Download Geometric and Spatial Reasoning baseline

Baseline Assessment: Geometric
Name ________________________________________
Grade_________________
1. What is the shape described below? Write your answer below the clues.
Clue 1:
Clue 2:
Clue 3:
Clue 4:
Clue 5:
Clue 6:
Clue 7:
Clue 8:
Clue 9:
It is a closed figure with 4 straight sides.
It has 2 long sides and 2 short sides.
The 2 long sides are the same length.
The 2 short sides are the same length.
One of the angles is larger than one of the other angles.
Two of the angles are the same size.
The other two angles are the same size.
The 2 long sides are parallel.
The 2 short sides are parallel.
Answer:
How did you know? What clues helped you the most?
Baseline Assessment: Geometric
2. A mat plan is a kind of blueprint with the number of cubes stacked on top of
each other written in each square. And the numbers are arranged in the
same floor pattern as seen in the 3-d shape.
a. For the following 3-d shape, an example of a mat plan is given to the
right. Notice that the 1s are in an L-shape in the mat plan, similar to
how the 3-d cubes are arranged with three in a row in front and one
placed behind the far left cube.
Mat Plan
1
1 1 1
Front
Front
b. For the following 3-d shape, fill in the mat plan in the grid provided.
Mat Plan
Front
Front
Baseline Assessment: Geometric
3. The Pythagorean Theorem is stated as follows:
The sum of the squares of the lengths of the legs on a right triangle is
equal to the square of the length of the hypotenuse. In other words, if
a is the length of one leg, and b is the length of the other leg, and c is
the length of the hypotenuse, then a 2  b 2  c 2 .
Given below are two incorrect
proofs of the Pythagorean Theorem.
Explain why both of them are incorrect.
Proof 1:
Proof 2:
Verify :
32  4 2  9  16  25
5 2  25
So 32  4 2  5 2.
Try another :
5 2  12 2  25  144  169
132  169
So 5 2  12 2  132.
We can try others and they will be the same.
Therefore a 2  b 2  c 2

Why is Proof 1 incorrect? Explain as
clearly as possible.
Why is Proof 2 incorrect? Explain as
clearly as possible.
Baseline Assessment: Geometric
Recording Student Responses
1. This problem enables you to see if students are at van Hiele Level 1 or 2.
Students at Level 1 get this problem incorrect, and students at Level 2 are
able to correctly determine the correct shape (a convex kite).
Grade level
9
10
11
12
Correct
Incorrect
Baseline Assessment: Geometric
2. This problem is meant to assess spatial reasoning ability. Students
must place the values in the correct orientation.
Grade level
9
10
11
12
Correct
Incorrect
Baseline Assessment: Geometric
4. This problem is meant to assess geometric reasoning ability. Student
responses may vary greatly. The first invalid proof attempts to avoid
geometry and essentially just checks a few special cases of numbers that
happen to be Pythagorean Triples. So this proof is not even a prof. The
second proof seems to show that the squares representing a 2 and b 2 can be
split into triangles which exactly fill up the square of size c 2 . However, this
diagram only works because the right triangle is also isosceles.


Response
Categories
Numbers of students
Proof 1
Not a Proof; just
arithmetic
Statements are
vague or
arithmetic is
incorrect
Proof doesn’t
work for all
cases
Not enough
algebra
Other

Proof 2