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 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.

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: 
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, 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_neg_0

5
standard_description: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
problem_activity: Optional activity
In the previous activity, students were given a map with a scale and the amount of time it took to get from one place to another. They used this to estimate the speed of the trip. In this activity, students work with the speed and a map with scale to find the amount of time a trip will take.
The main strategy to expect is to measure the distance between the two locations on the map and use the scale to convert this to the distance between the actual cities. Then students can calculate how long it will take at 15 mph.
Launch
Tell students that they will now use a scale drawing (a map) to solve a different problem about travel, this time focusing on how long it will take. Ask students what is the farthest they have ever biked. How long did it take? Do they know someone who has biked farther or for longer? If so, how far and how long?
Keep students in the same groups. Give students 4–5 minutes of quiet work time followed by partner and whole-class discussion.
Student Facing
A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from Garden City to Dodge City, Kansas?
[IMG]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Jada finds a map that says, “Note: This map is not to scale.” What do you think this means? Why is this information important?
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
The road from Garden City to Dodge City has many twists and bends. Students may not be sure how to treat these. Tell them to make their best estimate. Measuring many small segments of the road will have the advantage that those short segments are straight but it is time consuming. A good estimate will be sufficient here.
Activity Synthesis
First, have students compare answers with a partner and discuss their reasoning until they reach an agreement.
Next, invite students to share how they estimated the distance between the two cities (and how long it takes the cyclist to travel this distance). Ask students to consider the different distances students estimated the trip to be. What are some reasons for the differences? Possible explanations include:
Measurement error
The road is not straight and so needs to be approximated
For students who lay out the scale over and over again to cover the distance, it is difficult to estimate the fraction of the scale at the last step
Because of these different sources of inaccuracy, reporting the distance as 50 miles is reasonable; reporting it as 52 miles would require a lot of time and measurements; and reporting it as 51.6 miles is not reasonable with the given scale and map.
Speaking, Listening: MLR7 Compare and Connect.
As students work to determine the duration of the trip from Garden City to Dodge City, look for students with different strategies for estimating the distance between the two cities. As students investigate each other’s work, ask students to share what worked well in a particular approach. During this discussion, listen for any comments that make the estimation of the distance more precise. Then encourage students to make connections between the various uses of constant speed to calculate the duration of the trip. Amplify language students use to make sense of the cyclist’s constant speed and how it could be represented in the map. This will support constructive conversations as students compare strategies for calculating the duration of a trip and make connections between the quantity and visual representations of constant speed on the map.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


aligns: no