Grade 5 Core Standard III Assessment
Geometry, Measurement and Algebra
Name:
Date:
5.3.1 Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).
Use the triangles below to answer questions 1 through 4
A
B
C
D
E
1. Which triangles are right triangles?
_______________________________________________________________
2. How many triangles are isosceles?
_________________________________________________________________
3. How many triangles have exactly two acute angles?
____________________________________________
4. Which triangles are scalene?
________________________________________________________________________
5. Which type of triangle is not possible to create? Explain your reasoning.
A. acute scalene
B. obtuse equilateral
C. right isosceles
D. acute isosceles
It is NOT possible to create a/an ____________________________________________ triangle
because …
Name _______________________________
Date _______________________
6. Label each triangle based on the given angle measures.
7. Classify each triangle as isosceles, equilateral, or scalene.
4 feet
4 feet
7 feet
8. Josie drew a triangle using the information below.
• One angle measures 30° and one angle measures 60°.
• None of the sides have the same length.
Which best describes Josie’s triangle?
A) equilateral right triangle
B) isosceles right triangle
C) obtuse right triangle
D) scalene right triangle
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms.
9.
A triangle has a base of 8 inches and a height of 12 inches. What is the area of the triangle?
10. What is the area of the parallelogram shown below?
5m
9m
11. A triangle with the same base and height as the parallelogram below has an area of 32
square feet. What is the area of the parallelogram?
h
b
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by
the number of edges, faces, and/or vertices as well as types of faces.
12. Which shape does NOT have any faces, vertices, or edges?
A) Cone
C) Pyramid
B) Cylinder
D) Sphere
13. Complete the chart below:
Cube
Square Pyramid
Triangular Prism
Triangular
Pyramid
Faces
Vertices
Edges
5.3.4 Recognize volume as an attribute of three-dimensional space.
14. Which of these figures has volume?
A)
B)
C)
D)
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
15. Which measurement describes how much space is inside a triangular prism?
A) Area
C) Perimeter
B) Faces
D) Volume
5.3.5 Determine volume by finding the total number of same-sized units of volume that fill a three-dimensional shape without gaps or overlaps.
16.
Which same size unit would fill the rectangular prism to the
without any gaps or overlaps?
A)
B)
C)
right
D)
17. How many cubes like the one shown to the right will be
needed to fill the entire box? Show your work.
1 foot
1 foot
1 foot
4 feet
2 feet
8 feet
18. Draw a three dimensional shape with a volume of 40 cubic inches.
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.6 Recognize a cube that is one unit on an edge as the standard unit for measuring volume.
19. What is the volume of the figure below? Explain your reasoning.
= one cubic unit
20. What is the volume of the figure below? Explain your reasoning.
= one cubic unit
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.7 Determine the appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume.
21. What is the best estimate for the volume of the sphere shown in the cube below?
A) More than 125 cubic inches.
5 inches
B) Between 50 and125 cubic inches.
C) Between 10 and 50 cubic inches.
5 inches
5 inches
22. Which formula can be used to find the volume of the triangular prism shown below?
A)
20 (15 × 10 × 20)
B)
2
C)
20 (15 × 10)
2
23 × 10 × 20
2
D)
15 × 62 × 20
2
23. The dimensions of the block of ice are shown in the diagram below.
What units should be used to describe the volume of this block of ice?
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms.
24. Which barn roof has the greatest surface area?
20 feet
10 feet
10 feet
30 feet
25 feet
25. Describe a time when you compared the volume of two objects (draw a picture of each object in
the shaded area below and use the remaining space for your explanation).
Object 1
Object 2
______________________________________ ______________________________________
__
__
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
4/20/2011
Name _______________________________
Date _______________________
5.3.9 Identify and measure necessary attributes of shapes to use area, surface area, and volume formulas to solve problems (e.g., to find which of two gift
boxes needs the most wrapping paper or has the greater volume?).
26. Which box (A or B) will hold more sand? Explain your reasoning.
5 cm Box B
4 cm
Box A
2 cm
2 cm
7 cm
2 cm
27. Which box (1 or 2) would need more wrapping paper to cover completely without any gaps
or overlaps? Explain your reasoning.
4
Box 1
6
2
7
Box
2
3
NCSD Math Renewal: Grade 5 Core Standard 3: Geometry, Measurement, and Algebra Assessment
2
4/20/2011