few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
problem_activity: Optional activity
In this activity, students are given pictures and descriptions of planes cutting prisms and pyramids. Students are asked to draw cross sections freehand but this is not a skill that is required in order for students to be able to describe two-dimensional shapes created from cross sections, which is why this is an optional activity. Some pictures are of a moving plane. Students describe how the cross section changes as the plane moves.
If students have access to the digital activity there are applets to explore the cross sections.
Adapted from applets created in GeoGebra by
Anthony C.M. OR
.
Digital
Launch
Arrange students in groups of 2. Give students 3–5 minutes of quiet work time followed by time to discuss shapes of cross sections with a partner. Follow with a whole-class discussion.
Student Facing
Use the applet to draw each cross section and describe it in words. Start each one by dragging the gray bar on the left side across the screen until you see the whole 3D image on the left and the controls on the right.
Here is an applet with a rectangular prism, 4 units by 2 units by 3 units.
A plane cuts the prism parallel to the bottom and top faces.
The plane moves up and cuts the prism at a different height.
A vertical plane cuts the prism diagonally.
A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.
A plane cuts the pyramid parallel to the base.
A vertical plane cuts the prism.
A cube has an edge of length 4.
A plane cuts off the corner of the cube.
The plane moves farther from the corner and makes a cut through the middle of the cube.
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
Arrange students in groups of 2. Give students 3–5 minutes of quiet work time followed by time to discuss shapes of cross sections with a partner. Follow with a whole-class discussion.
Student Facing
Draw and describe each cross section.
Here is a picture of a rectangular prism, 4 units by 2 units by 3 units.
[IMG]
A plane cuts the prism parallel to the bottom and top faces.
[IMG]
The plane moves up and cuts the prism at a different height.
[IMG]
A vertical plane cuts the prism diagonally.
[IMG]
A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.
A plane cuts the pyramid parallel to the base.
[IMG]
A vertical plane cuts the prism.
[IMG]
A cube has an edge of length 4.
A plane cuts off the corner of the cube.
[IMG]
The plane moves farther from the corner and makes a cut through the middle of the cube.
[IMG]
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 drawings and descriptions. Consider asking some of the following questions:
“How did you figure out the shape of the cross section?”
“What helped you visualize the shape?”
“Were any of the shapes you drew here similar to the shapes you described in the previous activity?”
Conversing: MLR8: Discussion Supports.
To support a rich discussion while students are describing two-dimensional shapes created from cross sections, invite students to include details in their descriptions and drawings of each cross section. Provide sentence frames such as: “The cross section is ____ because . . .”, “A plane cuts _____ as shown by . . .”, or “The dimensions of a cross section are ______ since . . . .” This will help students make sense of complex language as they draw and describe cross sections shown in each figure.
Design Principle(s): Cultivate conversation


aligns: yes