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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Your response:
Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. 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.
B. 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.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Your response:
Thought: 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.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
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im_task_000157

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fl_problem_000674

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options: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
problem_activity: Optional activity
If students investigated the answers to their questions in the previous activity, they need access to their findings. They can either work with the questions generated by their group, or everyone can work from a master list of questions compiled by the teacher.
If students have access to a spreadsheet program, they can use it to find the results (MP5). Students need to communicate their findings clearly in graphical displays (MP6). They can choose to illustrate all or some of the questions in their graphical displays. Encourage the students to be creative with their displays. For example, if students are examining the question “How many people would live on each continent?” they might sketch the continents and place stick figures on the continents to represent the class. They might also draw a bar graph showing the same information in a different way.
Launch
Students work in same groups of 2–4 from previous activity. Provide access to four-function calculators. If students are doing their own research, provide access to internet-enabled devices. If conducting a gallery walk at the end, provide access to tools for making a visual display.
To give students a sense of the magnitude of the world versus the classroom, consider zooming in from Earth to North America, the United States, your state, your city, and finally your school.
Invite students to work on the question or questions that are of most interest to them either from their own group work on from the compiled list.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students are beginning to choose characteristics about the world’s population that are available to find, and that they can calculate percentages for the class for those characteristics.
Supports accessibility for: Memory; Organization
Student Facing
Suppose your class represents all the people in the world.
Choose several characteristics about the world’s population that you have investigated. Find the number of students in
your
class that would have the same characteristics.
Create a visual display that includes a diagram that represents this information. Give your display the title “If Our Class Were the World.”
Student Response
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Anticipated Misconceptions
Students may struggle with the difficult numbers for the percent of the world population with different characteristics. For example, there are about 1.2 billion people living in Africa. Ask them  to calculate
\(1.2 \div 7.4 \approx 0.162\)
. "What percent of the world population this is?" (16%). "If our class were the world, then about 16% of the class would live in Africa.  So how many students in our class would live in Africa?" (Since 16% of 25 is 4, that means that 4 students in our class would live in Africa.)
In some cases, there might be two acceptable answers to how many students in our class have a certain characteristic. About 10% of the world population is in Europe. For our class, we could have 2 students (8%) or 3 students (12%) that are in Europe. Either one is an acceptable answer. Make sure that students understand that 2.5 (10% of 25) is not a reasonable answer.
Activity Synthesis
Invite groups to share their displays. Consider doing a gallery walk and asking:
Were you surprised by any of your findings?
In what ways is the class actually representative of the world? (possibly gender distribution, religious adherence, etc.)
In what ways is it not? (age, place of residence, access to clean water, etc.)
Make sure to highlight the fact that having a small class limits the percentages that are possible. This can make deciding how many students in the class have a particular characteristic difficult. Consider asking:
What percentages are possible for students in the class? (0, 4, 8, . . . multiples of 4 up to 100)
There are 1 billion people living in the Americas. That’s a little more than 13.5% of the world population. If our class was the world, how many students in our class would be from the Americas? (3 students would be 12%, and 4 would be 16%. So 3 students is as close as we can get.)


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