IM 6.4.14 Lesson: Fractional Lengths in Triangles and Prisms
Find the area of Triangle A in square centimeters. Show your reasoning.
The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.
The area of Triangle C is 54/5 square units. What is the length of h? Show your reasoning.
Use cubes or the applet to help you answer the following questions.
Here is a drawing of a cube with edge lengths of 1 inch.
How many cubes with edge lengths of [math]\frac{1}{2}[/math] inch are needed to fill this cube?
What is the volume, in cubic inches, of a cube with edge lengths of [math]\frac{1}{2}[/math] inch? Explain or show your reasoning.[br]
Four cubes are piled in a single stack to make a prism. Each cube has an edge length of ½ inch. Sketch the prism, and find its volume in cubic inches.
For each prism, record in the table how many ½-inch cubes can be packed into the prism and the volume of the prism.
Examine the values in the table. What do you notice about the relationship between the edge lengths of each prism and its volume?
What is the volume of a rectangular prism that is [math]1\frac{1}{2}[/math]inches by [math]2\frac{1}{4}[/math]inches by 4 inches? Show your reasoning in the app below.
Show your reasoning.
A unit fraction has a 1 in the numerator.
[list][*]These are unit fractions: [math]\frac{1}{3}[/math],[math]\frac{1}{100}[/math],[math]\frac{1}{1}[/math].[/*][/list][list][*]These are [i]not[/i] unit fractions: [math]\frac{2}{9},\frac{8}{1},2\frac{1}{5}[/math].[br][/*][/list][br]Find three unit fractions whose sum is [math]\frac{1}{2}[/math]. An example is: [math]\frac{1}{8}+\frac{1}{8}+\frac{1}{4}=\frac{1}{2}[/math] How many examples like this can you find?[br]
Find a box whose surface area in square units equals its volume in cubic units. How many like this can you find?
IM 6.4.14 Practice: Fractional Lengths in Triangles and Prisms
Clare is using little wooden cubes with edge length [math]\frac{1}{2}[/math] inch to build a larger cube that has edge length 4 inches. How many little cubes does she need? Explain your reasoning.
The triangle has an area of [math]7\frac{7}{8}[/math]cm[math]^2[/math] and a base of [math]5\frac{1}{4}[/math]cm.[br]What is the length of [math]h[/math]? Explain your reasoning.[br][br][img]data:image/png;base64,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[/img]
Which expression can be used to find how many cubes with edge length of 13 unit fit in a prism that is 5 units by 5 units by 8 units? Explain or show your reasoning in the applet below.
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.
A builder is building a fence with [math]6\frac{1}{4}[/math]-inch-wide wooden boards, arranged side-by-side with no gaps or overlaps. How many boards are needed to build a fence that is 150 inches long? Show your reasoning.
Find the value of each expression. Show your reasoning and check your answer.
[math]2\frac{1}{7}\div\frac{2}{7}[/math]
[math]\frac{17}{20}\div\frac{1}{4}[/math]
Consider the problem: A bucket contains [math]11\frac{2}{3}[/math] gallons of water and is [math]\frac{5}{6}[/math] full. How many gallons of water would be in a full bucket? [br][br]Write a multiplication and a division equation to represent the situation. Then, find the answer and show your reasoning.
There are 80 kids in a gym. 75% are wearing socks. How many are [i]not[/i] wearing socks? If you get stuck, consider using a tape diagram.
Lin wants to save $75 for a trip to the city. If she has saved $37.50 so far, what percentage of her goal has she saved? What percentage remains?
Noah wants to save $60 so that he can purchase a concert ticket. If he has saved $45 so far, what percentage of his goal has he saved? What percentage remains?