Grade 05 Mathematics - EC: M05.D-M.3.1.2
Grade 05 Mathematics - EC: M05.D-M.3.1.2
Continuum of Activities
The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.
This continuum of activities offers:
- Instructional activities designed to be integrated into planned lessons
- Questions/activities that grow in complexity
- Opportunities for differentiation for each student’s level of performance
Grade Levels
5th Grade
Course, Subject
Mathematics
Activities
- Identify the dimensions of the base of the red rectangular prism.
- True or false. The volume of two rectangular prisms that are connected but not overlapping can be calculated by finding the volume of one and doubling it.
- True or false. The volume of two connected non-overlapping rectangular prisms can be calculated by calculating the volume of each prism then adding them together.
- What is the volume of two identical connected rectangular prisms with a base area of 24 cm2 and a height of 2 cm?
- The dimensions of the white rectangular prism are half the dimensions of the grey rectangular prism. What is the total volume?
- The shape below is comprised of two rectangular prisms. What is the volume in cubic centimeters?
- The figure below is two non-overlapping rectangular prisms. They have identical bases and different heights. Which expression can be used to find the total volume?
- The figure below is two non-overlapping rectangular prisms with identical bases. Which expression cannot be used to find the total volume?
- Sara is asked to find the volume of two connected rectangular prisms. Explain why it is very important for Sara to know if the prisms are overlapping or non-overlapping prisms.
- Explain how to calculate the total volume of the figure below. Be sure to include the answer in your explanation.
- Doug and Kirk are asked to find the volume of the connected, but not overlapping, set of two rectangular prisms. Who is correct? Identify the mistake made by the person who got it wrong.
Rectangular Prism 1: l = 12 in; w = 3 in; h = 7 in
Rectangular Prism 2: B = 24 in2; w = 2 ft.
Doug 12 x 3 x 7 = 252 Kirk 12 x 3 x 7 = 252 in3
24 x 2 = 48 24 x 24 = 576 in3
48 + 252 = 300 in2 252 + 576 = 828 in3
- There are nine 15 cm metal cubes and ten 25 cm metal cubes that are melted and poured into a 1 m iron cube. Will all the liquid metal fit in the box? If so, how much extra room is in the iron box? If not, how much metal overflows the iron box? Explain.
- The diagram below shows two non-overlapping rectangular prisms with the same height.
The volume of Prism #1 is 324 in3. Find the dimensions of Prism #1 and the total volume of the entire shape. Show all your work. Explain how you found the dimensions for Prism #1.
- Sara is asked to find the volume of two connected rectangular prisms. Explain why it is very important for Sara to know if the prisms are overlapping or non-overlapping prisms.
- Explain how to calculate the total volume of the figure below. Be sure to include the answer in your explanation.
- Doug and Kirk are asked to find the volume of the connected, but not overlapping, set of two rectangular prisms. Who is correct? Identify the mistake made by the person who got it wrong.
Rectangular Prism 1: l = 12 in; w = 3 in; h = 7 in
Rectangular Prism 2: B = 24 in2; w = 2 ft.
Doug 12 x 3 x 7 = 252 Kirk 12 x 3 x 7 = 252 in3
24 x 2 = 48 24 x 24 = 576 in3
48 + 252 = 300 in2 252 + 576 = 828 in3
- There are nine 15 cm metal cubes and ten 25 cm metal cubes that are melted and poured into a 1 m iron cube. Will all the liquid metal fit in the box? If so, how much extra room is in the iron box? If not, how much metal overflows the iron box? Explain.
- The diagram below shows two non-overlapping rectangular prisms with the same height.
The volume of Prism #1 is 324 in3. Find the dimensions of Prism #1 and the total volume of the entire shape. Show all your work. Explain how you found the dimensions for Prism #1.
Answer Key/Rubric
- 3 x 4
- False
- True
- 96 cm3
- A
- 5,376 cm3
- B
- C
- Acceptable responses may include, but are not limited to:
- If the figures are overlapping then the volume of the overlap is being counted twice.
- The volume of the each prism is calculated and then added together, therefore the overlap would be figured in each prism instead of only once
- Acceptable responses may include, but are not limited to:
- Volume = length x width x height
- The bottom prism has different measurements; change 1m into cm; 1 m = 100 cm
- The volume of the prism on the bottom is V = 8 x 6 x 100 which is 4,800 cubic centimeters.
- The volume of the prism on top is V = 12 x 8 x 6 (the 6 is the same width as the bottom prism) which is 576 cubic centimeters.
- Add the two prisms together: 4,800 + 576 = 5,376 cubic centimeters.
- Kirk is correct.
Doug’s mistake was he forgot to convert 2 ft. into 24 inches. Cannot use two different units of measure.
- The iron box will not overflow; 813,375 cubic centimeters of extra room
Acceptable explanations may include, but are not limited to:
- Volume of first set of cubes: 9 x 15 x 15 x 15 = 30,375 cm3
- Volume of second set of cubes: 10 x 25 x 25 x 25 = 156,250 cm3
- Total volume of melted metal cubes: 30,375 + 156,250 = 186,625 cm3
- Iron box measurement given in meters, must be converted to centimeters
- 1 m = 100 cm
- Volume of iron box: 100 x 100 x 100 = 1,000,000 cm3
- Since 186,625 cm3 is smaller than 1,000,000 cm3, the liquid metal will fit into the iron box
- Extra room: 1,000,000 - 186,625 = 813,375
- Dimensions of prism #1: h = 18 in; l = 2 in; w = 9 in
Total volume is 540 in3
Acceptable explanations may include, but are not limited to:
- Length of 2 inches was given in the diagram
- Height of 18 inches is from prism #2; told they are the same in the problem
- Width of 9 inches:
- Set up volume formula with known information: 324 = 2 x w x 18
- Simplify: 324 = 36w
- Divide both sides by 36 to get: w = 9