standard_description: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Narrative
The purpose of this activity is for students to think about and compare the capacities of containers. Students start by comparing two containers where it is visually obvious which one holds more. They use comparison language such as “The pitcher holds more than the cup.” Then, students consider containers that have capacities that are not easy to compare visually and they brainstorm ways to compare the capacities of the containers. Students may need to see the water poured between the two containers multiple times before they determine and can explain which container has more capacity. As students make predictions and then discuss and justify their comparisons, they share a mathematical claim and the thinking behind it (MP3).
MLR8 Discussion Supports.
Use multimodal examples to clarify what it means for a container to hold liquid. Use verbal descriptions along with gestures or drawings to show the meaning of the word hold in this context.
Advances: Listening, Representing
Required Materials
Materials to Gather
Containers of different sizes
Sticky notes
Required Preparation
Gather a larger pitcher and a small cup to display during the launch.
Gather 2 cups with capacities that are not easy to compare visually, such as a tall stemmed glass and a short, wide cup for the activity.
Launch
Groups of 2
Display a pitcher and a small cup.
“Diego’s class needs a lot of lemonade for a lemonade sale they are going to have at school. Which container do you think they should use to hold the lemonade? Why do you think that?” (The pitcher holds more lemonade because it is bigger. The cup is small.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“We think that the pitcher will hold more lemonade.”
Activity
Display 2 cups and give each student a sticky note.
“Which of these cups do you think would hold more lemonade? Put your sticky note by the cup that you think would hold more lemonade.”
3 minutes: independent work time
“People had different answers about which cup would hold more lemonade. What can we do to figure out which cup can hold more lemonade?”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Demonstrate filling one of the cups with water and then slowly pour that water into the other cup.
“I filled up the red cup and poured the same water into the blue cup, but the blue cup overflowed. Which cup do you think can hold more lemonade?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“The red cup can hold more lemonade than the blue cup.”
Student Response
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Activity Synthesis
“We can use water to help us figure out which cup can hold more lemonade.”


aligns: no