few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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?

shot_info: im_task_001477_pos_0

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im_task_000157_neg_0

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fl_problem_000674_pos_0

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standard_description: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
problem_activity: Warm-up
The goal of this opening activity is to activate, through a familiar context, what students know about functions from middle school.
Students first encounter a relationship in which two quantities—the number of bagels bought and price—do not form a function. They see that for some numbers of bagels bought, there are multiple possible prices. The relationship between the number of bagels bought and the
best
price, however, do form a function, because there is only one possible best price for each number of bagels.
Students contrast the two relationships by reasoning about possible prices, completing a table of values, and observing the graphs of the relationships.
Launch
Arrange students in groups of 4. Give students a few minutes of quiet time to think about the first question, and then a couple of minutes to share their thinking with their group. Pause for a class discussion.
Invite students to share an explanation as to how each person in the situation could be right. If possible, record and display students’ reasoning for all to see. After the reasoning behind each price is shared, direct students to the table in the second question. Ask students to write down “best price” in the header of the second column and then complete the table.
Student Facing
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A customer at a bagel shop is buying 13 bagels. The shopkeeper says, “That would be $16.25.”
Jada, Priya, and Han, who are in the shop, all think it is a mistake.
Jada says to her friends, “Shouldn’t the total be \$13.25?”
Priya says, “I think it should be \$13.00.”
Han says, “No, I think it should be \$11.25.”
Explain how the shopkeeper, Jada, Priya, and Han could all be right.
Your teacher will give you instructions for completing the table.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "br": [{}], "_values": ["number", "of\u00a0bagels"]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {}]}, {"td": [{"_value": "2"}, {}]}, {"td": [{"_value": "3"}, {}]}, {"td": [{"_value": "4"}, {}]}, {"td": [{"_value": "5"}, {}]}, {"td": [{"_value": "6"}, {}]}, {"td": [{"_value": "7"}, {}]}, {"td": [{"_value": "8"}, {}]}, {"td": [{"_value": "9"}, {}]}, {"td": [{"_value": "10"}, {}]}, {"td": [{"_value": "11"}, {}]}, {"td": [{"_value": "12"}, {}]}, {"td": [{"_value": "13"}, {}]}]}]}]}
Student Response
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Activity Synthesis
Consider displaying a table to summarize the different possibilities for calculating the price of 13 bagels (or the prices for 6 or more bagels), as well as the table showing the best price for each number of bagels bought.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "br": [{}], "_values": ["number", "of bagels"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["shopkeeper\u2019s", "price"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["Jada\u2019s", "price"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["Priya\u2019s", "price"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["Han\u2019s", "price"]}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {"_value": "1.25"}, {}, {}, {}]}, {"td": [{"_value": "2"}, {"_value": "2.50"}, {}, {}, {}]}, {"td": [{"_value": "3"}, {"_value": "3.75"}, {}, {}, {}]}, {"td": [{"_value": "4"}, {"_value": "5.00"}, {}, {}, {}]}, {"td": [{"_value": "5"}, {"_value": "6.25"}, {}, {}, {}]}, {"td": [{"_value": "6"}, {"_value": "7.50"}, {"_value": "6.00"}, {}, {}]}, {"td": [{"_value": "7"}, {"_value": "8.75"}, {"_value": "7.25"}, {}, {}]}, {"td": [{"_value": "8"}, {"_value": "10.00"}, {"_value": "8.50"}, {}, {}]}, {"td": [{"_value": "9"}, {"_value": "11.25"}, {"_value": "9.75"}, {"_value": "8.00"}, {}]}, {"td": [{"_value": "10"}, {"_value": "12.50"}, {"_value": "11.00"}, {"_value": "9.25"}, {}]}, {"td": [{"_value": "11"}, {"_value": "13.75"}, {"_value": "12.25"}, {"_value": "10.50"}, {}]}, {"td": [{"_value": "12"}, {"_value": "15.00"}, {"_value": "12.00"}, {"_value": "11.75"}, {"_value": "10.00"}]}, {"td": [{"_value": "13"}, {"_value": "16.25"}, {"_value": "13.25"}, {"_value": "13.00"}, {"_value": "11.25"}]}]}]}]}
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "br": [{}], "_values": ["number", "of bagels"]}, {"_attributes": {"scope": "col"}, "_value": "best price"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {"_value": "1.25"}]}, {"td": [{"_value": "2"}, {"_value": "2.50"}]}, {"td": [{"_value": "3"}, {"_value": "3.75"}]}, {"td": [{"_value": "4"}, {"_value": "5.00"}]}, {"td": [{"_value": "5"}, {"_value": "6.25"}]}, {"td": [{"_value": "6"}, {"_value": "6.00"}]}, {"td": [{"_value": "7"}, {"_value": "7.25"}]}, {"td": [{"_value": "8"}, {"_value": "8.50"}]}, {"td": [{"_value": "9"}, {"_value": "8.00"}]}, {"td": [{"_value": "10"}, {"_value": "9.25"}]}, {"td": [{"_value": "11"}, {"_value": "10.50"}]}, {"td": [{"_value": "12"}, {"_value": "10.00"}]}, {"td": [{"_value": "13"}, {"_value": "11.25"}]}]}]}]}
Ask students,
“’Number of bagels’ and ’price’ do not form a
function
, but ’number of bagels’ and ’best price’ do form a function. Why is this? What do you recall about functions?”
“If we graph the relationship between ’number of bagels’ and ’price,’ what do you think the graph would look like?”
“If we graph the relationship between ’number of bagels’ and ’best price,’ what would the graph look like?”
After students make some predictions, display the two graphs for all to see. In the first graph, solid blue dots represent the shopkeeper’s price, open green circles Jada’s price, red squares Priya’s price, and yellow triangles Han’s price. In the second graph, each X represents the best price for each number of bagel.
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Because there are multiple possible prices when the number of bagels is 6 or greater, price is not a function of the number of bagels bought.​​​​​​
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Because there is only one best price for a particular number of bagel, best price is a function of the number of bagels bought.
Emphasize that a function assigns one output to each input. Clarify that the word “function” in mathematics has a very specific meaning that does not necessarily agree with how “function” is used in everyday life (for instance, as in the sentence “The function of a bridge is to connect two sides of a river.”).


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