

different proportions.• Investigate and create models of thirds, sixths and ninths.• Use diagrams to represent linear models of thirds, sixths and ninths.• Investigate patterns associated with naming equivalent fractions among

thirds, sixths and ninths.• Count multiple thirds, sixths and ninths using materials and diagrams, e.g.

ability to:Create shapes by combining tangram pieces.

Learning alertsBe aware of:Students thinking that combining two triangles always makes a square.

Monitor students’ ability to:Represent fractions using materials and diagrams and count fractions.Label models of unit fractions and record equivalent fractions to one whole.

Learning alertsBe aware of:Students thinking that the larger the denominator, the larger the fraction piece or proportion of the whole.

tangram puzzles for students to develop the thinking associated with spatial visualisation.

Have students undertake paper folding activities or draw diagrams that can help establish the thinking required to name and identify equivalent fractions.

shapes in real-life contexts and re-create those shapes using tangram pieces.

Have students represent fractions from the third, sixth and ninth families using various materials (e.g. paper strips, string) and justify their choice.

ResourcesSupporting learning resource — Calculating multiplication problems using the area modelSheet — Grid paper: 1 cmbase 10 materials

ResourcesSupporting learning resource — Partitioning to investigate thirds, sixths and ninthsSheet — Naming fractionsLearning object — Number linematerials for linear fraction models, e.g. rope, ribbon, paper strips, pegs

numbers ‘0’, ‘1’, 13

, 16

, 19

written

on cardsSupporting learning resource —

and symbols.Form a generalisation about fractions equivalent to one whole.

Wilf: Model and represent thirds, sixths and ninths using a range of materials, diagrams and symbols?

Identify fractions equivalent to one whole?

Identify language associated with fractions?

Languagewhole numbers, consecutive numbers, benchmark numbers, half, thirds, sixths, ninths, partition, mixed, improper fraction, equal parts

Walt: Investigate the relative position of numbers by modelling the fractional numbers between whole numbers.Represent linear models of fractions along number lines and use these models

number lines.

• Identify and label models of unit fractions 13 , 16 , 19 .

Investigate equivalent fractions for one whole• Count multiple thirds, sixths and ninths.• Explore the term ‘equivalent fractions’ by establishing how many

repetitions of each fraction are required to make one original whole linear model or object.

• Record these equivalent fractions as symbols, e.g. 33 = 1.

• Develop a generalisation about equivalent fractions and one whole.

Lesson 15Fractions and decimals — Counting and representing thirds, sixths and ninths #Activities

Establish learning context• Consider the objectives of the lesson.• Review fraction types including unit and improper fractions and mixed

numbers.• Consolidate fractions equivalent to 1 and other whole numbers.

Investigate relative numbers• Practise identifying whole numbers between whole numbers.• Identify numbers (fractions) between two consecutive whole numbers.• Identify numbers (including fractional numbers) close to benchmark

numbers.

Represent mixed numerals on number lines• Apply partitioning and knowledge of thirds to represent the positions of

unit fractions 13

, 16

, 19

between 0 and 1 on number lines.

Monitor students’ ability to:Position numbers and fractions along number lines.Outline strategies to position numbers on the number line.

Learning alertsBe aware of:Students who cannot convert an equivalent mixed fraction to an improper fraction when counting along a number line.

Partition a physical number line, e.g. streamer or string, or partition rectangles to locate, identify and label improper fractions.

Have students continue to apply halving thirds to locate, label and count by twelfths, including in mixed numbers

Mathematics tool kit Years 3-6

ResourcesSupporting learning resource — Counting and representing thirds, sixths and ninthsSheet — Naming improper fractionsLearning object — Number linestring, cards with familiar numbers such as 0, 1, ½, ¼, ¾, ⅜, ⅝ and ⅞items that can be cut into halves, quarters or eighths for counting,

to count and solve simple fraction addition problems.

Wilf: Apply partitioning and represent fractions on number lines?Count by thirds, sixths and ninths along number lines?

Use number lines to solve simple addition fraction problems?Recognise and use patterns and relationships between fractions and whole numbers?

Languagehalve, half, quarter, eighth, equivalent, whole numbers, improper fraction, benchmark numbers, equal sharing, multiple groups

Walt: Compare and order fractions.Apply fractional understandings and principles to calculate and solve problems.

Wilf: Compare and order fractions in relation to benchmark numbers?

• Represent the positions of mixed numbers (thirds, sixths and ninths) between consecutive whole numbers.

Count by thirds, sixths and ninths• Apply partitioning to represent whole numbers and thirds as mixed

numbers between a range of two whole numbers on a number line, and then count by thirds along the number line.

• Repeat for sixths and then ninths.• Practise solving simple addition of fractions by counting on fractional

amounts along number lines.

Lesson 16Fractions and decimals — Solving fraction problems #Activities

Establish learning context• Consider the objectives of the lesson.• Consolidate understanding of numbers between other whole numbers

including consecutive whole numbers.

Use benchmark numbers to compare and order fractions

• Establish benchmark numbers of 12 and 1.

• Sort, compare and order fractions, improper fractions and their equivalent mixed numbers around these benchmark numbers.

Generate equivalent fractions in context• Investigate improper fractions equivalent to mixed numbers (correlate

with thirds, sixths and ninths) using materials and models.• Develop understanding of improper fractions equivalent to whole

numbers through contextualised problems.

Monitor students’ ability to:Apply fraction understanding to solve problems.

Learning alertsBe aware of:Students who are not able to convert improper fractions to equivalent mixed numbers and vice versa.

Have students use role play, materials or diagrams to work out solutions to problems.

Provide opportunities for students to create their own contextualised fraction problems using equivalent and improper fractions.

e.g. oranges, sheets of paperSupporting learning resource — Mathematics to ol kit Years 3-6

ResourcesSupporting learning resource — Solvi ng fr action problems Sheet — Comparing fractions on a number lineprepared contextualised fraction problemsassorted materials for modelling and representing solutions

Use modelling or diagrams to solve fraction problems?

• Develop strategies for recognising the relationship between improper fractions and mixed numbers using contextualised problems.

Supporting learning resource — Mathematics tool kit Years 3-6Helpful informationSupporting learning resource — Fractions https://learningplace.eq.edu.au/cx/resources/items/d71cc6ea-fd09-4406-a353-ea1769cc76f0/0/Mth_Y04_U1_SLR_Fractions.docx

https://learningplace.eq.edu.au/cx/resources/items/d71cc6ea-fd09-4406-a353-ea1769cc76f0/0/Mth_Y04_U1_SLR_Fractions.docx










Number & Place ValueMoney

&Financial

Mathematics

#Warm Ups

Lesson 17Number and place value — Multiplying and dividing by 3, 6 and 9#Activities

Establish learning context• Consider the objective of the lesson.

Continue number patterns• Use materials to model number patterns.• Make and view various patterns, state the rule for each one, then apply

the rule to continue the pattern.• Continue increasing and decreasing patterns, and fill in patterns with

missing terms (e.g. 1, 6, 11, 16, __, ___, ___).• Apply the inverse rule to find missing numbers at the beginning of

a pattern (e.g. ___, ____, ____, 25, 30, 35).• Show patterns on a number line.• Describe rules using an operation.

Create number patterns• Create a number pattern that can be represented pictorially.• Record the matching number pattern, e.g. 2, 4, 6.• Record the rule for the pattern, e.g. +2.

Create a number pattern on a number line. Establish learning context• Consider the objectives of the lesson.• Review the 9s fact family and related division facts.

Monitor students’ ability to:Solve multiplication and division problems.Use strategies to identify and complete number patterns resulting from multiplication.

Learning alertsBe aware of:Students lacking automaticity and using one way of thinking such as repeatedly adding 3 to recall all the 3s facts.Students lacking automaticity in recall of basic 9s facts and using fingers to recall answers.

L2B


Use counters to develop and illustrate how the 3s facts can build from the 2s facts, e.g.

Use counters to develop and illustrate how multiplication by 6 can build from doubling the 3s facts or from the known 5s facts.

Investigate the digit patterns among the 9s facts (e.g. the digits of the answer add to 9) or investigate the




Have students practise multiplying larger numbers by 3 using the ‘build up from a double’ strategy.Ask students to investigate and explain how multiplying by 3 can help when multiplying by 6.Ask students to investigate and explain how multiplying by 10 can help you multiply by 9.


ResourcesSupporting learning resource — Multiplying and dividing by 3, 6 and 9counters, word problems and number sentencesLearning object — Hundred boardLearning object — Tren's alien pet shopSheet — Absent facts Sheet — No show nines Slideshow — Multiplying and dividing by six Slideshow — Multiplying and dividing by nineSupporting learning resource — Scan-Think-DoSupporting learning resource — Mathematics tool kit Years

Languagemultiply, divide, facts, extended facts, fluency, patterns, repetition, strategy, part, whole, number sentence, operation, fact family.

Walt: Extend fluency of recall of the 3s, 6s and 9s facts.

Solve multiplication and division problems.

Wilf: Accurately and fluently recall the 3s, 6s and 9s facts?





Use estimation to find reasonable answers?

Languageround, calculation, split, compensate, strategy, estimate, solve, reasonable answer

Walt: Consider informal recording methods for calculating multiplication and division problems.

Apply computation strategies to solve word problems.

Wilf: Efficiently and accurately apply strategies to solve division problems?

Extend 3s, 6s and 9s facts• Fluently multiply and divide numbers by 6.• Practise extended 3s, 6s and 9s facts.• Investigate and form generalisations about extended facts that involve

multiplying and dividing by 9 (with no remainders).• Create and complete number sequences involving multiples of 9.

Solve multiplication and division word problems• Investigate multiplication and division word problems with no remainders,

identifying:o the whole and partso missing elementso the operation required to solve the problem.

• Record number sentences required to calculate word problems.• Apply personal methods to calculate problems.

#Warm Ups

Lesson 18Number and place value — Solving multiplication and division problems #Activities

Establish learning context• Review 3s, 6s and 9s facts and related division facts.

Revisit computation strategies• Review and practise informal written methods for recording the

application of computation strategies.

Apply strategies to solve problems• Practise computation, incorporating explicit application of strategies to

solve multiplication and division problems.• Ask questions using Scan–Think–Do, e.g.

Scano What do we know about the numbers?o What is the operation?o Does the answer need to be precise or approximate?

Thinko Can I do it mentally?

Monitor students’ ability to:Record informal solutions to division problems.

Learning alertsBe aware of:Overdependence on a narrow range of strategies.

relationship between the known 10s facts and the 9s facts.

Provide place value materials, such as MAB base 10, and a place value chart for students to model the partitioning of numbers, multiplicative concepts and to illustrate the thinking required to solve multiplication and division problems.

Have students record a range of different ways of applying the split strategy to calculate the one division problem.

3-6

ResourcesSupporting learning resource — Solvi ng multiplication and division problemsLearning object — Number expanderSheet — How would you solve a problem?calculators, butchers paper and markers for recording calculation methodsplace value materials, e.g. base 10 blocks/MAB, place value chartsLearning object — Tren's alien pet shopSupporting learning resource — Mathematics tool kit Years 3-6

Language

dollars, cents, coins, notes, equivalent amounts, change, tendered, count on, count back, subtract, estimate, round

Walt: Calculate change using a range of strategies.

Wilf: Apply strategies for calculating and rounding amounts tendered?Calculate change?

Languagedollars, cents, coins, notes, equivalent amounts, change, tendered, count on, count back, subtract, estimate, round

Walt:

o How will I know if the answer is reasonable?o Which strategy will I use?

Do• Solve the problem.• Check the answer is reasonable.

• Discuss possible strategies used to solve addition problems, e.g. jump, split or compensate, and personal methods.

Lesson 19Money and financial mathematics — Calculating change #Activities

Establish learning context• Consider the objective of the lesson.• Revise calculating the total value of combinations of Australian notes and

coins.

Round to five cents• Discuss reasons for estimating money amounts. Scenarios might include:

shopping, estimating total costs, ensuring that there is sufficient money to cover costs, making it manageable to split bills.

• Add and subtract money amounts, using rounding to the nearest whole dollar.

• Explore examples and the purpose of rounding amounts to the nearest five cents.

• Round prices to the nearest five cents.

Calculate change• Explore strategies to calculate change.• Count on from given amounts in dollars and cents to the nearest dollar.• Subtract the cost of purchases from the amount tendered.• Check calculations using a calculator.

Lesson 20Money and financial mathematics — Solving problems involving money #Activities

Establish learning context• Consider the objectives of the lesson.• Revisit strategies used for calculating change.

Monitor students’ ability to:Calculate change.

Learning alertsBe aware of:Students not recognising the decimal point as a marker to show dollars and cents.Suggested next steps for learningMatch notes and coins to amounts recorded on price tags.

Monitor students’ ability to:Calculate change using mental and written strategies.

Learning alertsBe aware of:Students making calculation errors when

Practise adding two items together and rounding the total cost to the nearest dollar.

Students find items from shopping catalogues that are priced under $5 and cut out the images. Students take turns as the

Students write out a tuckshop order for morning tea and lunch. Calculate the total cost of the items and calculate the change that would be received from $20, $10 and/or $5.

Students choose an amount to spend. Use shopping catalogues to buy items and calculate the total to make sure they are

ResourcesSupporting learning resource — Calculating changeLearning object — Australian money: Correct money and changeSheet — Using coins and notesimitation coins and noteseveryday items labelled with price tags

Estimate amounts of money using rounding.

Add and subtract money amounts using calculators and algorithms.

Solve problems involving purchases.

Wilf: Round money amounts and estimate total costs?

Apply an efficient strategy to add and subtract money amounts?

Languagedollars, cents, coins, notes, equivalent amounts, change, tendered, count on, count back, subtract, estimate, round, currency, foreign, comparison, decimal

Walt: Investigate currencies from different countries and cultures.

Wilf: Identify Australian and foreign currency as separate money systems?

Recognise money

Solve problems involving purchases and the calculation of change• Estimate the total costs of items by rounding prices to the nearest dollar.• Calculate addition and subtraction money problems using written

methods.• Calculate the cost of a set number of items using a given amount of

money, e.g. using a catalogue, students find five items that could be bought for under or exactly $20.

Lesson 21Money and financial mathematics — Representing money values in different ways #Activities

Establish learning context• Consider the objective of the lesson.• Revisit strategies used for calculating change.

Investigate coin combinations• Identify names and values of currencies around the world. Examples can

include the Japanese yen, Chinese yuan, Malaysian ringgit, New Zealand dollar or the European euro.

• Investigate coin combinations of an Asian currency and make simple comparisons with Australian coin values.

Trade coins for simple values• Trade coins for approximate equivalent values using Asian and Australian

currencies.• Develop a reference table to calculate approximate costs of items in

Australian dollars..

prices are presented as a combination of cents, whole dollars or dollar and cent combinations.

Monitor students’ ability to:Differentiate between Australian and foreign currencies.


Students not understanding why the value of the Australian dollar is not equal to the value of foreign currencies

customer and shopkeeper. The customer uses $5 and chooses an item to buy. The shopkeeper provides change by counting on and both students check the change using a calculator. Students swap roles and choose other items to buy and sell.

Create a matching game in which players match countries with their currencies.

within their budget. Add or delete items to get the total as close as possible to the chosen amount. Students calculate any change that would be received from the amount chosen.

Have students create a simple conversion table of assorted currency values equivalent to one dollar and one hundred dollars.

ResourcesSupporting learning resource — Solving problems involving moneySheet — Goods for saleSheet — Goods for sale: How much change?Slideshow — Zoo animals: Show me the moneyimitation coins and noteseveryday items labelled with price tags

ResourcesSupporting learning resource — Representing money values in different waysSlideshow — Shopping with Rocky Rhinoatlasnewspapersexamples of foreign currency

values? money (coins and notes to $20)

Summative Assessment Tasks

Modified13/3/19 Year 4 Unit 2

Assessment task — Recalling multiplication and division facts and using the properties of odd and even numbers

Name Class

Write your answers to the multiplication and division facts in the space provided.

a) 2 x 7 = __________(b) 18 ÷ 2 = __________(c) 6 x 7 = __________

(d) 30 ÷ 3 = _________ (e) 9 x 9 =__________ (f) 3 x 7 = __________

(g) 4 x 5 =__________ (h) 12 ÷ 6 = __________ (i) 12 ÷ 3 =__________

(j) 2 x 6 = x 3 (k) 21 ÷3 = ÷ 9 (l) 6 x = 9 x 4

Here are three statements. Two of the statements are true. One is a lie.

a) Circle the statement that is the lie:

Odd + odd = odd

Even + even = even

Odd + even = odd

b) Prove why the statement you have selected is the lie using numbers, words and/or drawings.

29 of 57Mth_Y04_U2_AT_ Recalling multiplication and division facts and using the properties of odd and even numbers

Question 1

Question 2

a) Caleb thinks that 3 x 24 will have an answer that is even. Is he correct? _______________

b) How do you know (use the properties of odd and even numbers in your explanation).

a) List all possibilities for the digits in the box to make the following statement true:

4 x 3 = an odd number


Question 3

Question 4

b) Explain why you chose these digits.

______________________________________________________________

______________________________________________________________

______________________________________________________________

__________________________________


Mathematics Year 4: Unit 2 — Recalling multiplication and division facts and using the properties of odd and even numbers

Name:

Purpose of assessment: To recall multiplication and division facts and use the properties odd and even numbers.

Aspect of Achievement Standard: Students recall multiplication facts to 10x 10 and related division facts. Students use the properties of odd and even numbers.

Understanding and Fluency Problem solving and Reasoning

Use properties of odd and even numbers.Recall multiplication facts to 10x10 and related division facts.

Use the properties of odd and even numbers.

Writes all possible digits to make the multiplication statement true. Q4a Apply and draw conclusions based on generalisations about adding odd and even numbers to solve unfamiliar problems. Q4b A

Calculate missing digits in a balanced equation. Q1j,k,lWrite one or two digits to make the multiplication statement true. Q4a

Use mathematical language to explain how you know whether an answer will be odd or even. Q 3b B

Use properties of odd and even numbers. Q2a, 3aRecall multiplication facts to 10x10 and related division facts. Q1a-i

Use properties of odd and even numbers to prove number statements true or false. Q2b C

Recalls some multiplication and division facts. Attempts to solve some problems by applying knowledge of odd and even numbers. D

Identifies some numbers as odd and even. E

Feedback:

32 of 57Mth_Y05_U2_AT Shape, angle, transformation concepts

Modified13/3/19 Year 4 Unit 2

Assessment task - Interpreting simple maps and classifying angles

Name Class

Task: Gnome Land

Question 1

Use the map of Gnome Land to complete the following:

a) Draw suitable symbols to represent the missing features in the legend.b) Find and circle the first aid tent in the middle of Gnome Land.c) Complete the compass rose on the map

Question 2

a) Position three rides, two food stalls and two eating areas on the map. (Think carefully about where to position these features.)

b) Describe the location of one of your food stalls in relation to other features on the map.

c) Justify the placement of the features using mapping language.

Question 3

Identify the toilet block nearest to the first aid tent. Describe the distance and direction from the first aid tent to the nearest toilet block using established pathways. Explain why you chose this toilet block.

Question 4

33 of 57Mth_Y04_U2_AT_Interpreting simple maps and classifying angles

Complete the following statements. The first one has been done for you.

a) The _________ is north of the first aid tent.

b) The _________ is west of the first aid tent.

c) The information kiosk is _______ of the first aid tent.

d) The ____________ is east of the first aid tent.

Question 5

Mark each of these steps on the map with arrows. You may pass through landmarks on your way.

1. Start at the information centre and walk 8 m north.

2. Make a quarter turn clockwise.

3. Continue walking for another 6 m.

4. Turn southward and proceed 4 m.

6. Place an X on the map at your finishing point.

Question 6

Your friend is at the information kiosk. Give directions to your friend to go to toilets in the south-west corner. Start from the information kiosk and use compass points, the language of transformation, features and scale to describe the shortest pathway.

1.

2.

3.

4.

5.


AnglesUse the map on Gnome land to answer these questionsQuestion 7

a. Position yourself at the first-aid tent and face north. If you point to the north with one arm and use the other arm to make a right angle, what might you be pointing to?

_____________________________________________________

b. Could there be more than one solution? YES / NO Explain your reasoning:

Question 8You will need a blue, red and green pencil for this question.Select the type of angle made if you:

a) Draw a BLUE line from train station 4 to train station 2 to train station 5. right angle not a right angle

b) Draw a RED line from train station 5 to train station 4 to train station 3.

right angle not a right angle

c) Draw a GREEN line from the cinema to the first-aid tent to the information stall

right angle not a right angle


Mathematics Year 4: Unit 2 — Interpreting simple maps and classifying angles Name:

Purpose of assessment: To interpret information contained in simple maps and make and classify angles

Aspect of the Achievement Standard: Interpret information contained in maps. Classify angles in relation to a right angle.


Classify angles in relation to a right angle.(Use simple scales, legends and directions.)

Interpret information contained in maps. (Describe locations and pathways.)

Uses knowledge of right angles to explain that two straight lines can create more than one right angle. Q7b

Describes location in relation to other features using combinations of mapping conventions. e,g. N, S, E, W, and possibly NE, SE, SW distance using grid. Q2b Interprets and describes pathways using a combination of directional language scale, legend and the language of transformation (anti-clockwise, ¾ turn). Q6

A

Describes distance and direction from one location to another using scale. Q3

Justifies decisions about location using the mapping language Q2cCompares distances to determine the most appropriate pathway. Q3 Describes an accurate pathway that accounts for the direction the person is travelling using simple language. Q6

B

Completes conventions of a simple map. Q1a-cPosition features on a map. Q2aUses compass points and a legend to determine positions of features. Q4b-dFollows simple directions. Q5Uses right angles to locate position of feature. Q7aClassify angles in relation to right angle. Q8a-c

Describes the positioning of new features on the map in relation to existing features using the mapping language. Q2bInterpret information contained in maps. Q3

C

Randomly positions additional features on the map. Describes locations and gives directions using everyday language. D

E

Feedback:

NOTE – Q2b, Q3 & Q6 contribute information to several markers- quality and content of response should be considered.

Mth_Y05_U2_MT_Solving problems using four operations

Mth_Y05_U2_MT_Solving problems using four operations

1

2

3

4

5

6

Monitoring Tasks

Year 4 Unit 1 & 2Assessment task — Investigating distance on maps

Name Class

Teacher Date

Task: To use simple strategies to reason and solve location inquiry questions.

During Semester 1, students completed two mathematical guided inquiries. They were:

Investigating the nature of 10 000. ‘How much is 10 000?’ (Unit 1), which focused on learning related to the substrand Number and place value

Investigating distance using maps. ‘What is the shortest distance around Australia?’ (Unit 2), which focused on learning related to the substrand Location and transformation.

As a monitoring task observe:

Mathematical guided inquiry

Link to relevant section of the achievement

standardQuality of student learning:

What is the shortest distance around Australia?

Students interpret information contained in maps.

Collect evidence that the student can:

understand mapping conventions apply mapping conventions to solve problems use scales on maps to calculate distances use appropriate units of measurement justify their answer to the problem with

mathematical evidence.

As an assessment task, the two inquiries and the attached Guide to making judgments can be used to report student learning (in line with the achievement standard) to parents. The specific aspect of the achievement standard is:

38 of 57Mth_Y04_U2_4_AT_MathGuidedInquiries

The two Mathematical guided inquiries identified can be used as tools to monitor or assess student understanding of Semester 1 work.

Schools can choose to:

use both inquiries as assessment with the Guide to making judgments (GTMJ) attached

choose to use one inquiry for monitoring and one for assessment

use both inquiries as monitoring tasks.

interpret information contained in maps.


Year 4 Mathematics: Unit 2 — Investigating distance on maps (MGI) Name:

Purpose of assessment: To use simple strategies to reason and solve location inquiry questions.


Perform calculations involving length.Connect and apply scale, legends and directional understanding to the inquiry question.

Use mathematical language and symbols.

Interpret, model and investigate scale, legends and direction on basic maps.Explain and justify conclusions using mathematical evidence.

Accurately transfers knowledge of simple scale, legend, direction and distance to calculate shortest route around Australia.Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Develops and applies methods to gather relevant evidence for a viable route to the shortest distance around Australia.Represents and presents evidence logically.Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

A

Recalls and uses appropriate simple scale, legend and direction understanding connected to the inquiry question.Consistently uses appropriate mathematical language, materials and diagrams.

Develops a method to gather evidence to support the shortest distance around Australia.Explains mathematical thinking including choices made, strategies used and conclusions reached.

B

Use simple scales, legends and directions to interpret information contained in basic maps.Uses appropriate mathematical language, materials and diagrams.

Chooses a known method to gather evidence to support the shortest distance around Australia.Represents and presents evidence.Describes mathematical thinking including strategies used and conclusions reached.

C

Finds a direction on a simple map.Uses aspects of mathematical language, materials or diagrams.

Follows a given method to gather evidence.Makes statements about choices or strategies used when prompted. D

Recognises features on a simple map.Uses everyday language. Makes isolated statements. E

Feedback:


Australian Curriculum

Foundation to 6 Maths - Year 4 Year 4 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 and explain strategies for finding 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.

Content Descriptors

Measurement and Geometry Number and Algebra

Shape

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

Geometric reasoning

Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089)

Location and transformation

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

Number and place value

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Investigate and use the properties of odd and even numbers (ACMNA071) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Recall multiplication facts up to 10 x 10 and related division facts (ACMNA075) Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

Money and financial mathematics

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

Fractions and decimals

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

Investigate equivalent fractions used in contexts (ACMNA077)


Curriculum Priorities - Pedagogy

ConsiderationsPrior and future curriculum

Relevant prior curriculum

Students require prior experience with: solving problems using efficient strategies for multiplication modelling and representing unit fractions identifying symmetry in the environment counting to and from 10 000 classifying numbers as odd or even recalling addition and multiplication facts for single-digit numbers continuing number patterns involving addition and subtraction making models of three-dimensional objects using mental and written strategies to solve problems using multiplication creating and interpreting simple grid maps identifying angles as measures of turn comparing angle sizes in everyday situations representing money values in different ways

Curriculum working towards

The teaching and learning in this unit work towards the following: choosing appropriate strategies for calculations involving multiplication and division recognising common equivalent fractions in familiar contexts using the properties of odd and even numbers recalling multiplication facts to 10 x 10 and related division facts locating familiar fractions on a number line continuing number sequences involving multiples of single-digit numbers solving problems involving multiplication of numbers by one- or two-digit numbers representing a remainder in division calculations creating number patterns with fractions and decimals using grid references to describe locations using degrees to measure angles..

General capabilitiesThis unit provides opportunities for students to engage in the following general capabilities.

Literacy

Comprehending texts through listening, reading and viewing Composing texts through speaking, writing and creating

Numeracy

Estimating and calculating with whole numbers


Curriculum Priorities - Pedagogy

Considerations Recognising and using patterns and relationships Using fractions, decimals, percentages, ratios and rates Using spatial reasoning

Information and communication technology (ICT) capability

Investigating with ICT

Critical and creative thinking

Inquiring - identifying, exploring and organising information and ideas Generating ideas, possibilities and actions Reflecting on thinking and processes Analysing, synthesising and evaluating reasoning and procedures

Personal and social capability

Social awareness

Intercultural understanding

Recognising culture and developing respectFor further information, refer to General capabilities in the Australian Curriculum and the Learning area specific advice

Cross-curriculum priorities

Aboriginal and Torres Strait Islander histories and cultures

Students will develop a knowledge, deep understanding and respect for Aboriginal peoples' and Torres Strait Islander peoples' history and culture and build an awareness that their histories are part of a shared history belonging to all Australians.The embedding of Aboriginal peoples' and Torres Strait Islander peoples' histories and cultures into the curriculum can be a challenging task. For further information, including pedagogical approaches, refer to C2C: Aboriginal peoples & Torres Strait Islander peoples Cross Curriculum Priority support https://oneportal.deta.qld.gov.au/EducationDelivery/Stateschooling/schoolcurriculum/Curriculumintotheclassroom/Pages/C2CAandTSICCPSupport.aspx.For access to model lessons to address Aboriginal and Torres Strait Islander histories and cultures visit the website YDM-CCP teacher resources (QUT) http://ydc.qut.edu.au/resources/YDM-CCP-teacher-resources.jsp

Username: CCPYDM Password: Curriculum#1

Asia and Australia's engagement with Asia




Assessment name: Using the properties of odd and even numbers

Assessment description: Students use the relationships between the four operations and odd and even numbers.

Assessment name: Recalling multiplication and division facts, interpreting simple maps and classifying angles

Assessment description: Students recall multiplication and division facts, interpret information contained in simple maps and classify angles in relation to a right angle.

Assessment name: Investigating distance on maps

Assessment description: Students use simple strategies to reason and solve location inquiry questions.

In this unit, assessment of student learning aligns to the following aspects 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 and explain strategies for finding 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.

Monitoring student learningStudent learning should be monitored throughout the teaching and learning process to determine student progress and learning needs.Each lesson provides opportunities to gather evidence about how students are progressing and what they need to learn next.Specific monitoring opportunities in this unit may include observations, consultations and samples of student work, for example:

represent, order and partition numbers identify which number is larger or smaller and have them explain how they know use strategies to solve addition and subtraction problems of whole numbers up to four digits use strategies to recall multiplication facts identify larger or smaller numbers identify numbers represented using non-standard partitioning apply number properties to check for reasonableness of answers when performing calculations use a range of strategies to identify and complete number patterns resulting from multiplication identify and sort numbers according to whether they are odd or even solve multiplication and division problems record solutions to division problems identify, represent and count fractions using materials and diagrams including number lines apply strategies to locate fractions on number lines


Monitoring description: Students solve simple problems involving the four operations using a range of strategies. They check for reasonableness of answers using estimation and rounding.Specific monitoring opportunities in this unit may include observations, consultations and samples of student work, e.g.

Calculate extended facts. Recall number facts and extended facts. Informally record strategies to solve problems. Solve simple problems involving the four operations using a range of strategies. Use strategies and informal recording for computation. Check the reasonableness of answers by using rounding and estimation. Represent fractions on a number line. Order decimals and locate them on number lines. Describe and apply patterning rules. Continue patterns by adding or subtracting decimals. Recognise and create two-dimensional representations of three-dimensional objects. Identify lines of symmetry in images and everyday contexts. Describe line and rotational symmetry or transformations of two-dimensional objects. Discuss and classify angles in relation to right angles. Estimate angle size. Use a protractor to measure angles. Collect and construct appropriate data displays. apply fraction understandings to solve problems in context label models of unit fractions and recordings of fractions equivalent to one and other whole numbers read and represent written and symbolic money amounts use mental and written strategies to calculate change understand calculating change understand Australian and other currencies identify, discuss and create diagrams of polygons and quadrilaterals create composite shapes from other 2D shapes identify 2D shapes and form generalisations about the shapes read and interpret scales on maps interpret and respond to directions involving the cardinal points of north, south, east and west use number facts to calculate distance understand mathematical language when finding locations and describing pathways interpret symbols in a legend and justify reasons for their use understand directional language and pathway representations present formulations and solutions to authentic problems involving location classify angles as greater than, less than or equal to right angles use a right angle finder understand angles.

Feedback


Feedback in this unit this may include: recall of 3s, 6s, 9s and 10s facts ability to partition and represent five-digit numbers in various ways strategies used to identify unknown quantities recognition and representation of fractions including equivalent fractions and mixed numbers identification of properties and features of 2D shapes strategies used to identify location.

Year 4 Semester 1 Term 2 Mathematics Report Card Comment Bank46 of 57Mth_Y05_U2_4_AT_MathGuidedInquiries

Assessment Task 4: Recalling multiplication and division facts and using the properties of odd and even numbers

A B C D E1M4A4 1M4B4 1M4C4 1M4D4 1M4E4

Recalling multiplication and division facts and using the properties of odd and even numbers

{Name} wrote all possible digits to make the multiplication statement true . {She,He} applied and drew conclusions based on generalisations about adding odd and even numbers to solve unfamiliar problems.


{Name} calculated missing digits in a balanced equation. {She,He} wrote one or two digits to make the multiplication statement true. {Name} used mathematical language to explain how you know whether an answer will be odd or even.


{Name} used properties of odd and even numbers. {She,He} recalled multiplication facts to 10x10 and related division facts. {Name} used properties of odd and even numbers to prove number statements true or false.


{Name} recalled some multiplication and division facts. {She,He} attempted to solve some problems by applying knowledge of odd and even numbers.


{Name} identified some numbers as odd and even.

Assessment Task 5: Interpreting simple maps and classifying angles

A B C D E1M4A5 1M4B5 1M4C5 1M4D5 1M4E5

Interpreting simple maps and classifying angles

{Name} used knowledge of right angles to explain that two straight lines can create more than one right angle. {She,He} described location in relation to other features using combinations of mapping conventions. e,g. N, S, E, W, and possibly NE, SE, SW distance using grid. {Name} interpreted and described pathways using a combination of directional language scale, legend and the language of transformation (anti-clockwise, ¾ turn).


{Name} described distance and direction from one location to another using scale. {She,He} justified decisions about location using the mapping language. {Name} compareed distances to determine the most appropriate pathway. {She,He} described an accurate pathway that accounted for the direction the person was travelling using simple language.


{Name} completed conventions of a simple map. {She,He} positioned features on a map. {Name} used compass points and a legend to determine the positions of features. {She,He} followed simple directions. {Name} used right angles to locate the position of a feature. {She,He} classified angles in relation to right angles. {She,He} described the positioning of new features on the map in relation to existing features using the mapping language. {Name} interpreted information contained in maps.


{Name} randomly positioned additional features on the map. {She,He} described locations and gives directions using everyday language.

No E Level on GTMJ or Comments


Maths Pre-ModerationYear 4 : Unit 2 Semester 1 Term 2 Title:

Curriculum Intent for the Unit (see unit /task description) In this unit students apply a variety of mathematical concepts in real-life, lifelike and purely mathematical situations.

Through the proficiency strands - understanding, fluency, problem-solving and reasoning - students have opportunities to develop understandings of:

Number and place value - recognise, read and represent five-digit numbers; identify and describe place value in five-digit numbers; partition numbers using standard and non-standard place value parts; compare and order five-digit numbers; identify odd and even numbers; make generalisations about the properties of odd and even numbers; make generalisations about adding, subtracting, multiplying and dividing odd and even numbers; recall 3s, 6s and 9s facts; solve multiplication and division problems; use informal recording methods and strategies for calculations; apply mental and written strategies to computation.

Fractions and decimals - revisit and develop understanding of the proportion and relationships between fractions in the halves family and thirds family, count and represent fractions on number lines, represent fractions using a range of models, solve fraction problems from familiar contexts.

Money and financial mathematics - read and represent money amounts, investigate change, round to five cents, explore strategies to calculate change, solve problems involving purchases and the calculation of change, explore Asian currency and calculate foreign currencies.

Shape - explore properties of polygons and quadrilaterals, identify combined shapes, investigate properties of shapes within tangrams, create polygons and combined shapes using tangrams.

Location and transformation - investigate the features on maps and plans; identify the need for legends; investigate the language of location, direction and movement; find locations using turns and everyday directional language; identify cardinal points of a compass; investigate compass directions on maps; investigate the purpose of scale; apply scale to maps and plans; explore mapping conventions, plan and plot routes on maps; explore appropriate units of measurement and calculate distances using scales.

Geometric reasoning - identify angles, construct and label right angles, identify and construct angles not equal to a right angle, mark angles not equal to a right angle.

Assessable Content (Must Know) (Refer to AAP or Unit Plan to source this Information)

Assessment Task 1: Recalling multiplication and division facts and using the properties of odd and even numbers

Understanding Fluency Use properties of odd and even numbers. Recall multiplication facts to 10x10 and related division facts.

Problem Solving and Reasoning

Use the properties of odd and even numbers.


Understanding Fluency Classify angles in relation to a right angle. (Use simple scales, legends and directions.)

Problem Solving and Reasoning Interpret information contained in maps. (Describe locations and pathways.)

Additional Targeted Teaching Priorities* Identified from previous assessment & post moderation of Semester 1 Mathematics unit 1 from Year 4 Data Wall. Were there any literacy / numeracy identified areas?


Scan and Assess

Prioritise

Develop and Plan

Feedback Guide/Assessment OpportunitiesSee Feedback that may relate to misunderstandings and commo alternative conceptions (in planning – Pre Moderating)Feedback in this unit this may include:

recall of 3s, 6s, 9s and 10s facts ability to partition and represent five-digit numbers in various ways strategies used to identify unknown quantities recognition and representation of fractions including equivalent fractions and mixed numbers identification of properties and features of 2D shapes strategies used to identify location.

Unit Success Criteria and DifferentiationHow will you know you students have succeeded?

Differentiation: CONTENT PROCESS PRODUCT

and ENVIRONMENT

‘C’ Year Level Achievement Standard – Success Criteria(Refer to GTMJ and relevant content descriptors (AAP) – including prior content – previous levels)

Assessment Task 1: Recalling multiplication and division facts and using the properties of odd and even numbersUnderstanding Fluency

Use properties of odd and even numbers. Q2a, 3a Recall multiplication facts to 10x10 and related division facts. Q1a-i

Problem Solving and Reasoning

Use properties of odd and even numbers to prove number statements true or false. Q2b


Understanding Fluency Completes conventions of a simple map. Q1a-c Position features on a map. Q2a Uses compass points and a legend to determine positions of features. Q4b-d Follows simple directions. Q5 Uses right angles to locate position of feature. Q7a Classify angles in relation to right angle. Q8a-c

Problem Solving and Reasoning Describes the positioning of new features on the map in relation to existing features using the mapping language. Q2b Interpret information contained in maps. Q3

‘B’ Standard – Success Criteria(Refer to GTMJ and relevant content descriptors)

Assessment Task 1: Recalling multiplication and division facts and using the properties of odd and even numbersUnderstanding Fluency

Describes distance and direction from one location to another using scale. Q3

Problem Solving and Reasoning Justifies decisions about location using the mapping language Q2c Compares distances to determine the most appropriate pathway. Q3 Describes an accurate pathway that accounts for the direction the person is travelling using simple language. Q6


Understanding Fluency Draws a net for a triangular prism 3b


Draws a 3 dimensional representation of a triangular prism 3c

Problem Solving and Reasoning Describes the (rotational) symmetry of a given design using some mathematical language 5a

‘A’ Standard – Success Criteria(Refer to GTMJ and relevant content descriptors + above)Assessment Task 1: Recalling multiplication and division facts and using the properties of odd and even numbersUnderstanding Fluency

Writes all possible digits to make the multiplication statement true. Q4a

Problem Solving and Reasoning Apply and draw conclusions based on generalisations about adding odd and even numbers to solve unfamiliar problems. Q4b


Understanding Fluency Uses knowledge of right angles to explain that two straight lines can create more than one right angle. Q7b

Problem Solving and Reasoning Describes location in relation to other features using combinations of mapping conventions. e,g. N, S, E, W, and possibly NE,

SE, SW distance using grid. Q2b Interprets and describes pathways using a combination of directional language scale, legend and the language of

transformation (anti-clockwise, ¾ turn). Q6

Support Plan or ICP Adjusted Content – Refer to ICPStudents:

Tasks: Supported Plan or ICPs Differentiated Assessment

Reporting Sentence: ‘Students working at Year x as per their Support Plan or ICP Plan Tasks and assessments.’


Maker Model Guiding Questions

Content What students need to learn (Select focus questions as required) Can I choose a familiar context to help make

connections or will I scaffold to broaden student world knowledge?

What links can I make to real life? Can I change the context to match student

interests? What prior learning experiences are required? How will I know what students already know?

Which data? Will students complete a Pre-test? Can I skim over some of the content or miss it

completely? How will I extend those students who already

have this knowledge? Will I accelerate students?

Process How students learn (Select focus questions as required) Can I tier the activities around concepts and skills

to provide different levels of support or opportunities to demonstrate deeper knowledge?

Do I need to vary the length of time students require to grasp a concept either by compacting the curriculum or extending the timeframe?

Can I provide opportunities for students to construct and demonstrate knowledge using digital resources and technologies?

Can I scaffold activities or break larger tasks down into smaller tasks?

Can I provide study guides or graphic organisers for targeted students?

Can I modify delivery modes for individuals or small groups?

Can I use peer tutoring?ProductHow students demonstrate what they know (Select focus questions as required) To complete the scheduled assessment task will

some students require more/less time? Can students be extended by communicating the

information in a more challenging way? E.g. change to authentic audience

Are there students who need the assessment task to be broken down for them?

Will some students need adjustments to the task e.g. having concrete materials at hand or access to digital technologies?

Will some students need feedback provided more frequently or in a different manner?

Environment How learning is structured (Select focus questions as required) Which of a range of flexible groupings: whole class, small group and individual, best suits this concept and skill set?Have I offered a range of materials and resources -including ICT's to reflect student diversity?Can I vary the level of class teacher support for some students?Would activities outside the classroom best suit this concept? E.g. Other learning spaces within the school, excursions, campsWhat routines can I put into place to assist students in developing independent and group work skills?What class structures can be modified e.g. team teaching or shared teaching and timetabling?Are there additional support provisions from specialist, teacher aide, mentor etc.?Can I provide visual cues for students e.g. content posters or list of instructions for students to follow?


Feedback: Evidence of Learning

Teaching Sequence FeedbackNumber and place value Lesson 1Exploring five- digit numbers Example learning sequence

Establish learning context Recognise and read five-digit numbers Make connections between representations of five-

digit numbers Identify and describe the place value of digits in

five-digit numbers

Evidence of learningCan the student:

Read and write five-digit numbers? Recognise the value of digits in five-digit numbers?

Number and place value Lesson 2Ordering and comparing five-digit numbers Example learning sequence

Establish learning context Compare numbers beyond 10 000 Order five-digit numbers


Identify numbers greater or less than a given number?

Use the symbols < and > to record information about numbers?

Order numbers on a number line? Locate numbers on a number line?

Number and place value Lesson 3Partitioning five-digit numbers Example learning sequence

Establish learning context Partition five-digit numbers into standard place

value parts Partition five-digit numbers into non-standard place

value parts


Show standard five-digit place value partitioning? Record standard place value partitions as number

sentences? Show non-standard five-digit place value

partitioning? Record non-standard place value partitions as

number sentences?

Number and place value Lesson 4Applying place value understanding to five-digit numbers Example learning sequence

Establish learning context Demonstrate place value understandings


Classify numbers using the symbols < and >? Position numbers correctly along a number line? Represent numbers using standard and non-

standard five-digit place value partitioning? Record standard and non-standard partitions as

number sentences?

Number and place value Lesson 5Working with five-digit numbers Example learning sequence

Establish learning context Consolidate place value understanding of five-digit

numbers Compare and order five-digit numbers Read, write and count five-digit numbers


Read and write numbers up to 10 000 and beyond? Represent numbers using materials? Identify the value of digits in five-digit numbers?

Number and place value Lesson 6 Solving addition and subtraction problems Example learning sequence

Establish learning context Recall addition and subtraction number facts Solve addition problems Solve subtraction problems


Solve addition and subtraction problems using a range of strategies?

Apply generalisations of odd and even numbers to check calculations?

Teaching Sequence Feedback


Number and place value Lesson 7Solving multiplication and division problems Example learning sequence

Establish learning context Practise recalling multiplication facts Use efficient strategies to solve multiplication

problems Use efficient strategies to solve division problems


Recall multiplication facts accurately? Apply multiplication facts to complete extended

facts? Solve multiplication and division problems?

Number and place value Lesson 8Identifying properties of odd and even numbers Example learning sequence

Establish learning context Identify odd and even numbers Investigate how odd and even numbers are used


Identify odd and even numbers and discuss their properties?


Number and place value Lesson 9Using the properties of odd and even numbers in addition and subtraction Example learning sequence

Establish learning context Investigate the properties of odd and even numbers

when adding and subtracting Add and subtract odd and even numbers



Apply generalisations about the structure and properties of odd and even numbers to check the accuracy of addition and subtraction?

Number and place value Lesson 10Using the properties of odd and even numbers in multiplication and division Example learning sequence

Establish learning context Investigate the properties of odd and even numbers

using multiplication and division Multiply and divide odd and even numbers



Apply number relationships to check the accuracy of operations?

Number and place value Lesson 11

Assessing student learningExample assessment sequence

Introduce and review the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purposeTo use the relationships between the four operations and odd and even numbers.

Location and transformation Lesson 22Describing location on simple maps and plans Example learning sequence

Establish learning context Investigate the features on maps and plans Identify the need for legends Find locations using turns and everyday directional

language Draw simple plans with symbols and legends


Describe and interpret features of maps? Develop a legend suitable for a school plan? Give and follow directions using everyday

language? Give and follow directions to find locations/objects

on maps?

Teaching Sequence FeedbackLocation and transformation Evidence of learning


Lesson 23 Using cardinal compass points Example learning sequence

Establish learning context Identify the cardinal points of a compass Investigate compass directions on maps

Can the student: Identify the cardinal points on a compass? Make connections between turns and compass

directions? Use compass points to locate positions and give

directions?

Location and transformation Lesson 24Using scale on maps Example learning sequence

Establish learning context Investigate the purpose of scale Apply scale to maps and plans


Identify the relationship between the distances on paper and the distances on the ground?

Use scale when giving and following directions?

Location and transformation Lesson 25 Using directional language to find locations and describe pathways Example learning sequence

Establish learning context Apply directional language in real-life contexts Use directional language with digital mapping

software


Read and use combinations of direction, compass points, legends and scale to find locations and give and follow instructions?

Geometric reasoning

Lesson 26

Exploring right anglesExample learning sequence

Establish learning context Identify angles Construct and label right angles


Relate a right angle to a quarter turn? Identify right angles? Recognise and use conventions for marking right

angles?

Geometric reasoning

Lesson 27

Comparing angles to a right angleExample learning sequence

Establish learning context Identify and construct angles not equal to a right

angle Mark angles not equal to a right angle


Construct angles not equal to a right angle? Use a right-angle finder to identify angles not equal

to a right angle? Use conventions for labelling angles not equal to a

right angle? Classify angles as equal to or not equal to a right

angle?

Geometric reasoning

Lesson 28

Summative AssessmentExample assessment sequence

Introduce and review the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purposeTo recall multiplication and division facts, interpret information contained in simple maps and classify angles in relation to a right angle.

Location and Transformation

Investigating distance on maps (MGI)

Lesson 29-32 (Monitoring Task)Example learning sequence

Establish learning context Identify the information required (Discover) Plan how to explore the MGI question (Devise) Follow plans (Develop) Explain (Defend) Explore further questions (Diverge)


Understand and apply mapping conventions to solve problems?

Use scales on maps to calculate distances? Use appropriate units of measurement?



Shape, Fractions and DecimalsLesson 12Identifying combined shapes Example learning sequence

Establish learning context Explore tangrams Use triangles to create combined shapes

Identify shapes in the environment


Identify the properties of 2D shapes? Create and record composite shapes? Identify combined shapes in the environment?

Shape, Fractions and DecimalsLesson 13Creating combined shapes Example learning sequence

Establish learning context Create shapes using tangram pieces


Combine tangram pieces to make new shapes?

Shape, Fractions and DecimalsLesson 14Partitioning to investigate thirds, sixths and ninths Example learning sequence

Establish learning context Investigate thirds, sixths and ninths

Investigate equivalent fractions for one whole


Model and represent thirds, sixths and ninths using a range of materials, diagrams and symbols?

Identify fractions equivalent to one whole? Identify language associated with fractions?

Shape, Fractions and DecimalsLesson 15Counting and representing thirds, sixths and ninths Example learning sequence

Establish learning context Investigate relative numbers Represent mixed numerals on number lines

Count by thirds, sixths and ninths


Apply partitioning and represent fractions on number lines?

Count by thirds, sixths and ninths along number lines?

Use number lines to solve simple addition fraction problems?

Recognise and use patterns and relationships between fractions and whole numbers?

Lesson 16Solving fraction problems Example learning sequence

Establish learning context Use benchmark numbers to compare and order

fractionsGenerate equivalent fractions in context


Compare and order fractions in relation to benchmark numbers?

Use modelling or diagrams to solve fraction problems?


Number & Place Value, Money and Financial MathematicsLesson 17Multiplying and dividing by 3, 6 and 9


Accurately and fluently recall the 3s, 6s and 9s facts?



Example learning sequence Establish learning context Extend 3s, 6s and 9s factsSolve multiplication and division word problems

Use estimation to find reasonable answers?

Number & Place Value, Money and Financial MathematicsLesson 18Solving multiplication and division problems Example learning sequence

Establish learning context Revisit computation strategies Apply strategies to solve problems


Efficiently and accurately apply strategies to solve division problems?

Number & Place Value, Money and Financial MathematicsLesson 19 Calculating change Example learning sequence

Establish learning context Round to five cents Calculate change


Apply strategies for calculating and rounding amounts tendered?

Calculate change?

Number & Place Value, Money and Financial MathematicsLesson 20Solving problems involving money Example learning sequence

Establish learning context Solve problems involving purchases and the

calculation of change


Round money amounts and estimate total costs? Apply an efficient strategy to add and subtract

money amounts?

Number & Place Value, Money and Financial MathematicsLessons 21 Representing money values in different ways Example learning sequence

Establish learning context Investigate coin combinations Trade coins for simple values


Identify Australian and foreign currency as separate money systems?

Recognise money values?

Post Moderation “Every Student Succeeding”


Objective: Develop professional knowledge and practice (Refer to Pialba state School Moderation and Reporting Policy)

Moderation ProtocolsRefer Appendix of Pialba State School Reporting and Moderation (pre-post) School Policy – Social Moderation Norms.

Moderation of Completed MATHS Assessment Samples Refer Appendix of School Policy – Making judgements using standards.

Previously agreed criteria (Pre Moderation) A-E given using the GTMJ On balance teacher judgement- poles Start at the C Move up or down according to the evidence in the sample. The achievement standard is the C standard. Compare each student sample to the standard not against other student samples Give an A-E grade for the task This sample will become part of the student’s portfolio of work

Where to next after Moderation Refer Appendix of School Policy – Moderation Reflection Tool. From the moderated samples information can then be used to plan for the next task. Complete in next Maths Unit the ADDITIONAL TARGETED TEACHING PRIORITIES

Identified from this terms assessment & moderation as well as the Show Me Tasks.


Scan and Assess

Act

Review

Prioritise

Review

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