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: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
problem_activity: Activity
In this activity students are presented with a series of questions like, “A person is 60 inches tall. Do you know their height in feet?” For some of the questions the answer is "yes" (because you can convert from inches to feet by dividing by 12). In other cases the answer is "no" (for example, “A person is 14 years old. Do you know their height?”). The purpose is to develop students’ understanding of the structure of a function as something that has one and only one output for each allowable input. In cases where the answer is yes, students draw an input-output diagram with the rule in the box. In cases where the answer is no, they give examples of an input with two or more outputs. In the Activity Synthesis, the word function is introduced to students for the first time.
Identify students who use different ways to describe the rules and different notation for the input and outputs of the final two problems.
Launch
Display the example statement (but not the input-output diagram) for all to see.
Example: A person is 60 inches tall. Do you know their height in feet?
Give students 30 seconds of quiet think time, and ask them to be prepared to justify their response. Select students to share their answers, recording and displaying different justifications for all to see.
Display the following input-output diagrams for all to see. Ask students if the rules in the diagrams match the justifications they just heard:
[IMG]
[IMG]
or
Tell students that they will draw input-output diagrams like these as part of the task. Answer any questions students might have around the input-output diagrams. Be sure students understand that if they answer yes to the question they will need to draw the input-output diagram and if they answer no they need to give an example of why the question does not have one answer.
Give students 8–10 minutes of quiet work time for the problems followed by a whole-class discussion.
Representation: Access for Perception.
Read all statements aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language
Student Facing
Say yes or no for each question. If yes, draw an input-output diagram. If no, give examples of two different outputs that are possible for the same input.
A person is 5.5 feet tall. Do you know their height in inches?
A number is 5. Do you know its square?
The square of a number is 16. Do you know the number?
A square has a perimeter of 12 cm. Do you know its area?
A rectangle has an area of 16 cm
2
. Do you know its length?
You are given a number. Do you know the number that is
\(\frac15\)
as big?
You are given a number. Do you know its reciprocal?
Student Response
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click here to register or sign in
for free access to Student Response.
Activity Synthesis
The goal of this discussion is for students to understand that functions are rules that have one distinct output for each input. For several problems, select previously identified students to share their rule descriptions. For example, some students might write the rule for finding the area of a square from its perimeter as "find the side length then square it" and others might write, "divide by four and then square it." Compare the different rules and ask students if they agree (or disagree) that the statements represent the same rule.
For the final two problems where the input is not a specific value, select previously identified students to share what language they used. For example, in the final problem some students may use a letter to stand for the input while others may just write "input" or "a number." Ask, "How can using a letter sometimes make it easier to represent the output?" (Writing "
\(\frac15 n\)
" is shorter than writing "
\(\frac15\)
of a number.")
Tell students that each time they answered one of the questions with a yes, the sentence defined a
function
, and that one way to represent a function is by writing a rule to define the relationship between the input and the output. Functions are special types of rules where each input has only one possible output. Because of this, functions are useful since once we know and input, we can find the single output that goes with it. Contrast this with something like a rolling a number cube where the input "roll" has many possible outputs. For the questions students responded to with no, these are not functions because there is no single output for each input.
To highlight how rules that are not functions do not determine outputs in a unique way, end the discussion by asking:
"Was the warm-up, where you have to square numbers, an example of a function?" (Yes, each input has only one output, even though some inputs have the same output.)
"Is the reverse, that is knowing what number was squared to get a specific number, a function?" (No, if a number squared is 16, we don't know if the number was 4 or -4.)
Speaking: MLR8 Discussion Supports.
Use this routine to support whole-class discussion. Call on students to use mathematical language to restate and/or revoice the rule descriptions that are presented. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer accurately restated their rule. Call students' attention to any words or phrases that helped to clarify the original statement. This will provide more students with an opportunity to produce language to describe functions.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no