few_shots: 
Example:
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 multiply multi-digit whole numbers using the standard algorithm.

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000674_pos_0

5
standard_description: Solve problems involving velocity and other quantities that can be represented by vectors.
problem_activity: Narrative
In this activity, students use rectangular diagrams and similar reasoning as in earlier activities to represent the multiplication of 2 two-digit numbers. They analyze a progression of diagrams, starting with those that represent multiplication of two-digit and one-digit numbers (18 and 6), a two-digit number and a ten (18 and 10), and then 2 two-digit numbers (18 and 16).
Students may decompose factors in different ways. For example, those who are familiar with multiples of 25 may find it intuitive to decompose
\(25 \times 46\)
as
\(25 \times 40\)
and
\(25 \times 6\)
, rather than decomposing 25 into
\(20 + 5\)
.
MLR8 Discussion Supports.
Pair gestures with verbal directions to clarify the meaning of any unfamiliar terms such as partial product.
Advances: Listening, Representing
Action and Expression: Develop Expression and Communication.
Give students access to base-ten blocks. If students use the blocks for the last question, ask them to also draw a diagram that represents their work with the blocks.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Launch
Display the three diagrams in the activity.
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Activity
“Take a few quiet minutes to work on the first problem. Then, share your thinking with your partner.”
3 minutes: independent work time
3 minutes: partner discussion
Invite students to share their responses: “What multiplication expression can be represented by each diagram?”
“Complete the rest of the activity.”
3 minutes: independent or partner work time
Monitor for students who decompose both factors into tens and ones and those who choose to keep one of the factors intact.
Student Facing
For each diagram, write a multiplication expression that the diagram can represent. Then, find the value of the expression. Use equations to show or explain your reasoning.
[IMG]
[IMG]
[IMG]
How are the diagrams alike? How are they different? Discuss with your partner.
Use a diagram to find each product.
\(13 \times 21\)
\(25 \times 46\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select two students to share their diagrams, solutions, and reasoning for the last problem.
“How did you decompose the factors and the diagram?” (I decomposed the 13 into 10 and 3 and the 21 into 20 and 1.)
“What expression could we write to show the partial product represented by each part of the diagram?”
“How do these partial products help us find the value of
\(13 \times 21\)
?” (Adding them gives us the value of
\(13 \times 21\)
:
\(200 + 10 + 3 + 60 = 273\)
)


aligns: no