Lesson 14: Fractional Lengths in Triangles and Prisms | Unit 4: Dividing Fractions

Open Ended

Clare is using little wooden cubes with edge lengths of $$\frac12$$ inch to build a larger cube that has edge lengths of 4 inches. How many little cubes does she need? Explain your reasoning.

Open Ended

The triangle has an area of $$7\frac{7}{8}$$ cm² and a base of $$5\frac{1}{4}$$ cm. What is the length of $$h$$ ? Explain your reasoning.

Multiple Choice

Which expression can be used to find how many cubes with edge lengths of $$\frac13$$ unit fit in a prism that is 5 units by 5 units by 8 units?

• $$\left(5\ \cdot\ \frac{1}{3}\right)\cdot\left(5\cdot\frac{1}{3}\right)\cdot\left(8\cdot\frac{1}{3}\right)$$

• $$5\cdot5\cdot8$$

• $$\left(5\ \cdot\ 3\right)\cdot\left(5\cdot3\right)\cdot\left(8\cdot3\right)$$

• $$\left(5\cdot5\cdot8\right)\cdot\left(\frac{1}{3}\right)$$

Open Ended

Mai says that we can also find the answer by multiplying the edge lengths of the prism and then multiplying the result by 27. Do you agree with her? Explain your reasoning.

Multiple Choice

What is the area of the right triangle shown in the image?

• 0.75 cm²
• 1.5 cm²
• 2 cm²
• 0.375 cm²

Open Ended

What is the height $$h$$ for the base that is $$\frac54$$ units long? Show your reasoning.

Draw

Draw a triangle on the grid with a base of $$5\frac12$$ units and an area of $$19\frac14$$ units^2.

Open Ended

Explain or show how you know the triangle you drew has an area of 19 1/4 units².

Open Ended

A shipping company is loading cube-shaped crates into a larger cube-shaped container. The smaller cubes have side lengths of $$2\frac12$$ feet, and the larger shipping container has side lengths of 10 feet. How many crates will fit in the large shipping container? Explain your reasoning.