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: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^(2) × 3^(–5) = 3^(–3) = 1/3^(3) = 1/27.
problem_activity: Warm-up
The purpose of this warm-up is to remind students that the translation of a line is parallel to the original line, and to plant the seed that a line can be taken to a parallel line by translating it. They inspect several lines to decide which could be translations of a given line. Then they describe the translations by specifying the number of units and the direction the original line should be translated.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet think time and access to geometry toolkits. Ask them to share their responses with a partner afterwards.
Student Facing
[IMG]
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
Which lines are images of line
\(f\)
under a translation?
For each line that is a translation of
\(f\)
, draw an arrow on the grid that shows the vertical translation distance.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may think that lines
\(i\)
and
\(h\)
can’t be images of line
\(f\)
because the part of
\(i\)
and
\(h\)
we can see is shorter than the part of
\(f\)
we can see. Tell these students that all of the lines go on indefinitely in both directions.
Activity Synthesis
Invite students to share how they know that lines
\(h\)
and
\(i\)
are translations of
\(f\)
. The main reason to bring out is that they are parallel to
\(f\)
. It might be worth demonstrating with a transparency that we can translate
\(f\)
to match up with
\(h\)
and
\(i\)
, but to match up with the other lines, we would need to rotate (or reflect) the transparency. If using a transparency to demonstrate the number of units to translate
\(f\)
up or down, it is helpful to draw a dot on a specific point on both the underlying graph and on the transparency.


aligns: no