Teacher Guide - ExploreLearning PD Blog



Florida MAFS-FSA Resource

Purpose: Teachers should utilize the ExploreLearning published Teacher Guide and Student Exploration Sheet to teach the content of this standard. This document is a supplemental resource designed to help support teachers in preparing students for content and various computer-based question mechanisms on the Florida Standards Assessment.

Guidelines: Below are select sample item stems from various sources, such as the Florida Department of Education (DOE). Teachers are encouraged to teach the standard/benchmark as recommended by their school district. Teacher may utilize the “Suggested Lesson Sequence” section in the ExploreLearning Teacher Guide and accompanying Student Exploration Sheet in teaching the content/concept.

In providing practice for MAFS FSA, teachers can use the question stems and facilitate the use of the Gizmo through various modes. Gizmo suggestions have been made for each question stem for whole-class facilitation. Contact your Project Manager or Sales Executive for professional development opportunities, such as classroom modeling.

|FL MAFS Content Standard |MAFS.912.G.-SRT.3.8 Use trigonometric ratios and the Pythagorean |

| |Theorem to solve right triangles in applied problems. |

| | |

| |MAFS.912.G.-SRT.3.6 Understand that by similarity, side ratios in|

| |right triangles are properties of the angles in the triangle, |

| |leading to definitions of trigonometric ratios for acute angles. |

| | |

| |MAFS.912.G.-SRT.3.7 Explain and use the relationship between the |

| |sine and cosine of complementary angles. |

|ExploreLearning Gizmo |Sine, Cosine, Tangent Ratios |

|[pic] |

|Sample Item Stem |Response Mechanism |Gizmo Suggestions |

|1. Lars rides a chairlift to the top of a mountain. The |Equation Editor Response |Introduce the concepts of Sine, Cosine, Tangent |

|chairlift rises at a constant angle of 37°. If the length| |by showcasing the Gizmo during whole class |

|of the chairlift ride is 1,392 m, what is the elevation | |instruction. Build student understanding for the |

|gain from the base of the chairlift to the top? | |mnemonic device “SOH-CAH-TOA” found in the |

| | |Teacher Guide – see suggested lesson sequence |

|Draw a right triangle to model this problem and use the | |section, Gizmo activity ELL adaptation. |

|Gizmo to find sin 37°. Show your work. | | |

| | |Complete activity A found in the Student |

|Elevation gain: | |Exploration Sheet by facilitating student usage |

| | |of the Gizmo using a wireless mouse or |

| | |interactive whiteboard, if available. Students |

| | |may also complete the activity 1:1 or 2:1 using |

|_______________ | |laptop carts, a computer lab, or BYOD. |

| | | |

| | |Debrief the answer to question 6 of Student |

| | |Exploration Sheet activity A using the Student |

| | |Exploration Sheet Answer Key. |

|2. A 12-foot ladder leans against a building. The top of |Equation Editor Response |Extend student learning (previous Gizmo |

|the ladder forms an angle of 19° with the top of the | |experience - activity A of the student |

|building, as shown. How high is the top of the ladder? | |exploration sheet) by completing activity B of |

| | |the student exploration sheet. Upon completion, |

|To solve the problem, make a sketch, write an equation | |allow time for students to review answers from |

|involving cosine, find the cosine value you need in the | |activities A and B in pairs. Emphasize the use of|

|Gizmo, and solve for the unknown height. Show your work | |the length and angle measurement tools of the |

|below. | |Gizmo. |

| | | |

| | |Debrief the answer to question 5 of Student |

| | |Exploration Sheet activity B using the Student |

| | |Exploration Sheet Answer Key. |

| | | |

| | |Use the Gizmo during a whole class |

| | |mini-lesson/review on Sine and Cosine. Have |

| | |students create a triple Venn Diagram – Sine, |

|Height of the top of the ladder: | |Cosine, Tangent. At the conclusion of the |

| | |mini-lesson, provide time for students to |

|______________________ | |evaluate Sine and Cosine and fill in as much as |

| | |they can on the Venn Diagram. |

|3. Gabriella and her friends are going camping. She is |Open Response |Allow time for students to work independently or |

|helping her friend pitch the tent. The support wire | |in pairs to problem solve the question stem. Once|

|needs to be at a 45° to the ground, and it is 8 ft long. | |students have problem solved on paper, students |

|How far away from the base of the tent does she need to | |can use the Gizmo to recreate the problem and |

|place the stake for the support wire? Choose the | |check their work. Start by selecting the “Cosine”|

|appropriate trigonometric ratio to solve the problem and | |Gizmo tab. Then use the angle slider to set the |

|justify your answer with an explanation. | |appropriate angle degrees. Click and drag point C|

| | |to make the “support wire” as close to 8 units as|

| | |possible (8.01). Select the “Show side lengths” |

| | |and “Show cosine computation” Gizmo options to |

| | |extend the learning opportunity. Use the |

| | |measurement tools when possible and associated |

| | |color coding of the Gizmo (adjacent = green, |

| | |hypotenuse = purple, opposite = red). |

|4. Joseph is measuring a tree. He walks 15.3 m from the |Multiple Choice Response |Extend student learning (previous Gizmo |

|base of the tree, lies on his stomach, and measures a 25°| |experiences - activities A and B of the student |

|angle of elevation. What is the height of the tree? | |exploration sheet) by completing activity C of |

| | |the student exploration sheet. Upon completion, |

|To solve the problem, write an equation using the correct| |allow time for students to review answers in |

|trigonometric ratio, use the Gizmo to find the value you | |pairs. Emphasize the use of the length and angle |

|need, and solve for the unknown height. | |measurement tools of the Gizmo. |

| | | |

|A. X ≈ 6.47 | |Debrief the answer to question 5 of Student |

|B. X ≈ 13.86 | |Exploration Sheet activity C using the Student |

|C. X ≈ 7.13 | |Exploration Sheet Answer Key. |

|D. X ≈ 8.35 | | |

| | |As an informal assessment, provide time for |

| | |students to ad onto and complete the triple Venn |

| | |Diagram they previously created. |

Name: ______________________________________ Date: __________________

Period # ___________

MAFS-FSA Student Task

Sine, Cosine, Tangent Ratios

MAFS.912.G.-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MAFS.912.G.-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

MAFS.912.G.-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles.

Math Tasks (Begin by exploring the Gizmo. Utilize the Gizmo to answer questions below.)

1. Lars rides a chairlift to the top of a mountain. The chairlift rises at a constant angle of 37°. If the length of the chairlift ride is 1,392 m, what is the elevation gain from the base of the chairlift to the top?

Draw a right triangle to model this problem and use the Gizmo to find sin 37°. Show your work.

Elevation gain:

2. A 12-foot ladder leans against a building. The top of the ladder forms an angle of 19° with the top of the building, as shown. How high is the top of the ladder?

To solve the problem, make a sketch, write an equation involving cosine, find the cosine value you need in the Gizmo, and solve for the unknown height. Show your work below.

Height of the top of the ladder: ___________

3. Gabriella and her friends are going camping. She is helping her friend pitch the tent. The support wire needs to be at a 45° to the ground, and it is 8 ft long. How far away from the base of the tent does she need to place the stake for the support wire? Choose the appropriate trigonometric ratio to solve the problem and justify your answer with an explanation.

4. Joseph is measuring a tree. He walks 15.3 m from the base of the tree, lies on his stomach, and measures a 25° angle of elevation. What is the height of the tree?

To solve the problem, write an equation using the correct trigonometric ratio, use the Gizmo to find the value you need, and solve for the unknown height.

A. X ≈ 6.47

B. X ≈ 13.86

C. X ≈ 7.13

D. X ≈ 8.35

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