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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
problem_activity: Narrative
The purpose of this warm-up is to elicit observations about differences in costs of living in different parts of the United States. It prepares students to look for and make sense of multiplicative comparisons later in the lesson. It also helps elicit what students know about how the different costs may be different depending on where you live.
Students may notice and wonder many things about the data in the table and both additive and multiplicative comparisons are likely to come up. Some students may note that an item costs “some dollars more” in San Francisco than in Fort Wayne, while others may say it costs “some number of times as much” based on the quantities or their estimation of the quantities. In the synthesis, focus student discussion on additive and multiplicative comparison.
Launch
Groups of 2
Display the table.
Activity
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
{"table": [{"_attributes": {"border": "1", "style": "width:95%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}}, {"_attributes": {"scope": "col", "style": "text-align:center; width:25%"}, "_value": "San Francisco, CA"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:25%"}, "_value": "Fort Wayne, IN"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "population"}, {"_value": "805,235"}, {"_value": "253,691"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "milk (1 gallon)"}, {"_value": "\\$4.45"}, {"_value": "\\$2.14"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "bread (1 loaf)"}, {"_value": "\\$3.54"}, {"_value": "\\$1.82"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "gasoline (1 gallon)"}, {"_value": "\\$3.70"}, {"_value": "\\$2.42"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "movie ticket"}, {"_value": "\\$15"}, {"_value": "\\$12"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "internet connection (1 month)"}, {"_value": "\\$70"}, {"_value": "\\$50"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "rent for a 3 bedroom apartment in the city center (1 month)"}, {"_value": "\\$6,000"}, {"_value": "\\$1,500"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "cost of a house"}, {"_value": "\\$1,400,000"}, {"_value": "\\$160,000"}]}]}]}]}
Student Response
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Activity Synthesis
“How could you compare the cost for renting an apartment in San Francisco to the cost in Fort Wayne? How could you use multiplication to compare the costs?”
As needed, “About how many more times as much is the cost of a house in San Francisco compare to the cost of a house in Fort Wayne?”
“The prices of the things you need to live, like food, clothing, and shelter, are called the cost of living. The cost of living can be very different depending on where in the world you live. Today we are going to compare the cost of living in different places around the world.”


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