New York State K-8 Mathematics M
New York State K-8 Mathematics Mentor Network
The class time for
group was 60
took about 1 1/2 to 2
Overhead projector and markers; Student
“Super-Star” 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.
Students will discover the patterns and relationships of similar, non-congruent 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.
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 “SUPER-STAR.” Teacher-made
exemplar (uncolored) is shown to students.
3. Model construction of the first leg of the ‘Super-Star,” as directions provide on
4. Students complete individual “Super-Stars.” 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 (10-15 minutes).
5. Pass out Super-Star 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 Super-Star) 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
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
14. Students are assigned the
overnight assignment to complete
I have used a 3 point rubric scale, which is as
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) Super-Star is properly drawn and cut, with all legs
b) Super-Star is colored using spatial estimation. An
obvious attempt was made to estimate the ratio of
1:2.6 for the copied design.
The in class activities will take a full, hard-working 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.
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.