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: 
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)

Answer: 
Yes. This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.

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_pos_0

1
standard_description: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
problem_activity: Activity
The purpose of this task is to introduce students to the idea of a proportional relationship. From previous work, students should be familiar with the idea of equivalent ratios, and they may very well recognize the table as a set of equivalent ratios. Here, we are starting to expand this concept and the language associated with it to say that there is a proportional relationship between the cups of rice and number of people as well as the number of spring rolls and number of people. More generally, there is a proportional relationship between two quantities when the quantities are characterized by a set of equivalent ratios.
The context in this activity and the numbers used are intended to be accessible to all students so that they can focus on its mathematical structure (MP7) and the new terms introduced in the lesson without being distracted.
While students are working, monitor for groups using each of these approaches:
Drawing that depicts 15 cups of rice and 45 people, organized into three people per cup. This representation of the problem can support all learners in moving forward. The teacher should highlight the organization of three people per cup, and identify correspondences between parts of the drawing and numbers in the table.
Moving down the table, multiplying both numbers in a row by the same number. “Since I multiply 2 by 5 to get 10, I will multiply 6 by 5 and get 30. Since 9 times 5 is 45, I will also multiply 3 by 5 to get 15.” If it comes up, the most appropriate name for the multiplier would be
scale factor
, but it is not necessary for students to call it this.
Calculation and use of a unit rate. “I reasoned that 1 cup of rice must serve 3 people. So 10 cups of rice must serve 30, and 15 cups must serve 45.”
Moving across the table. “It looks like we always multiply number of cups of rice by 3 to get the number of people it serves, so I will multiply 10 cups by 3 to get 30, and divide the 45 by 3 to get 15.”
Launch
Say, “Rice is a big part of the traditions and cultures of many families. Does your family cook rice, and if so, how?" Invite a student to describe the process (measure rice, measure water, simmer for a while). You use more rice for more people and less rice for fewer people. If students have trouble understanding or representing the context, show them the measuring cup so that they have a sense of its size, or draw a literal diagram that looks something like this:
[IMG]
Similarly, ask students if they have ever eaten a spring roll and invite them to describe what they are. While some spring rolls can be very large, the ones referred to in this activity are smaller.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because _____. Then, I….,” “I noticed _____ so I….,” and “I tried _____ and what happened was….”
Supports accessibility for: Language; Social-emotional skills
Student Facing
A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 10 cups of rice serve?
How many cups of rice are needed to serve 45 people?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "cups of rice"}, {"_attributes": {"scope": "col"}, "_value": "number of people"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "2"}, {"_value": "6"}]}, {"td": [{"_value": "3"}, {"_value": "9"}]}, {"td": [{"_value": "10"}, {}]}, {"td": [{}, {"_value": "45"}]}]}]}]}
A recipe says that 6 spring rolls will serve 3 people. Complete the table.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "number of spring rolls"}, {"_attributes": {"scope": "col"}, "_value": "number of people"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "6"}, {"_value": "3"}]}, {"td": [{"_value": "30"}, {}]}, {"td": [{"_value": "40"}, {}]}, {"td": [{}, {"_value": "28"}]}]}]}]}
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select students to share their approaches using the sequence listed in the Activity Narrative.
After students have shared their reasoning and connections have been drawn between the different approaches, introduce the term
proportional relationship
. For example, “Whenever we have a situation like this where two quantities are always in the same ratio, we say there is a proportional relationship between the quantities. So the relationship between the number of cups of rice and the number of people is a proportional relationship. The number of cups of rice is proportional to the number of people.” Write out some of these statements for all to see (in the next activity, students will need to write a statement like these about a different relationship). If the class has a word wall or students keep track of mathematical vocabulary in their notebooks, these new terms can be included there.
Notice that methods 2 and 3 involve identifying relationships of column entries, namely that the entry in the right-hand column is three times the corresponding entry in the left-hand column. This pattern can be explained in terms of the
unit rate
(people per cup of rice), which tells us how many people we can serve with a given amount of rice. The next activity is intended to build the understanding underlying this explanation.
After discussing the rice context thoroughly, ask students to share their solution approaches to the spring roll context. Ask students to identify and interpret the unit rate in this situation (0.5 people per spring roll may sound strange, but it means that 1 spring roll only halfway satisfies a person.)


aligns: no