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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Your response:
Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. 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.
B. 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.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


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

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Your response:
Thought: 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.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
problem_activity: Activity
In the previous activity, students commented on distributions on a dot plot and had opportunities to hear different ways to describe distributions. In this activity, they begin to think about how to characterize a distribution as a whole, in terms of its
center
and
spread
. Students learn that we can give a general description of a distribution by identifying a location that could be the center of the data, and by noting how alike or different the data points are.
Note that at this point “center” and “spread” can only be identified and described informally, via visual observation and intuitive reasoning about how data points are distributed. The lack of precise ways to identify center and spread helps to cultivate the need for more formal measures later.
In this activity, students evaluate and critique another's reasoning (MP3).
Launch
Keep students in groups of 2. Ask students to read the question in the stem, “How many hours do you generally spend on homework each week?” Then, ask students to explain why this is a statistical question. This is a statistical question because it can be answered by collecting data, and we can expect variability in the data.
Give them 6–7 minutes of quiet time to work on the first three questions, and then 4–5 minutes to share their responses with their partner and to complete the last two questions together. Be sure to leave at least 5 minutes for a whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge about calculating percentages. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Twenty-five sixth-grade students answered the question: “How many hours do you generally spend on homework each week?”
This dot plot shows the number of hours per week that these 25 students reported spending on homework.
[IMG]
[IMG]
Use the dot plot to answer the following questions. For each, show or explain your reasoning.
What percentage of the students reported spending 1 hour on homework each week?
What percentage of the students reported spending 4 or fewer hours on homework each week?
Would 6 hours per week be a good description of the number of hours this group of students spends on homework per week? What about 1 hour per week? Explain your reasoning.
What value do you think would be a good description of the homework time of the students in this group? Explain your reasoning.
Someone said, “In general, these students spend roughly the same number of hours doing homework.” Do you agree? Explain your reasoning.
Student Response
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Anticipated Misconceptions
Students may not recall how to find a percentage. Remind them that a percentage can be found if we know the size of a part and that of a whole. If needed, prompt them to determine the size of the entire data set.
Activity Synthesis
Ask a couple of students to share their thinking on what number of hours would be a good description of homework time for this group of students and why. Then, select a couple of other students to discuss how alike or different the lengths of homework time are.
Explain that sometimes it helps to describe a set of data generally, or to characterize it as a whole. One way to do that is by finding a value that describes the whole set reasonably well, or a value whose location can be considered the “center” of a distribution. Ask students:
“Where on the dot plot would you consider the center of the data? What is the value of that center?”
Another way to characterize a data set is by describing its “spread,” or the variability in the data points. The wider the spread (the more dispersed the data points are on a dot plot), the more variable or different they are. The narrower the spread (the more clustered together), the more alike they are. Ask students:
“Based on the dot plot, how would you describe the spread of the students’ homework time? Are the amounts of time they spend on homework alike or different?”
Tell students that we will continue to explore center and spread in upcoming lessons.
Representing, Writing: MLR7 Compare and Connect.
Ask pairs of students to prepare a display for a summary statement that generalizes the the number of hours spent on homework each week using the sentence frame, “Based on this data set, spending ___ hours on homework each week is typical for 6th graders because…”. Note a handful of sentences to highlight in the discussion. Give students opportunities to compare their statements with those shared and agree or disagree with each sentence, providing reasons for their agreement or disagreement supported by the data. Give students 1-2 minutes to revise their statements prior to collecting them for display. This will help students to develop conceptual understanding for “typical.”
Design Principle(s): Maximize meta-awareness, Cultivate conversation


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