IM 6.2.2 Lesson: Representing Ratios with Diagrams
Find the value of each expression mentally.
[math]24\div4[/math]
[math]\frac{1}{4}\cdot24[/math]
[math]24\cdot\frac{1}{4}[/math]
[math]5\div4[/math]
Here is a collection of snap cubes. Choose two of the colors in the image, and draw a diagram showing the number of snap cubes for these two colors.
Share diagrams with a partner. Write a sentence to describe a ratio shown in their diagram. Your partner will do the same for your diagram.
Share the sentence with your partner. If you disagree, explain your thinking.
Elena mixed 2 cups of white paint with 6 tablespoons of blue paint. Here is a diagram that represents this situation.
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[/img][br][br]Select [b]all[/b] the statements that correctly describe this situation.
Jada mixed 8 cups of flour with 2 pints of water to make paste for an art project. Draw a diagram that represents the situation.
Write at least two sentences describing the ratio of flour and water that Jada mixed.
The app below describes different recipes for spaghetti sauce. In the diagrams:[list][*]a circle represents a cup of tomato sauce[/*][*]a square represents a tablespoon of oil[/*][*]a triangle represents a teaspoon of oregano[/*][/list][list=1][*]Take turns with your partner to match a sentence with a diagram.[list=1][*]For each match that you find, explain to your partner how you know it’s a match.[/*][*]For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.[/*][/list][/*][*]After you and your partner have agreed on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.[/*][/list]
Drag the sentences or use the tools to match the sentence to the diagram.
There were two diagrams that each matched with two different sentences. Which were they?[list][*]Diagram _______ matched with both sentences ______ and ______.[/*][*]Diagram _______ matched with both sentences ______ and ______.[/*][/list]
Select one of the other diagrams and invent another sentence that could describe the ratio shown in the diagram.
Create a diagram in the applet below that represents any of the ratios in a recipe of your choice. Is it possible to include more than 2 ingredients in your diagram?
IM 6.2.2 Practice: Representing Ratios with Diagrams
Here is a diagram that describes the cups of green and white paint in a mixture.
[img]data:image/png;base64,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[/img][br][br]Select [b]all[/b] the statements that correctly describe this diagram
To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds. Create a diagram to represent the quantities of each ingredient in this recipe.
Use your diagram to complete each sentence.
The ratio of __________________ to __________________ to __________________ is ________ : ________ : ________.
To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds. Use your diagram to complete each sentence.[br][br]There are ________ cups of pretzels for every cup of raisins.
There are ________ cups of almonds for every cup of raisins.
A square is 3 inches by 3 inches. What is its area?
A square has a side length of 5 feet. What is its area?
The area of a square is 36 square centimeters. What is the length of each side of the square?
Find the area of this quadrilateral.
Explain or show your strategy.
Complete each equation with a number that makes it true.
[math]\frac{1}{8}\cdot8=[/math]
[math]\frac{3}{8}\cdot8=[/math]
[math]\frac{1}{8}\cdot7=[/math]
[math]\frac{3}{8}\cdot7=[/math]