##
* *Reflection: Diverse Entry Points
Scaling a Recipe - Section 1: Introduction

The manipulatives really helped students understand the introduction problem. Before we began working on the recipe, I gave students a chance to figure out the value of each pattern block based on the yellow hexagon being 1 whole.

Then, we read through the problem and discussed which block represented which ingredient. It is very important to write the color of the block next to the ingredient: 1 red = 1/2 cup of carrot juice; 1 blue = 1/3 cup of beet juice; 1 green = 1/6 cup of kale juice. Attend to precision!

The reason this is so important is that when beginning to scale the recipe we can say, for example, that a small used 1 cup of carrot juice or 2 reds. This helps students see that each ingredient is being scaled by a common factor. If a recipe uses 1 cup of beat juice, that requires 3 blue pieces or 1/3 * 3 = 1. So then, we also need 3 times the amount of the other ingredients.

In my first class we had a disruption by a misbehaving student. The class was particularly entertained by his antics. He was removed from class, but their focus was derailed. I had to stop the lesson and have a talk about our school values (Respect Integrity Self-Determination Engagement) and how they related to our mission of preparing 100% of our students for college, careers, and a successful life. That students behavior was not helping us reach any of these goals. This group will be coming in at recess to finish the lesson.

*Attending to Precision on the Introduction*

*Diverse Entry Points: Attending to Precision on the Introduction*

# Scaling a Recipe

Lesson 5 of 12

## Objective: SWBAT scale a recipe using bar models, double number lines, or arithmetic.

*45 minutes*

#### Introduction

*15 min*

This introduction is intended to provide students with more various models that could be used to solve proportional reasoning problems. The previous lessons have focused mostly on double number lines. This lesson will include double number lines, bar models, and even a concrete model using pattern blocks.

We will model the example problem in 4 ways moving from concrete to pictorial to abstract: 1) using pattern blocks; 2) using double number lines; 3) use bar models; 4) using multiplication.

I will distribute the following pattern blocks to pairs of students:

2 yellow (whole)

4 red (halves)

6 blue (thirds)

12 green (sixths)

We will read through the problem and then students will have to decide which pattern block could be used for which ingredient. The yellow one may confuse students because it does not represent an ingredient, it serves as a reference for 1 cup of the batch.

I will say that a small uses 1 cup of carrot juice. Model that with your blocks. How does this compare to the given ratio of ingredients? Answer: twice as much. So how much of the other ingredients should we use? Answer: twice as much. I will then ask students to model it and fill in the values. We will proceed in a similar manner for the other values.

Next we will use a double or perhaps triple number line.

Then we will use a bar model. The model can be fairly simple. For example we could represent beet juice by having one-third of a bar shaded. We see that a medium uses 1 cup of beets or 3/3 which means a medium uses 3 times the given amount. We can than apply this modeling to the other ingredients.

Finally, we can find each new amount simply by multiplying.

#### Resources

*expand content*

#### Problem Solving

*20 min*

Students will now be mostly on their own to solve this next problem. They should feel free to use any of the methods given, though the concrete will be a bit tricky for this problem

As students work I will be looking for which models they choose to employ and how accurately they are using the models.

I have noticed that some students have difficulty interpreting the table. They may need the teacher to point out that each batch or set of ingredients reads from top to bottom in a column. In other words, they may find it helpful to focus on 1 column at a time.

Students may need some prompting so I may ask questions like:

How much salt is used in batch 1? How does this compare to what was given in the recipe ratio? Show me.

For students who find this task exceptionally easy, I will given them an additional problem. How much of each ingredient will be used for a 24 cup batch? What about for a one-half cup batch?

As we review, I will look to display the various models used to solve the problems.

#### Resources

*expand content*

#### Assessment

*10 min*

This lesson assessment not only assesses how well students can scale a recipe but also apply what they have learned over the previous days. I think the assessment is a slightly easier problem that the one from the problem solving section.

There are 9 blanks for students to fill in. Therefore 7 out of 9 will be considered a successful assessment. Students are not required to simplify answers.

#### Resources

*expand content*

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- LESSON 1: Proportional Relationships of Whole Numbers
- LESSON 2: Proportional Relationships With Decimals
- LESSON 3: Proportional Relationships With Fractions
- LESSON 4: Finding Distances on Maps
- LESSON 5: Scaling a Recipe
- LESSON 6: Determine Equivalent Ratios - Scale Factor Between Ratios
- LESSON 7: Determine Equivalent Ratios - Scale Factor Between Terms
- LESSON 8: Determine The Graph of a Proportional Relationship
- LESSON 9: Determine Equivalent Ratios - Common Unit Rate
- LESSON 10: Writing The Constant of Proportionality Equation
- LESSON 11: Writing Equations for Proportional Relationships
- LESSON 12: The Distance Formula