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: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_neg_0

HS_0
standard_description: Recognize and represent proportional relationships between quantities.
problem_activity: Problem 1
The grocery store sells beans in bulk. The grocer's sign above the beans says, “5 pounds for $4.”
At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax.
Alberto said, “The ratio of the number of dollars to the number of pounds is 4:5. That's $0.80 per pound.”
Beth said, "The sign says the ratio of the number of pounds to the number of dollars is 5:4. That's 1.25 pounds per dollar."
Are Alberto and Beth both correct? Explain.
Problem 2
Claude and Dora go shopping at the same grocery store as Alberto and Beth.
Claude needs two pounds of beans to make soup. Show Claude how much money he will need.
Dora has $10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy.
Whose rate of change, Alberto’s or Beth’s, do you prefer to use to solve Claude’s problem? Dora’s problem? Explain.
Problem 3
Sanyukta can type 2 pages in 8 minutes.
a.   What are two rates associated with this ratio?
b.   Sanyukta has a deadline in 22 minutes, at which point she needs to be done typing an article. What is the greatest number of pages that Sanyukta can type before her deadline?
c.   Sanyukta has to type a 9-page article. How much time will it take her?
Problem 4
Solve each problem involving distance, speed, and time.
a.   Melanie drives at a constant speed of 35 miles per hour. How far does she travel in 2 hours?
b.   Nathan drives at a constant speed of 40 miles per hour. How long it take him to travel 60 miles?
c.   Oscar drives at a constant speed of 50 miles per hour. How far does he travel in 90 minutes?
d.   Penelope travels 14 miles in 30 minutes. At what constant speed is she driving?


aligns: no