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:
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} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
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?


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

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

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im_task_000157_pos_0

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fl_problem_000674_pos_0

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standard_description: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
problem_activity: Activity
During this activity students are asked to compute the perimeter of inscribed regular polygons given only the radius. They will need to figure out that drawing in the altitude will form a right triangle. Drawing this auxiliary segment shows students recognize the important structure of right triangles to calculate missing information (MP7). In this activity students are building towards an equation to approximate the value of
\(\pi\)
which they will complete in the next lesson.
Launch
Provide the definitions of a regular polygon (a polygon where all of the sides are congruent and all the angles are congruent), pentagon (5-sided polygon), and decagon (10-sided polygon) as needed.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. During the launch, take time to review terms that students will need to access for this activity. Invite students to suggest language or diagrams to include that will support their understanding of: regular polygons, pentagons, and decagons. Include definitions as well as diagrams for students to refer to throughout the lesson.
Supports accessibility for: Conceptual processing; Language
Student Facing
Here is a square inscribed in a circle with radius 1 meter. What is the perimeter of the square? Explain or show your reasoning.
[IMG]
What is the perimeter of a regular pentagon inscribed in a circle with radius 1 meter? Explain or show your reasoning.
What is the perimeter of a regular decagon inscribed in a circle with radius 1 meter? Explain or show your reasoning.
What is happening to the perimeter as the number of sides increases?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Here is a diagram of a square inscribed in a circle and another circle inscribed in the same square.
[IMG]
How much shorter is the perimeter of the small circle than the perimeter of the large circle?
If the square was replaced with a regular polygon with more sides, would your previous answer be larger, smaller, or the same? 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 Extension Student Response.
Anticipated Misconceptions
If students are spending too long attempting to draw the pentagon or decagon, provide them with a circle that has 10 equally spaced points.
If students are stuck after sketching the diagram ask them what helpful auxiliary lines they could draw. (Connect the center to the other vertices to make triangles. The altitude would create right triangles so I can use trigonometry.)
[IMG]
Activity Synthesis
Invite students to share their strategies. Focus on students who repeated the same strategy for multiple questions.
Use the applet to demonstrate what happens with the perimeter of the inscribed polygon as the number of sides increases.
Ask students what they noticed. Connect the generalizations they make with the noticing and wondering they did in the warm-up. If not mentioned by students, ask students what the circumference of the circle is. (
\(2\pi\)
) Build anticipation for calculating the value of
\(\pi\)
in the next lesson.
If students are not using workbooks tell them to be extra careful to put this work in a safe place because they will use it in the next lesson.
Writing, Listening, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to help students improve their writing, by providing them with multiple opportunities to clarify their explanations through conversation. Give students time to meet with 2–3 partners to share and get feedback on their work. Display prompts for feedback that students can use to help their partner strengthen and clarify their ideas. For example, "Your explanation tells me . . .", "Can you say more about why you . . . ?", and "A detail (or word) you could add is _____, because . . . ." Give students with 3–4 minutes to revise their initial draft based on feedback from their peers.
Design Principle(s): Optimize output (for explanation); Cultivate conversation


aligns: no