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: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
problem_activity: Narrative
The purpose of this activity is for students to consider the numbers when they choose a strategy to find the value of a product. Some students might choose to use the same strategy for any multiplication problem. In this activity, the numbers were chosen to encourage students to choose different strategies in order to generate discussion about why certain multiplication problems lend themselves to different strategies.
When students choose a multiplication strategy based on the factors, using the associative and commutative properties of multiplication and the distributive property, along with known facts, they make use of structure to facilitate their calculations (MP7).
MLR7 Compare and Connect.
Lead a discussion comparing, contrasting, and connecting the different strategies students chose to solve the problems. Ask, “Are there any benefits or drawbacks to one strategy compared to another?” and “Why did the different approaches lead to the same outcome?”
Advances: Conversing
Launch
Groups of 2
“Sometimes we use different strategies to solve problems, depending on the numbers in the problem. Without solving, look at the numbers in each expression and think about the strategy you would use to find the value.”
1–2 minutes: quiet think time
“Choose 2 problems you would solve using a different strategy and describe the strategy to your partner. Explain why you chose different strategies.”
1–2 minutes: partner work time
Activity
“Find the value of each expression. If you find the value mentally, record the steps you used in your head to arrive at the product.”
5–10 minutes: independent work time
Monitor for students who used different strategies for the same problem. For example, for
\(14\times25\)
, some students might multiply
\(14\times20\)
and
\(14\times5\)
and some students might double 25 and halve 14 and find
\(7\times50\)
.
8–10 minutes: partner work time
Student Facing
Find the value of each expression. Explain or show your reasoning.
\(14\times3\)
\(14\times101\)
\(14\times25\)
\(14\times9\)
\(14\times136\)
Student Response
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Activity Synthesis
Invite students to share their strategies for finding the value of
\(14 \times 101\)
.
“Is there a mental strategy you can use to find the value of this product?” (Yes. I know
\(14 \times 100\)
is 1,400 and then I can add 14 to that.)
Invite students to share their strategies for finding the value of
\(14 \times 136\)
.
“Which strategy did you use to find the value of
\(14 \times 136\)
? Why?” (I used the standard algorithm because I did not see a quick mental strategy for finding the value.)


aligns: no