standard_description: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
problem_activity: Narrative
The purpose of this activity is for students to ask a question that can be answered with the given information and then answer the question. There are many different questions students can ask including:
Who picked the most apples?
How many apples did they pick together?
Did Elena or Diego pick more apples?
How many apples did Diego pick?
These questions require all the given information to solve. Students may also ask questions which require only some of the information to solve, such as, “How many apples did Han pick?” The activity synthesis focuses on sharing different questions students asked and how they found the answer, with a focus on the multi-step problem “How many apples did they pick altogether?” Images are provided for display, however, student work should be used as much as possible in the synthesis.
Launch
Groups of 2
“Sometimes people buy apples at the market or grocery store, but sometimes people go to an apple orchard to pick apples.”
“Each person gets a basket to collect the apples they pick, and then they pay for the apples.”
“Apple picking can be a fun outing for families and friends.”
“You will be reading a story and asking questions about friends who went apple picking together.”
Activity
Read the problem.
“Think about the questions you could ask someone that this story could help them answer.”
5 minutes: independent work time
“Switch questions with your partner and find the answer.”
“Share your thinking and check to see if you agree about the answer.”
5 minutes: partner work time
Monitor for students who represent how many apples Han picked and students who represent how many apples Diego picked compared to Han to share in the synthesis as shown.
Student Facing
Elena picked 29 apples. Elena picked 14 fewer apples than Han. Han picked 15 more apples than Diego.
Write a question someone could answer based on this information.
Answer your question. Show your thinking using diagrams, symbols, or other representations.
Student Response
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Advancing Student Thinking
If students write a question that can’t be answered with the information given, consider asking:
“What is the story about?”
“What can be counted in the story?”
“What quantities do you know? What is unknown?”
Activity Synthesis
Invite students to share their questions.
Display a diagram that represents the number of apples Han picked, such as:
[IMG]
“What does the diagram represent?” (The number of apples Han picked since he picked 14 more than Elena.)
“How did you find how many apples Han picked?” (I added 30 to 14 to get 44 and then took away 1 to get 43.)
Display a diagram that represents the number of apples Diego picked compared to Han, such as:
[IMG]
“What does the diagram represent?” (How many apples Diego picked compared to Han.)
“How did you find how many apples Diego picked?” (I took 15 away from 43.)
“How did you find how many apples Elena, Han, and Diego picked altogether?” (I added 29, 43, and 28. I put all the tens together to get 80 and all the ones together to get 20 then added 80 and 20.)


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