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 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_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
problem_activity: Warm-up
This warm-up prepares students for the Info Gap activity that follows. First, students brainstorm what information they would need to know to solve a problem that involves constant speed. Then, the teacher demonstrates the process of asking a student why they need a specific piece of information before sharing it with them, in preparation for students following this procedure with their partner in the next activity.
Launch
Give students 1 minutes of quiet think time to brainstorm what information they would need to know to solve the problem, followed by a whole-class discussion demonstrating the procedure for the Info Gap activity.
Student Facing
Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?
What information would you need to be able to solve the problem?
Student Response
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Activity Synthesis
Ask students:
"What specific information do you need?"
"Why do you need that information?"
Share each piece of information with the class after a student specifically asks for it (and explains why they need to know it).
The race is 10,000 meters long.
The race started at 9:15 a.m.
In 1 minute, the person ran
\(156\frac{1}{4}\)
meters.
An equation relating distance and time is given by
\(d = 156\frac{1}{4} \boldcdot t\)
where
\(d\)
represents distance in meters and
\(t\)
represents time in minutes.
It takes 32 minutes for the person to run 5,000 meters.
The person runs at a pace of 6.4 minutes per kilometer (or 1,000 meters).
After you share each piece of information, ask the class whether they have enough information to be able to solve the problem. When they think they do, give them 2 minutes to solve the problem and then have them share their strategies. (The person should finish the race at 10:19 a.m.)
Tell students that they will be working in groups of two in the next activity and that they will be using the same procedure that you just demonstrated to solve a problem.


aligns: no