Student Page 2.5.2 Recipes and Proportional Reasoning
A proportional relationship that frequently arises in daily life is scaling recipes. As you work on Recipes and Proportional Reasoning, think about these questions: What does slope mean in this context? How can we find the slope in each representation, context, table, graph, and equation? How are the slopes for each of the ingredients in the guacamole recipe related?
1.
(a)
Have you had to make more or less of a recipe? Why did you alter it?
(b)
What did you do to rescale the recipe?
Guacamole.
2 medium avocados
1 teaspoon sea salt
2 tablespoons lemon juice (~ half a lemon)
\(1/4\) cup onion (~\(1/8\) a large onion)
1 medium tomato
\(1/2\) cup fresh cilantro leaves
Blend on low for 15 to 20 seconds. Do not over mix. Leave chunky. Garnish with diced tomato and parsley.
Yields 1.5 cups.
2.
Use the Guacamole recipe. Determine the amount of each ingredient you need for the number of recipes of guacamole shown in the first column. Complete Table 2.5.2.1.
| Ingredients | ||||
|---|---|---|---|---|
| Amount needed for \(n\)recipes with \(n =\) |
Avocados | Tomatoes | Lemons | Onions |
| \(\frac{1}{2}\) | ||||
| 1 | 2 | 1 | \(\frac{1}{2}\) | \(\frac{1}{8}\) |
| 2 | ||||
| 3 | ||||
| 4 | ||||
| \(n\) | ||||
3.
What patterns do you notice in the table?
4.
Graph the data by plotting the points, (Number of recipes, amount of ingredient needed). Use Figure 2.5.2.2
(a)
What scale should you use for each axis? How did you decide what the scale should be?
(b)
Label the scale on each axis. Write a title on each axis showing what it represents.
(c)
Graph each ingredient using a different color. Label each graph with the ingredient it represents.
5.
Compare the graphs. What do you notice? List as many relationships as you can.
6.
For each ingredient, find an equation that will predict the amount you will need for an unknown number of recipes. Write the equations in the last row of Table 2.5.2.1.
7.
You have 5 avocados.
(a)
How many recipes of guacamole can you make and use all of them?
(b)
How can you tell from the graph?
(c)
How can you tell from the table?
(d)
How can you tell from the equation?
8.
You have 1 onion but want to save half of the onion for salsa.
(a)
How many recipes of guacamole can you make?
(b)
How can you tell from the graph?
(c)
How can you tell from the table?
(d)
How can you tell from the equation?
9.
(a)
What does slope mean in the context of number of recipes versus amount of ingredients?
(b)
How can you find the slope from a table? From a graph? From the equation? From the recipe?
(c)
How are the slopes related for the ingredients in the guacamole recipe?