few_shots: 
Example 1:
Concept/skill: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

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: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Answer: 
Yes. This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.

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_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_pos_0

5
standard_description: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
problem_activity: Optional activity
In this activity, students use what they know about corresponding lengths and angles to show that one picture of a bird is
not
a scaled copy of the other. Unlike in previous tasks, minimal scaffolding is given here, so students need to decide what evidence is necessary to explain or show an absence of scaling. As students work, notice the different ways students use corresponding lengths and angles to think about scaling.
Identifying a specific measurement in one image and the corresponding measurements in the other (which show that one is not a scaled copy of the other) requires thinking about the structure of the pictures (MP7).
Monitor students for different approaches to show that one image is not a scaled copy of the other:
Identifying corresponding angles in the two images which have different measures
Identifying two pair of corresponding segments in the images with different scale factors
Select students who use these methods and ask them to present their approaches, in this sequence, during the discussion.
Digital
Launch
Arrange students in groups of 3–4. Provide access to geometry toolkits.
Give students 2 minutes of quiet work time followed by 1–2 minutes to discuss in groups how to find evidence that one picture is not a scaled copy of the other. Then, briefly discuss students’ ideas as a class. Consider listing the ideas for all to see and discussing which ones are likely to be most effective.
If students' ideas deviate from drawing corresponding points and segments and comparing distances and angles, guide them with some prompts. For example:
Pick a point that can be easily referenced (e.g., the tip of one wing) on one picture. Ask for the corresponding point on the other.
Ask if that pair of corresponding points could help them determine if one picture is scaled from the other. If not, ask what else might be needed.
Add another point and a segment connecting the two points. Ask if or how the segment could help, and so on.
Student Facing
Here are two pictures of a bird. Find evidence that one picture is not a scaled copy of the other. 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
Arrange students in groups of 3–4. Provide access to geometry toolkits.
Give students 2 minutes of quiet work time followed by 1–2 minutes to discuss in groups how to find evidence that one picture is not a scaled copy of the other. Then, briefly discuss students’ ideas as a class. Consider listing the ideas for all to see and discussing which ones are likely to be most effective.
If students' ideas deviate from drawing corresponding points and segments and comparing distances and angles, guide them with some prompts. For example:
Pick a point that can be easily referenced (e.g., the tip of one wing) on one picture. Ask for the corresponding point on the other.
Ask if that pair of corresponding points could help them determine if one picture is scaled from the other. If not, ask what else might be needed.
Add another point and a segment connecting the two points. Ask if or how the segment could help, and so on.
Student Facing
Here are two pictures of a bird. Find evidence that one picture is not a scaled copy of the other. Be prepared to explain your reasoning.
[IMG]
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
Students may draw two segments that do not share a point, or choose non-corresponding points and segments on the two figures. Refer students to earlier work involving polygons and point out pairs of distances that could be used for comparison and those that could not be. Remind them that we can only compare the corresponding parts, not just any two parts.
Activity Synthesis
Invite select students to share their reasoning. Ask how they knew that certain pairs of points in the images were corresponding points. Students could identify a unique feature such as the eyes or the tip of the wing. Make sure students understand that:
Corresponding angles on an image and a scaled copy have the same measure
Corresponding segments on an image and a scaled copy are related by the same scale factor
To conclude that an image is
not
a scaled copy of another, it is sufficient to find one pair of corresponding angle measures that are different or two pairs of corresponding segments with different scale factors.
Speaking: MLR8 Discussion Supports.
Give students additional time to make sure that everyone in their group can explain or justify why the copy of the bird is not a scaled copy. Then, vary who is called on to represent the ideas of each group. This routine will prepare students for the role of group representative and to support each other to take on that role.
Design Principle(s): Optimize output (for explanation)


aligns: no