Mathematics 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
G01 Students will be expected to derive proofs that involve the properties of angles and triangles.
G01.01 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology.
G01.02 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.
G01.03 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.
G01.04 Identify and correct errors in a given proof of a property involving angles.
G01.05 Verify, with examples, that if lines are not parallel the angle properties do not apply.
G01.06 Verify, through investigation, the minimum conditions that make a triangle unique.
G02 Students will be expected to solve problems that involve the properties of angles and triangles.
G02.01 Determine the measures of angles in a diagram that involves parallel lines, angles, and triangles and justify the reasoning.
G02.02 Identify and correct errors in a given solution to a problem that involves the measures of angles.
G02.03 Solve a contextual problem that involves angles or triangles.
G02.04 Construct parallel lines, using only a compass and straight edge or a protractor and straight edge, and explain the strategy used.
G02.05 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.
G03 Students will be expected to solve problems that involve the cosine law and the sine law, including the ambiguous case.
G03.01 Draw a diagram to represent a problem that involves the cosine law and/or sine law.
G03.02 Explain the steps in a given proof of the sine law and of the cosine law.
G03.03 Solve a problem involving the cosine law that requires the manipulation of a formula.
G03.04 Explain, concretely, pictorially or symbolically, whether zero, one or two triangles exist, given two sides and a non-included angle.
G03.05 Solve a problem involving the sine law that requires the manipulation of a formula.
G03.06 Solve a contextual problem that involves the cosine law and/or the sine law.
G01 was deemed non-foundational and is no longer included in Mathematics 11.
Additional Resources and Activities for G02 (properties of angles and triangles)
Angle Pairs from Math Teacher Mambo - A guided worksheet scaffolds the proof process by getting students to look at several angles and identify and explain their relationship. Completing this activity helps students get ready for two-column triangle proofs.
Lines, Transversals, and Angles Desmos Activity - In this activity, students explore the relationship among angles formed by a transversal and a system of two lines. In particular, they consider what happens when the two lines are parallel vs. when they are not.
Death Star Angles - A worksheet that asks students to use angle facts to find the missing angles. Shared by '@dooranran' on TES.
Polygon Angles - A worksheet for students to record their work as they discover the relationship between the sum of the interior angles and the number of sides in a convex polygon using the angle sum property. Shared by `Maths2Measure` on TES.
Show Me a Triangle Desmos Activity - A quick review of triangle vocabulary.
Parallel Lines, and Pairs of Angles - An interactive site that can be used to review the terminology.
Additional Resources and Activities for G03 (cosine law and the sine law, including the ambiguous case):
G03.04 (number of possible triangles given two sides and a non-included angle) was deemed non-foundational and is no longer included in Mathematics 11.
This means that ambiguous case is no longer part of outcome G03.
3 Fact Triangles and Teacher Notes - A 3 Fact triangle is one where 3 of the following facts are true: One side is 3cm; One angle is 90 degrees; One side is 4cm; One angle is 30 degrees. How many 3 fact triangles are there? What is the area and perimeter for each one. This is a great activity to practice sine and cosine law. From Jonny Griffith's RISP (Rich Starting Points for Math) Collection.
Sine Rule Target Table from Simply Effective Education - Test your pupils' knowledge of the sine rule with this differentiated target table. The aim is to reach a target score, set by you, by answering questions from the table. The questions are differentiated, with different point values, so pupils can choose their own difficulty level.
Triangle Problem Warm-up from Nat Banting - This problem can be a nice way to introduce the need for the ambiguous case. Students will not be able to solve this problem with an impossible triangle. They can then investigate when there would be a solution or two solutions for this triangle.
How High Is Mt. Ruapehu (application of sine/cosine rule) Desmos Activity - Calculate the height of mountains using non-right angle trigonometry. Students will have the freedom to take their OWN measurements using a virtual tape measure and clinometer then use their recorded measurements to find the heights of mountains -- including Mt. Ruapehu, New Zealand.
Non-Right Triangle Practice from Ms. Konstantine - This Google Slides has three pages of practice problems. One focused on triangle area, one on sine rule and one on cosine rule. From the MathsHKO blog.
Triangle Area Project from Girl Math - Students use Google Maps to locate an area of the world they are interested in. Select a plot of land in the shape of a non-rectangular quadrilateral (or more complex polygon for enrichment) and then use a virtual protractor to measure sides and angles. Students then calculate the area of this land and share their project on a Google Slide. Created by Girl Math. You might start this project off with a warm-up to remind students how to divide any polygon in to triangles.
My Unique Triangles Desmos Activity - Students will explore the conditions necessary to make unique triangles.
Unit 4 Cumulative Review
Trig Pile Up Including Sine and Cosine Rule from MathematicQuinn - A challenging Trig Pile up requiring the use of SOHCAHTOA, Pythagoras' Theorem, Sine rule, Cosine Rule and finding an obtuse angle with Sine.
Sine and Cosine Rule Trig Pile Up from MrGrayMaths - Work from the bottom to get an answer at the top! No “ambiguous” cases (where you need to use sin(x)=sin(180-x)).