Lesson 2
Introducing Proportional Relationships with Tables
Unit 2
Introducing Proportional Relationships
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2.1 Warm Up: Notice and Wonder- Paper Towels by the Case
Here is a table that shows how many rolls of paper towels a store receives when they order different numbers of cases.
What do you notice about the table? What do you wonder?
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Learning Targets
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1. A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
2.2 Feeding a Crowd
a. How many people will 10 cups of rice serve?
b. How many cups of rice are needed to serve 45 people?
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2. A recipe says that 6 spring rolls will serve 3 people. Complete the table.
2.2 Feeding a Crowd
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A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table as you answer the questions. Be prepared to explain your reasoning.
2.3 Making Bread Dough
1. How many cups of flour do they use with 20 tablespoons of honey?
2. How many cups of flour do they use with 13 tablespoons of honey?
3. How many tablespoons of honey do they use with 20 cups of flour?
4. What is the proportional relationship represented by this table?
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4 quarters are equal in value to 10 dimes.
2.4 Quarters and Dimes
1. How many dimes equal the value of 6 quarters?
2. How many dimes equal the value of 14 quarters?
3. What value belongs next to the 1 in the table? What does it mean in this context?
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Pennies made before 1982 are 95% copper and weigh about 3.11 grams each. (Pennies
made after that date are primarily made of zinc). Some people claim that the value of the
copper in one of these pennies is greater than the face value of the penny. Find out how
much copper is worth right now, and decide if this claim is true.
2.4: Are you ready for more?
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Lesson Summary
If the ratios between two corresponding quantities are always equivalent, the relationship between the quantities is called a proportional relationship.
This table shows different amounts of milk and chocolate syrup. The ingredients in each row, when mixed together, would make a different total amount of chocolate milk, but these mixtures would all taste the same.
Notice that each row in the table shows a ratio of tablespoons of chocolate syrup to cups of milk that is equivalent to 4:1.
The relationship between these quantities we could say:
-The relationship between amount of chocolate syrup and amount of milk is proportional.
-The relationship between the amount of chocolate syrup and the amount of milk is a proportional relationship.
-The table represents a proportional relationship between the amount of chocolate syrup and amount of milk.
-The amount of milk is proportional to the amount of chocolate syrup.
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Lesson Summary
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2.5 Cool Down: Green Paint
When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.
1. How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning.
2. Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green.
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2.5 Cool Down: Green Paint
3. What is the proportional relationship represented by this table?
4. What is the constant of proportionality? What does it represent?
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Reflections
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Practice Problems
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Lesson Video
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