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PIALBA STATE SCHOOL: MATHEMATICS YEAR 6 SEMESTER 2 UNIT 3 PLAN

Proficiency Strands

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: Money and financial mathematics - Connect fractions and percentage, calculate percentages and

discounts, calculate discounts of 10%, 25% and 50% on sale items. Number and place value - Identify and describe properties of prime, composite, square and

triangular numbers, multiply and divide using written methods including a standard algorithm, solve problems involving all four operations with whole numbers, locating and representing positive and negative integers and solving problems involving integers.

Location and transformation - Identify the four quadrants on a Cartesian plane, plot and locate ordered pairs in all four quadrants, applying one-step transformation and describe the effect of combinations of translations, reflections and rotations.

Patterns and algebra - Create and complete sequences involving fractions and decimals, describe the rule used to create the sequence and apply the order of operations to aid calculations when solving problems.

Fractions and decimals - Add and subtract fractions with related denominators, calculate a fraction of a quantity, multiply and divide decimals by powers of ten, add and subtract decimals, multiply decimals by whole numbers, divide numbers that result in tenths and hundredths and solve problems involving fractions and decimals.

Using units of measurement - Connect decimals to the metric system, convert between units of measure, comparing length and solve problems involving length and area and connect volume and capacity.

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 / monitoringDeep 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

Learning Interactive Objects (C2C Unit Resources G Drive)

Deep Learning Competency Focus: (Focus from 2019 beyond other than Year 4 NPDL Planning 2018)Collaboration Creativity Critical Thinking Citizenship Character Communication

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

1 D Show Me Term 3 Pre-Test

3 S Time: Duration of Weekly Events

6 S Data: Answering Questions

8 M Measurement (Mass): Shopping Bags

9 M Exploring Equivalence

10 M Investigating Duration of a Week

9 D Show Me Term 3 Post-Test

10 D Show Me Term 4 Pre-Test

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

KLA: MathsYear Level Team: add teacher names

Term 3: Semester 2Show Me Pre-test is to be completed, entered into Spreadsheet and unpacked with Year Level teachers prior to the commencement of the Unit

WALT/WILF/TIB(The What)

Active Learning Engagement(The How)

Check for Understanding

Internal monitoring data Formative (Feedback)

DifferentiationContent: What

Process: Pedagogy – HowProduct: Check for Understanding

Resources

L2B U2BMoney and Financial

Maths:Fractions, Decimals, Percent

Each lesson KWL and Vocab developmentSpend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.

ONGOING LEARNINGTHROUGHOUT THE TERM

Maths Warm Ups:

Activities: Investigate percentages Convert between fractions, decimals and

percentages Calculate percentage discounts using a

dual number line. Investigate fractions, decimals and

percentages Calculate percentages using written

strategies Calculate discounts Convert percentages Calculate discounts using digital

technologies (eg Calculator or spreadsheet)

Calculate percentage discounts for payment

Open Ended Problems:

Formative Assessment

Students will see that fraction, percentages and decimals are out of 100 and can calculate a discount.

Spend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.

Allow 'wait time' for the student to process information.

Plan for visual supports to instruction.Break tasks into smaller, achievable steps.

Use small group instruction and cooperative learning strategies.

Expose to more technical or specific Maths vocabulary.

Extend with students choice of extra study – ensure one-to-one conferences to allow student to share their work.

Use computers to reduce the additional practice of concepts and skills – Compact the curriculum where possible.

Independent Work

Peer Instruction

Tiered tasks

Mathematics Digital Resource Libraryhttps://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-5cb2-4db6-8fd2-43d3563ffe8a/3/Mathematics_Library/Number_Algebra.html

Supporting learning resource - Calculating percentage and discount

examples of sales catalogues newspapers, magazines and

catalogues

Vocabulary:

Walt: Students will connect fractions, decimals and percentages and calculate percentage discount.

Wilf: See that fraction, percentages and decimals are out of 100 and can calculate a discount.

Tib: In real life maths eg shopping students need to understand percentage calculations

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









Internal monitoring data Formative

(Feedback)



Resources

L2B U2BNumber and Place Value

Multiplication and DivisionEach lesson KWL and Vocab developmentSpend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.


Maths Warm Ups:

Activities:

Recognise properties of prime and composite numbers

Recognise properties of square and triangular numbers

Explore the relationship between square numbers and index notation



Can the student Locates a fraction on a number line where the denominator matches the intervals of the number line.Can the student choose appropriate units of measurement?

Allow 'wait time' for the student to process information


Plan for visual supports to instruction.

Break tasks into smaller, achievable steps.

Use small group instruction and cooperative learning strategies

.



Use computers to reduce the additional practice of concepts and skills

Compact the curriculum where possible.

Independent Work

Peer Instruction

Tiered tasks


Supporting learning resource - Exploring properties of whole numbers

Sheet - What I know about multiples!

Sheet - Square and triangular numbers investigations

Sheet - Divisibility rules Sheet - Hundred board: 0 to 99 Sheet - Game board: Snakes and

factors pencils coloured marker pens (felts,

whiteboard markers), A3 paper dice counters calculator

Vocabulary:

Walt: Students will use written strategies to multiply and divide, locate and represent integers on a number line and solve problems involving integers.

Wilf: Student will learned strategies to solve multiplication and division algorithms involving integers.

Tib: Using these algorithms is beneficial when solving mathematical problems in real life situations.

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Internal monitoring data Formative (Feedback)



Resources


Multiplication and DivisionEach lesson KWL and Vocab developmentSpend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.


Maths Warm Ups:

Activities: Consolidate a multiplication written strategy Apply a written algorithm for two-digit

multiplication Create and solve problems involving two-

digit multiplication Consolidate mental division strategies Revisit 1, 2, 5 strategy with and without

remainders Introduce a written expanded algorithm

(calculations with and without remainders) Introduce a written standard written

algorithm (calculations with and without remainders)

Consolidate a multiplication written strategy Apply a written algorithm for two-digit

multiplication Create and solve problems involving two-

digit multiplication Consolidate mental division strategies Revisit 1, 2, 5 strategy with and without



Can the student Locates a fraction on a number line where the denominator matches the intervals of the number line.Can the student choose appropriate units of measurement.

Can the student describe rules used in number sequences involving fractions and decimals.Solves problems involving decimal calculations.

Assessment purpose

To recognise the properties of prime, composite, square and triangular numbers, solve problems involving division and multiplication, calculate common percentage discounts on sale items and connect fractions, decimals and percentages as different representations of the






.





Independent Work

Peer Instruction

Tiered tasks


Using written methods for multiplication

Supporting learning resource - Written methods: Multiplication and division

Sheet - Two-digit multiplication playing cards (numbers only -

remove tens and picture cards) dice calculator pen and paper- Using written methods for division

Supporting learning resource - Calculating division using written methodsSheet - Written strategy 1, 2, 5

Slideshow - Using the 1, 2,5 strategy with no remainder

Slideshow - Using the 1, 2, 5 strategy with a remainder

Video - 1, 2, 5 written strategy for divisionVideo - 1, 2, 5 written strategy for division

2Sheet - 1, 2, 5 exemplarSheet - Record division

Mathematics Vocabulary:

Walt: Recognise the properties of prime, composite, square and triangular numbers, solve problems involving division and multiplication, calculate common percentage discounts on sale items and connect fractions, decimals and percentages as different representations of the same number.

Wilf: Locating a fraction on a number line where the denominator matches the intervals of the number line.

Choosing appropriate units of measurement.

Describing rules used in number sequences involving fractions and decimals.

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Solves problems involving decimal calculations.

Tib: Number concepts involving fractions and decimals are used in everyday real life situations.

(calculations with and without remainders) Introduce a written standard written

algorithm (calculations with and without remainders)

Understand the assessment Review the Guide to making judgments and

understand the standards Conduct the assessment


same number. Sheet - Division problems 1, 2, 5playing cards (numbers only-remove tens

and picture cards)

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(Feedback)



Resources


Pos / Neg NumbersEach lesson KWL and Vocab developmentSpend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.


Maths Warm Ups:

Activities:

Establish learning context (KWL and Vocab) Locate and position positive and negative

numbers on a number line Compare and order positive and negative

numbers

Create number lines involving integers Solve problems involving integers


Can the student locate positive and negative integers on a number line?

Can the student compare and order positive and negative integers






.





Independent Work

Peer Instruction

Tiered tasks


Supporting learning resource - Comparing and ordering positive and negative integers

Sheet - What is less than zero?

Sheet - Revise integers Sheet - Comparing and

ordering positive and negative numbers

Sheet - Numbers - 10 to 10 Sheet - Number lines (blank) one-metre length of string scissors Supporting learning

resource - Mathematics tool kit Years 3-6


Walt: Create number lines that allow the location and ordering of positive and negative integers so that comparisons can be made in order to solve real world problems.

Wilf: Locating of positive and negative integers on a number line?

Comparing and ordering of positive and negative integers.

Tib: Number concepts involving positive and negative

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integers and comparing them using a number line in order to solve problems are used in everyday real life situations.

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(Feedback)



Resources

L2B U2BLocation and Transformation

Cartesian Planes/One Step Trans/Combinations



Maths Warm Ups:

Activities:

Establish learning context Explore grid coordinates Introduce the first quadrant of the Cartesian

plane Introduce the second quadrant of the

Cartesian plane Introduce the third and fourth quadrants of

the Cartesian plane Establish learning context Draw shapes on the Cartesian plane Establish ordered pairs from table of values Represent polygons on the Cartesian plane Solve problems using the Cartesian plane


Can the student: Identify all four

quadrants of the Cartesian plane?

Locate points on the Cartesian plane?

Plot ordered pairs on all four quadrants of the Cartesian plane?

Complete a table of values and write ordered pairs?

Use ordered pairs to construct shapes on the Cartesian plane?

Solve problems using the Cartesian plane?






.





Independent Work

Peer Instruction

Tiered tasks


Supporting learning resource - Introducing the Cartesian plane

Learning object - Coordinates (1)

Learning object - Ordered pairs

Sheet - Empty coordinate grid

Sheet - Cartesian planes Sheet - Cartesian plane (-10

to 10) Sheet - Four-quadrant

battleship game Supporting learning

resource - Mathematics tool kit Years 3-6


________________________

Walt: Students will locate ordered pairs in any one of the four quadrants on the Cartesian plane.

Wilf: Students will understand the quadrants of a Cartesian plane using negative and positive integers and well as x and y axes

Tib: A basic knowledge of Cartesian planes provides the basis for more advanced knowledge of representing spatial positions and vectors

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(Feedback)



Resources

L2B U2BLocation and

TransformationEach lesson KWL and Vocab developmentSpend a short time at the start of each lesson revising concepts, facts or skills and enhancing understanding and fluency.


Maths Warm Ups:

Activities:

Establish learning context Investigate one-step transformations Apply transformations to create a tessellation

Establish learning context Apply combinations of transformations Create new shapes with multiple

transformations Create a transformation pattern


Can the student: Use the

appropriate language (e.g. translation, reflection, rotation) to describe transformations?

Use directional language to describe movement (e.g. quarter turn, 90° to the right, horizontally)?

Can the student: Identify a

combination of transformations?

Describe a combination of transformations?

Create a pattern by applying a combination of transformations to a shape?






.





Independent Work

Peer Instruction

Tiered tasks


Identifying transformations and symmetry

Sheet - Transforming a square

Video - Creating a tessellating shape

Sheet - More squares Sheet - Continue the

tessellating pattern Sheet - Which polygons

tessellate? Sheet - Square dot paper paper polygon shapes scissors pencils colours


Walt: Use appropriate mathematical directional language to solve patterns.

Wilf: Use the appropriate

language (e.g. translation, reflection, rotation) to describe transformations?


Identify a combination of transformations?

Describe a combination of transformations?

Create a pattern by applying a combination of transformations to a

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shape?

Tib: Students will describe the use of integers in everyday contexts, locate integers on a number line, locate an ordered pair in any one of the four quadrants on the Cartesian plane and describe combinations of transformations

Assessment PurposeStudents will describe the use of integers in everyday contexts, locate integers on a number line, locate an ordered pair in any one of the four quadrants on the Cartesian plane and describe combinations of transformations

Sheet - Transformation task Sheet - Cutting shapes Sheet - Transforming a

shape to tessellate Sheet - Regular polygon

template Sheet - Square dot paper

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Check for UnderstandingInternal monitoring data

Formative (Feedback)



Resources

L2B U2BPatterns and Algebra

Sequencing/Applying to Word Prob/Include

Fractions



Maths Warm Ups:

Activities: Establish learning context Identify and continue number

sequences involving fractions Identify and continue number

sequences involving decimals Record patterns involving fractions

and decimals in tables of values

Explore the order of operations Practise solving number sentences

using the order of operations

Revisit the order of operations

Describe a number sequence involving fractions and decimals with a rule?

Identify and apply the rule to a number sequence involving fractions and decimals?

Apply the order of operations to solve problems?

Write a number sentence, using order of operations correctly?

Apply the order of operations to solve problems?






.





Independent Work

Peer Instruction

Tiered tasks


Supporting learning resource - Creating and completing sequences involving fractions

Sheet - Follow the pattern Sheet - Fraction sequence Sheet - Number lines (blank) Sheet - Mixed decimal cards

(tenths) playing cards (ace to 10 only,

take out picture cards) dice Supporting learning resource

- Mathematics tool kit Years 3-6

Supporting learning resource - Exploring the effect of brackets

Sheet - Order of operations Sheet - Order of operations

(Independent activities) Sheet - Operation cards


Walt: Students will describe rules used in sequences involving fractions and decimals and write correct number sentences using brackets and order of operations.

Wilf: the ability to use correct mathematical language when describing fractions and solve order of operations problems involving brackets

Tib: Using correct mathematical language helps with understanding the value of fraction and equivalency

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Solve more complex equations involving order of operations


(make enough copies to give each player one card)

calculator

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(Feedback)



Resources

L2B U2BFractions and Decimals

Add Subtract/Find Quantity/Solve

Prob/Divide by Powers



Maths Warm Ups:

Activities: Establish learning context Add and subtract fractions with the

same and related denominators Use strategies to solve word problems

involving adding and subtracting fractions

Establish learning context Calculate a unit fraction of a quantity Calculate a fraction of a quantity Use digital technologies

Solve problems involving fractions

Multiply by powers of 10 Explore dividing by powers of 10

Add and subtract fractions with the same and related denominators?

Interpret a word problem?

Write a number sentence?

Solve word problems by adding or subtracting fractions with related denominators?

Calculate a fraction of a quantity?

Interpret a word problem to create a number sentence?

Add and subtract fractions with related denominators in different contexts?


Divide a decimal number by a






.





Independent Work

Peer Instruction

Tiered tasks


resource - Adding and subtracting fractions

Sheet - Fraction wall Sheet - Share the cakes Video - Use diagrams to add and

subtract fractions Sheet - Fraction problems Video - Solve problems with related

denominators Supporting learning resource -

Mathematics tool kit Years 3-6 Sheet - Fraction wall

Video - Calculating a unit fraction of a quantity

Sheet - Fraction problems Video - Solve problems with related

denominators

Sheet - Number slider: Thousandths Sheet - Place value chart


------------------------------------Walt: Students will solve problems involving the addition and subtraction of fractions with related denominators, calculate a fraction of a quantity and make connections between the powers of 10 and the multiplication and division of decimals.

Wilf: Students can add and subtractions, calculate quantities and use powers of 10 when multiplying and dividing fractions

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Tib: A basic understanding of fractions relates intimately to many aspects of theoretical and real world mathematics

Establish learning context Add and subtract decimals Investigate addition of hundredths Investigate subtraction of

hundredths


power of 10, using a place value chart?

Mentally divide a decimal number by a power of 10?

Calculate addition, using a written algorithm?

Learning object - Multiplying and dividing by 10, 100 and 1000 (1)

Learning object - Multiplying and dividing by 10, 100 and 1000 (2)

Sheet - Money operations Sheet - Decimal problems

Sheet - Multiplying with decimals

Sheet - Show how I can do itSheet - Problems with decimal answers

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(Feedback)



Resources

L2B U2BMeasurement

Length/Perimeter and Area/Volume and

Capacity



Maths Warm Ups:

Activities:

Establish learning context Explore the relationship between

length and perimeter Calculate areas of rectangles Solve problems involving area and

perimeter

Calculate perimeters of irregular shapes

Calculate areas of compound shapes Solve problems involving area and

perimeter

Measure the capacity of containers Conduct measurements to connect

millilitres to litres Connect capacity and volume

(millilitres to cubic centimetres

Calculate perimeters of regular shapes?

Calculate areas of rectangles?

Use appropriate units?

Identify the relationship between length and area through problem-solving?

Calculate perimeters of irregular shapes?

Calculate areas of compound rectangles?

Interpret and solve word problems?

Measure and record the capacity of containers, using metric units?

Explain that there are 1 000 mL in a litre?

Explain that 1 mL is equivalent to 1 cm3?






.





Independent Work

Peer Instruction

Tiered tasks


Supporting learning resource - Using units of measurement

Sheet - Place value chart: Hundreds of thousands

Sheet - Mass, length, capacity Learning object - Measure it: With

what? Learning object - Units of

measurement (1) Sheet - Length ladder measuring tape milk container ruler

Sheet - Place value chart: Hundreds of thousands

Sheet - Mass, length, capacity Learning object - Measure it: With

what? Learning object - Units of


Walt: Students will connect decimals to the metric system, convert between metric units, compare length and area, solve problems involving perimeter and area and connect volume and capacity.

Wilf: Student to be able to distinguish between different types of measurement, using correct terminology and solve problems is

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measurement

Tib: Real world situations frequently require the use and understanding of measurement terms.


Conduct Assessment

measurement (1)

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Year 6 Unit 3Assessment task — Calculating fractions and decimals

Name Date

Task

1. Place each fraction on the number line.

12

1112

14

2.

Calculate 13 of 27

3. Tom is saving for his camp which costs $364. He has saved 15 of the cost.

How much has Tom saved?

Show your working.

17 of 52Mth_Y06_U3_AT_FractionsDecimals

4. Joshua entered a pizza eating contest. He ate 12 of a meat lover pizza,

34 of a cheese pizza,

14 of a pepperoni

pizza and 38 of a chicken and bacon pizza.

a) Colour in the pizzas provided to show how much Joshua ate of each pizza.

b) Use the number line to calculate how much pizza Joshua ate altogether.

Write your answer as a fraction, improper fraction or mixed number.________________

5. Calculate the answer for 78 –

14 .

Show your working.

6. Karly has 1 13 packets of biscuits. She eats

16 of a packet and her friend eats

12of a packet.

What fraction of the biscuits has not been eaten?

Show your working.


7.

a) Write a number sequence to describe this pattern.

______________, _____________, _____________, ___________, ___________

b) Continue the pattern.

c) Write a rule which describes the pattern______________________________________

8.

Show a number sequence on the number line that follows this rule:

Start at 18

Increase by 14

9. Fill in the missing numbers to continue the number sequences. Write a rule to describe the pattern.

a) 0.78, ________, 0.74, 0.72, ______, 0.68 Rule:

b) _______, 0.2, 2, 20, ________, ________ Rule:

10. Select the best estimate for each of the following measurements:

a) Mass of apple: 20 g 120 kg 120 g

b) Capacity of paint tin: 4 mL 40 mL 4 L

11. Convert the following measurements into the units provided:

1.75 L 700 g


a) ________mL b) ________ kg

12. Three pieces of ribbon were needed for a costume. Their lengths were 35 mm, 15 cm and 1.25 m.

a) Estimate the total length of ribbon needed for the costume.

______________________________________________

b) Calculate the total length of ribbon needed for the costume.

Show your working

13. The capacity of the cream tub is 300 mL.

a) What is the volume of the cream tub?________________

b) Explain how you know what is the volume.

Explain the connection between capacity and volume.

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

14. Calculate the following:

a) 7.46 × 10 = b) 6.74 ÷ 10 = c) 53.76

+ 38.45

______

d) Iceblocks cost $2.85 each. Simone bought 7 iceblocks. How much did she spend?

e)

f) What is the difference between 5.6 and 7.282?

15. Jo had started her homework when Tanya came and rubbed out some of the numbers.

What numbers are missing?

Show your working.


74.97

Year 6 Mathematics: Unit 3 — Calculating fractions and decimals Name:

Purpose of assessment: To locate fractions on a number line, solve problems involving the addition and subtraction of related fractions, calculate a simple fraction of a quantity and describe rules for sequences involving fractions and decimals. To perform calculations on decimals including multiplying and dividing by powers of 10 and make connections between capacity and volume.

Understanding and Fluency Problem-solving and Reasoning

Add and subtract related fractions. Calculate a simple fraction of a quantity.Locate fractions on a number line. Convert between metric units. Perform calculations on decimals.

Solve problems involving addition and subtraction of related fractions.Describe rules used in number sequences involving fractions and decimals.Make a connection between capacity and volume.

Calculates involving decimals and missing addends.Estimates when converting metric units.

Explains the connection between capacity and volume.Solves multi-step problems involving addition and subtraction of related fractions.

A

Calculates a simple fraction of a quantity involving a decimal.Converts metric units to perform calculations.

Applies rules to continue number sequences.Applies relevant strategies to solve problems involving addition and subtraction of fractions.

B

Adds and subtracts related fractions.Calculates a simple fraction of a quantity.Locates fractions on a number line with related denominators.Multiplies and divides decimals by powers of 10.Converts between metric units.Performs calculations on decimals.

Solves problems involving addition and subtraction of related fractions.Makes a connection between capacity and volume.Describes rules used in number sequences involving fractions and decimals.Solves problems involving decimal calculations.

C

Locates a fraction on a number line where the denominator matches the intervals of the number line.Chooses appropriate units of measurement.

Uses diagrams to show addition of related fractions.Selects appropriate estimates for measurements. D

Writes a fraction on a number line. Uses a diagram to represent a fraction. E

Feedback:

Year 6 Unit 3Assessment task — Locating integers and describing transformations

Name Date

Task

1. Write an everyday situation where negative numbers are used:

2. Write the missing integer in the box.

a)

b)

3. Locate these integers on the number line.

4.

a) Plot each ordered pair on the Cartesian plane.

Label each point with the ordered pair.

A (1,5)

B (–4,–7)

b) Write ordered pairs for points S and T marked on the Cartesian plane.

22 of 52Mth_Y06_U5_AT_IntCartPlane

4–1 0

82–4

–5–1–73

S ___________________________

T ___________________________

5. Shannon plotted 4 points on a Cartesian plane.

Each point was in a different quadrant. She connected the points to create a rectangle.

What could the ordered pairs be?

Hint: Use the Cartesian plane to check your points if necessary.


6.

a) Could the following ordered pairs be the points for Shannon’s rectangle?

(5,5) (–4,7) (–2,–5) (2,–3)

b) Explain why or why not.

7.

a) What single transformation has been applied to shape A to get shape B?

b) What combination of transformations could be applied to get the same result?


BA

8. Doug was given shape A. He was asked to apply a translation to the right, then a 90 degree clockwise rotation. He drew shape B.

a) Is he correct? ____________________________

b) Explain why or why not using mathematical language and diagrams.


B

A

Year 6 Mathematics: Unit 3 — Locating integers and describing transformations Name:

Purpose of assessment: To describe the use of integers in everyday contexts, locate integers on a number line, locate an ordered pair in any one of the four quadrants on the Cartesian plane and describe combinations of transformations.


Identify everyday situations that use integers. Locate and represent integers on a number line. Locate ordered pairs in any one of the four quadrants of the Cartesian plane. Identify a transformation.

Solve problems involving ordered pairs on a Cartesian plane. Use mathematical language and diagrams to explain combinations of translations, reflections and rotations.

Plots and labels ordered pairs in all four quadrants on a Cartesian plane to create a rectangle.Locates and represents integers on a number line which does not have a scale.

Explains reasoning used to decide if a set of ordered pairs meets criteria.Justifies and explains combinations of transformations. A

Locates and represents integers on a number line where the intervals are more than one. Solves problems by plotting points in all four quadrants of the Cartesian plane. B

Writes an everyday context that uses integers.Locates integers on a number line.Plots and labels ordered pairs in a quadrant of the Cartesian plane.Correctly writes ordered pairs.

Describes combinations of transformations. C

Identifies a single transformation or writes a missing integer. Creates a shape on a Cartesian plane. D

Writes an ordered pair. Describes a transformation. E

Feedback:


Year 6 Unit 3Assessment task — Identifying number properties and calculating percentage discounts

Name Date

Task

1. Draw lines to match the number sequence to the number property.

Triangular 12, 14, 15, 16, 18

Composite 7, 11, 13, 17, 19

Even 510, 512, 514, 516, 518

Square 21, 28, 36, 45, 55

Prime 49, 64, 81, 100, 121

2. Choose one or more of the number properties below to label each number.

a) Write your choice or choices beside the number.

b) Use mathematical language and/or diagrams to show why your choice is correct.

196 62

41 36

28 of 52Mth_Y06_U5_AT_NumberProperties

Triangular Composite Square Prime

3. Draw a factor tree to find the prime factors of each number.

36 125

Solve each problem. Show how you worked it out.

4. Maya purchased 16 bags of apples. Each bag contained 24 apples. How many apples does she have altogether?

5. Riley has 468 marbles to give his friends. He wants to share them equally among his four friends. How many marbles will each friend receive?

6. Lan delivers papers two days a week. He delivers 33 papers one day and 77 papers the other day. Lan is paid $5 for every 10 papers he delivers. How much does Lan earn each week?

7. Anna’s car uses five litres of fuel per 100 km.

Her father’s car uses seven litres of fuel per 100 km. Petrol costs $2 a litre. Anna spends less than her father on a 500 km trip. How much less does she spend?


8. Fill in the table to show equivalent fractions, decimals and percentages.

Fraction Decimal Percentage

75%

0.5

610

25%

0.04

9. Write each number in the correct place on the number line.

a) 40% b)

310 c)

34 d) 0.7 e) 15%

10. Calculate the discount on these items. Show how you worked it out.

Cost of item Percentage discount Discount

50%

10%


11. Find out how much the family at Table 24 pays for their order. Show your working in the spaces below.

Show your working for all questions.

a) What is the total cost of the bill for the family without the discount?

b) What is the discount given to the family?

c) What amount does the family pay for their order?


Table 241× Entrée (Garlic bread)

1× Chicken pizza

1× Vegetarian pizza

1× Chocolate ice-cream

Year 6 Mathematics: Unit 3 — Identifying number properties and calculating percentage discounts Name:

Purpose of assessment: To recognise the properties of prime, composite, square and triangular numbers, solve problems involving division and multiplication, calculate common percentage discounts on sale items and connect fractions, decimals and percentages as different representations of the same number.


Identify and describe properties of prime, composite, square and triangular numbers. Make connections between equivalent fractions, decimals and percentages. Calculate percentage discounts of 10%, 25% and 50% on sale items.

Use mathematical language and diagrams to explain properties of whole numbers. Convert and compare fractions, decimals and percentages to solve problems. Solve problems involving percentage discounts, multiplication and division with whole numbers.

Calculates sale price of items after discount.Locates fractions, decimals and percentages on a number line.

Solves multi-step problems involving percentage discounts, multiplication and division.Correctly shows why all four numbers match their choices.

A

Identifies two numbers with more than one property.Lists all the prime factors of composite numbers.

Calculates percentage discounts as part of multi-step problems.Solves single step problems involving multiplication and division with working. B

Identifies number sequences as prime, composite, square and triangular.Makes connections between equivalent fractions, decimals and percentages.Calculates percentage discounts of 10%, 25% and 50%.Locates a fraction, decimal or percentage on a number line.

Explains the properties of numbers.Solves single-step problems involving multiplication and division. C

Identifies a number sequence as prime, composite, square or triangular. Shows why a number matches their choice of number property. D

Identifies a number sequence as even.Connects an equivalent fraction, decimal or percentage. Locates a fraction, a decimal or a percentage on a number line. E

Feedback:


Australian Curriculum

Mathematics - Year 6

Year 6 Achievement StandardBy the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages.

Content Descriptions

Measurement and Geometry Number and Algebra

Using units of measurement

Connect decimal representations to the metric system (ACMMG135) Connect volume and capacity and their units of measurement

(ACMMG138) Convert between common metric units of length, mass and capacity

(ACMMG136) Solve problems involving the comparison of lengths and areas using

appropriate units (ACMMG137)

Location and transformation

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

Money and financial mathematics

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Fractions and decimals

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

Multiply and divide decimals by powers of 10 (ACMNA130) Multiply decimals by whole numbers and perform divisions by non-zero

whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)

Solve problems involving addition and subtraction of fractions with the


same or related denominators (ACMNA126)

Number and place value

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

Patterns and algebra

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

Explore the use of brackets and order of operations to write number sentences (ACMNA134)


Curriculum Priorities - Pedagogy

Considerations

Prior and future curriculumRelevant prior curriculumStudents require prior experience with:

solving simple problems involving the four operations using a range of strategies checking the reasonableness of answers using estimation and rounding identifying and describing factors and multiples describing transformations of two-dimensional shapes using a grid reference system to locate landmarks ordering decimals and unit fractions and locating them on number lines adding and subtracting fractions with the same denominator continuing patterns by adding and subtracting fractions and decimals using appropriate units of measurement for length, area, volume, capacity and mass calculating perimeter and area of rectangles.

Curriculum working towardsThe teaching and learning in this unit work towards:

describing the use of integers in everyday contexts connecting fractions, decimals and percentages as different representations of the same number calculating common percentage discounts on sale items describing combinations of transformations locating an ordered pair in any one of the four quadrants on the Cartesian plane connecting fractions, decimals and percentages as different representations of the same number making connections between the powers of 10 and the multiplication and division of decimals making connections between capacity and volume solving problems involving length and area locating fractions and integers on a number line.


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

Comprehending texts through listening, reading and viewingNumeracy

Estimating and calculating with whole numbers Recognising and using patterns and relationships Using fractions, decimals, percentages, ratios and rates Using spatial reasoning Using measurement

Information and communication technology (ICT) capability Creating with ICT Managing and operating 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

For further information, refer to General capabilities in the Australian Curriculum and the Learning area specific advice.

Cross-curriculum prioritiesAboriginal and Torres Strait Islander histories and culturesStudents 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


Assessing student learningAssessment name: Identifying number properties and calculating percentage discountsAssessment description: Students recognise the properties of prime, composite, square and triangular numbers, solve problems involving division and multiplication, calculate common percentage discounts on sale items and connect fractions, decimals and percentages as different representations of the same number.Assessment name: Locating integers and describing transformationsAssessment description: Students describe the use of integers in everyday contexts, locate integers on a number line, locate an ordered pair in any one of the four quadrants on the Cartesian plane and describe combinations of transformations.Assessment name: Calculating fractions and decimalsAssessment description: Students locate fractions on a number line, solve problems involving the addition and subtraction of related fractions, calculate a simple fraction of a quantity and describe rules for sequences involving fractions and decimals. Students perform calculations on decimals including multiplying and dividing by powers of 10 and make connections between capacity and volume.In this unit, assessment of student learning aligns to the following aspects of the achievement standard.By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages.

FeedbackFeedback in this unit this may include:

ability to calculate percentage discounts on sale items using a variety of strategies to accurately plot ordered pairs on all four quadrants of the Cartesian plane ability to translate, reflect and rotate shapes using a variety of strategies to add and subtract fractions with related denominators ability to multiply and divide numbers by powers of 10 ability to identify rules to describe number sequences.


Year 6 Semester 2 Term 3 Mathematics Report Card Comment BankAssessment Task 1: Calculating Fractions and Decimals

A B C D E2M6A1 2M6B1 2M6C1 2M6D1 2M6E1

{Name} calculated involving decimals and missing addends.{She,He} estimated when converting metric units. {Name} explained the connection between capacity and volume.{She,He} solved multi-step problems involving addition and subtraction of related fractions.

{Name} calculated a simple fraction of a quantity involving a decimal. {She,He} converted metric units to perform calculations. {Name} applied rules to continue number sequences. {She,He} applied relevant strategies to solve problems involving addition and subtraction of fractions.

{Name} added and subtracted related fractions and calculated a simple fraction of a quantity.{She,He} located fractions on a number line with related denominators. {Name} multiplied and divided decimals by powers of 10. {She,He} converts between metric units and performed calculations on decimals. {Name}made a connection between capacity and volume. {She,He} described rules used in number sequences involving fractions and decimals. {Name} solved problems involving decimal calculations.

{Name} located a fraction on a number line where the denominator matches the intervals of the number line.{She,He} chose appropriate units of measurement.{Name} used diagrams to show addition of related fractions.{She,He} selected appropriate estimates for measurements.

{Name} wrote a fraction on a number line. {She,He} used a diagram to represent a fraction.


Assessment Task 2: Locating integers and describing transformation


{Name} plotted and labelled ordered pairs in all four quadrants on a Cartesian plane to create a rectangle.{She,He} located and represented integers on a number line which does not have a scale.{Name} explained reasoning used to decide if a set of ordered pairs meets criteria. {She,He} justified and explained combinations of transformations.

{Name} located and represented integers on a number line where the intervals are more than one. {She,He} solved problems by plotting points in all four quadrants of the Cartesian plane.

{Name} wrote an everyday context that uses integers.{She,He} located integers on a number line.{Name} plotted and labelled ordered pairs in a quadrant of the Cartesian plane. {Name}correctly wrote ordered pairs. {She,He} described combinations of transformations.

{Name} identified a single transformation or wrote a missing integer. {She,He} created a shape on a Cartesian plane.

{Name} wrote an ordered pair. {She,He} described a transformation.

Assessment Task 3: Identifying number properties and calculating percentage discounts


{Name} calculated sale price of items after discount. {She,He}located fractions, decimals and percentages on a number line. {Name} solved multi-step problems involving percentage discounts, multiplication and division. {She,He} correctly showed why all four numbers match their choices.

{Name} identified two numbers with more than one property.{She,He} listed all the prime factors of composite numbers. {Name} calculated percentage discounts as part of multi-step problems. {She,He} solved single step problems involving multiplication and division with working.

{Name} identified number sequences as prime, composite, square and triangular.{She.He} made connections between equivalent fractions, decimals and percentages.{Name} calculated percentage discounts of 10%, 25% and 50%.{She,He} located a fraction, decimal or percentage on a number line. {Name} explained the properties of numbers. {She,He} solved single-step problems involving multiplication and division.

{Name} identified a number sequence as prime, composite, square or triangular. {She,He} showed why a number matches their choice of number property.

{Name} identified a number sequence as even. {She,He} connected an equivalent fraction, decimal or percentage. {Name} located a fraction, a decimal or a percentage on a number line.


Maths Pre-ModerationYear: 6 Unit 3 Semester 2 Title: Mathematics

Curriculum Intent for the Unit (see unit /task description) In this unit students will learn and apply Maths knowledge and skills through guided play and tasks integrated and embedded into other key learning areas. Students apply a variety of mathematical concepts in real-life, lifelike and purely mathematical situations.

Learning opportunities support students to: Connect decimal representations to the metric system Connect volume and capacity and their units of measurement Convert between common metric units of length, mass and capacity Solve problems involving the comparison of lengths and areas using appropriate units Introduce the Cartesian coordinate system using all four quadrants Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness

of answers Compare fractions with related denominators and locate and represent them on a number line Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies Multiply and divide decimals by powers of 10 Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating

decimals, with and without digital technologies Solve problems involving addition and subtraction of fractions with the same or related denominators Identify and describe properties of prime, composite, square and triangular numbers Investigate everyday situations that use integers. Locate and represent these numbers on a number line Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four

operations with whole numbers Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence Explore the use of brackets and order of operations to write number sentences

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

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages.


Scan and Assess

Prioritise

Develop and Plan

Additional Targeted Teaching Priorities* Identified from previous assessment & post moderation of Semester 1 Maths Unit Term 2. Were there any literacy / numeracy identified areas?

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:

ability to calculate percentage discounts on sale items using a variety of strategies to accurately plot ordered pairs on all four quadrants of the Cartesian plane ability to translate, reflect and rotate shapes using a variety of strategies to add and subtract fractions with related denominators ability to multiply and divide numbers by powers of 10 ability to identify rules to describe number sequences.


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: Calculating Fractions and DecimalsAdds and subtracts related fractions.Calculates a simple fraction of a quantity.Locates fractions on a number line with related denominators.Multiplies and divides decimals by powers of 10.Converts between metric units.Performs calculations on decimals.Solves problems involving addition and subtraction of related fractions.Makes a connection between capacity and volume.Describes rules used in number sequences involving fractions and decimals.Solves problems involving decimal calculations.

Assessment Task 2: Locating Integers and describing transformationsWrites an everyday context that uses integers.Locates integers on a number line.Plots and labels ordered pairs in a quadrant of the Cartesian plane.Correctly writes ordered pairsDescribes combinations of transformations.

Assessment Task 3: Identifying number properties and calculating percentage discountsIdentifies number sequences as prime, composite, square and triangular.Makes connections between equivalent fractions, decimals and percentages.Calculates percentage discounts of 10%, 25% and 50%.Locates a fraction, decimal or percentage on a number line.Explains the properties of numbers.Solves single-step problems involving multiplication and division.

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

Assessment Task 1: Calculating Fractions and DecimalsCalculates a simple fraction of a quantity involving a decimal.Converts metric units to perform calculations.Applies rules to continue number sequences.Applies relevant strategies to solve problems involving addition and subtraction of fractions.

Assessment Task 2: Locating Integers and describing transformationsLocates and represents integers on a number line where the intervals are more than one.Solves problems by plotting points in all four quadrants of the Cartesian plane.

Assessment Task 3: Identifying number properties and calculating percentage discountsIdentifies two numbers with more than one property.Lists all the prime factors of composite numbers.Calculates percentage discounts as part of multi-step problems.Solves single step problems involving multiplication and division with working.


‘A’ Standard – Success Criteria(Refer to GTMJ and relevant content descriptors + above)

Assessment Task 1: Calculating Fractions and DecimalsCalculates involving decimals and missing addends.Estimates when converting metric units.Explains the connection between capacity and volume.Solves multi-step problems involving addition and subtraction of related fractions

Assessment Task 2: Locating Integers and describing transformationsPlots and labels ordered pairs in all four quadrants on a Cartesian plane to create a rectangle.Locates and represents integers on a number line which does not have a scaleExplains reasoning used to decide if a set of ordered pairs meets criteria.Justifies and explains combinations of transformations.

Assessment Task 3: Identifying number properties and calculating percentage discountsCalculates sale price of items after discount.Locates fractions, decimals and percentages on a number line.Solves multi-step problems involving percentage discounts, multiplication and division.Correctly shows why all four numbers match their choices.

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 FeedbackLesson 1Connecting fractions, decimals and percentagesExample learning sequence

Establish learning context Investigate percentages Convert between fractions, decimals and

percentages Calculate percentage discounts using a dual

number line

Evidence of learningCan the student:

Match a percentage to its fractional amount? Calculate the percentage of an amount? Calculate discounts of 10%, 25% and 50%?

Lesson 2Calculating percentage and discountExample learning sequence

Establish learning context Investigate fractions, decimals and percentages Calculate percentages using written strategies Calculate discounts


Calculate 10%, 25% and 50% of a quantity that is a multiple of 100?

Calculate 10%, 25% and 50% of a quantity that is not a multiple of 100?

Calculate 10%, 25% and 50% of a quantity that results in a decimal answer?

Convert between fractions, decimals and percentages?

Lesson 3Calculating the amount you payExample learning sequence

Establish learning context Convert percentages Calculate discounts using digital technologies Calculate percentage discounts for payment


Convert between fractions, decimals and percentages?

Calculate percentage discounts using a calculator? Calculate the price to be paid after the discount?

Lesson 4Exploring properties of whole numbersExample learning sequence

Establish learning context Recognise properties of prime and composite

numbers Recognise properties of square and triangular

numbers Explore the relationship between square numbers

and index notation


Calculate the prime factors of composite numbers? Write square numbers using index notation? Draw diagrams to represent square and triangular

numbers? Make the connection between consecutive

triangular numbers and a square number?

Lesson 5Using written strategies for multiplicationExample learning sequence

Establish learning context Calculate using mental and written multiplication

strategies Apply a written strategy for two-digit multiplication Solve problems involving multiplication


Apply a written method to solve two-digit multiplication questions?

Check the reasonableness of an answer using estimation?

Write a number sentence to represent a problem?

Lesson 6Calculating multiplication using a written strategyExample learning sequence

Establish learning context Consolidate a multiplication written strategy Apply a written algorithm for two-digit multiplication Create and solve problems involving two-digit

multiplication


Apply a written strategy to solve two-digit multiplication questions?

Check for reasonableness of an answer by estimating? Write a number sentence to represent the problem?


Teaching Sequence FeedbackLessons 7-8Using written strategies for divisionExample learning sequence

Establish learning context Consolidate mental division strategies Revisit 1, 2, 5 strategy with and without


(calculations with and without remainders) Introduce a written standard written algorithm

(calculations with and without remainders)


Apply written strategies to solve division questions?

Lesson 9Assessing student learningExample assessment sequence



Assessment purposeTo recognise the properties of prime, composite, square and triangular numbers, solve problems involving division and multiplication, calculate common percentage discounts on sale items and connect fractions, decimals and percentages as different representations of the same number

Lesson 10Locating and representing positive and negative numbersExample learning sequence

Establish learning context Locate and position positive and negative numbers

on a number line Compare and order positive and negative numbers


Provide examples of integers in real-life contexts? Use a number line to locate integers? Compare and order integers?

Lesson 11Solving problems involving integersExample learning sequence

Establish learning context Create number lines involving integers Solve problems involving integers


Accurately plot integers on a number line? Move between positive and negative numbers

along a number line? Solve problems involving integers?

Lesson 12Introducing the Cartesian planeExample learning sequence

Establish learning context Explore grid coordinates Introduce the first quadrant of the Cartesian plane Introduce the second quadrant of the Cartesian

plane Introduce the third and fourth quadrants of the

Cartesian plane


Identify all four quadrants of the Cartesian plane? Locate points on the Cartesian plane? Plot ordered pairs on all four quadrants of the

Cartesian plane?

Lesson 13Applying understanding using the Cartesian planeExample learning sequence

Establish learning context Draw shapes on the Cartesian plane Establish ordered pairs from table of values Represent polygons on the Cartesian plane Solve problems using the Cartesian plane


Complete a table of values and write ordered pairs?

Use ordered pairs to construct shapes on the Cartesian plane?

Solve problems using the Cartesian plane?


Teaching Sequence FeedbackLesson 14Applying a one-step transformationExample learning sequence

Establish learning context Investigate one-step transformations Apply transformations to create a tessellation


Use the appropriate language (e.g. translation, reflection, rotation) to describe transformations?


Lesson 15Applying a combination of transformationsExample learning sequence

Establish learning context Apply combinations of transformations Create new shapes with multiple transformations Create a transformation pattern


Identify a combination of transformations? Describe a combination of transformations? Create a pattern by applying a combination of

transformations to a shape?




Assessment purposeTo describe the use of integers in everyday contexts, locate integers on a number line, locate an ordered pair in any one of the four quadrants on the Cartesian plane and describe combinations of transformations.

Lesson 17Creating and completing sequences involving fractions and decimalsExample learning sequence

Establish learning context Identify and continue number sequences involving

fractions Identify and continue number sequences involving

decimals Record patterns involving fractions and decimals in

tables of values


Describe a number sequence involving fractions and decimals with a rule?

Identify and apply the rule to a number sequence involving fractions and decimals?

Lesson 18Applying the order of operations to word problemsExample learning sequence

Establish learning context Explore the order of operations Practise solving number sentences using the order

of operations


Apply the order of operations to solve problems? Write a number sentence, using order of

operations correctly?

Lesson 19Applying the order of operations to decimals and fractionsExample learning sequence

Establish learning context Revisit the order of operations Solve more complex equations involving order of

operations


Apply the order of operations to solve problems? Write a number sentence using order of

operations correctly?


Teaching Sequence FeedbackLesson 20Adding and subtracting fractionsExample learning sequence

Establish learning context Add and subtract fractions with the same and

related denominators Use strategies to solve word problems involving

adding and subtracting fractions


Add and subtract fractions with the same and related denominators?

Interpret a word problem? Write a number sentence? Solve word problems by adding or subtracting

fractions with related denominators?

Lesson 21Calculating a fraction of a quantityExample learning sequence

Establish learning context Calculate a unit fraction of a quantity Calculate a fraction of a quantity Use digital technologies to calculate unit fractions

of a quantity



Lesson 22Solving problems involving fractionsExample learning sequence

Establish learning context Solve problems involving fractions


Interpret a word problem to create a number sentence?

Add and subtract fractions with related denominators in different contexts?


Lesson 23Dividing decimals by powers of 10Example learning sequence

Establish learning context Multiply by powers of 10 Explore dividing by powers of 10


Divide a decimal number by a power of 10, using a place value chart?

Mentally divide a decimal number by a power of 10?

Lesson 24Adding and subtracting decimalsExample learning sequence

Establish learning context Add and subtract decimals Investigate addition of hundredths Investigate subtraction of hundredths


Calculate addition, using a written algorithm?

Lesson 25Multiplying decimals by whole numbersExample learning sequence

Establish learning context Multiply decimals by whole numbers Practise multiplying decimals by whole numbers


Apply a written algorithm to calculate numbers with tenths and hundredths?

Make reasonable estimates for multiplication questions?

Lesson 26Dividing dividends that result in tenths and hundredthsExample learning sequence

Establish learning context Calculate division of whole numbers Express remainders as decimals Introduce division resulting in hundredths Apply rounding to hundredths


Divide a whole number by another whole number? Convert a remainder to a fraction and decimal? Round a remainder to the hundredths place?


Teaching Sequence FeedbackLesson 27Connecting decimals to the metric systemExample learning sequence

Establish learning context Recognise equivalent measurements Use appropriate units of measurement


Recognise equivalent measurements in different units? Use appropriate units to record measurements?

Lesson 28Converting between metric unitsExample learning sequence

Establish learning context Identify and use correct operations when converting

units of measurement Explore prefixes in units of measurement to assist in

conversion understanding Convert between units of measurement


Use prefixes to assist in identifying equivalences? Convert between units of measurement?

Lesson 29Comparing length and areaExample learning sequence

Establish learning context Explore the relationship between length and perimeter Calculate areas of rectangles Solve problems involving area and perimeter


Calculate perimeters of regular shapes? Calculate areas of rectangles? Use appropriate units? Identify the relationship between length and area

through problem-solving?

Lesson 30Solving problems involving perimeter and areaExample learning sequence

Establish learning context Calculate perimeters of irregular shapes Calculate areas of compound shapes Solve problems involving area and perimeter


Calculate perimeters of irregular shapes? Calculate areas of compound rectangles? Interpret and solve word problems?

Lesson 31Connecting volume and capacityExample learning sequence

Establish learning context Measure the capacity of containers Conduct measurements to connect millilitres to litres Connect capacity and volume (millilitres to cubic

centimetres)


Measure and record the capacity of containers, using metric units?

Explain that there are 1 000 mL in a litre? Explain that 1 mL is equivalent to 1 cm3?


Understand the assessment Review the Guide to making judgments and understand

the standardsConduct the assessment

Assessment purposeTo locate fractions on a number line, solve problems involving the addition and subtraction of related fractions, calculate a simple fraction of a quantity and describe rules for sequences involving fractions and decimals.To perform calculations on decimals including multiplying and dividing by powers of 10 and make connections between capacity and volume.


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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