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# Formative Assessment: Formulas and Vectors

Lesson 6 of 12

## Objective: SWBAT solve problems using geometric trig formulas and vectors.

*50 minutes*

#### Math Grafitti

*20 min*

Today we are going to be taking a quiz over the formulas that we worked with in this chapter (Law of Sines and Cosines, Area = ½bcsin(A)) and the introductory information about vectors. To review for this quiz, I use a strategy called **Math Graffiti**. I write the following words and phrases on its own piece of poster paper:

*Law of Sines**Law of Cosines**Area = 1/2bcsin(A)**Vectors**Vector Addition and Subtraction*

Then I ask students to take ten minutes to move around the room and write as much information as they can about these topics on the posters. They can write things they know, things they don’t know, or questions they have. I make a point to clarify for students that the goal is not just writing down formulas - the first time I did this students just wrote down "*a*^{2} = *b*^{2} + *c*^{2} – 2*bc*sin*A*" and thought the Law of Cosines poster was done. I also want them to write about when we use the formulas, how they work, things we need to be careful about, etc.

Math Graffiti is a good way for them to get ready for today’s quiz. I find that this strategy helps to pinpoint misconceptions and over-generalizations that are present. Students are writing relatively anonymously, so they don’t feel too uncomfortable about sharing questions or ideas. I think that students are willing to graffiti questions that they might not ask in front of the whole class. **Be alert**: expect to catch something that a student thinks is true, but is not really.

After the ten minutes is up, I go around and scan each poster and pick some key ideas to talk to the whole class about. I pose questions that students wrote. I read statements and see if the class agrees or disagrees with them. This followup strategy is a great way to generate a lot of ideas and to notice general trends in the class. It is a great formative assessment to gauge how well your students understand these concepts.

Here are two examples (Law of Sines and Law of Cosines) of the posters that my students did. You can see that there is some deep thinking and some good questions that were raised. It is really nice when students build upon each others thoughts and clarify their thinking. In this video I talk more about this activity and how it helped my class even days after.

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#### Quiz

*30 min*

This quiz is just a short checkpoint to see how the students are doing with respect to the key ideas so far in the unit. I don’t give complicated problems. I want to assess student understanding of the formulas and knowledge of vectors at the midpoint of the unit. I will assess these topics more completely on the unit exam.

**Teacher's Note**: Quiz - Formulas and Vectors.docx provides sample problems that you may choose to use on your quiz.

#### Resources

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Triangles That Are Wrong Because They Are Not Right
- LESSON 2: The Law of Sines: More than Meets the Eye
- LESSON 3: Trigonometry from a Geometric Perspective
- LESSON 4: Airplane! - An Introduction to Vectors
- LESSON 5: Making Vector Operations Transparent
- LESSON 6: Formative Assessment: Formulas and Vectors
- LESSON 7: Resultant Vectors
- LESSON 8: Trigonometric Form of Complex Numbers
- LESSON 9: De Moivre's Theorem
- LESSON 10: Unit Review: Additional Trigonometry Topics
- LESSON 11: Unit Review Game: Categories
- LESSON 12: Unit Assessment: Additional Trigonometry Topics