**Developmentally appropriate questions and higher order thinking questions for Performance task**

I have been teaching and facilitating math courses ranging from pre-Algebra level to Calculus level for last 19 years. This year I have had an opportunity to teach

**to diverse learners’ .The greatest challenge has been getting students to improve their reasoning. Many students have difficulty processing information and writing formal proofs—a task that requires a good deal of reasoning.**

__self-contained Geometry__**In our math department, I was assigned the task of creating one performance task on concept of “Similar Triangles” and I had to develop**questions which are low- and high level, open-ended, text- or task-dependent and promote student thinking and understanding.

I developed discussion techniques which results in authentic text-based investigations and the questioning is at the level of complexity appropriate to the students’ age or grade or the content under study. I developed questions which require students to provide evidence of their thinking and construct viable arguments based on evidence.

Following is a list of questions I created which could be used by GEOMETRY TEACHERS while teaching and facilitating math topic on similar triangles and assess student understanding of concepts and skills by giving them performance task which I submitted on my site (Kalramathguru.weebley.com) and drive on February 26, 2015.

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__DOK 1 (recall): the most basic skills or definition__

**1.**What is ratio?

**2.**What is proportion?

**3.**When ratios are said to be in proportions?

**4.**What is angle sum property of triangle?

**5.**What are alternate interior and exterior angles?

**6.**

**7.**What are corresponding angles?

**8.**What is the difference between congruency and similarity?

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__DOK 2 (skill concept): using the information or conceptual knowledge__**1.**

**In what ways can I represent the relationships that exist between similar figures using the scale factors, length ratios, and area ratios?**

**2.**

**Under what conditions are similar figures congruent?**

**3.**

**When I draw a transversal through parallel lines, what are the special angle and segment relationships that occur?**

**4.**

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__DOK 3 (strategic thinking): reasoning or developing a plan; the task may have more than one answer__**1.**

**How can I tell if two figures are similar?**

**2 What strategies can I use to determine missing side lengths and areas of similar figures?**

**3. How can I be certain whether lines are parallel, perpendicular, or skew lines?**

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__DOK 4 (extended thinking): requires an investigation, collection of data and analysis of results; requires time to think and process__1.

**Why do I always get a special angle relationship when any two lines intersect?**

2.

**How can I apply understanding of concepts and skills related to similar triangles to find width of river, height of buildings and towers?**

3.

**In real life, which profession uses the concept of similar triangles in real life?**