few_shots: 
Example 1:
Concept/skill: 
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.

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.


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

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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


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

Example 3:
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.

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


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is for students to find areas of rectangles where one side is a whole number and the other side is a fraction that is greater than 1.  Students should solve the problems in a way that makes sense to them. Ask students to explain how the diagrams show the multiplication expressions.
Engagement: Provide Access by Recruiting Interest.
Synthesis: Optimize meaning and value. Invite students to share how they use the diagram to calculate the area of the desk or the garden and the method they used to do so with a classmate.
Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
Activity
5 minutes: individual work time
5 minutes: partner work time
Student Facing
Write a multiplication expression to represent the area of the shaded region.
[IMG]
What is the area of the shaded region?
Write a multiplication expression to represent the area of the shaded region.
[IMG]
What is the area of the shaded region?
Student Response
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Advancing Student Thinking
If students do not write multiplication expressions to represent the area of the shaded region, prompt them to explain how they found the area of the shaded region. Then, write expressions to represent the student’s strategy and ask, “How do these expressions represent your strategy?”
Activity Synthesis
Ask several students to share their responses to the second problem.
Display:
\(3 \times 3\frac{3}{4}\)
\(3 \times \frac{15}{4}\)
“How do these expressions represent the area of the shaded region?” (They are the width and length of the shaded region. In one, the length is a whole number and some fourths, and in the other, it is all fourths.)
“How is finding the value of these two expressions different?” (For the first one, I can multiply 3 by 3 and then 3 by
\(\frac{3}{4}\)
and add them together. For the second one, I can see how many fourths I have using multiplication.)


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