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.


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: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
problem_activity: Narrative
The purpose of this activity is for students to solve problems about a locker game by using the ideas of factors and multiples and by observing patterns in the numbers. The situation offers many possible explorations, but the questions around which lockers are touched and by how many people are designed to elicit understandings about multiplication.
Discussion about which lockers will be open or closed or by whom will likely move students away from thinking about factors and multiples and should not be the focus. The final question challenges students who are ready for more to look for additional patterns and generalize their observations. It is not expected that all students complete it. Students who are ready may simulate opening and closing the lockers in different ways, such as:
using actual lockers, if available
using a printed set of squares labeled 1 through 20
using two color counters and 10-frames, if available
using the head and tail sides of coins
MLR7 Compare and Connect
. Synthesis: Invite groups to prepare a visual display that shows the strategy they used to determine which lockers will be open. Encourage students to include details that will help others interpret their thinking. For example, specific language, using different colors, shading, arrows, labels, notes, diagrams or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students, “Which students open or close locker 10? What about locker 20? What patterns do you notice about the number of factors for a locker number and whether it is open or closed?”
Advances: Representing, Conversing
Representation: Internalize Comprehension
. Support students in transferring their knowledge to a new context. Begin by asking, “Does this problem remind anyone of the concepts we have been studying?” Invite students to reference the vocabulary display, and continue to refer them to it throughout the lesson.
Supports accessibility for: Conceptual Processing, Language, Attention
Launch
Groups of 3–4
“Let’s solve some problems about a game you read about earlier, where students take turns opening and closing lockers.”
“Silently read and think about each question.”
1 minute: quiet think time
“Work in your group to answer each question. Consider the representations you created or saw earlier to help you think about the problems.”
Activity
15–20 minutes: group work time
Monitor for students who:
represent each contact with the lockers in a systematic way
represent the open and closed lockers in various ways
reason about factors and multiples and use the vocabulary in their explanations
Encourage students who use a pattern to answer the final question to share their explanation. Invite them to consider a situation with more lockers such as 50 or 100.
Student Facing
The 20 students in Tyler’s fourth-grade class are playing a game in a hallway with 20 lockers in a row.
Your goal is to find out which lockers will be touched as all 20 students take their turn touching lockers.
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Which locker numbers does the 3rd student touch?
Which locker numbers does the 5th student touch?
How many students touch locker 17? Explain or show how you know.
Which lockers are only touched by 2 students? Explain or show how you know.
Which lockers are touched by only 3 students? Explain or show how you know.
Which lockers are touched the most? Explain or show how you know.
If you have time: Which lockers are still open at the end of the game? Explain or show how you know.
Student Response
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Activity Synthesis
“Take a few minutes to share your answers with students in a different group.”
Invite students to share how they kept track of the number of touches for each locker.
See lesson synthesis.


correct_option_index: 0