few_shots: 
Example 1:
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.


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.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
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} $

Concept/skill: 
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
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?

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K

im_task_000157_neg_0

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fl_problem_000674_pos_0

5
standard_description: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to make sense of different methods they can use to compare three-digit numbers. They analyze the thinking of others and make connections across representations (MP2, MP3). Although students have compared numbers using different representations in prior units, this activity offers them the opportunity to consider using the number line as a tool to compare three-digit numbers. In the synthesis, students will discuss which representation makes it easier to see the comparison. While students could make a case that each of the representations was easier for them, the focus is on Jada’s way, the number line.
MLR8 Discussion Supports.
Display sentence frames to support partner discussion. “_____ and _____ are the same/alike because . . .” and “_____ and _____ are different because . . . .”
Advances: Speaking, Conversing
Launch
Groups of 2
Activity
“Diego, Jada, and Clare were asked to compare 371 and 317. They each represented their thinking differently.”
“Take some time to look over their methods.”
2 minutes: independent work time
“Discuss with your partner how their methods are the same and different.”
4 minutes: partner discussion
“Now try Jada’s way.”
6 minutes: partner work time
Student Facing
Each student compared 371 and 317, but represented their thinking in different ways.
Diego
[IMG]
[IMG]
I see 3 hundreds for each number.
317 only has 1 ten, but 371 has 7 tens.
\(371 > 317\)
Clare
Each has 3 hundreds.
371 has 7 tens, but 317 only has 1 ten.
\(317 < 371\)
Jada
[IMG]
I can see that 371 is farther to the right on my number line, so I know it is greater than 317.
\(371 > 317\)
What is the same and different about these students’ representations?
Discuss with a partner.
Try Jada’s way.
Estimate the location of 483 and 443 on the number line.
Mark each number with a point. Label the point with the number it represents.
[IMG]
Use
\(>\)
,
\(=\)
, or
\(<\)
to compare 483 and 443.
______________________________
Student Response
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Advancing Student Thinking
If students write comparison statements that are not true, ask them to read their statements and consider asking:
“How did you decide which number was greater?”
“How does your statement match the number line?”
Activity Synthesis
“Clare, Diego, and Jada represented their thinking in different ways. Whose method made it easier to see that 371 is greater than 317? Explain.” (Jada’s because you just have to look at which number is farther to the right. You can see 371 is farther from 0. Diego’s because I use diagrams and I can see quickly that the hundreds are the same and there are more tens, but some things were the same.)
As needed, “Jada and Diego wrote
\(371 > 317\)
, but Clare wrote
\(317 < 371\)
. Who do you agree with? Explain.” (They both mean the same thing. 371 is greater than 317, so 317 is less than 371.)


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