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: 
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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
problem_activity: Warm-up
The mathematical purpose of this lesson is for students to motivate a conceptual understanding of the
addition rule
. Monitor for students discussing counting people twice.
Launch
Arrange students in groups of 2. Give students quiet work time and then time to share their work with a partner.
Student Facing
The table displays information about people at a neighborhood park.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}}, {"_attributes": {"scope": "col"}, "_value": "wearing sneakers"}, {"_attributes": {"scope": "col"}, "_value": "not wearing sneakers"}, {"_attributes": {"scope": "col"}, "_value": "total"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "wearing a hat"}], "td": [{"_value": "8"}, {"_value": "2"}, {"_value": "10"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "not wearing a hat"}], "td": [{"_value": "3"}, {"_value": "12"}, {"_value": "15"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "total"}], "td": [{"_value": "11"}, {"_value": "14"}, {"_value": "25"}]}]}]}]}
Andre says the number of people wearing sneakers or wearing a hat is 21, because there are a total of 10 people wearing a hat and a total of 11 people wearing sneakers. Is Andre correct? Explain your reasoning.
What is the probability that a person selected at random from those in the park is wearing sneakers or wearing a hat?
Student Response
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Activity Synthesis
The goal of this discussion is to use the context as a model to introduce a conceptual understanding of the addition rule. Ask previously identified students to explain why Andre counted some people twice when he stated that the number of people wearing sneakers or wearing a hat is 21.
Here are some questions for discussion.
“Why did Andre need to subtract 8 from 21 to get the correct answer?” (It needs to be subtracted because the 8 people that were wearing sneakers and wearing a hat were counted twice. We counted them twice when adding the column total for wearing sneakers and the row total for wearing a hat.)
“How could the number of people wearing sneakers or wearing a hat be represented using a Venn diagram?” (A Venn diagram could be made using two overlapping circles, one for wearing sneakers and one for wearing a hat. There would be 8 people in the middle where the two circles overlap. There would be an additional 3 people in the wearing sneakers circle representing those wearing sneakers but not a hat. There would also be an additional 2 people in the circle representing those wearing a hat but not sneakers.)
“What is the probability that a person selected at random is not wearing sneakers and not wearing a hat?” (
\(\frac{12}{25}\)
)


aligns: no