To introduce this lesson, and set up students to think critically, I write a Think-Pair-Share problem on the board:
Sophia has a puzzle piece that is shaped like a quadrilateral. The puzzle piece has two right angles, and one pair of parallel sides. What type of quadrilateral is the puzzle piece? Draw a diagram to support your answer.
Before I read the problem with students, we discuss puzzles the students have put together before, and what typical puzzle pieces look like. The students note that "baby" puzzles have fewer pieces, and they are easy.
I inquire as to what "easier" means. Students, with prompting, get to "less jagged". I read the problem aloud, and ask students to come up to the board to circle the key details of the problem. The goal is to model for my students how to engage with a problem. In order to "make sense" of our problem we need to closely read it, and we begin here by identifying these key details.
I tell my students that we were going to "dissect" the words in the problem. This word gets their attention. Some have older brothers and sisters doing dissection in high school, and are eager to get started.
**We start with the prefix "quad". I ask students to touch their quadricep muscles in their legs. Next, I write "triangle" and encourage students to find the prefix that tells them what it is (show me on your hands). A few students hold up four fingers but then remember "triangle" from yesterday's lesson. Once one student recognizes that one characteristic of the puzzle piece was to have right angles, I invite the students to show me with their arms a right angle. In doing this, I can quickly formatively assess who understands what a right angle is. Also, once a student points out a characteristic of parallel lines, then I invite students to show me parallel lines with their hands.
Pairs of students begin to solve the problem, using the model we have just practiced together. I circulate to prompt students if I see them trying to jump ahead without closely analyzing the entire problem.
Each group reports out what their puzzle piece looks like, and identifies each mandatory characteristic. The class determines that there are many correct answers.
**I incorporate a number of modalities when we review our vocabulary because I have a wide assortment of learning styles in my classroom. Most of my students are working significantly below grade level, and need to work with a real-world problem. Using their bodies helps them to make lasting connections.
The purpose in viewing Classifying Quadrilaterals, from Promethean Planet, is to show students the relationships between different quadrilaterals. This interactive resource includes definitions and a great labeling activity. Then we examine the properties of quadrilaterals below to decide which are parallelograms. I pose another, slightly easier, problem. My goal is to insure students are able to apply their learning, and so giving them a harder problem wouldn't be fair, nor would it insure that students could access it so that they can practice their learning.
Natalie wants to cut out a parallelogram to use in her collage. What types of quadrilaterals can Natalie use?
Students use the chart of Special Quadrilaterals to assist them. Using color codes, students highlighted the characteristics special to each quadrilateral. Students analyze which special quadrilaterals have the same properties of a parallelogram, and therefore determine that Natalie can use a parallelogram, a rectangle, a rhombus, or a square. To further extend students' thinking, students are asked to tell which other special quadrilaterals have those properties. Also, students are asked to determine which types of quadrilaterals are parallelograms that Natalie could use that has no right angles. This took students a bit of time to hypothesize; you can see one student's notes in the file. Students were encourages to use scrap paper to draw and cut out shapes, especially my remedial students, to manipulate the shapes.
For Independent Practice, students answer two word problems, and have to justify/explain their answers. I assign only two problems so that students can focus on each problem objectively. It's not how much work they do, it is the quality of their work that is important. I believe students know the difference between "busy work" and meaningful practice. In order to give me critical data on each student's development of understanding, questions range from basic comprehension to application throughout the entire lesson. For the following problems, I allow for a Think-Pair-Share.
1. O'Neika has a puzzle piece that is shaped like a quadrilateral. The puzzle piece has two right angles and one pair of parallel sides. What type of quadrilateral is the puzzle piece? Draw a model, and support your answer. (It's a trapezoid; drawings will vary.) Here, students use MP5: use appropriately tools strategically. Students will sketch a diagram that fits the given description in order to classify the figure. Here, I ask students: "What information did you know about the quadrilateral? How did this information help you determine your answer?" "Did each of you use a similar approach when you were working individually?" "Did you all reach the same conclusion? If not, how did you agree on an answer as a pair?" I point out to students after we all come back together as a class, that students approached the problem in a variety of ways, but there is only one type of quadrilateral that meets the correct criteria.
2. Colton earned a polygonal boy scout badge. The badge has three sides that are the same length. Each angle in the triangle measures 60 degrees. What is the shape of his badge? (It's an equilateral triangle; all angles are acute.) Here, students use MP 7: look for and make use of structure. Students sort through given information to classify a triangle. By writing this problem on the board, and underlining the sentence: The badge has three sides that are the same." helps greatly in solving this problem.
As a class, we review the answers to the Independent Practice word problems. I use cold calling (drawing name sticks) to ensure equity in calling upon students. Without telling students specifically what Mathematical Practice we're focusing on, I encourage them to consider more than one mathematical practice when attending to problems. Here, students share out to other groups how they solved the problems.
Together, we fill out the Quadrilateral Family Tree to describe the relationship between quadrilaterals. Students will then utilize this as a study guide.