Mathematics- Unit Planner Exemplar Year Level: 3 Year:

KEY CONCEPTS (What do we want our students to know and be able to do?) General capabilities and cross-curriculum priorities

Exploring Shapes and AnglesStudents identify and use their knowledge and understandings of angles, symmetry and three-dimensional shapes to design a robot that meets a design brief.The big idea of this unit is exploring the way angles and symmetry in shapes can be used to create or enhance designs.Inquiry questions for the unit: What is an angle? What is symmetry? Where do angles and symmetry exist in natural and built environments? How can you use angles and symmetry to create or enhance a design? What are key features of three-dimensional shapes?

Literacy Recognise different types of content words belonging to Mathematics Recognise adjectives that carry a high load of conceptual and abstract

meaning Interpret graphic information in designs Classify different shapes according to their features Compose visual texts (labelled design)

Numeracy See mathematics as important to everyday living Recognise angles and symmetry in the environment and apply

knowledge within a range of real-life contexts Apply geometric understanding to design

ICT capability Experiment and use ICTs to create a response to the design brief Represent ideas, information and thinking Develop imaginative responses Record evidence of learning Recognise some elements of images in communication Apply basic formatting strategies

Critical and creative thinking Interpret the design brief Create responses or solutions to the design brief Identify angles and symmetry Justify choices within design

PROFICIENCIES (How the content will be explored?)Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetryFluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positionsProblem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patternsReasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays

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Curriculum - Highlight the content descriptions to be covered

Number and Algebra Measurement and Geometry Statistics and ProbabilityNumber and Place ValueInvestigate the conditions required for a number to be odd oreven and identify odd and even numbers (ACMNA051)

Using Units of MeasurementMeasure, order and compare objects using familiar metricunits of length, mass and capacity (ACMMG061)

ChanceConduct chance experiments, identify and describe possibleoutcomes and recognise variation in results (ACMSP067)

Recognise, model, represent and order numbers to at least10000 (ACMNA052)

Tell time to the minute and investigate the relationshipbetween units of time (ACMMG062)

Data representation and interpretationIdentify questions or issues for categorical variables. Identifydata sources and plan methods of data collection andrecording (ACMSP068)

Apply place value to partition, rearrange and regroupnumbers to at least 10000 to assist calculations and solveproblems (ACMNA053)

ShapeMake models of three-dimensional objects and describe keyfeatures (ACMMG063)

Collect data, organise into categories and create displaysusing lists, tables, picture graphs and simple column graphs,with and without the use of digital technologies (ACMSP069)

Recognise and explain the connection between addition andsubtraction (ACMNA054)

Location and transformationCreate and interpret simple grid maps to show position andpathways (ACMMG065)

Interpret and compare data displays (ACMSP070)

Recall addition facts for single-digit numbers and relatedsubtraction facts to develop increasingly efficient mentalstrategies for computation (ACMNA055)

Identify symmetry in the environment (ACMMG066)

Recall multiplication facts of two, three, five and ten andrelated division facts (ACMNA056)

Geometric ReasoningIdentify angles as measures of turn and compare angle sizesin everyday situations (ACMMG064)

Represent and solve problems involving multiplication usingefficient mental and written strategies and appropriate digitaltechnologies (ACMNA057)Fractions and DecimalsModel and represent unit fractions including ½ ,¼, 1/3, 1/5and their multiples to a complete whole (ACMNA058)Money and financial mathematicsRepresent money values in multiple ways and count thechange required for simple transactions to the nearest fivecents (ACMNA059)Patterns and AlgebraDescribe, continue, and create number patterns resultingfrom performing addition or subtraction (ACMNA060)

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ACHIEVEMENT STANDARDBy the end of Year 3, Students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays. Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.

Assessment (How will we know they have learned it?) Make judgments

Describe the assessment Assessment date Unit teachers will design a rubric reflecting A-E achievement relating to geometric reasoningProperties of 2D and 3D shape ieSymmetryAngle

Mathematical investigation: Journal (Written)Investigate shapes and angles.Students create angles and recognise equivalence in angles. They identify the occurrence of symmetry in the environment and use symmetry to create symmetrical pictures and shapes.Student journals may include samples of work that: identify and recognise the occurrence of angles and symmetry in the natural and built

environment identify, recognise and label right, straight and equivalent angles and symmetry in

given design represent design ideas or plans for a robot within an environment that meets a design

brief based on angles and symmetry.The assessment package Exploring 3D objects, angles and symmetry in the QSA Assessment Bank could be used in this unit.

Week 8-9

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Teaching and Learning- Teaching strategies and learning experiences

LessonLearning Intentions

Warm Up Teaching strategies and learning experiences Sharing/PlenaryQuestioning

Resources

To find out what we know about 2D shapesIdentify purpose of unit through explanation of assessment and necessary mathematical understandings and processes. Ie Aust curric descriptions and standards

What am I? shape quiz Provide opportunities for students to apply knowledge of features of 2-D shapes to draw models of 2-D shapes as revision and consolidation of prior learning.

Set up mathematical learning log to record all evidence of learning throughout unit

Create a word bank of vocabulary used to discuss and describe 2-D and 3-D shapes and their properties including edges, corners, surfaces, angles (right, straight and equivalent), nets and symmetry (classroom word wall & student learning log).

2-D shapes learning log word wall

To find out what we know about 3D shapes

Shape hunt . Revise properties of 3-D shapes and identify objects within the school environment that are common 3-D shapes.

Make models of 3-D shapes from nets provided by the teacher and discuss features of the shapes. Brainstorm the features

and properties of 3D shapes and add to word wall

Collection of shapes within the environment

To explore how lines intersect to form a definition of angles

To begin the lesson, the class should discuss what a line is. The class should understand that a line goes on forever in two directions. Revise different types of lines

Parallel

Perpendicular

Diagonal

Vertical/horizontal

The class can determine what parallel lines are. They can be given two licorice strips and be allowed to demonstrate what parallel lines look like. Their samples should not intersect. The class can next discuss what perpendicular lines are. They can demonstrate with their strips. Make sure the student samples intersect to create right angles. Halfway through the lesson, introduce the concept of angles as two rays that join together at a vertex. Pass out three pipe cleaners to each of the students.The students can manipulate the pipe cleaners to make different angles after they are introduced by the teacher.. The students will enjoy manipulating the pipe cleaners as they develop greater spatial sense with this lesson.

*Does a line have a beginning or end.*how do we describe line segments?*Can someone show me an example of parallel lines?*What are perpendicular lines?

Licorice strips

pipecleaners

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Teaching and Learning- Teaching strategies and learning experiences

LessonLearning Intentions

Warm Up Teaching strategies and learning experiences Sharing/PlenaryQuestioning

Resources

What kinds of lines do clock hands make?

Giant string hand for groups of 3 to work with

Tell time to the minute, and discuss angles of the hands on analogue clocks.

Understand the relationship between half turns and 30 minutes on the analogue clock, and quarter turns and 15 minutes.

Recall and recognise angles in natural and built environments to build a bank of descriptors for angles, including quarter turn, clockwise and anti-clockwise direction of turn and equivalence of angles.

Clocks

To classify and name angles

http://www.mathsisfun.com/angles.html

Create angle tester and test on 2-D and 3-D shapes and then in the environment (see resources).

Take photos of angles in the environment and create a pictorial bank or draw on post-its.

Use the various angle testers to identify angles in the natural and built environment .

Sort and group the angles found . Connect to clock labels of classification.

Introduce the correct terminology for classification of angles

String,overhead sheets, pins

Pipe cleaners

Paper plates

I-pads/ cameras

Post-its

To explore symmetry within 2D shapes

Viewing powerpoint of symmetrical designs in art and the environment

Cutting a range of 2-D shapes in half to see if they match, and create definitions in the learning log. Sharing of individual

definitions to create a class definition

Symmetry powerpoint

To recall and identify symmetry in the natural and built environment.

Property Loops relating to symmetry Recognise symmetry in the environment. Take photos of symmetry in the environment and

create a pictorial bank (learning log).

Share photos and discuss various types of symmetry eg. Line symmetry and rotational symmetry

I-pads/cameras

To design, construct and analyse a design based

Co-construct a design of an object, e.g. car, boat, bike, ripstick (peer evaluation).

Use guided questioning to identify choice of strategies for angle and symmetry recognition within design.

Conduct a PMI to evaluate and provide feedback

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Teaching and Learning- Teaching strategies and learning experiences

LessonLearning Intentions

Warm Up Teaching strategies and learning experiences Sharing/PlenaryQuestioning

Resources

on use of geometric features

Choose modelled and guided strategies (use of angle testers and labels) to identify angles and symmetry within given design, with oral justification.

Choose modelled and guided strategies (use of angle testers and labels) to identify angles and symmetry within given design, with oral justification.

Interpret the design brief and identify requirements of design task (highlighting, numbering or underlining strategies).

Using chosen software application, apply new understandings to create individual robot design in alignment with design brief.

After their first draft, use feedback strategies (PMI) for peer evaluation of design.

Reflect upon peer evaluation (learning log) and apply changes to enhance their design.

Present final design and/or created robot to adult to effectively communicate and justify design choices, including identification of angles and symmetry in design

Design brief

Variety of equipment

REFLECTIVE PRACTICE/ Adjustments for needs of learners: Explain adjustments that will be made to the learning experiences to cater for the varied needs, abilities, interests and experiences of students. What activities/assessment worked well? What modifications would you make? What common misconceptions did students demonstrate?

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