Fill It Up!
Find the volume: 3 units by 2 units by 4 units
24 units3
A prism has dimensions 2 ft × 3 ft × 4 ft.
If you make 2 identical prisms, what is the total volume?
48 feet3
Find the area: 4 inches long and 1/2 inch wide
Area = 2 in2
A shape has 4 sides and one pair of parallel sides.
What type of shape could it be?
Trapezoid
A rectangle has an area of 12 units2.
One side is 3 units. What could the other side be? Explain.
4 units
A rectangular prism has a length of 5 units, a width of 2 units, and a height of 3 units. What is the volume?
30 units3
A rectangular prism has a volume of 36 units3.
It is made of 3 equal layers. What is the volume of each layer?
12 units3
Find the area: 8 inches long and 3/4 inches wide
Area = 6 in2
True or False:
All squares are rectangles. Explain why.
True: squares have 4 right angles, which makes them rectangles
True or False:
A shape with 4 equal sides is always a square. Explain.
False: it could be a rhombus
A box has a volume of 48 units3. The length is 4 units, and the width is 3 units. What is the height?
4 units
A shape is made of two rectangular prisms:
What is the total volume?
36 units3
Find the area: 2/3 ft long and 3/5 ft wide
Area = 2/5 ft2
A shape has:
- Opposite sides parallel
- Opposite sides equal
- NO right angles
What is the most specific name for this shape?
Parallelogram
A rectangular prism has a volume of 24 units3.
Give two different sets of dimensions that could make this prism.
1 x 1 x 24 units
1 x 2 x 12 units
1 x 3 x 8 units
1 x 4 x 6 units
2 x 2 x 6 units
2 x 3 x 4 units
There are two boxes:
- Box A: 2 units by 3 units by 4 units
- Box B: 1 unit by 6 units by 4 units
Which has the greater volume?
Trick Question - Both boxes have the same volume! (24 units3)
A composite figure is made of two prisms stacked on top of each other:
Instead of adding volumes separately, explain how you could use multiplication to find the total volume more efficiently. Then solve.
Combine the two heights together: 3 + 1 = 4 units tall
Volume: 5 units x 2 units x 4 units = 40 units3
A rectangle has side measurements of 4 ft long and 1 1/2 ft wide. What is the area?
Area = 6 ft2
A quadrilateral has:
- 4 equal sides
- Opposite angles equal
- Angles are NOT all 90°
What is the shape?
Rhombus
A rectangle has side lengths of 1/2 ft and 8 ft.
Another rectangle has side lengths of 1 ft and 4 ft.
Compare their areas. What do you notice?
Both rectangles have the same area: 4 ft2
You are filling a fish tank that is 2 1/2 feet by 4 feet by 3 feet. How much water can it hold?
30 feet3
You are building a storage unit made of two connected rectangular prisms:
Part A: Find the total volume.
Part B: Explain how addition and multiplication both help solve this problem.
Bottom section: 24 ft3
Top: 18 ft3
Total Volume = 42 ft3
Explanation:
You are designing a small garden that is 2 1/2 meters long and 1 1/2 meters wide. What is the area of the garden?
Area = 3 3/4 m2
A builder is choosing tiles for a floor. He has two options:
- Tile A: 4 equal sides, 4 right angles
- Tile B: 4 equal sides, no right angles
Part A: Name each shape.
Part B: Which of those shapes are also parallelograms? Explain.
Tile A: Square
Tile B: Rhombus
Both squares and rhombuses are parallelograms because they have two pairs of parallel sides.
You are designing a dog pen using rectangular sections.
You put them together to make a 3D rectangular prism that is 2 meters tall.
Part A: What is the total area of the base?
Part B: What is the volume of the prism?
Part C: Explain how area and volume are connected in this problem.
Part A: 6 + 3 = 9 square meters
Part B: 9 × 2 = 18 cubic meters
Part C: The area of the base is multiplied by the height to get the volume.