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: 
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.

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

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_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
problem_activity: Optional activity
In this activity, students use the data from the previous activity and draw a scatter plot and a line that fits the data. The given data show a clear linear association, so it is appropriate to model the data with a line. Students can use a piece of dried linguine pasta or some other rigid, slim, long object (for example, wooden skewer) to eyeball the line that best fits the data. (The line of best fit has a variance of
\(R^2=0.94\)
.) Even though different answers will have slightly different slopes and intercepts, they will be close to each other.
Launch
Students in same groups of 3–4. Provide access to pieces of dried linguine pasta.
Representation: Internalize Comprehension.
Provide a range of examples and counterexamples for a best fit line. Consider displaying charts and examples from previous lessons to aide in memory recall.
Supports accessibility for: Conceptual processing
Student Facing
Make a scatter plot of the data.
[IMG]
Describe any patterns of association that you notice.
Draw a line that fits the data. Write an equation for this line.
Student Response
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Anticipated Misconceptions
If a student is stuck on making the scale on the graph, remind them to look at the range from the previous problem.
Activity Synthesis
At the start of the discussion, make sure students agree that there seems to be a negative association that looks like a line would fit the data nicely before moving on.
Invite several groups to share the equations they came up with and how they found them. They will likely have slightly different slopes and intercepts. Ask students to explain where those differences come from. (Not everyone chose the same points to guide the trendline they drew for the data.) The differences should be small and the different models give more or less the same information. In the next activity, students will be using the model (equation and graph) to make predictions.
Representing, Conversing: MLR8 Discussion Supports.
After students complete their scatter plots from the data, they should meet with a small group of 3–4 students to share and compare. While each student shares, circulate and encourage students to look for commonalities and to discuss their differences in displays. Tell students to generate an agreed on response for the equation and the visual display of the line even though they may have differences. Tell students that one member will share out, but they won’t know who, so they all need to be prepared to share and explain. During the whole-class discussion, amplify use of mathematical language such as “slope”, “intercept”, “equation”, “graph”, and “negative association”. Use this to help students develop their explanations of associations and differences that they see in how the data is interpreted.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


aligns: no