standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Optional activity
This activity gives students more practice writing an equation that represents the proportional relationship examined in a previous lesson: the amount of flour and honey in a recipe. Students can then use their equation to answer additional questions about the situation.
Launch
Tell students that this activity revisits a context from an earlier lesson. Give students quiet work time followed by partner discussion.
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension of the baking situation, without solving it for students. In the first read, students read the prompt with the goal of comprehending the situation (e.g., there is always the same ratio of honey to flour; different days have different numbers of batches). Delay asking students to complete the table. In the second read, ask students to analyze the prompts to understand the mathematical structure by naming quantities. Listen for, and amplify, the two important quantities that vary in relation to each other in this situation:
f
is the number of cups of flour;
h
is the number of tablespoons of honey. After the third read, ask students to brainstorm possible strategies to determine the amount of flour needed if you know how much honey will be used.
Design Principle(s): Support sense-making
Student Facing
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.
If
\(f\)
is the cups of flour needed for
\(h\)
tablespoons of honey, write an equation that relates
\(f\)
and
\(h\)
.
How much flour is needed for 15 tablespoons of honey? 17 tablespoons? Explain or show your reasoning.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "honey (tbsp)"}, {"_attributes": {"scope": "col"}, "_value": "flour (c)"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {}]}, {"td": [{"_value": "8"}, {"_value": "10"}]}, {"td": [{"_value": "16"}, {}]}, {"td": [{"_value": "20"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "55"}, "_value": "\\(h\\)"}]}, {}]}]}]}]}
Student Response
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Activity Synthesis
Ask students to compare answers with their partner and discuss their reasoning until they reach an agreement.
Then, invite students to share how they used their equation from question 2 to answer question 3 with the whole class.


aligns: no