few_shots: 
Example 1:
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.


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:
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} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
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?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

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

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im_task_000157_pos_0

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fl_problem_000674_neg_0

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standard_description: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
problem_activity: Activity
In this activity, students examine relationships shown in graphs. They consider different types of events that cause repeated outputs (MP2). They examine one situation which is periodic (the distance of a car from the start line as it goes around a racetrack) and two situations which are not periodic, but do rise and fall at regular intervals. The long-term goal in this unit is to develop mathematical tools which can help model these complex phenomena.
Monitor for students who connect the repetitive nature of these graphs to the context of the clock hands or Ferris wheel from earlier lessons.
Launch
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select 2 of 3 to complete. Chunking this task into more manageable parts may also support students who benefit from additional processing time.
Supports accessibility for: Organization; Attention; Social-emotional skills
Student Facing
Here are some relationships that produce graphs that have a repetitive nature. For each situation, describe the dependent and independent variable. How does the dependent variable change? What might cause this change?
This is the graph of the distance of a race car from the starting line as it goes around a track.
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This is the graph of the temperature in a city in Australia over 21 days.
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This is the graph of two populations over time.
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Student Response
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Student Facing
Are you ready for more?
A ladybug is resting at the tip of a clock’s minute hand, which is 1 foot long. When it is 12:15, the ladybug is 10 feet above the ground.
Calculate how far above the ground the ladybug is at 12:00, 12:30, 12:45, and 1:00.
Estimate how far above the ground the ladybug is at 12:10, 12:20, and 12:40.
Plot the distances of the ladybug from the ground from 12:00 to 1:00.
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If the ladybug stays on the minute hand, predict how its distance from the ground will change over the next hour (from 1:00 to 2:00). What about from 2:00 to 3:00?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Some students may be unsure how to read the axes for all but the first relationship, as they look different than what students have seen so far. Encourage these students to focus on a specific coordinate on a graph to help them make sense of the axis labels as a way to get started.
Activity Synthesis
Begin the discussion by selecting previously identified students to share their observations about connections between the repeating nature of these graphs and the clock hands or Ferris wheel contexts from earlier lessons. If no groups make this connection, invite students to do so now—for example, by comparing the period of the race car to the period of the minute hand on a clock or by contrasting how the height of a point on a Ferris wheel always moves between the same high and low while the city high and low temperatures change from day to day.
Display the graphs for all students to see. Here are some questions for discussion:
“What similarities do you see between the graphs representing these situations?” (There are highs and lows in all the graphs, and these highs and lows come at pretty regular intervals.)
“Do these graphs all represent functions? How can you tell?” (Yes, in these situations for each time, there is a single value.)
“What do you think it means for a function to be
periodic
?” (The output values follow a repeating pattern.)
“What other words could you use to describe this type of behavior?” (repeating, cyclic)
Conclude the discussion by reminding students that previously, we named functions whose values repeat at regular intervals
periodic functions
. The graph of the race track is an example of what a periodic function can look like. The other two situations shown, temperature and population over time, are not quite periodic functions since the output values are not the same over and over again, but they have a definite periodic pattern to them.


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