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: 
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.

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

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fl_problem_000674_pos_0

5
standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Optional activity
This activity is similar to the previous activity in that students are interpreting a graph and making sense of what situation the graph is representing. The difference here is that the specificity with numbers has been removed, so students need to think a bit more abstractly about what the changes in the graph represent and how they connect to the situation.
Monitor for students describing the graph with different levels of detail, particularly for any students who state that the car got up to speed faster than the car slowed down to 0.
Teacher Notes for IM 6–8 Math Accelerated
This activity is required.
Launch
Give students 1–2 minutes of quiet work time, followed by a whole-class discussion.
Engagement: Develop Effort and Persistence.
Break the class into small discussion groups and then invite a representative from each group to report back to the whole class. All group members should be prepared to share if invited.
Supports accessibility for: Attention; Social-emotional skills
Student Facing
[IMG]
The graph shows the speed of a car as a function of time. Describe what a person watching the car would see.
Student Response
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Student Facing
Are you ready for more?
The graph models the speed of a car over a function of time during a
3-hour trip. How far did the car go over the course of the trip?
There is a nice way to visualize this quantity in terms of the graph. Can you find it?
[IMG]
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
The purpose of this activity is for students to connect what is happening in a graph to a situation. Display the graph for all to see. Select previously identified students to share the situation they came up with. Sequence students from least descriptive to most descriptive. Have students point out the parts on the graph as they share their story about the situation.
Consider asking the following questions:
“Did the car speed up faster or slow down faster? How do you know?” (The car sped up faster because the first part of the model is steeper than the third part of the model.)
“How did you know that the car stayed that speed for a period of time?” (The graph stays at the same height for a while, so the speed was not changing during that time.)
Reading, Writing, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to provide students with a structured opportunity to revise and refine the explanation of their thinking about the shape and patterns in the graph. After students have written a response to the task statement, ask students to meet with 2–3 partners in a row for feedback. Each time, partners should explain their thinking without reading from their written work. Provide students with prompts for feedback that will help students strengthen their ideas and clarify their language (e.g., “How do you know that from the graph?”, “What in the graph makes you think that?”, “Can you give an example?”, etc.). Students can borrow ideas and language from each partner to strengthen their final version.
Design Principle(s): Optimize output (for explanation)


aligns: no