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: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
problem_activity: Activity
In the previous activity, students found that negative real numbers have two imaginary square roots. In future lessons, students will use the quadratic formula to find complex solutions, which involves interpreting expressions like
\(\sqrt{\text-36}\)
. In this activity, students learn and apply the convention that for any positive real number
\(a\)
,
\(\sqrt{\text-a}=i\sqrt{a}\)
.
Launch
Explain to students that sometimes negative numbers end up inside of the square root symbol as a result of the steps used to solve equations. In the previous activity, we saw that negative numbers have two square roots, one on the positive imaginary axis, and one on the negative imaginary axis. By convention, the
\(\sqrt{}\)
symbol with a negative number inside refers to the square root on the positive imaginary axis. For example,
\(\sqrt{\text-4}=2i\)
.
Student Facing
Write these imaginary numbers using the number
\(i\)
.
\(\sqrt{\text- 36}\)
\(\sqrt{\text- 10}\)
\(\text- \sqrt{\text- 100}\)
\(\text- \sqrt{\text- 17}\)
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 need to work through some intermediate steps in order to express the square roots in terms of
\(i\)
. For example, students could break a square root apart like this:
\(\sqrt{\text-36} = \sqrt{\text-1}\boldcdot \sqrt{36} = i \boldcdot 6 = 6i\)
.
Activity Synthesis
Select students to share their responses and encourage students to show that their answers make sense by squaring. Mention that for answers that involve
\(i\)
multiplied by a radical, it is customary to write the
\(i\)
first so it doesn’t look like it might be part of the radicand. For example,
\(\sqrt{\text-15}\)
is usually written as
\(i\sqrt{15}\)
rather than
\(\sqrt{15}i\)
.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because . . .”, “I noticed _____ so I . . .”, “Why did you . . .?”, “I agree/disagree because . . . .”
Supports accessibility for: Language; Social-emotional skills


aligns: no