Quiz + Similar Figures
Lesson 14 of 21
Objective: SWBAT use corresponding sides and proportions to find unknown sides of similar figures.
Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables and are given the option to use cardboard dividers and noise canceling head phones. Instructions on the powerpoint displayed at the board notify students that they will only have 30 minutes to complete this quiz (a timer will be displayed). They will also be reminded to watch out for units, vocab terms, and to check their work. At the end of the quiz, all students will be asked to turn in their quizzes, and the Class Work will be distributed.
This quiz will assess student knowledge of calculating/interpreting the constant of proportionality or unit rate, calculating equivalent ratios, comparing ratios, as well as writing an equation and creating a graph to represent a proportional relationship. The last question in this quiz proved to be the toughest for students. I make sure to create more spiraled material for future lessons to continue reviewing questions like these. This is an ideal question which pushes students to high levels of understating linear relationships. Within one context, downloading songs, students are pushed to interpret the meaning of k (Krystal can download 2.4 songs per minute), the structure of an equation which describes this relationship (y=2.4x), as well as the structure of the line which represents all the possibilities for songs downloaded in a given time lapse. Students who do not answer this question correctly are failing to see how it all connects. They may, however, understand bits and pieces, as evidenced by their accuracy on the previous questions in the quiz. This makes data analysis very important. A student who missed a few questions in #s 1 – 7 understands bits and pieces and needs help putting it all together. These students need small group remediation no more than two times the following week. Students who struggled with most of this Quiz are most likely struggling to understand basic building blocks such as how to calculate the unit rate. This group of students needs intensive remediation and will be invited to after school study groups with the opportunity to make up the quiz.
To save time on note taking today, students are given a sheet from the Glencoe math text along with a set of highlighters. I run the powerpoint through the 3rd and 4th slides which summarize the definition of similar figures as shapes with corresponding sides that are proportional and corresponding angles which are congruent. Students are asked to find this information on their sheet and highlight it. Then I distribute their class journals.
I ask all students to turn to a fresh sheet, on the right side of the journal, and title our first example Corresponding sides are proportional, highlighting the title at the top of the paper in the journal. Then I ask them to draw trapezoid DEFG from the first example in their worksheet, making sure to label the sides given. Next, I ask them to fold the worksheet over so that they are covering the solution to this example. We will be working out the solution on our own, and then checking it against their solution.
My goal through this activity is to get students used to reading examples from a textbook and working them out on their own to gain understanding of the process without mindlessly reading through it. The video below shows how we would construct this journals entry so that students can use it to study and gain better understanding of the process.
The next example is titled corresponding angles are congruent. I first have students define the word congruent as equivalent for this example. We draw two similar, right triangles (one smaller than the other) and highlight the angles in the triangle. Then I have students label the two acute triangles 45 degrees each and the right angle 90 degrees. We only complete this example with congruent angles and I explain to students that we will be doing more work with angles after the state test.
Practice + Closing
I ask students to next complete the “check your progress” example at the bottom of the worksheet by copying it into their journal and completing it like we did the first example. This example may be completed with partners. Once students have completed this example they are to review the back of the worksheet. Each of the two examples given (finding sides of similar triangles and a real world example) includes a “check your progress” problem for students to try. I give them a lined sheet of paper and ask them to write a heading at the top along with the title Exit Ticket. Students must return these two “check your progress” problems completed to me before the end of class. If they finish early they may receive their homework to start ahead of time. I will be using the exit tickets to inform my instruction as I prepare to teach scale drawings in the following week.
With 5 minutes left in class, all students will receive their homework and be dismissed for the next class.