Deliver instruction (Block 7)
Agile Mind materials Opening the lesson
activities Further questions
Framing questions
Lesson
Agile Mind materials
Using ratios:
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MARS Task: Cereal
Featured essay: MARS Task: Cereal by Linda Fisher
Opening the lesson
Bring in at least two cereal boxes, each with different quantities of protein per serving.
Encourage students to speculate on which is more nutritious by looking at the front images, then
narrow their attention to using the nutrition labels.
Framing questions
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Have you ever used the nutrition labels to make decisions about which foods to eat?
What are some things that you might consider in choosing a cereal?
Why might you want to find a cereal with a high ratio of protein grams to total grams?
Lesson activities
MARS task: Cereal
About this task. This task reinforces the ideas explored in the previous blocks of instruction in
this topic. Students will build on their understanding of ratio and proportional reasoning by
engaging in the context of comparing protein per serving of two different brands of cereals. The
two questions in this task will not take more than 10-15 minutes for students to answer. Most
students will answer the first question quickly; however, the second question is more challenging
with multiple steps. The richness of this task is in the wide variety of approaches that students
will have. If you have not already set classroom norms for good written explanations, you can
use this task to do that. This task provides opportunities for students to build proficiency with
these Standards for Mathematical Practice from the Common Core State Standards for
Mathematics:
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Make sense of problems and persevere in solving them. (SMP.1)
Construct viable arguments and critique the reasoning of others. (SMP.3)
Model with mathematics. (SMP.4)
Attend to precision. (SMP.6)
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Use the opening and framing questions to set the stage and generate student interest in the
task.
As you set students to task, clarify that both questions require that students show their
work and the second task requires students to provide a written explanation of their
thinking.
Have students begin the task by working individually for about 5-10 minutes. This
individual time will promote deeper individual student engagement and a wider variety of
approaches.
Classroom strategy. As students are working, monitor their progress. Encourage
students to make sense of the problem by explaining to themselves or to you the meaning
of the two questions (SMP.1). Observe how students are modeling with mathematics. For
example, some students may model the situation with ratios written as fractions, others
may create a table, diagram or other model (SMP.4). Think about which models you want
to highlight during your debrief of the task.
The most common misunderstanding that students make when working with ratios is to
apply additive reasoning rather than multiplicative reasoning. If this occurs, encourage
students to restate the meaning of the numbers in the scenario and then ask, “How many
grams of protein would be in 2 servings? 3 servings? 10 servings?”
Some students may struggle with interpreting the meaning of the numbers involved in
this scenario. For example, some students may analyze a ratio by dividing the numerator
into the denominator. This strategy can lead to a correct answer, but some students may
not realize that this calculation yields the grams of cereal per gram of protein. Encourage
students to describe the meaning of the numbers in the original ratios and the reason for
the operations that they are choosing to use. Using precise language and units can help
them describe the meaning of the numbers.
Another common error is that students may make imprecise calculations. The ratios in
question 2 are not easily compared by inspection. Encourage students to verify their
conjectures numerically.
After students have had sufficient time to engage in both of the questions in the task, ask
them to pair up with a classmate and share their strategies and their answers. Remind
students that they will need to include their written explanations in their final work
product. Also tell students that they should be prepared to share their strategy with the
rest of the class.
Classroom strategy. Some students may not have had many experiences in providing
written explanations of their mathematical thinking. To get students started, encourage
them to tell a neighbor their strategy and then record the idea in writing. By requiring
students to communicate their thinking clearly, using appropriate language and
representations, to their classmates, you can promote the practice of attending to
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precision (SMP.6). For this scenario, the comparisons will require careful attention to the
meanings of the numbers within the context.
As pairs are sharing their ideas and individual students are recording their thinking,
determine which students you will ask to share their thinking and strategies with the
class. Identify 3-5 different approaches.
Classroom strategy. Encourage students’ active listening during the debrief of this task.
For example, after a student has shared his or her answer or strategy engage students by
saying; “Raise your hand if you understand Michael’s strategy.” Then call on one of
those students to restate the student’s strategy in their own words. This process can help
to establish norms for classroom discourse while also setting the expectation that all
students listen carefully to each other’s ideas. As students or pairs of students are sharing
their answers and strategies with the rest of the class, encourage students to critique the
reasoning of others (SMP.3) and to compare the various strategies.
Collect students’ work. The featured essay MARS Task: Cereal includes an optional
process for analyzing students’ work in order to determine the instructional implications.
This process will enable you to gain insight into students’ depth of understanding and
their readiness for future topics. For example, although not explicitly discussed in the
topic, some students may find unit rates for each of the cereals, which is the big idea in
Topic 2.
Suggested assignment
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Guided assessment, page 6
Further questions
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How many servings of Cornbits would you have to eat in order to get the same number of
grams of protein as there are in one serving of Tasty Oats?