few_shots: 
Example:
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.

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?

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

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

shot_info: im_center_000269_pos_0

2
standard_description: Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
problem_activity: Warm-up
This Math Talk encourages students to think about the relationship between base 10 logarithms and exponential expressions. Students have a chance to rewrite decimals, fractions, and base 10 numbers as powers of 10 in order to see which power of 10 the number is equal to and so find its base 10 logarithm. They will use this skill later in the lesson and in future lessons in order to calculate or estimate different logarithms.
Launch
Remind students that logarithms with no specified base are base-10 logarithms.
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
Evaluate mentally.
\(\log 10\)
\(\log 10,\!000\)
\(\log 0.1\)
\(\log \frac{1}{1,000}\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate
\(\underline{\hspace{.5in}}\)
’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”
If not already mentioned, make sure students recall that numbers such as 0.1 and
\(\frac{1}{1,000}\)
are still powers of 10 but they have negative exponents (that is, 0.1 is
\(10^{\text -1}\)
, and
\(\frac {1}{1,000}\)
is
\(\frac{1}{10^3}\)
or
\(10^{\text-3}\)
). This suggests that the logarithms of numbers that are less than 1 would be negative.
Speaking: MLR8 Discussion Supports.
Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because…” or "I noticed _____ so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no