few_shots: 
Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Recognize and represent proportional relationships between quantities.

Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

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

shot_info: fl_problem_000972_neg_0

6
standard_description: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Warm-up
This warm-up introduces students to a scale without units and invites them to interpret it using what they have learned about scales so far.
As students work and discuss, notice those who interpret the unitless scale as numbers having the same units, as well as those who see “1 to 100” as comparable to using a scale factor of 100. Invite them to share their thinking later.
Launch
Remind students that, until now, we have worked with scales that each specify two units—one for the drawing and one for the object it represents. Tell students that sometimes scales are given without units.
Arrange students in groups of 2. Give students 2 minutes of quiet think time and another minute to discuss their thinking with a partner.
Student Facing
A map of a park says its scale is 1 to 100.
What do you think that means?
Give an example of how this scale could tell us about measurements in the park.
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 might think that when no units are given, we can choose our own units, using different units for the 1 and the 100. This is a natural interpretation given students’ work so far. Make note of this misconception, but address it only if it persists beyond the lesson.
Activity Synthesis
Solicit students’ ideas about what the scale means and ask for a few examples of how it could tell us about measurements in the park. If not already mentioned by students, point out that a scale written without units simply tells us how many times larger or smaller an actual measurement is compared to what is on the drawing. In this example, a distance in the park would be 100 times the corresponding distance on the map, so a distance of 12 cm on the map would mean 1,200 cm or 12 m in the park.
Explain that the distances could be in any unit, but because one is expressed as a number times the other, the unit is the same for both.
Tell students that we will explore this kind of scale in this lesson.


aligns: no