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.


Standard options: 
A. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. 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.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
problem_activity: Problem 1
What is the measure, in wedges, of the following angle?
[IMG]
A ray that turns all the way around its endpoint and back to its starting place has made a full turn. We say that the ray has turned 360
degrees
.
[IMG]
How many degrees has the ray turned from where it started?
[IMG]
[IMG]
[IMG]
Problem 2
Determine how many degrees the wedge created in Lesson 5 measures, and use that to create a makeshift protractor to measure benchmark angles.
Use a similar process to create a makeshift protractor that measures in increments of 45°.
Problem 3
Using the makeshift protractors you made in Anchor Task #2, find the measure, in degrees, of each of the following angles. If an angle can’t be measured precisely with either protractor, make an estimate.
| 1.            |https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png|  |https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png| image:: https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png |     1.            |https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png|  |https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png| image:: https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png      |
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| 1.            |https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png|  |https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png| image:: https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png | 1.                     |https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png|  |https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png| image:: https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png |


correct_option_index: 0

2