revisit angle relationships · web view2019. 3. 17. · pialba state school: mathematics year 6...

PIALBA STATE SCHOOL: MATHEMATICS YEAR 6 SEMESTER 1 UNIT 2 TERM 2 PLAN

Proficiency Strands

At this Year level:

• understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations

• fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables

• problem-solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles

• reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

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 1 Pre-Test

2 S Investigating the design of pyramids (MGI)

3 M Below Zero (Integers)

4 S Order of Operations

6 S Investigating Angles

9 M Patterns Rules

10 D Show Me Term 1 Post-TestShow Me Term 2 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 6 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 8 & 9

Check for Understanding Differentiation ResourcesALL RESOURCES HAVE BEEN UPLOADED TO ONENOTE

SHAPEClassify & Construct Nets of 3D

objectsConstructing prisms & pyramids

#Warm Ups

#Activities - Classifying and constructing nets of 3D objectsClassify three-dimensional objects according to their features Sort three-dimensional objects into groups in more

than one way and explain the sorting. Sort three-dimensional objects into prisms, pyramids

and others and explain the sorting criteria.

Identify nets of three-dimensional objects Review understanding of nets. Identify nets of three-dimensional objects.

Construct three-dimensional objects using nets Construct nets of a cube. Construct nets of a rectangular prism. Define and identify pyramids. Investigate nets of a pyramid.

Constructing prisms and pyramidsEstablish learning context• Consider the objective of the lesson.

Construct solid models of prisms and pyramids• Build models of prisms and pyramids using modelling

materials.• Evaluate the results by checking the accuracy of the

features and comparing with geometric solids or everyday examples.

Construct skeletal models of prisms and pyramids

Monitor students’ ability to:Identify features of three-dimensional objects, in particular prisms and pyramids.Identify and draw nets of prisms and pyramids.

Check the accuracy of the features of their models.

Learning alertsBe aware of:Students failing to identify the base of three-dimensional objects.Students being unable to visualise the three-dimensional object from its net and vice versa.

Students not attending to the length of the sides and the size of the angles in their models, resulting in inaccurate models.

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

Provide charts of three-dimensional objects with features labelled.

Encourage students to match the features on the charts with the features of everyday three-dimensional objects.

Play barrier games such as ‘Guess my shape’

Allow students

U2BReading calendars

Linking months of the year to seasons

Expose to more technical or specific Maths vocabulary.

Independent Work

Peer Instruction

Tiered tasks

Introduce less familiar prisms (e.g. pentagonal prisms, hexagonal prisms) and encourage students to identify the bases, then use the shape to name the prisms.

Encourage students to build other types of prisms besides rectangular and triangular prisms.

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

ResourcesSupporting learning resource — Constructing nets of 3D objectsSheet — Prism or not?models of three-dimensional objects (e.g. geometric solids or everyday examples such as boxes, dice, balls, soft drink cans)pictures of three-dimensional objectstwo or more hoops, blank cards to be used as labels for groupsLearning object — Nets: cube and rectangular prismSheet — Nets of 3D objectsLearning object — Nets for 3-D shapes (2)Sheet — 3D objects and their netsexamples or models of three-dimensional objects

Supporting learning resource — Constructing prisms and pyramids modelling materials (reusable modelling clay, playdough, modelling clay)materials for constructing prisms

Languageprism, pyramid, polygon, base, vertex, apex, edge, face, net, cube, square-based prism, rectangular prism, 3D, three-dimensional, square-based prism, rectangular prism, triangular-based prism

Walt: Classify three-dimensional objects according to their features.

Identify three-dimensional objects.

Identify and draw nets of three-dimensional objects.

Construct solid and skeletal models of prisms and pyramids.

Wilf: Explain how the features of a three-dimensional object determine whether it is a prism or a pyramid?

Identify nets of threedimensional objects?

Draw a net of a cube, rectangular prism and pyramid?

Use the features of prisms and pyramids to evaluate their models?

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



• Collect appropriate material for building skeletal models (e.g. collect 12 toothpicks for prisms with 12 edges).

• Compare the features of the skeletal models to those of solid models and geometric solids and adjust as required.

• Emphasise the need for accuracy in reproducing the features.

to work with a partner to facilitate building and evaluating skeletal models.

and pyramids (e.g. toothpicks and reusable modelling clay, straws and sticky tape, paper for rolling into tubes)





Active learning Engagement(The How)C2C Lessons 10 - 13

Check for Understanding

Differentiation ResourcesALL RESOURCES HAVE BEEN UPLOADED TO ONENOTE

MEASUREMENTVolume & Capacity

Guided Investigation (Pyramids)

#Warm Ups

Using units of measurement — Comparing volume and capacity #Activities

Establish learning context• Consider the objectives of the lesson.

Compare the terms volume and capacity• Define the terms ‘volume’ and ‘capacity’. For example, capacity is

the amount a container can hold. It is often used in relation to the volume of a liquid. Volume is a measure of the amount of space taken up by an object.

• Discuss misconceptions of volume and capacity to establish the relationship between them by comparing and contrasting both terms.

Use materials to define volume and capacity in real-life contexts• Display examples of objects to establish units of measurement for

volume.• Discuss appropriate units of measurement (millilitres, litres, cubic

centimetres and cubic metres) for specific items (medicine on a teaspoon, tea in a cup, water in a jug, water in a swimming pool, load of gravel).

Measure volume and capacity using materials• Estimate capacities of containers and measure using appropriate

instruments and appropriate units (millilitres, litres)• Measure the volume of objects (e.g. empty milk container) by filling

them with 1 cm cubes.• Use cubic centimetres (cm3) as the unit for recording volume. Guided Investigation Assessment TaskUsing units of measurement — Investigating the design of pyramids (MGI)

Establish learning context

Monitor students’ ability to:Make connections between capacity and volume.

Learning alertsBe aware of:Students confusing ‘volume’ and ‘capacity’ which might cause them to incorrectly label the container’s capacity as ‘volume’.

Guided Investigation Assessment Task

Monitor students’ ability to:Formulate and solve authentic problems using area, capacity and volume.

Learning alertsBe aware of:

L2B



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




Use technology to record students work; e.g. digital photography, tape and video.

Use non-standard units to estimate and measure capacities (e.g. How many marbles will fit in the jar?)Students use




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

Provide opportunities to estimate and measure larger volumes and capacities and make connections with dimensions


Resources

Supporting learning resource — Comparing volume and capacity

Sheet — Investigating capacity

Sheet — Building volume

variety of containers

1 cm cubesLearning object — Measure it: With what?

Resources for Guided Inquiry

Assessment task — Investigating pyramids and measurement

Assessment task — Investigating pyramids and measurement: Model response

Supporting learning resource — Guided inquiry poster

Supporting learning resource — Evidence cycle

Languagemeasurement, volume, capacity, appropriate unit, millilitres, litres, mL, L, cubic centimetres, cm³, cubic metres, m³

Walt: Define the terms ‘volume’ and ‘capacity’.

Measure volumes using appropriate units of measurement.

Estimate and measure volumes.

Problem-solve and reason by conducting an inquiry task to design the ‘biggest’ pyramid from an A3 sheet.

Wilf: Explain the difference between volume and capacity?

Choose appropriate units?

Make reasonable estimations?

Accurately measure volumes?

Develop a plan to solve an inquiry question?

Identify appropriate mathematical strategies to calculate and compare




pyramid size (e.g. by measuring capacity and converting to volume)?

Justify pyramid design using evidence collected?

• Inquiry question: What is the biggest pyramid you can make from an A3 sheet?

Explore contexts such as pyramids around the world (Discover)• Introduce and analyse the inquiry question.• Discuss how ‘biggest pyramid’ might be interpreted.• Investigate Egyptian pyramids and discuss different types of

geometric pyramids.• Discuss A3 paper size.

Plan how to answer the question (Devise)• Develop a work plan.• Identify appropriate mathematical methods that could be used to

help solve the problem.• Identify different designs that could be used, such as nets, or

disassembled sides which can be cut out and taped together to make a pyramid.

• Identify strategies for measuring size (e.g. measuring height, measuring volume by filling the pyramid with sand or similar and then pouring it into a measuring cylinder).

• Identify conversions between units of capacity and volume.

Collect and review evidence (Develop)• Implement the plan.• Investigate and trial various pyramid designs and sheet layouts.• Record mathematical evidence collected and flow of decisions made

to identify the best design.• Measure and assess pyramid size (e.g. by measuring capacity or area

of unused paper).• Review processes and plans and amend strategy if required.• Review if the evidence is sufficient to form conclusions.

Draw conclusions (Defend)• Construct the biggest pyramid and replicate the design/plan on

another A3 sheet.• State the size of the pyramid.• Justify the design chosen using the evidence collected (e.g. refer to

layout or shape).• Present and/or explain the mathematics used to support the

response.• Reflect on what has been learned and how it could be improved in

the future.

Extend learning or apply learning to other areas (Diverge)

Students confusing ‘volume’ and ‘capacity’.

nets rather than disarticulated designs. Students compare size using simple measures of size such as relative size or area of base, or height.

of containers.

Students consider pyramids with other polygon base shapes (e.g. hexagons and triangles). Students consider a range of measures of size, such as area of paper used, height and volume/capacity.

Supporting learning resource — Investigating pyramids and measurement

pourable substance such as sand or flour

model and net of a pyramid

capacity measuring containers

A3 paper and/or poster cardboard

A4 and/or A5 sheets of paper

measuring implements, including 30 cm rulers and protractors (if the ‘angle method’ is used to draw the nets)

Learning object — 3D shapes from different views

Sheet — Pyramids and Sphinx of Giza

Helpful information

Supporting learning resource — Guided Inquiry: 5Ds https://learningplace.eq.edu.au/cx/resources/items/e485f3ba-f8d8-4d99-9556-cecf2846a464/0/Mth_HI_InquiryApproach.docx

Supporting learning resource — Guided Inquiry FAQ https://learningplace.eq.edu.au/cx/resources/items/f4ced56b-8641-477a-a3fb-f22d0ebc1f81/0/Mth_HI_InquiryFAQs.docx

https://learningplace.eq.edu.au/cx/resources/items/f4ced56b-8641-477a-a3fb-f22d0ebc1f81/0/Mth_HI_InquiryFAQs.docx



https://learningplace.eq.edu.au/cx/resources/items/e485f3ba-f8d8-4d99-9556-cecf2846a464/0/Mth_HI_InquiryApproach.docx



• Can a larger pyramid be made by increasing the number of sides?• Does the shape of the sheet make a difference? Is a square sheet

(354 x 354 mm) the same size as an A3 sheet of paper?• How do the volume, height and base area change if the same design

is used to construct a pyramid from an A4 sheet of paper?• Amend your plan based on feedback and new ideas gained from

viewing the work of other students to make a larger pyramid.• Add design and colour to the outside of the pyramid.• Apply learning to other areas.








NUMBER & PLACE VALUE

Square & Triangular Nos.

Less than zero (Number Line)

Positive & Negative Nos.

#Warm Ups

Number and place value — Exploring square and triangular numbers #Activities

Establish learning context• Consider the objective of the lesson.

Explore arrays of numbers• Represent numbers less than ten in arrays.• Discuss the shapes that are created (rectangular, square).• Write the factors that can be represented by the arrays (1 x 1, 2 x 2, etc.)

Explore square numbers• Define a square number.• Create the first five square numbers as arrays (1, 4, 9, 16 and 25).• Discuss the growth number pattern that occurs.• Identify a square number as a number multiplied by itself.• Find the square number of the numbers one to ten.• Create a visual representation of square numbers; e.g. cut square

numbers from dot paper.

Find square numbers from one to 100• Find all square numbers on a multiplication grid.

Represent triangular numbers• Introduce triangular numbers.• Demonstrate the triangular shape.• Create the first three triangular numbers with counters.• Discuss the growth pattern.

Find triangular numbers between one and 100• Record triangular numbers in a table.• Investigate and discuss patterns observed.

Monitor students’ ability to:Construct a square number using materials and visual models.

Construct a triangular number using materials and visual models.

Learning alertsBe aware of:Students misinterpreting the rule ‘a square number is the answer you get when you multiply a number by itself’.Students not familiar with number facts.

When recorded as an exponent (e.g. 5²) students multiply the whole number by the exponent (e.g. 5 x 2 = 10).

Students connecting the term number with the triangular number, e.g. the second triangular number is 3.Students adding more than one counter to the next row.

Monitor students’ ability to:

L2B








Work with small square and triangular numbers and materials.






Independent Work

Peer Instruction

Tiered tasks

Work with large square numbers and identify patterns among the sequence of square numbers.Work with large


Resources

Supporting learning resource — Exploring square and triangular numbers

Sheet — Square dot paper

Sheet — Grid paper:1 cm

Audio — A square meal for a squeaky alien

Sheet — Multiplication grid

counters, scissors, chess board

Sheet — Hundred board

Sheet — Square dot paper

Sheet — Patterns in triangular numbers

counters

Languagesquare number, equal, factor, ‘multiplied by itself’, integers, positive, negative, temperature, number lineWalt: Investigate square and triangular numbers.

Wilf: Create arrays to show a square number?

Represent a triangular number?

Apply square and triangular number patterns to predict the next square number?




Walt: Position positive and negative whole numbers on a number line.Use a number line to solve problems involving positive and negative numbers

Wilf: Represent positive and negative numbers on a number line?Use the number line to represent and solve problems?

Walt: Demonstrate understanding of positive and negative numbers and their position on a number line.

Wilf: Locate positive and negative numbers on a number line?

Interpret positive and negative numbers in a real-life situation?

• Investigate the pattern within the rows of triangular numbers.• Use patterns to predict the next triangular number.• Identify the triangular numbers between one and 100.

Number and place value — Solving problems less than zero on a number line#Activities


Explore numbers less than zero• Establish the concept of numbers having a value of less than zero.• Brainstorm real-life examples of situations where numbers less than zero

are used.

Locate positive and negative numbers on a number line• Position number cards from –10 to 10 on a number line.• Compare the value of numbers based on their position on the number

line.

Number and place value — Solving problems less than zero on a number line#Activities


Revisit positive and negative numbers on a number line• Review the position of integers relative to zero.• Students position numbers on a number line.• Form generalisations about movement along a number line.

Show understanding of integers (Monitoring task)• Solve problems involving integers using an everyday example of a number

line.

Identify everyday situations where negative numbers are used.

Use strategies to solve problems.Use a number line to solve problems.

Learning alertsBe aware of:Students incorrectly assuming that negative numbers are fractions of positive numbers.

Students thinking that numbers less than zero are non-existent numbers.

Suggested next steps for learningEmphasise real-life scenarios that involve numbers less than zero such as temperature scale or finance.Play games that involve a scoring system where players can lose more points than they earn.

Monitor students’ ability to:Locate positive and negative numbers on a number line.

Learning alertsBe aware of:Students incorrectly assuming that negative numbers are fractions of positive numbers.

Students work with pictorial representations and engage in physical activities that involve moving either side of zero.

Students work with pictorial representations and engage in physical activities that involve moving either side of zero.

triangular numbers.

Create number lines to model differences between positive and negative numbers.

Students create number lines appropriate for the range of numbers in a variety of problems.

Resources

Supporting learning resource — Solving problems on a number line

Sheet — What is less than zero?

Sheet — Numbers -10 to 10 (print and cut)

rope or tape to create a number line on the floor

Sheet — Positive and negative numbers

Learning object — Number linerope or tape (to create a number line on the floor long enough for 21 students to stand along)

Resources

Monitoring task — Describing integers in everyday contexts

Supporting learning resource — Locating positive and negative numbers on a number line

Sheet — Thredbo thermometers

Sheet — Numbers –10 to 10

rope

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






PATTERNS & ALGEBRAOrder of

OperationsProblems

Assessment Task

##Warm Ups

Patterns and algebra — Introducing order of operations #Activities

Establish learning context• Consider the objective of the lesson.• Explain that operations in expressions are worked on in order of

their sophistication. For example, multiplication is worked on before addition, because it is a more sophisticated operation.

• Establish conventions for the order of operations, e.g.

1. Do the calculations inside the brackets.2. Do multiplication and division before adding and subtracting.3. Work left to right.

Investigate the left to right convention• Investigate the commutative property for addition and

multiplication and how it does not apply to subtraction and division.• Establish the importance of working left to right when solving

expressions containing subtraction and division, e.g. 28 – 4 – 3 = .

Explore ordering multiple operations

Monitor students’ ability to:Solve expressions containing multiple operations.Identify why a convention is needed to inform the order of calculations.

Learning alertsBe aware of:Students working from left to right rather than using the order of operations conventions.

L2B






Use small group instruction and cooperative







Resources

Supporting learning resource — Introducing order of operations

calculators

Sheet — Order of operations

Sheet — Operation cards (Note: Make enough copies to give each player one card.)

Sheet — Using the order of operations

Languageorder of operations, expression, equation, brackets, multiply, divide, add, subtract

Walt: Explore and apply conventions used to calculate expressions containing multiple operations.

Identify that brackets may be needed to change the order in which operations are completed.

Wilf:




Demonstrate the importance of applying conventions when calculating expressions containing multiple operations?

Explain the effect of brackets on the order of operations in an expression?

Walt: Apply conventions when solving problems involving multiple operations

Wilf: Demonstrate the correct order of conventions when solving problems involving multiple operations?

• Calculate answers for equations containing multiple operations.• Investigate reasons for having a correct order for working when

expressions have multiple operations, e.g. 8 – 3 x 2 = .• Demonstrate the convention of working multiplication and division

before addition and subtraction.

Identify the effect of using brackets• Investigate the effect of using brackets, e.g.

(8 – 3) x 2 = 10, 8 – (3 x 2) = 2• Identify whether brackets are required when solving expressions

containing multiple operations.

Solve equations using the order of operations• Solve equations and problems associated with the order of

operations.

Patterns and algebra — Solving problems using the order of operations#Activities

Revisit order of operations• Review the order of operations for calculating expressions with

multiple operations. Conventions:o Do the calculations inside the brackets.o Do multiplication and division before adding and subtracting.o Work left to right.

• Depending on your students, it may be relevant to investigate acronyms and their limitations (e.g. BOMDAS, BODMAS, PEMDAS).

Solve problems using the order of operations• Solve problems using the order of operations.• Create equations using order of operations to reach a target

number.• Consolidate knowledge through independent activities.

Patterns and algebra — 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

Monitor students’ ability to:Apply the order of operations to solve problems.

Learning alertsBe aware of:Students working from left to right rather than using the order of operations.

Assessment Task

Assessment purposeTo write and apply the correct use of brackets and order of operations in number sentences.

learning strategies


Provide students with problems and have them explain the steps to solve them.

Independent Work

Peer Instruction

Tiered tasks

Extend the complexity of the expressions by including more operations and brackets.

Extend the complexity of the expressions by including more operations and brackets. Resources

Supporting learning resource — Solving problems using the order of operations

calculator

six-sided dice

playing cards

Sheet — Order of operations

Sheet — What order?

Resources

Assessment task — Applying the order of operationsAssessment task — Applying the order of operations: Model response

the assessment.

Conduct the assessment• Students individually complete the test to demonstrate their

understanding of the conventions used when calculating expressions containing multiple operations.







NUMBER & PLACE VALUEMental Strategies when dividing (no remainder)

Applying written strategy

#Warm Ups

Number and place value — Applying mental strategies when dividing with no remainder #Activities

Revisit divisibility rules Review divisibility rules as guidelines for determining if

one number is divisible by another using an understanding of number sense and place value.

Use divisibility rules to find factors for various numbers.

Consider parts of a division number sentence and provide students with dividends to which they must find divisors that divide equally.

Revisit mental strategies for division Review mental strategies for division. Review estimating with division using front-ending and

rounding strategies. Introduce, model and apply the ‘think multiplication’

strategy, e.g. 130 ÷ 5 = 5 x ? = 130). Introduce, model and apply the split strategy, e.g.

180 ÷ 5 = (100 ÷ 5) + (50 ÷ 5) + (30 ÷ 5) = 20 + 10 + 6 =

Monitor students’ ability to:Choose appropriate mental strategies for division.Estimate a result when dividing.

Learning alertsBe aware of:Students not connecting division with the corresponding multiplication fact.

Students not knowing their multiplication number facts, possibly causing difficulty when recalling related facts for division.

L2B






Use small group instruction and cooperative





Independent Work

Peer Instruction

Tiered tasks

Use more complex and


Resources

Supporting learning resource — Applying mental strategies to dividing with no remainder

Sheet — Divisibility rules

Sheet — Division with no remainders

calculator

counters

Languagedivide, divisor, quotient, dividend, factorise, ‘think multiplication’, partition, split, estimate, factors, multiples

Walt: Apply mental strategies to divide whole numbers by one-digit divisors.

Apply the 1, 2, 5 strategy for dividing whole numbers by onedigit divisors.

Express a remainder as a whole number

Wilf: Estimate with accuracy?




Choose strategies to divide with consistent accuracy?

Divide using the 1, 2, 5 strategy with consistent accuracy?

36). Apply strategies to division word problems.

Number and place value — Applying a written strategy when dividing without and with a remainder

Revisit mental strategies for division• Discuss the relationship between multiplication and

division.• Revise the ‘split’

(e.g. 180 ÷ 5 = (100 ÷ 5) + (50 ÷ 5) + (30 ÷ 5) = 20 + 10 + 6 = 36) and ‘think multiplication’ (e.g. 130 ÷ 5 = 5 x ? = 130) strategies for calculating division mentally.

Review the 1, 2, 5 written strategy for division without a remainder• Review the 1, 2, 5 strategy for solving division

questions that don’t require a remainder.• Use the 1, 2, 5 strategy to solve division questions

without a remainder.

Use the 1, 2, 5 strategy for division with a remainder• Review remainders that are written as whole numbers.• Investigate and use the 1, 2, 5 strategy for division

with a remainder.• Solve division questions that require a remainder

written as a whole number. (Remainders written as proper fractions will be taught in later units.)

Monitor students’ ability to:Use the 1, 2, 5 strategy.

Learning alertsBe aware of:Students not connecting division with the corresponding multiplication fact.Students not knowing their multiplication number facts, possibly causing difficulty when recalling related facts for division.

learning strategies

Provide base 10 materials or counters to link division and multiplication facts.

Provide base 10 materials and place value charts to illustrate division process and steps required to divide larger numbers.

larger numbers with multiple factors.

Use larger numbers that require answers with remainders.

Supporting learning resource — Applying a written strategy when dividing without and with a remainder

Sheet — 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

Sheet — 1, 2, 5 exemplar

Video — Using the 1, 2, 5 strategy with no remainder

Video — Using the 1, 2, 5 strategy with a remainder

base 10 materials

calculator








GEOMETRIC REASONING

Investigating AnglesVertically Opposite : Calculate Unknown

AnglesAssessment Task

#Warm Ups

Geometric reasoning — Investigating angles on a straight line #Activities

Define ‘adjacent’ and ‘supplementary’ Explore the term ‘adjacent’. Introduce the term ‘supplementary’.

Make generalisations about angles on a straight line Use models to investigate angles on a straight line. Estimate, then measure angles on a straight line. Make a generalisation about angles that form a straight line. Test the generalisation by proving angles on a straight line equal 180°.

Calculate unknown angles on a straight line Explore methods to calculate unknown angles on a straight line. Apply methods to calculate unknown angles on a straight line.

Geometric reasoning — Investigating vertically opposite angles#Activities

Generalise about angles made by intersecting lines

Monitor students’ ability to:Identify a pattern and make a generalisation.Calculate unknown angles on a straight line.

Learning alertsBe aware of:Students who cannot see a pattern.Students who cannot describe a pattern.Students who cannot write a statement that generalises the pattern.

Monitor students’ ability to:

L2B






Use small group instruction and





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


Resources

Supporting learning resource — Investigating angles on a straight line

Sheet — Calculating unknown supplementary angles

Sheet — Identify supplementary angles

Learning object — 360º protractor

Languageangle, vertex, ray, labelling angles ABC , AB/BC rays, protractor, acute, right angles, obtuse, straight, reflex, revolution, straight line, revolution, angles at a point, vertically opposite, supplementary, intersecting lines, angles at a pointWalt: Make a generalisation about angles on a straight line.




Make a generalisation about vertically opposite angles.

Wilf: Make a generalisation about angles on a straight line?

Calculate unknown angles on a straight line?

Identify the angle relationship involved in calculating unknown angles on a straight line?

Identify vertically opposite angles?Calculate unknown vertically opposite angles?

Make a generalisation about vertically opposite angles?

Walt: Make a generalisation about angles at a point.

Wilf:Identify and calculate unknown angles at a point?

Make a generalisation about angles at a point?

Identify the angle relationship involved in calculating unknown angles at a point?

• Discuss angles formed by two intersecting lines using the terms ‘vertically opposite’, ‘intersecting lines’, ‘acute’, ‘obtuse’, ‘right-angled’ and ‘equal’.

• Classify the angles formed by two intersecting lines.

Explore angle relationships in vertically opposite angles• Estimate then measure vertically opposite angles.• Form a generalisation about vertically opposite angles.• Test the generalisation, by proving vertically opposite angles are equal.

Calculate unknown vertically opposite angles• Explore methods to determine and calculate unknown vertically

opposite angles.Apply methods to determine and calculate unknown vertically opposite angles

Geometric reasoning — Investigating angles at a point#Activities

Explore angles at a point• Use materials to investigate the sum of angles at a point.• Estimate, then measure, angles at a point.

Make a generalisation about the relationship between angles at a point• Form a generalisation about angles at a point.• Test the generalisation by proving that angles at a point add to 360°.

Calculate unknown angles at a point• Explore methods to calculate unknown angles at a point.• Apply methods to calculate unknown angles at a point.• Investigate angles formed by three and more intersecting lines.

Geometric reasoning — Calculating unknown angles

Identify a pattern and making a generalisation.Calculate vertically opposite angles.

Learning alertsBe aware of:Students who cannot describe a vertically opposite angle.Students who cannot identify the size of angles due to being unfamiliar with alternative orientations of vertically opposite angles.

Monitor students’ ability to:Identify a pattern and make a generalisation.Calculate unknown angles at a point.

Learning alertsBe aware of:Students confused about angles at a point being associated with angles in a circle.

cooperative learning strategies


To link size of the angle and the concept of rotation, students can use full circle protractor with a moveable line.

Provide visual aids of angle types for proportional understanding.

where possible.

Independent Work

Peer Instruction

Tiered tasks

Introduce real-life contexts for calculating unknown angles.

Introduce real-life contexts for measuring unknown angles.

Introduce real-

Sheet — Geometry rules posters

Supporting learning resource — Investigating vertically opposite angles

protractors

Learning object — 360 protractor

Sheet — Vertically opposite angles


Resources

Supporting learning resource — Investigating angles at a point

Sheet — Bird’s-eye view of a

Walt: Calculate unknown angles using angle relationships.

Wilf:Identify angle relationships?Calculate unknown angles using angle relationships?

#Activities

Revisit angle relationships• Review angles on a straight line, vertically opposite angles and angles at

a point.

Apply angle relationships• Apply methods to calculate unknown angles at a point.

Calculate unknown angles using relationships• Explore real-life examples of angles to establish contexts for calculating

unknown angles.• Calculate simple unknown angles using angle relationships.

Geometric reasoning — 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• Students individually complete the assessment to demonstrate their

understanding of angles on a straight line, vertically opposite angles and angles at a point.

Monitor students’ ability to:Calculate unknown angles using angle relationships.

Learning alertsBe aware of:Students misinterpreting how angles are classified.Students assuming that angle relationships are isolated from one another.

Assessment Task

Assessment purposeTo solve problems using the relationships between angles on a straight line, vertically opposite angles and angles at a point.

Provide visual aids of angle types for proportional understanding.

life contexts for calculating unknown angles.

roundabout

Sheet — Angles at a point

Sheet — Unknown angles at a point



Resources

Supporting learning resource — Calculate unknown angles

Sheet — Angles quiz


Learning object — Measuring angles (2)





Resources

Assessment task — Investigating anglesAssessment task — Investigating

angles: Model response







FRACTIONS & DECIMALSSolving Problems

Powers of 10Add, Sub, Multiply, Divide

#Warm Ups

Fractions and decimals — Adding decimals involving tenths #Activities

Revisit tenths

Monitor students’ ability to:Add decimals and check for reasonableness of answers.

Learning alertsBe aware of:

L2B


Explicitly teach the vocabulary use picture clues with explanation





Compact the curriculum where


Resources

Languagetenths, addition, subtraction, decimal, regrouping, split, jump, compensate, powers of 10, multiplication, patterns, place value, generalisations, tenths, hundredths, estimate




Review the value of digits in the tenths column.

Explore strategies for adding tenths Use decimal models and place value charts to add

decimals without regrouping. Model how to use the jump and split strategies to add

decimals without regrouping. Use estimation and rounding to check reasonableness

of answers.

Apply strategies to addition questions Use a variety of strategies to solve decimal addition

questions without regrouping

Fractions and decimals — Subtracting decimals involving tenths #Activities

Explore strategies for subtracting tenths• Use decimal models and place value charts to subtract

decimals with and without regrouping.• Use the jump and split strategies to subtract decimals

without regrouping.• Use estimation and rounding to check reasonableness

of answers.

Apply strategies to subtraction questionsUse a variety of strategies to solve decimal subtraction questions, without regrouping

Fractions and decimals — Solving problems involving decimals #Activities

Revisit strategies for adding and subtracting decimals

• Review the jump and split strategies to add and subtract decimals without regrouping.

• Use estimation and rounding to check reasonableness of answers.

Use an efficient strategy to solve problems

• Use an efficient strategy to solve addition and subtraction involving decimals without regrouping.

Students who use similar thinking to whole numbers and add decimals without taking note of place value, e.g. thinking 0.9 + 0.3 = 0.12

Monitor students’ ability to:Apply strategies to subtract decimals and check for reasonableness of answers.

Learning alertsBe aware of:Students not using place value when subtracting but simply ignoring the decimal marker and using whole number processes.Students taking the larger number from the smaller number.

Monitor students’ ability to:Solve problems involving decimals.

Learning alertsBe aware of:Students not taking note of place value and using whole number concepts when adding and subtracting decimals.



Use decimal fraction models and place value charts to represent decimals and additive situations.



possible.

Independent Work

Peer Instruction

Tiered tasks

Add larger numbers with regrouping and provide increasingly sophisticated additive problems for students to solve.

Subtract larger numbers with regrouping and provide increasingly sophisticated additive problems for students to solve

Use problems with larger numbers with regrouping.

Supporting learning resource — Adding decimals involving tenths

Sheet — Place value chart

Sheet — Place value chart to tenths

Sheet — Empty number lines

decimal fraction models

Learning object — Abacus

Learning object — Number line

Supporting learning resource — Subtracting decimals involving tenths

Sheet — Place value chart to tenths

Sheet — Subtracting using number lines


place value materials, e.g. MAB

Sheet — Empty number lines

Learning object — Abacus

ResourcesSupporting learning resource — Solving problems involving decimalsSheet — Place value chart to

Walt: Add decimals (to tenths).Use estimation to check for reasonableness of answers.

Wilf: Add decimals?

Recognise if answers are reasonable?

Walt: Subtract decimals involving tenths?Recognise if answers are reasonable?

Wilf: Subtract decimals involving tenths?


Walt: Add and subtract numbers involving decimals.Use estimation to check for reasonableness of answers.

Wilf: Select appropriate strategies to solve addition and subtraction questions?


Walt: Multiply whole numbers by powers of 10.

Wilf: Identify the change in value of whole numbers multiplied by powers of 10?

Solve problems involving multiplication by powers of 10?

Make generalisations about the relationship between positions on the place value chart and powers of 10?

Walt: Multiply decimals by powers of 10.

Wilf: Identify the change in value of

Fractions and decimals — Multiplying whole numbers by powers of 10#Activities

Revisit strategies for multiplication with whole numbers• Discuss strategies used for multiplication facts, e.g.

doubling, skip counting, using known facts, making arrays.

Multiply single digits by powers of ten• Demonstrate change in place value when multiplying a

digit by 10, 100 and 1 000.• Identify visual patterns using a place value chart.• Develop understanding of the place value system

based on multiples of ten.

Multiply two-, three- and four-digit numbers by powers of 10• Reinforce place value understanding using number

sliders.• Explain powers of 10 based on the number system.• Record multiplication horizontally.• Use calculators to model patterns.

Use number facts and powers of 10• Model splitting numbers into factors using powers of

10.• Solve problems involving basic facts and powers of 10.

Consolidate understanding of multiplying by powers of 10• Form generalisations about whole numbers multiplied

by powers of ten.• Solve problems with and without digital technology

Fractions and decimals — Multiplying decimals by powers of 10#Activities

Revisit multiplying whole numbers by powers of 10• Review the effect on whole numbers when multiplying

by powers of 10.

Monitor students’ ability to:Multiply whole numbers by powers of 10.

Learning alertsBe aware of:Students indiscriminately adding zeros to numbers when multiplying by powers of 10.

Monitor students’ ability to:Multiply decimals by powers of 10.

Learning alertsBe aware of:Students indiscriminately

Work with one- and two-digit numbers multiplied by powers of 10 using number sliders.

Work with materials like number sliders, calculators and place value charts to support

Have students mentally solve multiplication problems by powers of 10

Have students solve calculations mentally.

tenthsSheet — Empty number linesa number line from 0 to 4 with tenths marked (the number line needs to be large enough to accommodate students’ name tags and counters)dicefive name tags for each student/teama different coloured counter for each student/team

Resources

Supporting learning resource — Multiplying whole numbers by powers of 10

Learning object — Number slider

Sheet — Number slider


calculators (one per student)

decimals multiplied by powers of 10?

Solve problems involving multiplication of decimals by powers of 10?

Walt: Multiply decimals by one-digit whole numbers.

Wilf: Apply multiplication strategies to questions involving decimals (with tenths)?

Make reasonable estimates for multiplication questions?

Solve problems involving multiplication of decimals by one-digit whole numbers?

• Discuss the use of ‘0’ as a space holder.

Multiply tenths by powers of 10• Explore the change in place value when multiplying

tenths by 10, 100 and 1 000.• Identify visual patterns using a number slider.

Multiply hundredths and thousandths by powers of 10• Predict patterns for multiplying hundredths by powers

of 10.• Reinforce place value understanding using number

sliders.• Record multiplication horizontally.• Use calculators to model patterns.

Consolidate understanding of multiplying by powers of 10• Identify multipliers in multiplication expressions.• Form generalisations about decimals multiplied by

powers of ten.

Fractions and decimals — Multiplying tenths by one-digit whole numbers #Activities

Revise multiplying whole numbers by one-digit whole numbers• Use familiar multiplication strategies to solve

problems.

Multiply tenths by one-digit• Investigate multiplying tenths using a place value

chart.• Model language used for place names.

Multiply decimals by one-digit whole numbers• Make estimations.• Explore grid strategies to solve problems.• Record multiplication horizontally.• Use calculators to check answers.

Compare the multiplication of whole numbers and decimals

counting zeroes and moving the decimal point rather than the number.

Monitor students’ ability to:Use mental strategies for performing calculations.

Learning alertsBe aware of:Students counting how many digits after the decimal point in the numbers being multiplied, rather than using place value understanding to determine the position of the decimal in the answer.

students to see and describe what is occurring when numbers are multiplied by powers of ten.

Concentrate on multiplying only tenths and renaming when necessary to develop language.

Students use written strategies to solve multiplication with larger numbers.

Resources

Supporting learning resource — Multiplying decimals by powers of 10


Sheet — Number slider

Sheet — Number slider to hundredths


Sheet — 0 to 9 digit cards (prepare extra ‘0’ cards)

3 power cards with labels: ‘x10’, ‘x100’, ‘x1000’, calculators, a decimal point card, a chair

Resources

Supporting learning resource — Multiplying tenths by one-digit whole numbers

Sheet — Place value chart to

Walt: Multiply decimals by multiples of 10.

Wilf: Apply multiplication strategies to questions involving hundredths and thousandths?


Solve problems involving multiplication of decimals by multiples of 10?

• Form generalisations about the value (e.g. hundredths, tenths …) of decimals multiplied by powers of ten.

• Solve multiplication problems.

Fractions and decimals — Multiplying tenths by one-digit whole numbers #Activities

Revisit multiplying tenths by one-digit whole numbers• Apply multiplication strategies to solve problems using

digital technology.

Multiply hundredths by one-digit whole numbers• Explore multiplying hundredths using a place value

chart.• Model language used for place names.

Multiply decimals by one-digit whole numbers• Multiply money amounts using cents and dollars.• Solve problems involving multiplying hundredths by

one-digit whole numbers.• Record multiplication horizontally.• Use calculators to check answers.

Multiply decimals by multiples of 10• Make links to powers of ten.• Make estimates.• Complete multiplication expressions.

Monitor students’ ability to:Use mental strategies for performing calculations.

Learning alertsBe aware of:Students counting how many digits after the decimal point in the numbers being multiplied rather than using place value understanding to determine the position of the decimal in the answer.

Concentrate on multiplying by one-digit whole numbers and renaming when necessary to develop multiplicative language.Work with materials like number sliders, calculators and place value charts to support students to see and describe what is occurring when numbers are multiplied by powers of ten.

Students use written strategies to solve multiplication with larger numbers.

tenths

counters

calculators (one per student)

• Learning object — Multiplication of decimals (1)

Resources

Supporting learning resource — Multiplying decimals by multiples of 10

Sheet — Place value chart to hundredths

Sheet — Multiplication patterns

Sheet — Mighty animals

counters, calculators



Key Learning

Area: Maths

Year Level Team: Year 6 Term: 2

Show 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)




PATTERNS & ALGEBRA

Patterns using a table of valuesDecimal patterns

Whole number and applying pattern understanding

#Warm Ups Monitoring Task

L2B


Explicitly teach the vocabulary to ensure the

U2B

Compact the curriculum where possible.

Independent Work

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



Patterns and algebra — Exploring whole number patterns #Activities

Revisit square and triangular number patterns Identify square and triangular number patterns. Review the meaning of a ‘term’. Record the first five triangular and square numbers.

Represent number patterns using materials Discuss simple number patterns (e.g. 2, 4, 6, 8 or 3, 6, 9, 12). Model geometric patterns using materials. Discuss strategies to identify a rule. Record the pattern. Repeat with other examples.

Patterns and algebra — Exploring patterns using a table of values#Activities


Represent patterns in tables of values• Discuss the purpose of a table of values.• Model a table of values using the values from a previous pattern (e.g. patterns

made in the previous lesson).

Show patterns in tables of values• Describe the relationship between the numbers in the first row (or column) of

the table, describe the relationship in the second row (or column) of the table and describe the relationship between the corresponding numbers in the two rows (or columns), e.g.

• Extend the table of values and predict unknown quantities.• Complete a table of values using other examples to demonstrate understanding.

Patterns and algebra — Exploring decimal patterns

Monitor students’ ability to:Identify the rule in the pattern.

Learning alertsBe aware of:Students who cannot identify patterns or sequences or are unable to continue the pattern.

Monitor students’ ability to:Describe a pattern represented in a table of values.

Learning alertsBe aware of:Students who are unable to identify a pattern or the relationship used to create the pattern

students have the required prior knowledge.

To support student to see patterns use materials such as counters to represent patterns and also organise information into a table

Use simple patterns and rules.

Peer Instruction

Tiered tasks

Use complex sequences, which include two-step rules (e.g. multiply by 3 and add 2) or multiplicative patterns (e.g. exponential growth patterns).

Create complex patterns and two-step rules.

index.html

Resources

Supporting learning resource — Exploring whole number patterns

Sheet — Patterns in tables

counters

toothpicks

pattern blocks

Resources

Supporting learning resource — Exploring patterns using a table of values

Sheet — Patterns

counters

toothpicks

pattern blocks

Languagepatterns, term, continue, create, relationship, rule

Walt: Describe, continue and create number patterns.

Wilf: Make a general statement describing a pattern?

Walt: Identify patterns and describe the rule from a table of values.

Wilf: Represent patterns in a table of values?Identify the rule used to create number patterns?


Walt: Describe, continue and create number patterns involving decimals.

Wilf: Create and continue a pattern involving decimals?Describe patterns using rules?Solve problems by applying rules identified?

Walt: Describe, create and continue number patterns involving whole and decimal numbers.

Wilf: Identify the rule used to create number patterns and use it to continue the pattern?

Organise known information about the pattern into

#Activities

Reinforce writing rules to describe patterns• Discuss examples of number sequences that do / do not have patterns.• Create patterns using word problems or visual images.• Identify the start and the change for each pattern.• Write a rule to describe the pattern.

Note: Encourage students to find the multiplicative relationship between the two variables and write a rule using this relationship.

Create patterns involving decimals• Create simple decimal patterns (e.g. 0.5, 0.7, 0.9 …)• Continue decimal number patterns.• Organise what is known about the pattern into a table to help determine the

unknown numbers in each sequence.• Provide contexts involving decimals and model how to create patterns to

represent the situation.

Describe and continue patterns involving decimals• Create a decimal word problem.• Examine the table of values and determine the rule.• Use and explain a rule to identify values in a pattern sequence.

Patterns and algebra — Exploring decimal patterns#Activities


Reinforce patterns• Organise known information about a pattern by creating a table of values.• State the rule that describes the mathematical processes used to determine

unknown values.• Describe mathematical processes using symbols and/or words.• Communicate mathematical ideas using multiple representations.• Continue sequences and identify unknown values in recursive patterns.

Investigate a pattern problem (Monitoring task)• Identify patterns to solve problems.• Explain and provide reasons to problem solutions.• Complete a task to demonstrate understanding of patterns and tables of values.

Monitor students’ ability to:Create and continue a decimal pattern.

Learning alertsBe aware of:Students unable to identify a pattern or the relationship used to create the pattern.Students simply identifying a counting sequence.

Monitor students’ ability to:Describe the rule used to create a number pattern and use the rule to continue the pattern.

Learning alerts

Be aware of:Students unable to identify a pattern or the relationship between quantities used to create the pattern.

Use simple decimal patterns and describe the patterns using language of place value (e.g. 12 tenths, 15 tenths, 18 tenths …)

Use materials or diagrams to represent simple patterns and have students describe the rules.

Use complex decimal patterns with two step rules.

Use complex patterns and rules.

Resources

Supporting learning resource — Exploring decimal patterns

Resources

Monitoring task — Describing number patterns and rules

Supporting learning resource — Applying pattern understanding

Sheet — Patterns in tables

tables or organised lists to identify unknown values?

Modified

13.03.2019 Year 6 Unit 2Assessment task — Applying the order of operations

Name Class

Question 1

Solve the equations:

a) 3 + 5 - 6 = b) 5 + 5 x 6 = c) 12 + 4 – 2 x 5 =

d) 20 ÷ 5 x 2 + 8 = e) 6 + (7 x 3) = f) 2 x (9 + 2 + 6) – 5 =

Question 2

Add brackets to the following expressions to make them true.

a) 4 + 4 + 2 ÷ 5 = 2

b) 12 x 3 + 2 – 5 = 55

c) Jodie and Ben were solving 6 + 14 ÷ 2. Ben calculated from left to right 6 + 14 ÷ 2 = 10. Jodie used brackets 6 + (14 ÷ 2) = 13. Jodie’s method was the most accurate. Explain why:

Question 3

Complete these number sentences by adding the correct operation symbol (+, -, x or ÷). Each operation symbol can only be used once for each question.

a) 3 6 2 = 20 b) 14 6 2 = 26

c) 14 3 1 10 = 7 d) 7= 3 20 5

e) 8 40 2 = 4 7

25 of 59Mth_Y06_U2_AT_Applying the Order of Operations

Question 4

Travis asked his mother for a new toy. He was given $34 straight away and then $2 pocket money each week for the next 12 weeks. How much money did he have after 12 weeks of saving?

Shade the bubble that represents the word problem:

Question 5

Here are two word problems. Write an equation that could be used to solve for each:

a) Jake had 34 lollies and gave 12 to his friends at school. He gave half of what was left to his brother. How many lollies did his brother receive?

b) Trent had saved $34 in his money box. He took half of his money out to go shopping. He bought a burger meal for $12 and an ice-cream for $2. How much money was left in his pocket?

Question 6

Explain why two children may arrive at different answers for this equation. 8 + 16 ÷ 4 =

26 of 59Mth_Y06_U2_AT_Applying the Order of Operations

2 x 12 + 34 = 58

34 + 2 x 12 = 58

Show possible workings. Justify your thinking with reference to order of operations.

34 + 12 – 2 = 44

12 + 34 x 2 = 80 W

Working Space

Year 6 Mathematics: Unit 2 — Applying the order of operations Name:

Purpose of assessment: To write and apply the correct use of brackets and order of operations in number sentences.

Understanding and Fluency Problem-solving and Reasoning

(Write correct number sentences using brackets and order of operations. Solves problems involving all four operations with whole numbers.) Applies knowledge of order of operations and brackets.

Chooses appropriate operations to correctly complete a complex unfamiliar equation such as balanced equations. Q3e

Uses mathematical language to justify the appropriate method for calculating using the order of operations. Q6 A

Chooses appropriate operations to correctly complete a complex familiar equation Q3c, 3d

Explains how the use of brackets in equations assists with accurate calculation Q2cWrite equations (mixed operations) to match complex familiar word problems Q5b if written as a single equation.

B

Correctly sequences the order in which operations with and without brackets are calculated. Q1 a-f Solves answers involving operations with whole numbers Q3a, 3b

Adds brackets to expressions to make them true Q2 a,b Matches equations (mixed operations) with word problems. Q4Write correct number sentences using brackets and order of operations. 5aWrite equations (mixed operations) to match complex familiar 5b if written as a series of equations.

C

Calculates some simple familiar operations with and without using order of operations. Uses everyday language to describe methods. D

Makes attempts to calculate with whole numbers in a left to right sequence. Makes attempts to explain mathematical thinking E

Mth_Y06_U2_AT_InvestigatingAngles

Modified13/3/19

Year 6 Unit 2Assessment task — Investigating angles

Name Class

Task

1. Without using a protractor, find the size of the unknown angles.

x =

z =

Explain how you got your answer:

2. Find the size of the unknown angles.


a) b)

a)

c=

d=

e=

f=

g=

Explain how you got your answer:

3. True or False?Below are two true statements and one false statement about the diagram on the left.

Statement 1: c + d = 180◦

Statement 2: a + b + c + d +

e = 380◦

Statement 3: c + d = e + a + b Which statement is false? Explain why:


b)

5. 6. a)

x and y are straight lines.

j and k are equal angles.

Find the size of the unknown angles.

h = j =

i = k =

b) Explain how you got your answer.


4. In this diagram ∠AEB + ∠BEC + CED = 180◦

a. Extend the ray BE below the line AED. Label the end of the ray as F.

b. Name the angle formed by the new ray and the ray ED.

c. Using the extended ray (F), name two sets of angles that add to 180.

7.


6. In the diagram on the left:

a + c = 90

a = c

b = 12 of 90

6a) What is the sum of these angles?

∠WOX + ∠WOY + ∠WOZ =

6b) Show your thinking:

a = b = c

d is closest to (tick one box):

60 30 45

Explain how you worked it out.

GMA Year 6 Mathematics: Unit 2 — Investigating angles Name:

Purpose of assessment: Solve problems using the properties of angles.

Understanding and Fluency Problem-solving and Reasoning

(Identify and apply the angle relationships for angles on a straight line, vertically opposite angles and angles at a point.)

Solve problems using the properties of angles. (Communicates mathematical reasoning for answers)

Uses inferred angle knowledge to calculate unknown angle measurements (Q7)Applies angles knowledge of a straight line, right angles and vertically opposite angles to find unknown angles in a complex, unfamiliar context and support explanations by using mathematical reasoning. Q7

A

Calculates unknown angles requiring multi-step thinking. Q5a 6aNames two sets of angles that add to 180◦ Q4c

Uses problem-solving strategies to calculate the sum for three angles. Q6aExplain how the size of an unknown is determined. Q5b, 6b B

Uses knowledge of angle properties to calculate angles measures Q1a, 1b, Q2a, 2b, Q3, Q4a, 4b.Recognise angles of revolution embedded in diagrams. Q3

Solves problems using the properties of angles. Q3.Communicate mathematical reasoning for answers to angle problems.Q1b, 2b, Q3 C

May identify some angle measurements involving single step calculations. May use a combination of everyday and mathematical language to explain thinking. D

Makes attempts to identify angle measurements Makes attempts to explain mathematical thinking E

Feedback:

32 of 59Mth_Y06_U2_AT_MathGuidedInquiries

Year 6 Unit 2Assessment task — Investigating pyramids and measurement

Name Class

During Semester 1, students will complete two Mathematical guided inquiries. They are:

Investigating measurement problems involving area. ‘How many chairs best fit into the school hall for a concert?’ (Unit 1) which focused on learning related to the sub strand Using units of measurement

Investigating pyramids and measurement. ‘What is the biggest pyramid you can make from an A3 sheet’ (Unit 2) which focuses on learning related to the sub-strands Using units of measurement and Shape.

As a monitoring task observe:

Mathematical guided inquiry

Link to relevant section of the achievement standard

Quality of student learning:

Investigating pyramids and measurement

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 construct simple prisms and pyramids.

Collect evidence that the student can:

identify the volume a container can hold as the capacity

recognise that 1 mL is equivalent to 1 cm3

recognise a pyramid identify the differences between a prism and a

pyramid construct prisms and pyramids including using nets formulate a plan to solve an authentic measurement

problem explain the thinking they used to solve the problem justify their answer to the problem with mathematical

evidence.

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

connect decimal representations to the metric system choose appropriate units of measurement to perform a calculation make connections between capacity and volume


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

Schools can choose to:

• use both inquiries as assessment with the GTMJ attached• choose to use one inquiry for monitoring and one for assessment

or

• use both inquiries as monitoring tasks.

construct simple prisms and pyramids.


Year 6 Mathematics: Unit 2 — Investigating pyramids and measurement Name:

Purpose of assessment: To use simple strategies to reason and solve a shape and measurement inquiry question.

Understanding and Fluency Problem-solving and ReasoningConstruct simple prisms and pyramids.Connect and apply shape and measurement understanding to the inquiry question.Use mathematical language and symbols.

Interpret, model and investigate area, volume, capacity and shape.Explain and justify conclusions using mathematical evidence.

Accurately transfers knowledge of shape and measurement connected to the inquiry question.Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Develops and applies methods to gather relevant evidence for a viable conclusion.Represents and presents evidence logically.Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

A

Recalls and uses appropriate shape and measurement understanding connected to the inquiry question.Consistently uses appropriate mathematical language, materials and diagrams.

Applies a method to gather evidence to support a conclusion.Explains mathematical thinking including choices made, strategies used and conclusions reached.

B

Uses and applies shape and measurement understanding to design and construct prisms and pyramidsUses everyday language and some appropriate mathematical language, materials and diagrams.

Chooses a known method to gather evidence to support a conclusion.Represents and presents evidence.Describes mathematical thinking including strategies used and conclusions reached.

C

Finds an area of a two-dimensional shape on a prism or pyramid.Uses aspects of mathematical language, materials or diagrams.

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

Recognises a two-dimensional shape.Uses everyday language. Makes isolated statements. E

Feedback:

Monitoring Tasks:

MathematicsMonitoring task — Describing integers in everyday contexts Year 6 Unit 2

Name Date

Teacher information


Students describe the use of integers in everyday contexts.

They locate integers on a number line.

MaterialsOptional: Rather than using the pictures listed in the task, provide:

a range of frozen food packs links to relevant websites, or

supermarket catalogues.

Teacher note:

This task provides an opportunity to gather evidence about student learning. It is expected that teachers provide each student with a copy of the task listed on the following pages.

Task:Look for evidence that the student can:

identify everyday situations that use negative integers order integers

locate integers on a number line.

Answers:

1 and 2. 4 °C –1 °C 3 °C –4 °C –2 °C 12 °C

–4 °C –2 °C –1 °C 3 °C 4 °C 12 °C

3. Student marks zero and an appropriate scale on the thermometer and then marks the 12 °C correctly.

4. Student marks –4 °C on the thermometer and moves 10 degrees up the thermometer to get 6 °C.

5. The lasagne is stored correctly because it is below 0 °C which is the Australian standard, or because –3 °C is below –2 °C.

Describing integers in everyday contexts

The storage of hot and cold foods must meet an Australian standard.

The thermometer shows the acceptable temperatures for storage of hot, cold and frozen foods.

1. Make a list of the temperatures listed on the food packs.

2. Circle the lowest temperature. Write how you know.

3. Order the temperatures from lowest to highest.

4. Mark the highest temperature on the thermometer. (Remember to mark a scale on the thermometer.)

5. What temperature is 10 °C higher than the lowest temperature?

6. Tom’s Corner Store stored the lasagne at –3 °C. Is the lasagne stored correctly? Explain how you know.

MathematicsMonitoring task — Describing number patterns and rules Year 6 Unit 2

Name Date

Teacher information


Students describe rules used in sequences involving whole

numbers.

Teacher note:

This task provides an opportunity to gather evidence about student learning. It is expected that teachers provide each student with a copy of the task listed on the following pages.

Task:

Look for evidence that the student:

completes a table of values to describe a pattern identifies an additive pattern in a table of values writes a rule (including a start value and a change) to describe a pattern

applies the rule to answer a question.

Note: Some students may bypass the additive relationship and write a rule using the multiplicative relationship between the two variables. This is to be encouraged and fostered as this is what will be expected in Year 7.

Alternative patterns

Rather than using the question given, use a financial situation, e.g. Bruce earns $15 per hour. How much will he earn in a 20-hour week?

Use materials (e.g. matchsticks or counters) to illustrate patterns.

Answers:

1.

Time (hrs) 1 2 3 4 5 6 7 8 9

Distance (m) 3.5 7 10.5 14 17.5 21 24.5 28 31.5

2. Start at 3.5 m and add on 3.5 m for each extra hour. Some students may write the number of hours times 3.5.

3. The caterpillar crawls 24.5 metres in seven hours.

4. Students use repeated addition or multiplication to show that in 24 hours the caterpillar crawls 84 metres.

Describing number patterns and rules

Use a table of values to answer the following:

A caterpillar crawled at a speed of 3.5 m per hour.

1. Use the information in box to complete the table of values.

Time (hrs) 1 2 3 4 5 6 7

Distance (m)

2. Write a rule to describe the pattern.

3. How far has the caterpillar crawled after seven hours?

4. How far did the caterpillar travel in one day (24 hours)? Show working for how you found your answer.

Australian Curriculum

Foundation to 6 Maths - Year 6

Year 6 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.

Content Descriptors

Measurement and Geometry Number and Algebra

Using units of measurement

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)

Geometric reasoning

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141)

Shape

Construct simple prisms and pyramids (ACMMG140)

Fractions and decimals

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

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)

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:

ordering decimals and unit fractions and locating them on a number line continuing patterns by adding and subtracting decimals and fractions connecting three-dimensional objects with their two-dimensional representations solving simple problems involving the four operations using a range of strategies checking the reasonableness of answers using estimation and rounding measuring and constructing different angles.

Curriculum working towardsThe teaching and learning in this unit work towards the following

rounding describing the use of integers in everyday contexts locating integers and fractions on a number line making connections between the powers of 10 and the multiplication and division of decimals adding and subtracting decimals constructing simple prisms and pyramids solving problems involving all four operations with whole numbers describing rules used in sequences involving whole numbers, fractions and decimals solving problems using the properties of angles writing correct number sentences using brackets and order of operations.

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 Recognising and using patterns and relationships Using fractions, decimals, percentages, ratios and rates Using spatial reasoning Interpreting statistical information Using measurement

Critical and creative thinking Inquiring - identifying, exploring and organising information and ideas

Curriculum Priorities - Pedagogy

Considerations Generating ideas, possibilities and actions Reflecting on thinking and processes Analysing, synthesising and evaluating reasoning and procedures

Personal and social capability Self-management Social managementFor 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 learning

Assessing student learning

Assessment name: Investigating pyramids and measurement

Assessment description: Students use simple strategies to reason and solve a shape and measurement inquiry question

Assessment name: Applying the order of operations

Assessment description: Students write and apply the correct use of brackets and order of operations in number sentences.

Assessment name: Investigating angles

Assessment description: Students solve problems using the relationships between angles on a straight line, vertically opposite angles and angles at a point

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.

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 nextSpecific monitoring opportunities in this unit may include observations, consultations and samples of student work, for example:

use the 1 2 5 division strategy apply understanding of place value and multiplication to make calculations represent square and triangular numbers with materials interpret square and triangular number patterns position and compare integers on a number line locate, order and compare related fractions consider place value when adding and subtracting decimals add and subtract decimals multiply decimals by powers of 10 and multiples of powers of 10 identify the rule used to create a pattern represent a pattern in a table of values make models of prisms and pyramids and check accuracy of features calculate angles on a straight line, opposite each other and at a point estimate and measure angles.

Monitoring task

Monitoring name: Describing integers in everyday contexts (Below Zero)

Monitoring description: Students identify integers in an everyday context and locate and order them using a number line.

Monitoring name: Describing number patterns and rules (Patterns Rules)

Monitoring description: Students describe, create and continue number patterns involving whole and decimal numbers.

FeedbackFeedback may relate to misunderstandings and common alternative conceptions. Feedback in this unit this may include:

using strategies for multiplying and dividing whole numbers finding unknown angles applying the order of operations to calculate continuing and creating number sequences and identifying the rules used using effective strategies for adding and subtracting decimals applying understanding of powers of 10 to multiplying decimals constructing accurate features of prisms and pyramids applying the rules for square and triangular numbers to continue the patterns positioning and ordering integers correctly on a number line.

Year 6 Semester 1 Term 2 Mathematics Report Card Comment Bank

Assessment Task 4: Investigating pyramids and measurement

A B C D E1M6A4 1M6B4 1M6C4 1M6D4 1M6E4


{Name} accurately transfers knowledge of shape and measurement connected to the inquiry question. {She,He} consistently and clearly used appropriate mathematical language, materials and diagrams. {Name} developed and applied methods to gather relevant evidence for a viable conclusion. {She,He} represented and presented evidence logically. {Name} clearly explained their mathematical thinking including choices made, strategies used and conclusions reached.


{Name} recalled and used appropriate shape and measurement understanding connected to the inquiry question. {She,He} consistently used appropriate mathematical language, materials and diagrams. {Name} applied a method to gather evidence to support a conclusion. {She,He} explained their mathematical thinking including choices made, strategies used and conclusions reached.


{Name} used and applied shape and measurement understanding to design and construct prisms and pyramids. {She,He} used everyday language and some appropriate mathematical language, materials and diagrams. {Name} chose a known method to gather evidence to support a conclusion. {She,He} represented and presented evidence. {Name} described their mathematical thinking including strategies used and conclusions reached.


{Name} found an area of a two-dimensional shape on a prism or pyramid. {She,He} used aspects of mathematical language, materials or diagrams. {Name} followed a given method to gather evidence. {She,He} made statements about choices made and strategies used, when prompted.


{Name} recognised a two-dimensional shape. {She,He} used everyday language. {Name} made isolated statements.

Assessment Task 5: Applying the order of operations


Applying the order of operations

{Name} chose appropriate operations to correctly complete a complex unfamiliar equation such as balanced equations. {She,He} used mathematical language to justify the appropriate method for calculating using the order of operations.


{Name} chose appropriate operations to correctly complete a complex familiar equation. {She,He} explained how the use of brackets in equations assists with accurate calculation {Name} wrote equations (mixed operations) to match complex familiar word problems.


{Name} correctly sequenced the order in which operations with and without brackets are calculated. {She,He} solved answers involving operations with whole numbers. {Name} added brackets to expressions to make them true. {She,He} matched equations (mixed operations) with word problems. {Name} wrote correct number sentences using brackets and order of operations. {She,He} wrote equations (mixed operations) to match complex familiar.


{Name} calculated some simple familiar operations with and without using order of operations. {She,He} used everyday language to describe methods.


{Name} made attempts to calculate with whole numbers in a left to right sequence. {She,He} made attempts to explain their mathematical thinking.

Assessment Task 6: Investigating angles


Investigating angles

{Name} used inferred angle knowledge to calculate unknown angle measurements. {She,He} applied angles knowledge of a straight line, right angles and vertically opposite angles to find unknown angles in a complex, unfamiliar context and support explanations by using mathematical reasoning.


{Name} calculated unknown angles requiring multi-step thinking. {She,He} named two sets of angles that add to 180. {Name} used problem-solving strategies to calculate the sum for three angles. {She,He} explained how the size of an unknown is determined.


{Name} used knowledge of angle properties to calculate angles measures {She,He} recognised angles of revolution embedded in diagrams. {Name} solved problems using the properties of angles. {She,He} communicated mathematical reasoning for answers to angle problems.


{Name} maybe able to identify some angle measurements involving single step calculations. {She,He} may have used a combination of everyday and mathematical language to explain thinking.


{Name} made attempts to identify angle measurements. {She,He} made attempts to explain their mathematical thinking.

Maths Pre-ModerationYear 6 : 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 - select and apply mental and written strategies and digital technologies to solve problems involving multiplication and division with whole numbers, and identify, describe and continue square and triangular numbers.

Fractions and decimals - apply mental and written strategies to add and subtract decimals, solve problems involving decimals, make generalisations about multiplying whole numbers and decimals by 10, 100 and 1 000, apply mental and written strategies to multiply decimals by one-digit whole numbers, and locate, order and compare fractions with related denominators and locate them on a number line.

Patterns and algebra - continue and create sequences involving whole numbers and decimals, describe the rule used to create these sequences and explore the use of order of operations to perform calculations.

Using units of measurement - make connections between volume and capacity. Shape - problem-solve and reason to create nets and construct models of simple prisms and pyramids. Geometric reasoning - make generalisations about angles on a straight line, angles at a point and vertically

opposite angles, and use these generalisations to find unknown angles.

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


Understanding Fluency Construct simple prisms and pyramids. Connect and apply shape and measurement understanding to the inquiry question. Use mathematical language and symbols..

Problem Solving and Reasoning Interpret, model and investigate area, volume, capacity and shape. Explain and justify conclusions using mathematical evidence.


Understanding Fluency (Write correct number sentences using brackets and order of operations. Solves problems involving

all four operations with whole numbers.)

Problem Solving and Reasoning Applies knowledge of order of operations and brackets..


Understanding Fluency (Identify and apply the angle relationships for angles on a straight line, vertically opposite

angles and angles at a point.)

Problem Solving and Reasoning Solve problems using the properties of angles. (Communicates mathematical reasoning for

answers)

Scan and Assess

Prioritise

Develop and Plan

Additional Targeted Teaching Priorities* Identified from previous assessment & post moderation of Semester 1 Mathematics unit 1 from Year 6 Data Wall. 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:

using strategies for multiplying and dividing whole numbers finding unknown angles applying the order of operations to calculate continuing and creating number sequences and identifying the rules used using effective strategies for adding and subtracting decimals applying understanding of powers of 10 to multiplying decimals constructing accurate features of prisms and pyramids applying the rules for square and triangular numbers to continue the patterns positioning and ordering integers correctly on a number line.

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)


Understanding Fluency Uses and applies shape and measurement understanding to design and construct prisms and pyramids Uses everyday language and some appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Chooses a known method to gather evidence to support a conclusion. Represents and presents evidence. Describes mathematical thinking including strategies used and conclusions reached.


Understanding Fluency Correctly sequences the order in which operations with and without brackets are calculated. Q1 a-f Solves answers involving operations with whole numbers Q3a, 3b

Problem Solving and Reasoning Adds brackets to expressions to make them true Q2 a,b Matches equations (mixed operations) with word problems. Q4 Write correct number sentences using brackets and order of operations. 5a Write equations (mixed operations) to match complex familiar 5b if written as a series of equations.


Understanding Fluency Uses knowledge of angle properties to calculate angles measures Q1a, 1b, Q2a, 2b, Q3, Q4a, 4b. Recognise angles of revolution embedded in diagrams. Q3

Problem Solving and Reasoning Solves problems using the properties of angles. Q3. Communicate mathematical reasoning for answers to angle problems.Q1b, 2b, Q3

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


Understanding Fluency Recalls and uses appropriate shape and measurement understanding connected to the inquiry question. Consistently uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Applies a method to gather evidence to support a conclusion. Explains mathematical thinking including choices made, strategies used and conclusions reached.


Understanding Fluency Chooses appropriate operations to correctly complete a complex familiar equation Q3c, 3d

Problem Solving and Reasoning Explains how the use of brackets in equations assists with accurate calculation Q2c

Write equations (mixed operations) to match complex familiar word problems Q5b if written as a single equation.


Understanding Fluency Calculates unknown angles requiring multi-step thinking. Q5a 6a Names two sets of angles that add to 180◦ Q4c

Problem Solving and Reasoning Uses problem-solving strategies to calculate the sum for three angles. Q6a Explain how the size of an unknown is determined. Q5b, 6b

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


Understanding Fluency Accurately transfers knowledge of shape and measurement connected to the inquiry question. Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Develops and applies methods to gather relevant evidence for a viable conclusion. Represents and presents evidence logically. Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.


Understanding Fluency Chooses appropriate operations to correctly complete a complex unfamiliar equation such as balanced equations. Q3e

Problem Solving and Reasoning Uses mathematical language to justify the appropriate method for calculating using the order of operations. Q6


Understanding Fluency Uses inferred angle knowledge to calculate unknown angle measurements (Q7)

Problem Solving and Reasoning

Applies angles knowledge of a straight line, right angles and vertically opposite angles to find unknown angles in a complex, unfamiliar context and support explanations by using mathematical reasoning. Q7

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 8Classifying and constructing nets of 3D objects Example learning sequence

Classify three-dimensional objects according to their features

Identify nets of three-dimensional objects Construct three-dimensional objects using nets

Evidence of learningCan the student:

Explain how the features of a three-dimensional object determine whether it is a prism or a pyramid?

Identify nets of three-dimensional objects? Draw a net of a cube, rectangular prism and

pyramid?

Lesson 9Constructing prisms and pyramids Example learning sequence

Establish learning context Construct solid models of prisms and pyramids Construct skeletal models of prisms and pyramids


Use the features of prisms and pyramids to evaluate their models?

Lesson 10Comparing volume and capacity Example learning sequence

Establish learning context Compare the terms volume and capacity Use materials to define volume and capacity in real-

life contexts Measure volume and capacity using materials


Explain the difference between volume and capacity?

Choose appropriate units? Make reasonable estimations? Accurately measure volumes?

Lessons 11-13Investigating the design of pyramids (MGI)

Guided Investigations Assessment

Example learning sequence Establish learning context Explore contexts such as pyramids around the

world (Discover) Plan how to answer the question (Devise) Collect and review evidence (Develop) Draw conclusions (Defend) Extend learning or apply learning to other areas

(Diverge)

Evidence of learning

Can the student: Develop a plan to solve an inquiry question? Identify appropriate mathematical strategies to

calculate and compare pyramid size (e.g. by measuring capacity and converting to volume)?

Justify pyramid design using evidence collected?

Guided Investigations Assessment

Lesson 14Exploring square and triangular numbers Example learning sequence

Establish learning context Explore arrays of numbers Explore square numbers Find square numbers from one to 100 Represent triangular numbers Find triangular numbers between one and 100


Create arrays to show a square number? Represent a triangular number? Apply square and triangular number patterns to

predict the next square number?

Teaching Sequence Feedback

Lesson 15Solving problems less than zero on a number line Example learning sequence

Establish learning context Explore numbers less than zero Locate positive and negative numbers on a number

line


Represent positive and negative numbers on a number line?

Use the number line to represent and solve problems?

Lesson 16Locating positive and negative numbers on a number line

Monitoring TaskExample learning sequence

Establish learning context Revisit positive and negative numbers on a number

line Show understanding of integers (Monitoring task)


Locate positive and negative numbers on a number line?

Interpret positive and negative numbers in a real-life situation?

Lesson 17Introducing order of operations Example learning sequence

Establish learning context Investigate the left to right convention Explore ordering multiple operations Identify the effect of using brackets Solve equations using the order of operations


Can the student: Demonstrate the importance of applying

conventions when calculating expressions containing multiple operations?

Explain the effect of brackets on the order of operations in an expression?

Lessons 18-19Solving problems using the order of operations Example learning sequence

Establish learning context Revisit order of operations Solve problems using the order of operations


Demonstrate the correct order of conventions when solving problems involving multiple operations?

Lesson 20Assessing student learning

Example learning sequence Understand the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purposeTo write and apply the correct use of brackets and order of operations in number sentences

Lesson 21Applying mental strategies when dividing with no remainder Example learning sequence

Establish learning context Revisit divisibility rules Revisit mental strategies for division


Estimate with accuracy? Choose strategies to divide with consistent

accuracy?

Lesson 22-23Applying a written strategy when dividing without and with a remainder Example learning sequence

Establish learning context Revisit mental strategies for division Review the 1, 2, 5 written strategy for division

without a remainder Use the 1, 2, 5 strategy for division with a remainder


Divide using the 1, 2, 5 strategy with consistent accuracy?

Teaching Sequence FeedbackLesson 24 Evidence of learning

Investigating angles on a straight line Example learning sequence

Establish learning context Define 'adjacent' and supplementary' Make generalisations about angles on a straight line Calculate unknown angles on a straight line

Can the student: Make a generalisation about angles on a straight

line? Calculate unknown angles on a straight line? Identify the angle relationship involved in calculating

unknown angles on a straight line?

Lesson 25

Investigating vertically opposite angles Example learning sequence

Establish learning context Generalise about angles made by intersecting lines Explore angle relationships in vertically opposite

angles Calculate unknown vertically opposite angles

Evidence of learning Can the student: Identify vertically opposite angles? Calculate unknown vertically opposite angles? Make a generalisation about vertically opposite

angles?

Lesson 26

Investigating angles at a point Example learning sequence

Establish learning context Explore angles at a point Make a generalisation about the relationship

between angles at a point Calculate unknown angles at a point


Can the student: Identify and calculate unknown angles at a point? Make a generalisation about angles at a point? Identify the angle relationship involved in calculating

unknown angles at a point?

Lesson 27

Calculating unknown angles Example learning sequence

Establish learning context Revisit angle relationships Apply angle relationships Calculate unknown angles using relationships


Can the student: Identify angle relationships? Calculate unknown angles using angle

relationships?

Lesson 28

Assessing student learning Example learning sequence

Understand the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purposeTo solve problems using the relationships between angles on a straight line, vertically opposite angles and angles at a point.

Lesson 1

Subtracting decimals involving tenths Example learning sequence

Establish learning context Revisit tenths Explore strategies for adding tenths Apply strategies to addition questions


Add decimals? Recognise if answers are reasonable?

Lesson 2

Adding decimals involving tenths Example learning sequence

Establish learning context Explore strategies for subtracting tenths Apply strategies to subtraction questions


Can the student: Subtract decimals involving tenths? Recognise if answers are reasonable?


Lesson 3

Solving problems involving decimals


Select appropriate strategies to solve addition and subtraction questions?

Example learning sequence Establish learning context Revisit strategies for adding and subtracting

decimalsUse an efficient strategy to solve problems


Lesson 4

Multiplying whole numbers by powers of 10Example learning sequence

Establish learning context Revisit strategies for multiplication with whole

numbers Multiply single digits by powers of ten Multiply two-, three- and four-digit numbers by

powers of 10 Use number facts and powers of 10 Consolidate understanding of multiplying by powers

of 10


Can the student: Identify the change in value of whole numbers

multiplied by powers of 10? Solve problems involving multiplication by powers of

10? Make generalisations about the relationship

between positions on the place value chart and powers of 10?

Lesson 5

Multiplying decimals by powers of 10Example learning sequence

Establish learning context Revisit multiplying whole numbers by powers by 10 Multiply tenths by powers of ten Multiply hundredths and thousandths by powers of

10Consolidate understanding of multiplying by powers of 10


Identify the change in value of decimals multiplied by powers of 10?

Solve problems involving multiplication of decimals by powers of 10?

Lesson 6

Multiplying tenths by one- digit whole numbers Example learning sequence

Establish learning context Revise multiplying tenths by one-digit whole

numbers Multiply tenths by one-digit Multiply decimals by one-digit whole numbers

Compare the multiplication of whole numbers and decimals


Can the student:

Apply multiplication strategies to questions involving decimals (with tenths)?


Solve problems involving multiplication of decimals by one-digit whole numbers?

Lesson 7

Multiplying decimals by multiples of 10Example learning sequence

Establish learning context Revisit multiplying tenths by one-digit whole

numbers Multiply hundredths by one-digit whole numbers Multiply decimals by one-digit whole numbers

Multiply decimals by multiples of 10


Apply multiplication strategies to questions involving hundredths and thousandths?


Solve problems involving multiplication of decimals by multiples of 10?

Lesson 29

Exploring whole number patterns Example learning sequence

Establish learning context Revisit square and triangular number patterns Represent number patterns using materials


Can the student: Make a general statement describing a pattern?


Lesson 30

Exploring patterns using a table of values Example learning sequence

Evidence of learning Can the student: Represent patterns in a table of values? Identify the rule used to create number patterns?

Establish learning context Represent patterns in tables of values Show patterns in tables of values

Lesson 31

Exploring decimal patterns Example learning sequence

Establish learning context Reinforce writing rules to describe patterns Create patterns involving decimals Describe and continue patterns involving decimals


Create and continue a pattern involving decimals? Describe patterns using rules? Solve problems by applying rules identified?

Lesson 32

Applying pattern understanding

Monitoring Task

Example learning sequence Establish learning context Reinforce patterns Investigate a pattern problem (Monitoring task)


Identify the rule used to create number patterns and use it to continue the pattern?

Organise known information about the pattern into tables or organised lists to identify unknown 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

revisit angle relationships · web view2019. 3. 17. · pialba state school: mathematics year 6...

Documents