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:
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
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Activity
In the previous activity, students calculated the scaled distances they would need to create a scale drawing, but did not actually create the scale drawing. In this activity, they create two different scale drawings of the state of Utah and notice how the scale impacts the drawing. One of the reasons choice of a scale is important is that we want to see the appropriate level of detail within a fixed space.
Launch
Display the outline of Utah and ask students “What do you notice? What do you wonder?”
[IMG]
Ask students to describe the shape: a rectangle with a smaller rectangle removed in the upper right corner.
Give students 5–6 minutes of quiet work time followed by whole-class discussion.
Student Facing
A rectangle around Utah is about 270 miles wide and about 350 miles tall. The upper right corner that is missing is about 110 miles wide and about 70 miles tall.
Make a scale drawing of Utah where 1 centimeter represents 50 miles.
Make a scale drawing of Utah where 1 centimeter represents 75 miles.
How do the two drawings compare? How does the choice of scale influence the drawing?
Student Response
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Anticipated Misconceptions
Some students may get a shape that is not closed or does not have right angles if they did not measure carefully enough. Prompt them to double-check their measurement for a particular side of the state if you can easily tell which side is drawn incorrectly.
Students may think that a scale of 1 centimeter to 50 miles will produce a smaller scale drawing than a scale of 1 centimeter to 75 miles (because 50 is less than 75). Ask them how many centimeters it takes to represent 75 miles if 1 centimeter represents 50 miles (1.5) and how many centimeters it takes to represent 75 miles if 1 centimeter represents 75 miles (1).
Activity Synthesis
Ask students what the two scale drawings share in common. Answers include: they both represent Utah, they both have the same shape, and they both can be used to measure distances in the actual state of Utah.
Ask students how the two scale drawings differ. The one at a scale of 1 centimeter to 50 miles is larger than the one at a scale of 1 centimeter to 75 miles.
Some students may notice that the scale drawing at a scale of 1 centimeter to 75 miles is actually a scaled copy of the other drawing, with a scale factor of 1.5. If so, ask them to share their observation linking scale drawings with scaled copies.
Representation: Internalize Comprehension.
Use color coding and annotations to highlight connections between representations in a problem. For example, annotate a display of the two scale drawings to make visible what the drawings share in common, and how they differ.
Supports accessibility for: Visual-spatial processing
Reading, Speaking: MLR3 Clarify, Critique, Correct.
Before presenting the correct scale drawings of Utah, present an incorrect drawing and written explanation. For example, present a rectangle approximately 5.4 cm wide and 7 cm tall that is missing an upper right corner which is approximately 1.4 cm wide and 2.2 cm tall, and provide the statement: “Since 1 cm represents 50 miles, I divided 110 and 70 each by 50, and got 2.2 and 1.4. The small rectangle that is missing is 2.2 cm tall and 1.4 cm wide.” Ask students to identify the error, critique the reasoning, and revise the statement so that the drawing is a scale drawing of Utah. This will remind students about the characteristics of scale drawings discussed in previous lessons and how to determine whether a drawing qualifies as a scale drawing of an actual object.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness


aligns: no