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
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_lesson_009431_pos_0

1
standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
Previously, students classified fractions based on their relationship to
\(\frac{1}{2}\)
and 1 (whether they are less than or more than these benchmarks). They used these classifications to compare fractions. In this activity, students are presented with fractions that are in the same group (for example, both less than
\(\frac{1}{2}\)
, or both greater than
\(\frac{1}{2}\)
but less than 1), so they need to reason in other ways to make comparisons.
Students can reason in a number of ways—by thinking about size and number of parts, drawing a diagram or number line, or reasoning numerically, but in most cases, they need to also rely on the idea of equivalence.
MLR7 Compare and Connect.
Synthesis: After each strategy has been presented, lead a whole-class discussion comparing, contrasting, and connecting the different approaches. Ask, “Did anyone solve the problem the same way, but would explain it differently?” and “Why did the different approaches lead to the same outcome?”
Advances: Representing, Conversing
Representation: Internalize Comprehension.
Activate background knowledge. Invite students to review the strategies they know for comparing fractions (reasoning about denominators or numerators, comparing to a benchmark, and writing equivalent fractions). Record students’ strategies on a visible display, including details (words or pictures) that will help them remember how to use the strategy.
Supports accessibility for: Conceptual Processing, Memory, Attention
Launch
Groups of 2
“Here are some fractions you’ve sorted in an earlier lesson. We compared them to
\( \frac{1}{2}\)
and 1.”
“What do the fractions in group 3 have in common? Why might they be in the same group?” (They are all greater than 1.)
“How are the fractions in group 1 different than those in group 2?” (Those in group 1 are less than
\( \frac{1}{2}\)
, and those in group 2 greater than
\( \frac{1}{2}\)
but less than 1.)
“We can tell that the fractions in group 2 are greater than those in group 1, and the fractions in group 3 are greater than those in the other groups.”
“Now compare the fractions in each group.”
Activity
“Take a few quiet minutes to work on the problems. Afterward, share your responses with your partner.”
7–8 minutes: independent work time
5 minutes: partner discussion
Monitor for students who:
reason by drawing number lines or tape diagrams
reason about the distance of each fraction from 0,
\(\frac{1}{2}\)
, or 1
reason about equivalent fractions (even if they don’t write out the multiplication numerically)
reason about equivalent fractions numerically by writing out the multiplication
Student Facing
Here are some pairs of fractions sorted into three groups. Circle the greater fraction in each pair. Explain or show your reasoning.
Group 1:
\(\frac{2}{10}\)
or
\(\frac{26}{100}\)
\(\frac{2}{5}\)
or
\(\frac{11}{100}\)
Group 2:
\(\frac{2}{3}\)
or
\(\frac{7}{12}\)
\(\frac{4}{5}\)
or
\(\frac{7}{10}\)
Group 3:
\(\frac{11}{5}\)
or
\(\frac{26}{10}\)
\(\frac{11}{3}\)
or
\(\frac{26}{12}\)
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 who used different strategies to share their responses.
“How do we compare two fractions that are in the same group—say, both less than
\( \frac{1}{2}\)
or both greater than 1?” (We can think about how close or far away from
\( \frac{1}{2}\)
each fraction is.)
Highlight how equivalent fractions came into play in each strategy. For example, ask, “When comparing
\(\frac{2}{3}\)
and
\(\frac{7}{12}\)
, why was it helpful to think of the
\(\frac{2}{3}\)
as
\(\frac{8}{12}\)
?” Or, “When comparing
\(\frac{7}{10}\)
and
\(\frac{4}{5}\)
, why did you think of
\(\frac{4}{5}\)
as
\(\frac{8}{10}\)
?”
If no students mention that it is often easier to compare two fractions when they have the same denominator, ask them about it.


aligns: no