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I like that the overall goal is to be able to prove similarity and proportional polygons. That would be the independent work a student would complete. Even if there is some struggle in fully getting everything set up, but that is the joy of a proof. You can conclude through several different ordering of steps.

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This is a particularly interesting Unit Design because it incorporates a real world use of similarity. Many humans are fascinated with buildings or structures, so this would be a great unit plan for honing in on similarity.

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a.) Understand similarity in terms of similarity transformations

1. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar.

2. Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

b.) Prove theorems involving similarity

Apply logical reasoning and analytical skills

Work effectively with others

Cooperate for a common purpose

That proportions between similar figures can only be set up one way.

That similar is the same as congruent.

Students will take a summative test created by the department.
The test will be in a traditional format and will cover the above stated content standards.

Students will take the test individually.

ONE TIME ASSESSMENTS:

This is assessing the students' ability to apply scale factors to real world scenarios. Our follow up discussion to this activity will assess the students' understanding of the 21 st century skill: why we collaborate for a common purpose. Students will relate the collaboration that they do as students to the collaboration a real life contractor would have to do as part of their job.

I will assess the group work for both 21 st century and literacy skills. Students will self-evaluate how well they worked in groups and how effective they were in their role. The actual group work that they turn in will inform me of how well they were able to use logic to solve the new problem (literacy objective).

DAILY ASSESSMENTS:

This ongoing assessment will enlighten students to their (mis)understandings throughout the unit. They have the opportunity to ask questions on problems they do not understand and thus reconcile those misunderstandings. This kind of self-assessment helps to develop metacognitive processes in students, an important component to student success. Also, research shows that homework is most effective when it is graded.

I monitor student progress constantly. Sometimes I do that with a "fist to five". Sometimes I have students write what they think they know on a piece of paper and share it with a partner, and then we discuss what people are confused about. I am constantly monitoring student progress in different ways.

are your students headed?Where have they been?How will you make sure the students know where they are going?

Thus far, the students have studied congruence relationships. They have learned how to prove whether two shapes are congruent and then how that can help them to solve for missing components of a figure. Now, they will be learning about similarity relationships. This is like the congruence relationship but has key differences. Students will learn how side lengths are related when shapes are similar and how to prove similarity. Some ideas will transfer directly from the congruence relations but many will be different.
They also learned about proportions and scaling in middle school but never in the geometry context. Now they will be taking components of previous concepts and merging them with new information.

How will you hook students at the beginning of the unit?

I will tell students that what we are learning in this unit has many real world applications. One of those applications is in architectural building design. To pique their interest, I will show the students a series of pictures of collapsed buildings and bridges that happened as a result of calculation error. This will help to illustrate the importance of the unit.
http://www.cnbc.com/id/44231749/page/1

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?

Students will explore scale drawings by pretending to be building contractors that are following an architects scaled blue prints. They will have to answer real world questions based on the blue print design. I will equip them with the skills to do this in the lesson prior.

Students will also explore similar triangles in a group activity where they will try to prove that two triangles are similar based on a small amount of criteria. They will have to justify why that criteria is or is not sufficient for determining similarity. This exploration will come prior to the lesson on proving similarity in triangles. It is their past lessons on proofs that has equipped them for this exploration. I will facilitate the investigation and then call the class together to discuss our findings and clarify.

How will you cause students to reflect and rethink?How will you guide them in rehearsing, revising, and refining their work?

Students will first learn one method for approaching imbedded triangles. However, later in the unit, we will discover the "Side-Splitter Theorem" that will cause them to rethink our original approach in favor of something more direct. The Side Splitter Theorem will combine their new knowledge with concepts they have learned from past units.

Students will also be reflecting on what they learned when proving congruency in triangles and how that must be revised and adapted for proving similarity instead.

How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?

Students will exhibit their skills through homework that is graded and discussed daily. Students will also be given frequent formative assessments so that students can self-evaluate their understanding.

How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?

I will be able to scaffold the in-class activities by walking around and providing additional support to the students who need it. Also, since students will be working in groups for inquiry activities, they will not be left to struggle on their own. However, each student will still be held accountable for their own learning since they will be graded on their individual work.

I will also vary the lessons from day to day to meet different learning styles. Some days we will be exploring; other days will be more of a straight forward lesson. I will ensure that students will be given constant "brain breaks" as well.

How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?

I will have exploration activities spaced well throughout the unit so that there are never too many consecutive "lecture" type lessons. Students will also be given formative assessments throughout the unit.

See my timeline below for a more in-depth explanation of sequencing.

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UbD Unit Plan - Kirsten's Teacher Work Sample

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a.) Understand similarity in terms of similarity transformations Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

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Many students I have seen struggle with order of operations and some struggle with the properties (even if not given what type of property). I especially liked the end when it said "all rules are out, come up with as many solutions as you can" because I have been practicing asking students "what if a friend came to this answer?" as a way for them to further explain how their own answer is the correct solution.

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I find this lesson plan intriguing because many humans are fascinated by architecture. Not only that, but students would have to incorporate budgeting based on the amount of material needed which would be laid out by area. There are also rubrics used to help students attain their goal.

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The WHERETO in Stage 3 is really thought out and organised.

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Understanding by Design - Unit Plan for Polygons and Quadrilaterals

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Use of UbD format to plan a Geometry unit for all ability levels on polygons, then quadrilaterals in particular.