Sample Lesson Plan

5 E’s Lesson Plan

Standard(s) Addressed:

Ratios and proportional relationships

Grade 6: Ratios and Proportional Relationships, extension lesson (fun facty)

6.RP.3

Practice standards used: 

2—Reason abstractly and quantitatively.

5—Use appropriate tools strategically.

7—Look for and make use of structure.

Lesson Objective 

The Ratio that Tops them All

1. What will students discover
1. Students will discover the Golden Ratio and then we will use technology to explore different areas that it appears through the use of applets
2. How will they discover it?
1. Students will find ratios for familiar items, as well as unfamiliar ones, to discover the “Golden Ratio” of Mathematics.
3. How will you measure their understanding? (Use measurable verbs.)
1. I will ask them high cognitive demand questions throughout the lesson, as well as observe their group work. There should be not only algebra worked out, but also pictures of their thinking.

Use the above to help you write the Content Objective.

Students will be able to analyze data about geometric shapes and discover the Golden Ratio by manipulating figures & comparing their lengths with applets and demonstrate this knowledge by sharing ideas out loud in groups where they will have not only algebra, but also pictures to reason their findings. 

Materials Used (be specific):

Paper, writing utensil, chart handout, document camera, ruler, measuring tape, images for historical content, computers for students, access to math applets about the Golden Ratio & Fibonacci numbers

Classroom Management (how will you get the attention of the class?; pass out and collect supplies?; will students be working with a partner? in groups? when?): 

I will let students know, at the start of class, which techniques I will be using, such as a countdown timer on the board, clap once to get everyone’s attention, individual vs. group work vs. class work. Knowing when to listen and when to share ideas. To keep track of time, I will project a timer on the board during group or individual work so that students can see how much longer they have to work, as well as the buzzer will go off and that will get their attention. If an activity is not being timed, then gauge how much more time students need and proceed as necessary.

ENGAGE:  Connect to Prior Knowledge and Experience, Create Emotionally Safe Learning Environment, Excite Students about Today’s Learning Objective Estimated time: 5 minutes Description of Engage: The students will be shown a picture of da Vinci’s Vitruvian Man and asked what they know about it.
Teacher’s Role	Teacher Questions	Students’ Role & Answers to Teacher Questions
Show students the image of the Vitruvian Man. Ask them what they know about it. See what their prior knowledge consists of and build on what the students share. Share where da Vinci’s motivation came from for this picture. This goes along with notes based on the work of the architect Vitruvius. Ratios discussed. First History Component The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. Called Proportions of Man and is only displayed to the public occasionally. Vitruvius determined that the ideal body should be 8 heads high.	Have we seen this before? What do we know about this? What do the shapes around the man mean? Why are those there? Do they tell us anything about the picture? What are some things that you notice about the picture? What observations did you make?	Yes, on TV. Fingertip to fingertip is a person’s height, it is symmetrical. The circle and the square show that certain lengths are equal. They help show equal parts of the body. The circle has equal radius all the way around, so the distances are the same. Students will respond to questions and listen to others’ thoughts.
EXPLORE: Hands-On Learning, Contextualize Language, Use of Scaffolding (Graphic Organizers, Thinking Maps, Cooperative Learning), Use of Multiple Intelligences, Check for Understanding                                                                               Estimated time: 20 minutes Description of Explore: Students will be given a worksheet and various objects to measure.
Teacher’s Role	Teacher Questions	Students’ Role & Answers to Teacher Questions
Give instructions about the task. Do not yet pass out materials (they will get distracted). Model the first measurement, reminding students that a must be greater than b when they document it on their table. Keep in mind to the nearest tenth. Students will work in groups of four and each will have a role. These roles include: -Big ideas person (pulls group back to focus) -Clarifier (monitors concept comprehension, measure lengths) -Explainer (measures group progress, records information) -Peacekeeper (controls the floor) EVERYONE: questioner They will have a list of items to measure: phone, table, notebook/paper, face, +6 of your own! Once instructions are given and instructional questions are clarified, one student will grab a meter stick and chart, then GO! Using the Google timer, still have 8 minutes to measure, then 4 minutes to complete calculations & interpret/compare/contrast data (find similar ratios). They will record at least 1 result on the board that has not yet been recorded. Students will fill out a table for the following values: object, length a, length b (where a>b), a/b on a worksheet.	Why are you measuring that part? Why did you choose to measure this? What other shapes can we try? Do we see a pattern? What else do we notice? Do we see commonalities?	We only need the height and width/we might need the diameter and circumference/etc. We like the shape/this is something everyone uses/etc. Circle/square/rectangle/oval. Yes, these numbers are all kinda close to 1.5 here, none of them are above three. Students will be measuring objects inside the classroom and writing down their numbers. Then, they will work with their group to try to find a pattern. They will be working with each other to see if one object is in the Golden Ratio or not.
EXPLAIN: Listening, Speaking, Reading, and Writing to Communicate Conceptual Understanding, Define Vocabulary                                                        Estimated time: 10 minutes Description of Explain: Students will explain their method of finding a pattern in groups and share in a whole class discussion, then see a short video about a few different appearances of the Golden Ratio.
Teacher’s Role	Teacher Questions	Students’ Role & Answers to Teacher Questions
Let students Think-Write-Pair-Share about their findings. Then when we bring it to the whole class conversation, everyone will already have their thoughts written down. Implementing this strategy is good for ELL or students with special needs because it allows them to write down and rehearse their thoughts so they do not feel uncomfortable when speaking in front of the class. Press on student thinking to further their methods. Realign students to be on the right path. Try to help them discover a pattern in their ratios. Guide a class discussion based on compare and contrast statements from students about their findings. Mini lecture (more in the form of historical fun facts) will be present in this section in order to introduce students to the “Golden Ratio,” since they have not seen it before the video. They will also learn about the different methods and historical events that led up to the finalization of the Golden Ratio. These include Pythagoras, Euclid and da Vinci. Show video! http://www.mathsisfun.com/numbers/golden-ratio.html Pythagoras: Pentagons, each of the lengths of the pentagram can be in golden measure with another. Also, the picture shows that by taking one pentagram, you can create a sequence of smaller or larger pentagrams based off of the sides. Fibonacci: How his numbers give the ratio Euclid: Extreme & mean ratio: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less. da Vinci: The Vitruvian man, revisited. He referred to it as the “Divine Proportion” based off of appealing aesthetics and ratios of objects and parts of the body in comparison to one another.	Where are you starting? Knowing that gives us pi, do we see anything similar with non-circles? Why did you start there? What did our ratios tell us? Why does this number keep showing up?! What do we see in common with these three mathematicians? What is different?	We took the circumference and divided it by the diameter, which gives us pi. Well, we only have a height and a width, so maybe we can do something with those numbers? The only two values we were given. Some of them are similar, but others do not really fit the pattern we found. They all found the same number. Some of them use shapes, others lines or area and another used a human, which is more easier to understand in person. Students are discussing with each other the phenomena they have measured and discovered, as well as what they have seen from the video. They will use various applets that help them see patterns and discover the interesting ratios that appear from the applets. Then, they will listen to a mini lecture of historical fun facts relating to the Golden Ratio.
EVALUATE: Thinking Maps, Summarize Lesson and Review Vocabulary, Variety of Assessment Tools, Games to Show Understanding, Test Students on the Learning Objective                      Estimated time: Done throughout  Description of Evaluate: Listen to student responses and press their thinking for mastery of material.
Teacher’s Role	Teacher Questions	Students’ Role & Answers to Teacher Questions
Teacher will evaluate students throughout the entire process, ranging from class discussion, to group discussion, to individual work, to conversations heard around the room. For individual assessment, students will complete a ticket-out-the-door write up about their knowledge. I will ask them to respond to one of the following prompts to turn in, choose either 1, 2 or 3: What do you understand best? What are you still confused about? What are you curious about?	Why do you think this happens? What have you found? What method are you trying? Do we see a common number?	These look like they have similar proportions. The rectangles and circles are related to each other, but we don't see pi in the rectangles. We are dividing height by width. We’re getting about 1.5 as our scale factor. Students will respond to the questions and participate in discussion throughout the class period. Then, they will complete their ticket-out-the-door by using complete sentences.
EXTEND/ELABORATE: Group Projects, Plays, Murals, Songs, Connections to Real World, Connections to Other Curricular Areas                                                   Estimated Time: 5 minutes Description of Extend/Elaborate: Show students a video and tell them to find other shapes at home to measure and see which one is closest to the Golden Ratio.
Teacher’s Role	Teacher Questions	Students’ Role & Answers to Teacher Questions
Give instructions about finding 5-10 items at home to measure and see how close they can get to finding the Golden Ratio. Bring them to class tomorrow and we will see who gets the closest!	What do we think will give us the best ratio? Now we know what the number is, make a conjecture in your math journal about which items you want to measure and which ones you think will have the closest match to the Golden Ratio. Are the instructions clear?	Yes, I’m going to try the television. I want to see how close my windows/bed/desk/table are to the Golden Ratio. Students will complete this part at home and be sure to bring the information to the following class.