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: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
problem_activity: Activity
This practice activity is similar to the last activity in the associated Algebra 1 lesson, except that students are asked to find specific information about the contexts before being asked to compare them.
To give students a greater opportunity to communicate their thinking verbally and listen to the reasoning of others, we recommend assigning each student to either work on function
\(m\)
or
\(p\)
for the first question, and then get together in groups of 2–4 to tackle the remaining questions.
Launch
Arrange students in groups of 2. In each group, one partner completes the first question for function
\(m\)
, and the other partner for function
\(p\)
. Then, partners should work together using the information they found in the first question to complete the remaining questions.
It’s a judgment call about whether to ask students to find the maximum of function
\(m\)
without a graphing calculator or provide access to graphing calculators. In the associated Algebra 1 lessons, there are times when students are asked to answer such a question without graphing.
Student Facing
Two objects are thrown into the air. The height of object M in meters is modeled by the function
\(m(x)=(5+10x)(1.5-x)\)
with
\(x\)
representing time in seconds. The height of object P in meters is modeled by the function
\(p\)
, represented by the graph.
[IMG]
For each object, determine:
the time at which the object hit the ground
the height from which the object was thrown
the maximum height of the object
the time at which the object reached its maximum height
Which object was launched from a greater height? Explain your reasoning.
Which object hit the ground first? Explain your reasoning.
Which object reached a greater maximum height? Explain your reasoning.
Student Response
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Activity Synthesis
Much of the conversation will take place within groups. Time permitting, invite students to create a visual display of their solutions and explanations. Give students an opportunity to review other groups’ work, and time to revise and refine their own work. If desired, select a few exemplary visual displays to keep posted in the classroom to support students in later lessons.


aligns: yes