few_shots: 
Example 1:
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.

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.


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

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
problem_activity: Activity
This activity is similar to what students did in the previous activity; however, here the conditions given are 2 angles and 1 side.
Launch
Keep students in the same groups. Tell students that this activity is similar to the previous one, and they should pay close attention to what they find different here. Provide access to geometry toolkits. Give students 2–3 minutes of quiet work time followed by time to discuss their explanations with a partner. Follow with a whole-class discussion.
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, “Both _____ and _____ are alike because . . .”, “ _____ and _____ are different because . . . ."
Supports accessibility for: Language; Social-emotional skills
Student Facing
Examine this set of triangles.
[IMG]
What is the same about the triangles in the set? What is different?
How many different triangles are there? Explain or show 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.
Anticipated Misconceptions
Some students may say there are only 2 different triangles in this set, because they do not notice the slight size difference between the smaller two groups of triangles. Prompt them to look at where the
\(80^\circ\)
angle is located in comparison to the 6 cm side.
Activity Synthesis
Ask a few students to share how many different triangles they think are in this set. Select students to share the similarities and differences between triangles in the set. If necessary, trace a few triangles from the set and show how you can turn, flip, or move some of them to line up while others cannot be lined up. Ask students what this means about all the triangles in the set (they are not all identical to each other).
To highlight the differences among the triangles ask students:
“What differences do you see between the triangles in this activity and the triangles in the previous activity?” (The given conditions here were 2 angles and 1 side, the previous activity was 2 sides and 1 angle.)
“What similarities do you see between the triangles in this activity and the triangles in the previous activity?” (These triangles have all the same conditions but in a different order, and they made different triangles as was seen in the previous activity.)
If time permits, consider asking students to use a protractor to measure the unlabeled angle from each of the three different triangles. Discuss what they notice about the third angle. (It’s the same size in every triangle.)
Explain to students that here we see another example of different triangles that can be made using the same conditions (2 angles and 1 side) in different orders (side between the two angles, side next to the 40 degree angle and side next to the 80 degree angle). Tell them that in upcoming lessons we will continue to investigate what they noticed here with the addition of drawing the different triangles.
Speaking: MLR8 Discussion Supports.
Use this routine to amplify mathematical uses of language to communicate about similar triangles. As students share the similarities and differences they noticed about the triangles, invite other students to press for details, challenge an idea, elaborate on an idea, or give an example of their own process. Revoice student ideas to demonstrate mathematical language when necessary. This will help students produce and make sense of the language needed to communicate their own ideas.
Design Principle(s): Optimize output (for explanation)


aligns: no