TIPS4Math Grade 8 Circles Overall Expectations Students will: • Determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder (8m31) • Demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world (8m40) Specific Expectations Students will: • Solve problems that require conversions involving metric units of area, volume, and capacity (i.e., square centimetres and square metres; cubic centimetres and cubic metres; millilitres and cubic centimetres) (8m33) • Measure the circumference, radius, and diameter of circular objects, using concrete materials (8m34) • Determine, through investigation using a variety of tools and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas [i.e., Circumference of a circle = π x diameter; Area of a circle = π x (radius)2] (8m35) • Solve problems involving the estimation and calculation of the circumference and the area of a circle (8m36) • Construct a circle, given its centre and radius, or its centre and a point on the circle, or three points on the circle (8m44) Specific Lesson Learning Focus Expectations Circles • Estimate and measure the circumference, radius, and diameter of circular 8m34 objects using a variety of concrete tools (e.g., string, tape measure) Circumference • Through investigation determine the relationship for calculating the 8m35 circumference of a circle (i.e. measure diameter and circumference and investigate the ratio of circumference to diameter (C:d = π :1) o use a variety of tools (e.g. cans and string, dynamic geometry software) and strategies • Generalize to develop the formula Circumference= π x diameter Circumference Problems • Solve problems involving the estimation and calculation of circumference 8m36 using real-life contexts o include problems where circumference is given and diameter or radius is required Area of a Circle • Through investigation determine the relationship for calculating the area of a 8m35 circle o Use a variety of tools (e.g., cans and string, dynamic geometry software) and strategies (e.g., paper cutting, grid overlays • Generalize to develop the formula Area = π x radius2 EduGAINS-Mathematics Page 1 of 14 TIPS4Math Grade 8 Circles (continued) Specific Lesson Learning Focus Expectations Area of a Circle Problems • Solve problems involving the estimation and calculation of area 8m33 • Solve area problems requiring conversions between square units 8m36 • Solve problems where area is given and radius or diameter is required Circumference versus Area • Solve problems involving the estimation and calculation of circumference and 8m33 Problems area within contexts 8m36 o these contexts should require determining whether area or circumference is needed • Solve circumference and area problems involving real-life contexts that require conversions between metric units • Solve problems involving real-life contexts where area or circumference is given and radius or diameter is required Construct Circles • Construct a circle given its centre and radius 8m44 • Construct a circle from its centre and a point on the circle • Construct a circle from three points on the circle Consolidation and Summative Tasks EduGAINS-Mathematics Page 2 of 14 TIPS4Math Grade 8 Circles Specific Expectations: 8m34 Learning Focus Blended Learning Other Resources Teacher Guide TIPS4RM Grade 8 Unit 3: Unit 2 Activity 1: Circles Introduction From Powers to Circles OERB ID: ELO1477250 • Day 5: Talking About Minds • Identify parts of a circle Unit 2 Activity 1: Minds On Circles On o radius OERB ID: ELO1476960 o diameter • Circles o circumference o explore connections between radius, diameter, circumference and area • Journal entry Action • Estimate and measure the Unit 2 Activity 1: Action circumference, radius, and • Pi, Please, with a Side of Baseball diameter of circular objects OERB ID: ELO1416660 using a variety of concrete o circumference and diameter relationship tools (e.g., string, tape measure) Unit 2 Activity 1: Consolidation • Circle Relationships Activity o hands on exploration o journal Consolidation Unit 2 Activity 1: Action • Assignment 1: Parts of a Circle o explaining relationships between radius and diameter, diameter and circumference o real-life connection • Anchor Chart – circumference and area of circle EduGAINS-Mathematics Page 3 of 14 TIPS4Math Grade 8 Circumference Specific Expectations: 8m35 Learning Focus Blended Learning Other Resources Teacher Guide TIPS4RM Grade 8 Unit 3: Unit 2: Measurement From Powers to Circles OERB ID: ELO1477250 • Day 6: Mysterious Circles • Unit 2: Activity 1: Circles Introduction • Unit 2 Activity 2: Circles – Circumference and Homework Help Area • Circles: Finding the Minds • Develop familiarity with dynamic Unit 2 Activity 2: Minds On Circumference Given the On tools for creating circles and OERB ID: ELO1476970 Diameter measuring their diameter and • Review circumference o parts of a circle Gizmos o circumference • Circumference and Area • Discussion of Circles o translate into words and explain why it is appropriate: C = π x d Geometer’s Sketchpad Action • Through investigation Unit 2 Activity 1: Action • Bike Wheel determine the relationship for • Pi, Please, with a Side of Baseball • Circles and Pi calculating the circumference of a OERB ID: ELO1416660 circle (i.e. measure diameter and o circumference and diameter relationship GeoGebra circumference and investigate the • Rolling a Circle to Find Pi ratio of circumference to diameter Note: supplementation required for developing (π)) familiarity with dynamic tools for creating circles Desmos o use a variety of tools (e.g. cans and measuring their diameter and circumference • Measuring Circles and string, dynamic geometry software) and strategies Gap Closing I/S Student • Generalize to develop the formula Book: 2D Measurement Circumference= π x diameter pp 3 – 6, 21 – 27 Consolidation Gap Closing I/S Facilitator’s Guide: 2D Measurement pp 4 – 6, 23 – 29 EduGAINS-Mathematics Page 4 of 14 TIPS4Math Grade 8 Circumference Problems Specific Expectations: 8m36 Learning Focus Blended Learning Other Resources Minds • Review circumference formula and TIPS4RM Grade 8 Unit 3: From On how to determine the circumference Powers to Circles for a given diameter or radius • Day 6: Mysterious Circles Action • Solve problems involving the estimation and calculation of Gap Closing I/S Student Book: circumference using real-life 2D Measurement contexts pp 3 – 6, 21 – 27 o include problems where circumference is given and Gap Closing I/S Facilitator’s Guide: diameter or radius is required 2D Measurement pp 4 – 6, 23 – 29 Consolidation EduGAINS-Mathematics Page 5 of 14 TIPS4Math Grade 8 Area of a Circle Specific Expectations: 8m35 Learning Focus Blended Learning Other Resources Teacher Guide TIPS4RM Grade 8 Unit 3: From Unit 2: Activity 2: Circles – Circumference and Area Powers to Circles OERB ID: ELO1477250 • Day 7: Circulating Problems Minds • Develop familiarity with • Day 8: Parts and Wholes On dynamic tools for creating circles and measuring their Homework Help diameter and area • Circle Measurement Action • Through investigation Unit 2 Activity 2: Action determine the relationship OERB ID: ELO1476970 Gizmos for calculating the area of a • Toss Me a Circle • Circumference and Area of circle OERB ID: ELO1413950 Circles • Use a variety of tools (e.g., o discover and determine area of a circle cans and string, dynamic • Circus Circus Geometer’s Sketchpad geometry software) and OERB ID: ELO1413960 • Circles and Pi strategies (e.g., paper o multiple choice questions about radius, diameter, cutting, grid overlays circumference and area GeoGebra • Generalize to develop the • Discussion • Explore the Area of a Circle formula Area = π x radius2 o write a problem about calculating area and • Area of a Circle circumference • Anchor Chart NCTM Illuminations o add new area and circumference information • Circle Tool Unit 2 Activity 2: Consolidation Consolidation Gap Closing I/S Student Book: • Assignment 1: Toilet Paper Roll Challenge – Part 1 2D Measurement o circumference, perimeter and area questions pp 3 – 6, 21 – 27 Gap Closing I/S Facilitator’s Guide: 2D Measurement pp 4 – 6, 23 – 29 EduGAINS-Mathematics Page 6 of 14 TIPS4Math Grade 8 Area of Circles Problems Specific Expectations: 8m33, 8m36 Learning Focus Blended Learning Other Resources Minds • Review Area formula and how to TIPS4RM Grade 8 Unit 3: From Powers On determine the area for a given to Circles diameter or radius • Day 8: Parts and Wholes • Day 9: Unusual Dart Board Action • Solve problems involving the • Day 10: Composition with Circles estimation and calculation of area • Solve area problems requiring Geometer’s Sketchpad conversions between square units • Composite Shapes • Solve problems where area is given and radius or diameter is Geogebra required • Explore the Area of a Circle Consolidation • Area of a Circle NCTM Illuminations • Circle Tool Gap Closing I/S Student Book: 2D Measurement pp 3 – 6, 21 – 27 Gap Closing I/S Facilitator’s Guide: 2D Measurement pp 4 – 6, 23 – 29 EduGAINS-Mathematics Page 7 of 14 TIPS4Math Grade 8 Circumference versus Area Problems Specific Expectations: 8m33, 8m36 Learning Focus Blended Learning Other Resources Minds • Review circumference and area Homework Help On formulas • Circle Measurement Quiz • Identify contexts that relate to circumference • Identify contexts that