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: 
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.

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

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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Order three objects by length; compare the lengths of two objects indirectly by using a third object.
problem_activity: Narrative
The purpose of this activity is for students to create a connecting cube tower that is the same length as a given image. In the activity synthesis, students transition from describing the length of an object by comparing it to another object ("The earthworm is the same length as a tower of 8 cubes.") to describing the length of an object as a measurement ("The earthworm is 8 cubes long.").
Required Materials
Materials to Gather
Connecting cubes
Materials to Copy
Lengths of Creepy, Crawly Things
Launch
Groups of 2
Give each student connecting cubes and a copy of the blackline master.
Activity
“We just saw a picture that showed a pencil that was the same length as the purple tower. Use connecting cubes to build a tower that is the same length as each creepy, crawly thing.”
10 minutes: partner work time
Monitor for students who carefully line up the cubes with the endpoints of the images.
Student Response
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Activity Synthesis
Invite previously identified students to share.
Display the image of the caterpillar.
“How did you measure the caterpillar?” (I lined the first cube up with the end of the caterpillar. Then I added cubes until I got all the way to the other end of the caterpillar.)
“Since the tower of 4 cubes is the same length as the caterpillar and each cube has the same length, we can say the caterpillar is 4 cubes long.”
For each animal, invite students to say, “The ______ is ___ cubes long.”


aligns: no