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: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Activity
Students solved equations of the form
\(x+p = q\)
and
\(px=q\)
in grade 6, but the equations only involved positive values. This activity bridges their understanding of a solution to an equation as a value that makes the equation true with their understanding of operations involving negative numbers from this unit. This activity builds on the work students have done in this lesson evaluating expressions at different values.
Monitor for students who:
take an arithmetic approach by substituting in values and evaluating. (Does
\(\text-2 \boldcdot (\text-4.5) = \text-9\)
?)
take an algebraic approach by writing an equivalent equation using an inverse operation (If
\(\text-2 \boldcdot x=\text-9\)
, then
\(x=\text-9 \div \text-2\)
.)
Digital
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to a value that makes it true by dragging the answer to the corresponding equation. Be prepared to explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to its solution.
\(\frac12 x=\text-5\)
\(\text-2x=\text-9\)
\(\text-\frac12 x=\frac14\)
\(\text-2x=7\)
\(x+\text-2 = \text-6.5\)
\(\text-2+x=\frac12\)
\(x = \text-4.5\)
\(x = \text-\frac12\)
\(x = \text-10\)
\(x = 4.5\)
\(x = 2 \frac12\)
\(x=\text-3.5\)
Be prepared to explain your reasoning.
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 an equation for which there is a student who took an arithmetic approach and a student who took an algebraic approach. Ask students to share their reasoning for why a solution is correct. Sequence arithmetic approaches before algebraic approaches. An example of an arithmetic approach: “I know that -3.5 is the solution to
\(\text-2x=7\)
, because I know that
\(\text-2 \boldcdot (\text-3.5)=7\)
. An example of an algebraic approach: “If
\(\text-2x=7\)
, then I know that
\(x=7 \div \text-2\)
.) Record their work, side by side, for all to see. If there are no equations for which students took both approaches, present both approaches anyway. Tell students that either approach is valid, but that in the next unit they will see some more complicated equations for which one approach might be simpler than the other.
Representing, Conversing, Listening: MLR7 Compare and Connect.
Use this routine to support whole-class discussion. Ask students, “What is the same and what is different?” about how they matched the expressions. Connect strategies by showing the different ways operations are used in each approach (e.g., arithmetic method by substituting in values and evaluating; algebraic method by using an inverse operation). Use gestures, and color on the display to highlight these connections. This helps students use mathematical language as they reason about their strategies to evaluate equivalent equations.
Design Principle(s): Maximize meta-awareness; Support sense-making


aligns: no