Ms. Mofield’s 7th grade math class: 1 hour and a half (block periods)Purpose: To gain an appreciation for mathematical concepts of proportion and ratio to find similar figures in the real world and to adapt the lesson today into new and upcomingmath lessons. (we will discuss how proportion and ratio are used to create similar figures in the real world) Objective: Students will work in groups to explore and discuss similar and congruent figures and form predictions so that they are able to discover properties of each, identify, describe, find, and construct similar and congruent figures. Students can use measurement to explore the meaning of similarity and later to apply the concept to solve problems.Essential Question(s): 1. What are the properties of similar figures?2. Are congruent objects similar? 3. Are all similar objects congruent?4. What are the properties of congruent figures?5. How can you prove figures are similar? Procedure…Attention Getter: Teacher will toss two Styrofoam balls of the same size and one bigger ball (beach ball) to three students in the class. Desks are arranged in a semi-circle set up for classroom discussion and an easier way to pass the balls around the room. As the balls are being passed around the room, students will brainstorm characteristics of the balls, focusing on similarities and differences (other than color). (3 min)Body:- Teacher will call on students to provide ideas of similarity and write the ideas on aPost-It chart. Teacher and students will engage in a conversation about the ideas listed and develop a definition for the term similar. At this stage, students will recognize similar as being objects of the same shape (look the same), but not necessarily the same in size. (5 min)- Students will think relate the term similar to prior knowledge about the word by thinking about what the term similar means outside of math class, objects found inthe “real world” and discuss how similar figures are used in real life. (Possible answers might be the photo enlargement/reducer machine, copy machines that alter the size of pictures, Christmas ornaments, bricks….) (3 min)- Teacher will hold up objects of the same size and shape and have students write down characteristics of these objects. After listing the characteristics, students will share and guess the definition to label objects of the same size and shape. Students will understand this definition to be congruent. (3 min)- Teacher will show students the similar and congruent signs.- Students will work in predetermined groups to discover properties of similar figures and congruent figures. (10 minutes)- Groups will be 4-5 students each- Each group will get a bag of similar objects and a bag of congruentMs. Mofield’s 7th grade math class: 1 hour and a half (block periods)objects, a sheet of measurements, a compass, and a ruler. - Students will measure objects in the bag, predicting relationships of similar figures.- Teacher will walk around the room to guide students in their thinking - Students and teacher will discuss the predicted relationships found in the similar figures; students will share their predicted relationships. (8 min)- Students will recognize the definition of similar figures as two figures that have the same shape, corresponding, congruent angles, and having corresponding sides that are proportional in length. Students will recognize that congruent figures have exactly the same side lengths and angle measurements. - What does proportional mean? Students will share what they believe proportionalto be and understand that proportional is (having the same ratio). Students will explain ratio (which they found working in groups). Students will answer these student directed questions if they do not come up with the correct definition for ratio: How did you know the figures were similar? What numbers did you use from both of the figures? What did they look like when you set them up mathematically? What was your final answer? What do you think you just did? Students will understand that they found the ratio by dividing the lengths of the corresponding sides and the end result is expressed as a fraction or can be written as 2:1 (ex.), with the : meaning to. Teacher will provide examples on the board, drawing a figure and labeling sides, dividing to show/reinforce students answer to proportionality and ratio. Students will understand that when matching corresponding sides of similar figures and dividing the corresponding sides, the ratios will be equal. (5 min)- Groups will alternate between the computer lab and the artistic lab, in which they find and create similar figures. Students will continually ask themselves, “why are these figures similar?” Students already know the rules of group work and how to operate GSP, so the rules will be quickly reviewed. (30 min)- Teacher will explain to students the directions for both activities. Three groups will do the computer activity while three groups work on the handson activity. Groups 1-3 will be on computers first and groups 4-6 will be doing the hands on activity 1st. Students will switch at the sound of the classroom buzzer. - The computer activity: Students will open GSP and click on: Similar figures in our classroom. Students will use measurement tools to find 3 different sets of similar objects. Students will find 2 different sets of congruent objects. Students will then construct one set of similar classroom objects and one set of congruent objects. Each individual student must take at least one turn to be the mouse operator (measurer) as group members watch/help so that there is not one dominant worker. Students will recall the property of similar figures—corresponding congruent angles. There are multiple similar (caution: students may forget to check angles, and just depend on side lengths…make sure to question them to get them to understand that they need to recall and use allof the properties of similar and congruent figures)- The art activity: Each student in each group will create 2-3 different similar objects and 4 different congruent objects out of given materials.Ms. Mofield’s 7th grade math class: 1 hour and a half (block periods)(construction paper, magazines, paper plates….) After constructing a shape, how will you construct a similar object? (caution: students will probably start out measuring and cutting out one figure and get stuck