Unit Overview: Aiming for the Stars
Aim: How can algebra and trigonometry be used to help us find speed and distance traveled by our model rockets?
Objectives: Students will use trigonometry to find the altitude of right triangles. Given distance and time traveled, students will use algebra to find speed.
Grade Levels: Fourth-fifth
Number of 90-Minute Periods: The unit takes place over three weeks and is usually taught three times a week for 90 minutes per period. Therefore the total unit lasts nine lessons or so. This is somewhat variable depending on the class and the rate at which they are learning the material.
Source: Teacher developed, refined, and aligned with the NCTM and National Science Teachers Association (NSTA) standards.
- • Teaching and Learning, Access and Equity, Curriculum, Tools and Technology, Assessment NCTM Mathematics Standards: Add Trig?
- • Algebra: Represent and analyze mathematical situations and structures using algebraic symbols.
- • Measurement: Apply appropriate techniques, tools, and formulas to determine measurements.
- 4.OA.A.1-A.3. Use the four operations with whole numbers to solve problems.
- 4.MD.A.2. Use the four operations to solve word problems involving distances.
- • Represent Measurement Quantities Using Diagrams.
- 4. MD.C.6. Measure angles in whole-number degrees using a protractor. Sketch angles
of specified measure.
5. NBT.B.5-B.7. Perform operations with multidigit whole numbers and with decimals
6. EE.A.1-A.2. Apply and extend previous understandings of arithmetic to algebraic
6.EE.B.5-B.7. Reason about and solve one-variable equations.
NCTM Processes/CCSSM Mathematical Practices
• Problem Solving
SMP1: Make sense of problems and persevere in solving them.
- • Communication SMP6: Attend to precision.
- • Representation
SMP4: Model with mathematics.
SMP5: Use appropriate tools strategically.
- • Replacing variables with numbers in a formula
- • Using a ruler, tape measure, protractor, and calculator
- • Collecting and recording data
- • A willingness to trust the teacher that the students will be guided through material that on the surface appears too difficult for them (This is really a key component to this lesson.)
Mathematical Concepts: Students apply the distance-rate-time formula to find the speed of their model rockets. Students use the formula (altitude = tangent of the angle x base) to find the altitude reached by their model rockets.
Materials and Tools
• Per group: ruler, tape measure, protractor, calculator, table of tangent values, stopwatch, assembled model rocket. Per class: rocket launch system, electronic protractor, radio, videotape of October Sky.
- • Assign students to groups of two to four to conduct activities, to assemble model rockets, and to solve problems.
- • Engage parent/teacher volunteers to assist with building and launching rockets and with other activities as needed.
- • Assign exercises for practice in applying formulas to find speed and altitude.
- • Give very clear guidelines regarding behavior and performance to the students.
Assessment: Circulate to observe and question students' work. Check written work for accuracy in using formulas to find speed and altitude. Use checklist to assess rocket quality control. Use a paper-and-pencil test covering the mathematics content of the unit. Have the students write about the project that they do. This writing can take the form of a letter to their parents explaining the project. Administer a self-assessment at the end of all the projects. This self-assessment asks the following questions:
- 1. What was the easiest part of the unit for you? Why?
- 2. What was the hardest part of the unit for you? Why?
- 3. What would you do differently next time? Why?
- 4. What grade do you think you deserve?
- 5. What reasons can you give to justify your answer?