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.


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.


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.


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.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
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: Activity
The purpose of this task is to give students a good reason to compute a rate “per 1.” Since the task statement doesn't provide all the information needed to answer the question and does not suggest a solution pathway, it is an opportunity for students to make sense of the problem (MP1) and engage in some aspects of mathematical modeling (MP4).
Students learn about the Burj Khalifa, the tallest high-rise in the world, and try to determine how long it would take to wash all of its 24,348 windows given a specific rate of work by a window-washing crew. The fact that the total number of windows is not a multiple of the corresponding value in the given ratio (15 windows in 18 minutes) motivates students to identify the rate for 1 and then scale that number to answer the question.
This activity does not specify which “per 1” rate students should find. Some students are likely to first calculate
\(\frac56\)
windows per minute instead of
\(1\frac15\)
or 1.2 minutes per window. Students are not expected to name the above quantities as “rates per 1” or “unit rates” at this time. As students work, ask them to explain what the quantity they calculated (either windows per minute or minutes per window) means and how they plan to use it. If students are unsure where to start with the problem, ask, “At this rate, how long will it take the crew to finish 90 windows? 300 windows?”
Launch
Ask students to close their workbooks or devices, and ask if they know what the Burj Khalifa is. Allow students who are familiar with the building to share what they know.
Then, display a picture of the building and a map of its location.
[IMG]
Once students see that the Burj Khalifa is the tallest artificial structure in the world and is located on the coast of the Arabian Gulf, surrounded by desert, ask what else they wonder about the building. Pause here to allow students time to think of a question. Keep the photo and map of the Burj Khalifa displayed.
Select students to share their questions, limiting it to one question per student. Record 5–10 questions for all to see. If no students wonder about the number of windows, say that you also have a question about the building and add to the list: “How long does it take to wash all the windows on the Burj Khalifa?”
Explain that your question came to mind after watching an online video of a window washing crew on the Burj Khalifa, using brushes and squeegees to clean the windows while harnessed to ropes.
Tell students they will now try to answer a question about the window washing. Give students 3–5 minutes of quiet think time to do so.
Answering the question requires knowing how many windows the Burj Khalifa has. The amount,
24,348 windows
, is readily available through online searches if students are allowed and able to go online. Otherwise, have the number ready to share, and consider announcing the value to the whole class only after several students have requested the information. Recognizing missing information and the steps needed to acquire it is part of the mathematical modeling process.
Some facts on the Burj Khalifa:
Height: 2,722 ft (829.8 meters)
Tallest artificial structure in the world (as of January 2016)
154 usable floors, 9 maintenance floors, 46 spire levels, 2 below-ground parking lots (Wikipedia)
57 total elevators
It took 6 hours for an individual to climb to the top of the Burj Khalifa in 2011.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, ask students to identify the rate for 1 window or 1 minute. Next, ask students to find how long it would take to wash a portion of the windows, such as 100 or 1000. After that, ask students how long it would take to wash all the windows of the Burj Khalifa.
Supports accessibility for: Organization; Attention
Speaking: MLR7 Compare and Connect.
Use this routine when students present their strategy and representations to find how long it will take to wash all the windows. Ask students to consider what is the same and what is different about each approach. Draw students’ attention to the different quantities they calculated (either windows per minute or minutes per window). These exchanges can strengthen students’ mathematical language use and reasoning to make sense of strategies used to compute a rate “per 1.”
Design Principle(s): Maximize meta-awareness
Student Facing
[IMG]
A window-washing crew can finish 15 windows in 18 minutes.
If this crew was assigned to wash all the windows on the outside of the Burj Khalifa, how long will the crew be washing at this rate?
Student Response
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Anticipated Misconceptions
Students may get stuck when they try to find the minutes per window because 15 does not divide evenly into 18. Help them reason in terms of equivalent ratios or recall grade 5 methods for determining a quotient that is not a whole number.
Activity Synthesis
Invite a few students to explain their reasoning and solutions. Ask students who used both
\(1\frac15\)
or 1.2 minutes per window and
\(\frac56\)
windows per minute to share. Emphasize that both quantities are valid and have purpose, depending on the question you are answering.
Focus the discussion on strategies for identifying and correcting errors. As rate problems grow more complex, students become more likely to mix up numbers, calculate less-helpful rates per 1, or make arithmetic mistakes that are left unquestioned. If possible, have several students share approaches that did not work, and errors that were made, and ask them to explain how they knew they must have made an error.
If no students offer to share, have an example of a student error ready to display for the class. For example, a student may incorrectly calculate
\(\frac56\)
minutes per window instead of
\(1\frac15\)
minutes per window. Ask students to discuss with a partner what they think the error is and how they would help the student. Select 1–2 students to share their ideas with the class; while they share, make the corrections for all to see.
Lastly, students may point out that the answer, 29,217.6 minutes, is a total time and is not representative of how many normal work days it would take the crew to do the job. Time permitting, pursue this valuable line of thinking, as it shows that students are thinking about the math and the context (MP2).


correct_option_index: 2