few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
problem_activity: Warm-up
This warm-up reminds students of previous work with tape diagrams and encourages a different way to reason with them. Students are given only a tape diagram and are asked to generate a concrete context to go with the representation.
Students’ stories should have the following components:
the same unit for both quantities in the ratio
a ratio of
\(7:3\)
scaling by 3, or 3 units per part
They may also have a quantity of 30 that represents the sum of the two quantities in the ratio.
As students work, identify a few different students whose stories are clearly described and are consistent with the diagram so that they can share later.
Launch
Ask students to share a few things they remember about tape diagrams from the previous lesson. Students may recall that:
We draw one tape for every quantity in the ratio. Each tape has parts that are the same size.
We draw as many parts as the numbers in the ratio show (e.g., a
\(2:3\)
ratio: we draw 2 parts in a tape and 3 parts in another tape).
Each part represents the same value.
Tape diagrams can be used to think about a ratio of parts and the total amount.
Tell students their job is to come up with a valid situation to match a given tape diagram. Give students some quiet thinking time, and then time to share their response with a partner.
Student Facing
Describe a situation with two quantities that this tape diagram could represent.
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Student Response
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Anticipated Misconceptions
Students may misunderstand the meaning of the phrase “with two quantities” and simply come up with a situation involving ten identical groups of three. Point out that the phrase means that the row of seven groups of three should represent something different than the row of three groups of three.
Students may also come up with a situation involving different units, for example, quantity purchased and cost, or distance traveled and time elapsed. Remind them that the parts of tape are meant to represent the same value, so we need a situation that uses the same units for both parts of the ratio.
Activity Synthesis
Invite a few students to share their stories with the class. As they share, consider recording key details about each story for all students to see. Then, ask students to notice similarities in the different scenarios.
Guide students to see that they all involve the same units for both quantities of the ratio, a ratio of 7 to 3, and either 3 units per part or scaling by 3. They may also involve an amount of 30 units, representing the sum of the two quantities.


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