few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_001477_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Use the relation i^(2) = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
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
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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