few_shots: 
Example:
Concept/skill: 
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¬¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Problem/activity:
Stage 1: Money
 Required Preparation
 Materials to Copy
 Blackline Masters
 Would You Rather Stage 1 Spinner
 Would You Rather Stage 1 Recording Sheet
 
 Narrative
 The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.

Answer: 
Yes. In this activity, students write word problems that compare coin amounts.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_center_000269_pos_0

2
standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Optional activity
The purpose of this activity is for students to find a fractional percent increase.
Look for students who calculate the percentage first and then add them together, and students who multiply by 1.08 and 1.008, respectively.
Launch
Students in groups of 2. 4 minutes of quiet work time followed by partner and then whole-class discussion.
Representation: Internalize Comprehension
. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?
The population of city B was approximately 7,150,000, and it increased by 0.8% in one year. What was the new population?
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 who want to multiply by
\(1 + \frac{p}{100}\)
may have trouble determining where to put the decimal. Have them think about the problem in steps. How can you find 8%? (Multiply by 0.08.) How can you find 0.8%? (Multiply by 0.008.)
Activity Synthesis
Have selected students show solutions, starting with a solution where the percentage is found first and then added to the initial amount, then the approach where one multiplies by 1.08 or 1.008, respectively. Make sure everyone understands both methods. Help students see the connections between these strategies.
Representing, Speaking: MLR7 Compare and Connect.
Use this routine after students present their solutions for calculating the new population of each city. Ask students, "what is the same and what is different about these approaches?" Call students' attention to the different ways students represented the percent increase in their strategies. These exchanges strengthen students' mathematical language use and reasoning based on percent increases with and without fractional amounts.
Design Principle(s): Maximize meta-awareness


aligns: no