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 following problem or activity 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: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
problem_activity: Narrative
The purpose of this activity is for students to practice finding the perimeter of shapes that have labeled side lengths. The synthesis focuses on methods students have for efficiently finding the perimeter of shapes with some or all side lengths having equal length. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).
Monitor and select students who find the perimeter of the hexagon by:
adding the individual side lengths around the shape
adding the two 8–inch side lengths together and the four 4–inch side lengths together and then adding those sums together
multiplying like side lengths, then adding, such as
\(2 \times 8\)
for the long sides and
\(4 \times 4\)
for the short sides and then adding those products together
using symmetry to split the shape in half horizontally and adding
\(4 + 8 + 4 = 16\)
for the top half of the shape and then doubling that for the sides on the bottom half of the shape
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?” (Students may notice: One rectangle has numbers on the sides. One rectangle has tick marks on the sides. The rectangles are the same size. Students may wonder: Why are the sides of the rectangles marked differently? Could we find the distance around the rectangle with the numbers on the sides?)
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Activity
“Work with your partner to find the perimeter of each shape.”
5–7 minutes: partner work time
As students work, consider asking:
“How does having sides of the same length help us find the perimeter?”
“Can you multiply to find the perimeter?”
Student Facing
What do you notice? What you wonder?
[IMG]
Find the perimeter of each shape. Explain or show your reasoning.
[IMG]
[IMG]
[IMG]
[IMG]
[IMG]
Student Response
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for free access to Student Response.
Activity Synthesis
Ask previously identified students to share their strategies for finding the perimeter of the hexagon. Arrange the presentations in the order listed in the activity narrative.
Give students a chance to ask questions about each strategy as it is shared.
“How does having sides of the same length help us find the perimeter?”
Consider asking:
“Why does this strategy work with this shape?”
“Did anyone else find the perimeter of this shape in a different way?”
“Was it easier to find the perimeter of some shapes in this activity than others? Why?” (Yes, some of the shapes had several sides that are the same length, so we could multiply. In a rectangle, we can add two sides and then double the result to find the whole perimeter.)


aligns: no