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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_001477_pos_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Narrative
The purpose of this activity is for students to convert between measurements in milliliters and liters, providing practice multiplying and dividing by 1,000. Students work with numbers in many forms including whole numbers, decimals, fractions, and numbers in exponential form.
Engagement: Internalize Self-Regulation.
Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, provide students with a partially completed chart to compare their answers and talk about the similarities and differences with their partners.
Supports accessibility for: Attention; Memory; Social-Emotional Functioning
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?” (There are different sized water bottles. There are numbers underneath the water bottles. How much more water does the big one hold than the little one? How many milliliters are in a liter?)
Display a table like this one:
{"table": [{"_attributes": {"border": "1", "style": "width:40%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "1,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.1"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "100,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}]}]}]}]}
“What numbers go in the empty boxes in the table?”
30 seconds quiet think time
“Explain your thinking to a partner.”
Fill in the table and leave it displayed for students to refer to during the lesson.
{"table": [{"_attributes": {"border": "1", "style": "width:40%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "1,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "10,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.1"}, {"_attributes": {"style": "text-align:center"}, "_value": "100"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "100"}, {"_attributes": {"style": "text-align:center"}, "_value": "100,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.01"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}]}]}]}]}
Activity
3–5 minutes: independent work time
1–2 minutes: partner discussion
Monitor for students who:
compare the quantities by converting milliliters to liters
compare by converting liters to milliliters
Student Facing
[IMG]
Complete the table.
{"table": [{"_attributes": {"border": "1", "style": "width:50%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "6.3"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.95"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(10^2\\)"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "800,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(10^6\\)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "65"}]}]}]}]}
Decide if the two measurements are equal. If not, choose which one is greater. Explain or show your reasoning.
15 mL and 0.15 L
2,500 mL and 2.5 L
200 mL and
\(\frac{1}{4}\)
L
1 mL and
\(\frac{1}{1,000}\)
L
15,600 mL and 15.5 L
Student Response
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Advancing Student Thinking
If students confuse the operations they need to use to convert milliliters to liters or liters to milliliters, refer to the table from the launch and ask, “What patterns do you notice?”
If necessary, add rows to the table and ask them to explain how many milliliters of water are in 2 liters of water and 3 liters of water, and 0.001 liter of water.
Activity Synthesis
Invite selected students to share how they compared the measurements.
Display: 15,600 mL and 15.5 L
“How many liters are 15,600 milliliters? How do you know?” (15.6 since I divide by 1,000)
“How many milliliters are 15.5 liters? How do you know?” (15,500 since there are 1,000 milliliters in each liter so that’s 15,000 and half of a thousand which is 500.)
“Which is greater? 15,600 milliliters or 15.5 liters? How do you know?” (15,600 mL because I can compare them using either liters or milliliters.)
“When you solved this problem, did you convert from milliliters to liters or from liters to milliliters? Why?” (I converted from liters to milliliters because multiplying by 1,000 is more comfortable than dividing by 1,000.)


aligns: no