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.


Your response:
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.


Your response:
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.


Your response:
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: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
problem_activity: Optional activity
The purpose of this activity is for students to make preparations to create their scale drawings. They sketch a rough floor plan of the classroom.
In groups, they plan the steps for making measurements and then carry out their plan.
Some things to notice as students work:
As they draw their sketch, encourage them to focus on big-picture elements and not on details. It is not important that the sketch is neat or elaborate. What matters more is that it does not omit important features like the door.
As they make plans for measuring and recording, encourage them to work systematically to minimize omissions and errors.
Urge students to measure twice and record once. It is better to take a little more time to double check the measurements than to find out during drawing that they are off.
Launch
Give students 1–2 minutes to read the task statement individually and to ask any clarifying questions. Consider displaying a floor plan sketch of another room in the school. Emphasize that the sketch serves a similar purpose as an outline in writing. It does not need to be to scale, accurate, or elaborate, but it should show all the important pieces in the right places so it can be a reference in creating the scale drawing.
Arrange students in groups of 2–4. Smaller groups means that each individual student can be more involved in the measuring process, which is a benefit, but consider that it might also make the measuring process more time consuming (as it would mean more groups moving about in a confined space).
Distribute blank paper and give students 4–5 minutes to draw a sketch and to share it with a partner. Provide access to measuring tools. Give students another 4–5 minutes to plan in groups, and then time to measure (which may vary depending on size of classroom and other factors).
Representation: Internalize Comprehension.
Activate or supply background knowledge about measurement. Check to see that students are able to use measuring tools and record measurements accurately.
Supports accessibility for: Memory; Conceptual processing
Student Facing
On a blank sheet of paper, make a
rough sketch
of a floor plan of the classroom. Include parts of the room that the class has decided to include or that you would like to include. Accuracy is not important for this rough sketch, but be careful not to omit important features like a door.
Trade sketches with a partner and check each other’s work. Specifically, check if any parts are missing or incorrectly placed. Return their work and revise your sketch as needed.
Discuss with your group a plan for measuring. Work to reach an agreement on:
Which classroom features must be measured and which are optional.
The units to be used.
How to record and organize the measurements (on the sketch, in a list, in a table, etc.).
How to share the measuring and recording work (or the role each group member will play).
Gather your tools, take your measurements, and record them as planned. Be sure to double-check your measurements.
Make your own copy of all the measurements that your group has gathered, if you haven’t already done so. You will need them for the next activity.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
After groups finish measuring, ask them to make sure that every group member has a copy of the measurements before moving on to the next part.
Consider briefly discussing what was challenging about doing the measuring. A few important issues which may come up include:
Making sure that the measuring device stays in a straight line.
It is hard to be accurate when the measuring device needs to be used
multiple
times in order to find the length of something long, such as a wall.
Taking turns with other groups that are trying to measure the same thing.
The measurements are not exact and need to be rounded.
Speaking: MLR8 Discussion Supports.
As students describe their process for measuring features of the room, press for details in students’ explanations by requesting that students challenge an idea, elaborate on an idea, or give an example of their measuring process. Provide a sentence frame such as: “It was challenging to measure ______ because . . . .” This will help students to produce and make sense of the language needed to communicate their own ideas.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 1