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New York State K8 Mathematics M
New York State K8 Mathematics Mentor Network
K2  35  68  Timeframe: The class time for my accelerated group was 60 minutes. Planning took about 1 1/2 to 2 hours. 
Materials: Overhead projector and markers; Student “SuperStar” worksheets and worksheet transparency; Tag board with small star in center for each student; Transparency of construction instructions; Sample drawings and creations of engineering design. (OPTIONAL); Student protractors; Pencil; Calculator ; Ruler ; Scissors. 

Purpose: Students will discover the patterns and relationships of similar, noncongruent figures through construction and design of a “Super Star.” Students will determine through deductive reasoning that all angles of both figures (small and large star) are of equal measure, and that any two similar length measurements between the two stars will be proportionate. Students have just finished a chapter on proportions and ratios , and will need to use this knowledge to complete the activities. 

PreActivities/Introduction: 1. Provide a brief summary of scaling and similar figures using engineering documents and the actual parts made (Brass Hammer) OPTIONAL. 2. Students are given a set of directions by overhead projector, along with all necessary teacher and student provided supplies to make a “SUPERSTAR.” Teachermade exemplar (uncolored) is shown to students. 3. Model construction of the first leg of the ‘SuperStar,” as directions provide on overhead instructions. 4. Students complete individual “SuperStars.” Those who finish early are given directions to explore their stars (small and large) using a protractor and English/metric ruler, in search of any patterns or relationships (1015 minutes). 

Activity: 5. Pass out SuperStar worksheet. Introduction is read aloud. Directions are given. Students are to work in pairs or individually to complete the first two columns of the worksheet (10 minutes given). 6. Teacher replaces constructive transparency with worksheet transparency and calls upon selected students to read measurements and visually correlate to the stars. 7. Teacher asks students for visible patterns. Students will see that similar angles have the same measure. Students may see that measurements correlate equally (proportionate). 8. Students are to find the unit ratio of the measurements (small star to SuperStar) using a calculator if necessary . Students use knowledge from previous chapter, but a brief review may be necessary (10 mm.). 9. Record findings on the overhead worksheet. Students will see that the ratio is near 1:2.6 for all similar length measurements, given room for small human error. Call upon students to make impressions. Teacher describes this relationship as proportional. 10. Students are given directions to complete the bottom half of the worksheet to list similarities and differences of the two stars . Common traits are listed in the star labeled (BOTH STARS). 

Summary: 11. Teacher models these stars as summary of the activity . BOTH STARS must have: a) angles are same/congruent, and b) measurements have the same ratio OR measurements are proportionate. Other answers are accepted, but a) and b) are the objectives of the activity. 12. Students are now introduced to the follow up activity, which is being graded on a rubric. They will create similar designs between the two stars using spatial estimation. Students will draw a pattern or unique design on the smaller star and then copy that design to the larger star. 13. Exemplar (colored teacher version) is shown and rubric is introduced to students (see part 5 of outline). 14. Students are assigned the overnight assignment to complete the miniproject. 
Assessments/Rubrics: I have used a 3 point rubric scale, which is as follows: 0: Incomplete or missing 1: Complete, but shows an incomplete understanding of both objectives. If quality of craftsmanship is poor, some may meet one of the objectives and fall into this category. 2: Complete with demonstration of one objective, but shows an incomplete understanding of the second. If quality of craftsmanship is poor, some may meet both objectives and fall into this category. 3: Complete understanding, with good craftsmanship and demonstration of both objectives: a) SuperStar is properly drawn and cut , with all legs congruent b) SuperStar is colored using spatial estimation. An obvious attempt was made to estimate the ratio of 1:2.6 for the copied design. 

Instructional/Environmental
Modifications: The in class activities will take a full, hardworking 60 minutes, and was completed in that time successfully in my situation. This activity was presented to an accelerated 6th grade program, which runs alongside the 7th grade curriculum. To meet the needs of the sixth grade curriculum, the superstars may need to be pre made, since they need to be accurately drawn and cut for the activity to meet the objectives. Similarity and ratios/ proportions are both part of the 6th grade curriculum in Newfane. So this may be used as an expository activity at the regular 6th grade level. There are very high expectations for this class. Extra time may be necessary in slower working situations. 

Teacher Reflections: I wanted to complete a scaling activity from the center of an object. The easiest way that I found for the kids was to extend the legs of the stars by the width of the ruler . Without accurate measurement procedure, some kids had a hard time spatially constructing this. I decided to include this in the rubric because I spent a great deal of class time helping students and modeling. They should have been responsible to fix the shapes at home. This was told to them. The products were very creative, with few similarities between them. We used these throughout our scaling unit. It provided the students with the basic ideas behind similar scaled objects. This can be extended to a geometry unit with endless possibilities. 
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