few_shots: 
Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001392_pos_0

8
standard_description: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
problem_activity: Warm-up
The purpose of this warm-up is for students to review plotting and labeling points that include negative coordinates and use repeated reasoning to generalize patterns in the coordinates of points in each quadrant (MP8).
Digital
Launch
Arrange students in groups of 4. Assign each person in a group a different quadrant. Tell students you will give them 2 minutes to plot and label at least three points in their assigned quadrant, and up to six if they have time. Give students 2 minute of quiet work time. Give students 4 minutes to share their points and their coordinates with their small group and look for patterns in the coordinates of points in each quadrant. Follow with whole-class discussion.
Though the paper and pencil version may be preferred, a digital applet is available for this activity.
Student Facing
Plot points in your assigned quadrant and label them with their coordinates.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Arrange students in groups of 4. Assign each person in a group a different quadrant. Tell students you will give them 2 minutes to plot and label at least three points in their assigned quadrant, and up to six if they have time. Give students 2 minute of quiet work time. Give students 4 minutes to share their points and their coordinates with their small group and look for patterns in the coordinates of points in each quadrant. Follow with whole-class discussion.
Though the paper and pencil version may be preferred, a digital applet is available for this activity.
Student Facing
Plot points in your assigned quadrant and label them with their coordinates.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The focus of the discussion is for students to explain why the following patterns emerge:
In quadrants I and IV, the x-coordinate of a point (or the first number in an ordered pair) is positive.
In quadrants II and III, the x-coordinate of a point is negative.
In quadrants I and II, the y-coordinate of a point (or the second number in an ordered pair) is positive.
In quadrants III and IV, the y-coordinate of a point in is negative.
Ask the students to share any patterns they noticed among the coordinates of the points in each quadrant. After each student shares, ask the rest of the class if they noticed the same pattern within their small group. Record and display these patterns for all to see. If possible, plot and label a few example points in each quadrant based on students' observations.


aligns: no