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: 
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

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_neg_0

3

fl_problem_000674_neg_0

5
standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Activity
The goal of this activity is to practice applying the definition of rotation. In this activity, students rotate a segment around its endpoint to create an isosceles triangle. By rotating a segment around one endpoint, students can observe that the distance between the center of rotation and a point is the same as the distance between the center of rotation and the image of that point. This observation is later captured in the formal definition of rotation.
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).
Digital
Launch
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to aide students who benefit from support with organizational skills in problem solving. For example, present one question at a time and ensure students complete each step correctly before moving on to the next step.
Supports accessibility for: Organization; Attention
Student Facing
Draw a segment. Label the endpoints
\(A\)
and
\(B\)
.
Rotate segment
\(AB\)
clockwise around center
\(B\)
by 90 degrees. Label the new endpoint
\(A’\)
.
Use the Polygon tool to draw triangle
\(ABA'\)
.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Draw a segment. Label the endpoints
\(C\)
and
\(D\)
.
Rotate segment
\(CD\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’\)
.
Rotate segment
\(C’D\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’’\)
.
Use the Polygon tool to draw triangle
\(CDC’’\)
.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure. An equilateral triangle is an example of a
regular polygon
: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Print
Launch
Briefly demonstrate how to create an angle of a given measure with a protractor and ask students to use their protractors along with you.
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5). You may wish to demonstrate using GeoGebra Geometry in Math Tools.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to aide students who benefit from support with organizational skills in problem solving. For example, present one question at a time and ensure students complete each step correctly before moving on to the next step.
Supports accessibility for: Organization; Attention
Student Facing
Draw a segment. Label the endpoints
\(A\)
and
\(B\)
.
Rotate segment
\(AB\)
clockwise around center
\(B\)
by 90 degrees. Label the new endpoint
\(A’\)
.
Connect
\(A\)
to
\(A’\)
and lightly shade in the resulting triangle.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Draw a segment. Label the endpoints
\(C\)
and
\(D\)
.
Rotate segment
\(CD\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’\)
.
Rotate segment
\(C’D\)
counterclockwise around center
\(D\)
by 30 degrees. Label the new endpoint
\(C’’\)
.
Connect
\(C\)
to
\(C’’\)
and lightly shade in the resulting triangle.
What kind of triangle did you draw? What other properties do you notice in the figure? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
You constructed an equilateral triangle by rotating a given segment around one of its endpoints by a specific angle measure. An equilateral triangle is an example of a
regular polygon
: a polygon with all sides congruent and all interior angles congruent. Try to construct some other regular polygons with this method.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may not notice any properties other than that rotation preserves distances to the center of rotation. Encourage these students to use tracing paper to make other conjectures about side lengths or angles.
Activity Synthesis
Display an isosceles triangle
\(ABC\)
with base
\(BC\)
.
Here are some key conjectures and observations students should come away from the discussion with:
Rotations preserve the distance to the center of rotation.
The angle bisector of angle
\(A\)
is also the perpendicular bisector of the base (
\(BC\)
) of an isosceles triangle.
The two base angles (angle
\(B\)
and angle
\(C\)
) of an isosceles triangle are congruent.
An isosceles triangle where angle
\(A\)
is 60 degrees is also equilateral.
It is not necessary at this time to formalize the language of these ideas. This will come later as students prove some of these statements in a subsequent unit.


aligns: no