10TH GRADE
GEOMETRY AND SPATIAL SENSE ANSWERS
1
Question 21
Alex wanted to find a pattern to predict the total number of diagonals in a convex
polygon. He used each of the figures below to determine the number of diagonals in the
4-sided convex polygon and the 5-sided convex polygon shown below.
2
a. Create a table like the one shown below in your Student Answer Booklet.
Complete the table to show the relationship between the number of sides, the
number of diagonals drawn from each vertex, and the total number of diagonals
in each of the convex polygons listed.
Number of sides
4 5 6 7 8
Number of diagonals from each vertex 1 2 3
Total number of diagonals
2 5 9
b.
c. What is the total number of diagonals that a convex polygon of 12 sides has?
d. Write an expression which represents the number of diagonals that a convex
polygon of n sides has.
Scoring Guide
Score
Description
4
The student response demonstrates an exemplary understanding of the
geometrical concepts underlying the task.
3
The student response demonstrates good understanding of the geometrical
concepts underlying the task. Although there is significant evidence that the
student was able to work with the concepts involved, some aspect of the response
is flawed. As a result the response does not merit a top score.
2
The student response contains fair evidence of understanding some of the
geometrical concepts and skills underlying the task. While some aspects of the
task are completed correctly, others are not. The mixed evidence provided merits
no more than 2 points.
1
The student response contains only minimal evidence of understanding the
geometrical concepts/skills underlying the task.
0
The student response contains insufficient evidence of understanding the
geometrical concepts underlying the task to merit any points.
Blank No Response.
3
Grade 10 Mathematics
Question # 21 - Score Point 4
4
5
6
7
8
9
Answer: 1
Answer: 4
10
Answer: 3
11
Answer:
Answer:
12
Answer: 2
Answer: 4
13
Answer: 3
14
Answer:
Answer:
15
Answer:
4pts-
3pts-
2pts-
1pt-
0pts-
16
Answer: C
Answer: C
17
Answer: C
Answer: B
18
Answer: D
19