Math at Work 10 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Math at Work 10 - 12 and related Math 7 - 9 Outcomes *Updated May 2024*
Math at Work 10 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
A01 - This is not an outcome that can be taught in isolation but must be integrated as a foundational concept within each of the units in the course.
G03 Students will be expected to demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons. [C, CN, PS, V]
G03.01 Determine, using angle measurements, if two or more regular or irregular polygons are similar.
G03.02 Determine, using ratios of side lengths, if two or more regular or irregular polygons are similar.
G03.03 Explain why two given polygons are not similar.
G03.04 Explain the relationships between the corresponding sides of two polygons that have corresponding angles of equal measure.
G03.05 Draw a polygon that is similar to a given polygon.
G03.06 Explain why two or more right triangles with a shared acute angle are similar.
G03.07 Solve a contextual problem that involves similarity of polygons.
G04 Students will be expected to demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by applying similarity to right triangles, generalizing patterns from similar right triangles, applying the primary trigonometric ratios, and solving problems. [CN, PS, R, T, V]
G04.01 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the side adjacent are equal, and generalize a formula for the tangent ratio.
G04.02 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the hypotenuse are equal, and generalize a formula for the sine ratio.
G04.03 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side adjacent to the length of the hypotenuse are equal, and generalize a formula for the cosine ratio.
G04.04 Identify situations where the trigonometric ratios are used for indirect measurement of angles and lengths.
G04.05 Solve a contextual problem that involves right triangles, using the primary trigonometric ratios.
G04.06 Determine if a solution to a problem that involves primary trigonometric ratios is reasonable.
A01 Students will be expected to solve problems that require the manipulation and application of formulas related to perimeter, area, the Pythagorean theorem, primary trigonometric ratios, and income. [C, CN, ME, PS, R]
(It is intended that this outcome be integrated throughout the course.)
A01.01 Solve a contextual problem that involves the application of a formula that does not require manipulation.
A01.02 Solve a contextual problem that involves the application of a formula that requires manipulation.
A01.03 Explain and verify why different forms of the same formula are equivalent.
A01.04 Describe, using examples, how a given formula is used in a trade or an occupation.
A01.05 Create and solve a contextual problem that involves a formula.
A01.06 Identify and correct errors in a solution to a problem that involves a formula.
Additional Resources and Activities for G03 (similar polygons):
Similar Rectangles with Currency - Hey, remember those bank notes from around the world that you used for currency exchange rates? Almost all bills are rectangles but are they similar rectangles? Why do you think bank notes are printed in a rectangular shape? Break those bills out again and measure them (outcome M03) to see if any of the rectangles are similar. If you have any US bills, you can use paper folding to find that the ratio of the length to width is root 3 to 4. If you do this activity, let me know what you come up with! Ask students to create their own currency with each bill a different but similar rectangle.
Measuring Heights of Objects Using Mirrors and Similar Triangles - Give each group a tape measure and a mirror, and a list of tall objects around your school (flagpole, basketball hoop, etc.). They will place the mirror on the ground between them and the object. One student will position himself so that he can see the top of the object reflected in the mirror. The other students measure the distance from the mirror on the ground to the base of the object and from the mirror on the ground to the observing student’s feet. By measuring the height of the observing student’s eyes, they can use similar triangles to calculate the height of the object. How accurate do you think this method of indirect measurement is? Where are the sources of error? You could later compare this to a measurement taken using a clinometer and the tangent function. A nice Brightstorm video explains the procedure.
Additional Resources and Activities for G04 and A01 (trig ratios):
*Note G04.5 (contextual problem) and G04.6 (reasonableness of solutions) are no longer expectations of MTW10.
Stomp Rocket Activity - Build a simple stomp rocket and then launch them. Use a clinometer and trigonometry to measure the height that the rocket travels.
Guess the Height of a Lamp Pole from Dan Meyer - Students use estimation and similar triangles to try to determine the height of a lamp pole from a photo. Mimio file.
Sorting Right Triangles - An introductory task for trigonometry. Sort right-angled triangles into two groups of similar triangles and consider their angles and sides to discover that the ratios remain equal. From Teachit Maths
Practical Trigonometry Problem Solving Desmos Activity - Armed with a clinometer and a tape measure, students are required to solve a series of trigonometry problems.
Development of Trigonometry Ratios Desmos Activity - Development of the Sine, Cosine, and Tangent ratios by looking at similar triangles. This activity leads into the development of the Trigonometric Table and introduces its use in solving for unknown angles in right triangles.
CEMC Courseware Lesson 3: Tangent Ratio and Lesson 4: Sine and Cosine Ratios - The Centre for Education in Mathematics and Computing (CEMC) has developed online mathematics courseware.
How far off the ground did your kite go? from John Stevens - Students use trig ratios and angles of elevation by flying a kite (from Mrs. Burt at Etiwanda High School).