few_shots: 
Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Concept/skill: 
Recognize area as an attribute of plane figures and understand concepts of area measurement.

Answer: 
No. This activity does not teach students area as an attribute of plane figures. Instead, the activity focuses on solid, three-dimensional figures.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_lesson_009431_neg_0

1
standard_description: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^(2 )+ y^(2) = 3.
problem_activity: In Class Launch
Use after Unit 2, Lesson 23
Solicit information that students already know about heating buildings, which they will use in this task. Here are some possible questions for discussion:
“How are buildings heated?” (fireplaces, boilers, gas furnaces)
“What kinds of energy can be used to heat buildings?” (electricity, natural gas, solar power)
“When in the year do you think our school uses the most power for heating?” (probably right before or after winter break, when it’s pretty cold and there are still people in the building for most of the day)
Tell students that in this task they will investigate energy costs for some different heating systems. They will begin by considering a homeowner’s current heating system, and compare some other systems the homeowner could use instead. Tell students that energy is measured in kilowatt-hours, which is abbreviated kWh.
Then give students a preview of some of the calculations they’ll need to do by showing why the homeowner currently pays
$
975/year to heat the house. Tell students that the current system is 60% efficient, which means that for every 100 kWh it uses, it only produces 60 kWh of heat. Display this statement for all to see:
“For every 100 kWh of energy a certain heating system uses, it produces 60 kWh of heat. If the system has to produce 11,700 kWh of heat to heat a house for the winter, how many kWh of energy will it use?”
Ask students to think about how they would find an answer to this question. They do not need to calculate an answer, only think of a strategy. After some quiet think time, ask students to share their thoughts with a partner. Then invite students to share strategies with the class. Use one of the suggested strategies to calculate the answer, and write the steps for all to see. Here is one possible way:
\(\displaystyle \begin{align*}{} \dfrac{100 \text{ kWh input}}{60 \text{ kWh output}} &= \dfrac{x \text{ kWh input}}{11,\!700 \text{ kWh output}} \\  \dfrac{100 \text{ kWh input}}{60 \text{ kWh output}} \boldcdot 11,\!700 \text{ kWh output} &= x \text{ kWh input} \\ 19,\!500 \text{ kWh} &= x \end{align*} \)
To find out how much this will cost the homeowner, we need to know how expensive the fuel is. If we assume natural gas costs
$
0.05 per kWh, then multiplying 19,500 by 0.05 will give us the total cost of
$
975.
Teacher Instructions
Students will need to do a lot of independent research for this task. One way to make the research less time-consuming would be to have students suggest other ways of heating the house, like solar panels or geothermal heating and cooling systems, and have each group investigate one of the ideas. Students do not have to limit themselves to alternative heating systems—if they wish, they can also look at ways the homeowner could reduce the amount of heat needed, for example by insulating their walls. Once the groups are done researching, they can report their results to the class so that everyone can use the same information to do their analysis, or new groups can form so that each member of the group researched a different idea, and the group can work together to use the information each member found.
Students will need to be very careful not to confuse the amount of energy a system uses with the amount it produces, and in their research they will see many ways of describing the energy that is used and produced, such as British thermal units, therms, and Joules. If students struggle with the calculations, it may help if they make a table with column headings like “energy used” and “energy produced” so they can fill in the values they know for each system and calculate the unknown ones.
Student-Facing Statement
A homeowner wants to replace their old heating system. Energy is measured in kilowatt-hours (kWh). It takes about 11,700 kWh of energy to heat the house for the winter. The current heating system uses natural gas and is 60% efficient, which means that for every 100 kWh of natural gas it uses, it produces 60 kWh of heat. With the homeowner’s current system, it costs
$
975 to heat the house.
Research at least two other options available in your area that this homeowner could replace their heating system with. Assume that natural gas costs
$
0.05/kWh and electricity costs
$
0.21/kWh. The house is 2,500 square feet.
The homeowner also has an air conditioner that uses 2,500 kWh of electricity per year and produces 290 kWh of cooling for every 100 kWh it uses. They also have a water heater that uses 4,300 kWh of electricity per year and produces 90 kWh of heat for every 100 kWh it uses. These systems could also be replaced if there is a cheaper option, but it isn’t necessary.
Which system would you recommend? Make a graph to convince the homeowner to switch to this system.
If the homeowner switches to the system you recommend, how long will it take them to save as much money as the new system cost?
Teacher Instructions
Students will need to be very careful not to confuse the amount of energy a system uses with the amount it produces. If students struggle with the calculations, it may help if they make a table with column headings like “energy used” and “energy produced” so they can fill in the values they know for each system and calculate the unknown ones.
Student-Facing Statement
A homeowner wants to replace their old heating system. Energy is measured in kilowatt-hours (kWh). It takes about 11,700 kWh of energy to heat the house for the winter. The current heating system uses natural gas and is 60% efficient, which means that for every 100 kWh of natural gas it uses, it produces 60 kWh of heat. With the homeowner’s current system, it costs
$
975 to heat the house. Assume that natural gas costs
$
0.05/kWh and electricity costs
$
0.21/kWh.
The homeowner also has an air conditioner that uses 2,500 kWh of electricity per year and produces 290 kWh of cooling for every 100 kWh it uses. They also have a water heater that uses 4,300 kWh of electricity per year and produces 90 kWh of heat for every 100 kWh it uses. These systems could also be replaced if there is a cheaper option, but it isn’t necessary.
Here are three other types of heating systems the homeowner could replace their current system with:
A new furnace which also runs on natural gas and is more efficient. For every 100 kWh of natural gas it uses, it produces 95 kWh of heat. This system costs
$
5,000 to install.
A geothermal heat pump. This system uses electricity instead of natural gas, but it produces 4 kWh of heat for every 1 kWh of electricity it uses. It costs
$
14,000, but it’s very low-maintenance and it also replaces the air conditioner and water heater.
A grid-tied solar array. This system is connected to the electrical grid so that when it generates more energy than the house needs, the extra electricity can be sold back to the grid. Over the whole year, the house will use as much electricity as is sold back, which means the homeowner would basically be heating and cooling the house for free. It costs
$
16,000 to install.
Which system would you recommend? Make a graph to convince the homeowner to switch to this system.
How long will it take to save as much money as the new system cost?


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