few_shots: 
Example:
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: fl_problem_000674_pos_0

5
standard_description: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
problem_activity: Narrative
This activity serves two main purposes. The first is to allow students to apply their understanding that the result of
\(a \times \frac{1}{b}\)
is
\(\frac{a}{b}\)
. The second is for students to reinforce the idea that any non-unit fraction can be viewed in terms of equal groups of a unit fraction and expressed as a product of a whole number and a unit fraction.
The activity uses a “carousel” structure in which students complete a rotation of steps. Each student writes a non-unit fraction for their group mates to represent in terms of equal groups, using a diagram, and as a multiplication expression. The author of each fraction then verifies that the representations by others indeed show the written fraction. A
s students discuss and justify their decisions they create viable arguments and critiqe one another’s reasoning (MP3).
MLR8 Discussion Supports.
Display sentence frames to support small-group discussion after checking their fraction diagram and equation: “I agree because . . .”, “I disagree because . . . .”
Advances: Conversing
Required Materials
Materials to Gather
Paper
Launch
Groups of 3
“Let's now use the patterns we saw earlier to write some true equations showing multiplication of a whole number and a fraction.”
Activity
3 minutes: independent work time on the first set of problems
2 minutes: group discussion
Select students to explain how they reasoned about the missing numbers in the equations.
If not mentioned in students' explanations, emphasize that: “We can interpret
\(\frac{5}{10}\)
as 5 groups of
\(\frac{1}{10}\)
,
\(\frac{8}{6}\)
as 8 groups of
\(\frac{1}{6}\)
, and so on.”
“In an earlier activity, we found that we can write any fraction as a multiplication of a whole number and a unit fraction. You'll now show that this is the case using fractions written by your group mates.”
Demonstrate the 4 steps of the carousel using
\(\frac{7}{4}\)
for the first step.
Read each step aloud and complete a practice round as a class.
“What questions do you have about the task before you begin?”
5–7 minutes: group work time
Student Facing
Use the patterns you observed earlier to complete each equation so that it’s true.
\(5 \times \frac{1}{10} =  \underline{\hspace{0.5in}}\)
\(8 \times \frac{1}{6} = \underline{\hspace{0.5in}}\)
\(4 \times  \underline{\hspace{0.5in}} = \frac{4}{5}\)
\(6 \times  \underline{\hspace{0.5in}} = \frac{6}{10}\)
\( \underline{\hspace{0.5in}} \times \frac{1}{4}= \frac{3}{4}\)
\( \underline{\hspace{0.5in}} \times \frac{1}{12}= \frac{7}{12}\)
Your teacher will give you a sheet of paper. Work with your group of 3 and complete these steps on the paper. After each step, pass your paper to your right.
Step 1: Write a fraction with a numerator other than 1 and a denominator no greater than 12.
Step 2: Write the fraction you received as a product of a whole number and a unit fraction.
Step 3: Draw a diagram to represent the expression you just received.
Step 4: Collect your original paper. If you think the work is correct, explain why the expression and the diagram both represent the fraction that you wrote. If not, discuss what revisions are needed.
Student Response
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Activity Synthesis
See lesson synthesis.


aligns: no