Year 9-01 Geometrical Representation OCR Past Paper PDF

Unit of Learning: Year 9 – 01. Geometrical Representation Duration 5 weeks Start date: Completed date: Outcomes: MAO-WM-01, MA5-GEO-C-01, MA5-GEO-P-01, MA5-NET-P-01...

Unit of Learning: Year 9 – 01. Geometrical Representation Duration 5 weeks Start date: Completed date: Outcomes: MAO-WM-01, MA5-GEO-C-01, MA5-GEO-P-01, MA5-NET-P-01 Life skills: MALS-GEO-01 MA5-GEO-C-01: explores 2-dimensional shapes and 3-dimensional objects MALS-GEO-01 explores 2-dimensional shapes and 3-dimensional objects MA5-GEO-P-01: establishes conditions for congruent triangles and similar triangles and solves problems relating to properties of similar figures and plane shapes MA5-NET-P-01: solves problems involving the characteristics of graphs/networks, planar graphs and Eulerian trails and circuits This program of learning addresses content from the focus areas of Properties of geometrical figures A, as well as Path focus areas, Properties of geometrical figures B and Introduction to networks. The lessons and sequences in this program of learning are designed to allow students to understand and use geometrical representations, applying concepts including proportion, scale factors, similarity and connections (networks) to represent real-life objects, spaces, situations and concepts. Core Syllabus Content Background Knowledge Properties of geometrical figures A Identify and describe the properties of similar figures Describe similar figures as having the same shape but not necessarily the same size Verify and explain that in similar polygons, the corresponding angles are equal and the corresponding side lengths are in the same proportion Name the vertices in matching order when using the similar symbol ( in a similarity statement Match the corresponding sides and angles of similar polygons Key Terms Solve problems using ratio and scale factors in similar figures Apply an appropriate scale to enlarge or reduce a diagram Determine the scale factor for pairs of similar polygons and circles Apply knowledge of scale factor to find unknown sides in similar polygons Solve problems involving unknown lengths and scale factors of similar figures and related practical problems Assessment Solve problems involving scale drawings, with or without digital tools In-class assessment: Applies the properties of congruent and similar triangles to solve mathematical Properties of geometrical figures B (Path) partial problems involving plane shapes Develop and apply the minimum conditions for triangles to be similar Examine the minimum conditions needed and establish the 4 tests for 2 triangles to be similar Apply the minimum conditions needed and determine whether 2 triangles are similar using an appropriate test Summative assessment: Exam Establish and apply properties of similar shapes and solids Solve problems involving areas and volumes of similar shapes and solids Introduction to networks (Path) partial Examine and describe a graph/network Describe a network as a collection of objects (nodes or vertices) interconnected by lines (edges) that can represent systems in the real world Examine real-world applications of networks such as social networks, supply chain networks and communication infrastructure, and explore other applications of networks Identify and define elements of a graph including vertex, edge and degree Explain that a given graph can be drawn in different ways Lesson sequence Duration  Lesson Teaching and Learning Activity (no. of Core Path lessons) 01. how long is a blue Students explore the concept of proportion by exploring relationships between their own height 1 whale? and objects they can't easily see or measure. 02. scaled copies or Students define similarity by exploring the concept of scaled versus distorted copies. 1 fakes? 03. similar figures in Students are provided with opportunities to explore similar figures and scale in art. 2 art Students construct triangles and explore the minimum requirements to know 2 triangles are 04. how many angles? similar. 1 05. corresponding Students are introduced to formal similarity statements for corresponding sides and angles 2 sides and angles through explicit teaching with faded examples. Students are first introduced to the definition of scale factor, then utilise their prior knowledge 06. scale factor of corresponding sides to apply the scale factor and find the scale factor between 2 similar 2 figures. 07. scale factor in Students explore similar triangles in routine and non-routine problems, with a focus on 2 similar triangles exploring shadows. 08. movie magic Students apply scale in non-routine ways. Students explore scale models used in The Lord of the 1 Rings and the Harry Potter movies and answer questions using a scale given as a ratio. 09. maps and scale Students explore and solve problems involving various graphical representations, including maps 2 and floor plans. 10. comparing Students explore the similarities and differences between maps and network diagrams. 1 representations 11. scale factor and Students explore the relationship between scale factor and area. Students can take this further 1 area with an investigation into the relationship between scale factor and surface area and volume. Lesson sequence and details Learning episode 1 – how long is a blue whale? Teaching and learning activity Students explore the concept of proportion by exploring relationships between their own height and objects they can't easily see or measure. Syllabus content Solve problems involving scale drawings, with or without digital tools Table 1 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Whales and chihuahuas Tape measure or trundle Duration: 1 lesson wheel Learning intention Mini whiteboards and markers To visualise lengths by comparing familiar objects. Device per pair of students Success criteria and internet access I can make approximate comparisons between familiar Printed class set of Appendix lengths and unseen long and short objects. A I can estimate the length of objects larger and smaller than Whales and chihuahuas me. PowerPoint for displaying I can visualise proportion to check if my answers are logical. images Learning episode 2 – scaled copies or fakes? Teaching and learning activity Students define similarity by exploring the concept of scaled versus distorted copies. Syllabus content Describe similar figures as having the same shape but not necessarily the same size Verify and explain that in similar polygons, the corresponding angles are equal and the corresponding side lengths are in the same proportion Table 2 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Scaled copies or fakes? Devices with internet access Duration: 1 lesson (preferably one per student) Learning intention Rulers (one per student) Printed class sets of To be able to describe characteristics of similar figures. Appendix A and Appendix B Success criteria Scaled copies or fakes? I can identify similar figures. PowerPoint for displaying I can explain why figures are similar or not similar. images Learning episode 3 – similar figures in art Teaching and learning activity Students are provided with opportunities to explore similar figures and scale in art. Syllabus content Match the corresponding sides and angles of similar polygons Solve problems involving scale drawings, with or without digital toolsTable 3 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Similar figures in art Rulers (one per student) Duration: 2 lessons Printed class sets of Learning intentions Appendix A and Appendix B Similar figures in art To explore the use of similar figures and scale. PowerPoint for displaying To explore the meaning behind symbols used in Aboriginal images artwork. Success criteria I can use a grid to draw similar figures. I can use a vanishing point to draw similar figures. I can recognise symbols in Aboriginal artwork and appreciate their meaning. Learning episode 4 – how many angles? Teaching and learning activity Students construct triangles and explore the minimum requirements to know 2 triangles are similar. Syllabus content Verify and explain that in similar polygons, the corresponding angles are equal and the corresponding side lengths are in the same proportion Match the corresponding sides and angles of similar polygons Examine the minimum conditions needed and establish the 4 tests for 2 triangles to be similar (Path) Apply the minimum conditions needed and determine whether 2 triangles are similar using an appropriate test (Path) Table 4 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes How many angles? Straight pasta, for example, Duration: 1 lesson spaghetti (1–2 packets for Learning intention the class) Sticky tape To be able to determine if 2 triangles are congruent, similar, Ruler or neither based on the number of angles known. Printed class set of Appendix Success criteria A I can determine if 2 triangles are congruent, similar, or Printed and cut class set of neither. Appendix B I can state whether 2 triangles will be similar based on the number and position of congruent angles. Learning episode 5 – corresponding sides and angles Teaching and learning activity Students are introduced to formal similarity statements for corresponding sides and angles through explicit teaching with faded examples. Syllabus content Verify and explain that in similar polygons, the corresponding angles are equal and the corresponding side lengths are in the same proportion Name the vertices in matching order when using the similar symbol (~) in a similarity statement Match the corresponding sides and angles of similar polygons Table 5 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Corresponding sides and angles Printed set of Appendix A (one sheet to 4 students) Duration: 2 lessons Printed class sets of Learning intentions Appendices B, C and D To match corresponding sides and angles of similar figures. Corresponding sides and To write similarity statements using appropriate notation. angles PowerPoint for Success criteria displaying images I can locate sides and angles indicated using labelled vertices. I can identify corresponding sides and angles within similar figures. I can explain the meaning of symbols used in similarity statements. I can write similarity statements. Learning episode 6 – scale factor Teaching and learning activity Students are first introduced to the definition of scale factor, then utilise their prior knowledge of corresponding sides to apply the scale factor and find the scale factor between 2 similar figures. Syllabus content Determine the scale factor for pairs of similar polygons and circles Apply knowledge of scale factor to find unknown sides in similar polygons Table 6 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Scale factor A device with internet access for Desmos activity Duration: 2 lessons (preferably one device per Learning intentions student) To understand and be able to determine the scale factor Printed class sets of between 2 similar figures. Appendix A and Appendix B To be able to use scale factors to find missing sides in similar figures. Scale factor PowerPoint for displaying images Success criteria I can identify and name corresponding sides of similar figures. I can use a scale factor to find missing sides in similar figures. I can use given information to determine the scale factor between 2 similar figures. Learning episode 7 – scale factor in similar triangles Teaching and learning activity Students explore similar triangles in routine and non-routine problems, with a focus on exploring shadows. Syllabus content Solve problems involving unknown lengths and scale factors of similar figures and related practical problems Solve problems involving scale drawings, with or without digital toolsTable 7 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Scale factor in similar triangles Optional activities require Duration: 2 lessons additional resources: Learning intention o a device with internet To solve routine and non-routine problems involving similar access for GeoGebra triangles. activity Success criteria o chalk o tape measures I can solve routine problems using similar triangles. I can recognise problems I can solve using similar triangles. Printed class set of Appendix A Scale factor in similar triangles PowerPoint for displaying images Learning episode 8 – movie magic Teaching and learning activity Students apply scale in non-routine ways. Students explore scale models used in The Lord of the Rings and the Harry Potter movies and answer questions using a scale given as a ratio. Syllabus content Apply an appropriate scale to enlarge or reduce a diagram Solve problems involving unknown lengths and scale factors of similar figures and related practical problems Solve problems involving scale drawings, with or without digital tools Table 8 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Movie magic Printed class sets of Duration: 1 lesson Appendices A, B and C Learning intentions Movie magic PowerPoint for displaying images To develop students’ understanding of scale. To solve problems involving ratios and scales. Success criteria I can describe how scale is used in real life situations. I can solve scale problems using ratios. Learning episode 9 – maps and scale Teaching and learning activity Students explore and solve problems involving various graphical representations, including maps and floor plans. Syllabus content Apply an appropriate scale to enlarge or reduce a diagram Solve problems involving scale drawings, with or without digital tools Table 9 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Maps and scale A device with internet Duration: 2 lessons (minimum of one device Learning intentions between 2 students) Printed class sets of To explore the similarities and differences of various Appendix A and Appendix B graphical representations. Maps and scale PowerPoint To apply scale in context. for displaying images Success criteria I can read various graphical displays, including maps and floorplans. I can solve scale problems using ratios. Learning episode 10 – comparing representations Teaching and learning activity Students explore the similarities and differences between maps and network diagrams. Syllabus content Describe a network as a collection of objects (nodes or vertices) interconnected by lines (edges) that can represent systems in the real world (Path) Examine real-world applications of networks such as social networks, supply chain networks and communication infrastructure, and explore other applications of networks (Path) Identify and define elements of a graph including vertex, edge and degree (Path) Explain that a given graph can be drawn in different ways (Path) Table 10 – lesson details Visible learning Required resources Registration, adjustments and evaluation notes Comparing representations Printed class set of Appendix Duration: 1 lesson A Learning intention Comparing representations PowerPoint for displaying To recognise the similarities and differences between images networks and maps. Success criteria I can explain the similarities and differences between networks and maps. I can use network diagrams to solve problems. Learning episode 11 – scale factor and area Teaching and learning activity Students explore the relationship between scale factor and area. Students can take this further with an investigation into the relationship between scale factor and surface area and volume. Syllabus content Solve problems involving unknown lengths and scale factors of similar figures and related practical problems Solve problems involving areas and volumes of similar shapes and solids (Path) Table 11 – lesson details Visible learning Required Resources Registration, adjustments and evaluation notes Scale factor and area Pattern tiles or a device with Duration: 1 lesson internet Learning intention Printed class sets of Appendices A, B and C To solve problems involving similar figures and area. Success criteria I can solve problems involving similar figures and area. I can use scale factor to calculate the areas of similar figures.  UNIT EVALUATION Teacher Evaluation Comments / variations How does the unit rate in these areas? Google form – click here Time Allocation and Pacing Resources appropriate Record any variation made: Cognitive Load Theory considered Use of Digital Technologies Cross-Curriculum Integration Differentiation for Diverse Learners Use of Numeracy Strategies Literacy Strategies & activities Recommendations to improve this program: Formative Assessment Strategies Student Engagement Levels Connects concepts to real-world contexts Incorporation of group activities Feedback strategies Data monitoring of student progress Date commenced: / / Date completed: / / Teacher name: _____________________________ Head Teacher name: ___________________________ Teacher’s signature: Head Teacher’s signature: