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)
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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: 
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.

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} $

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

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


Answer: 
Yes. This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.

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

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im_task_000157_neg_0

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standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Activity
The purpose of this activity is for students to use double number line diagrams to represent situations of percent increase and decrease. Additionally, students identify the original and new amount in the double number lines to reinforce that the original amount pertains to 100%.
As students work on the task, monitor for students who created various equations for the last question.
Launch
Arrange students in groups of 2. Give 5–8 minutes of quiet work time. After 5 minutes allow students to work with a partner or to continue to work alone.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, present one question at a time and monitor students to ensure they are making progress throughout the activity.
Supports accessibility for: Organization; Attention
Student Facing
For each problem, complete the double number line diagram to show the percentages that correspond to the original amount and to the new amount.
The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s tank hold?
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At a movie theater, the size of popcorn bags decreased 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold?
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A school had 1,200 students last year and only 1,080 students this year. What was the percentage decrease in the number of students?
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One week gas was \$1.25 per gallon. The next week gas was \$1.50 per gallon. By what percentage did the price increase?
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After a 25% discount, the price of a T-shirt was \$12. What was the price before the discount?
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Compared to last year, the population of Boom Town has increased 25%. The population is now 6,600. What was the population last year?
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Student Response
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Anticipated Misconceptions
Students may continue to struggle to recognize the original amount and new amount with the proper percentages on the double number line.  Remind them that the original amount always corresponds to 100%.
Activity Synthesis
Select students to share the values they identified as original amount and the new amount for a few problems. Discuss how 100% always corresponds to the original value and when there is an increase in the value the new value corresponds to a percentage greater than the original 100%.
Select students to share the different equations they came up with. Discuss how the distributive property is useful for finding the percentage that corresponds with the new value instead of the percentage of the change.
Discuss how solving problems about percent change may require either multiplying or dividing numbers. It can be confusing, but it helps to first express the relationship as an equation and then think about how you can find the unknown number. Looking at the examples below, the first two require multiplication, but the others require division.
Using the structure A% of B is C:
\((1.5) \boldcdot 12 = c\)
\((0.80) \boldcdot 15 = c\)
\(a \boldcdot (1,\!200) = 1,\!080\)
\(a \boldcdot (1.25) = 1.50\)
\((0.75) \boldcdot b = 12\)
\((1.25) \boldcdot b = 6,\!600\)
Representing, Speaking: MLR7 Compare and Connect.
Use this routine after selected students share the values they identified for the original amount and the new amount for a few problems. Ask students what is the same and what is different about the ways double number lines were used to represent percent increase and decrease for the different situations. Call students' attention to how the original amount is represented as 100% in the tape diagrams and in some of the equations. This will help strengthen students' mathematical language use and reasoning based on percent increase and decrease.
Design Principle(s): Maximize meta-awareness


aligns: no