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.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response:
Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

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} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

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?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response:
Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
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im_task_000157

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fl_problem_000674

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options: Relate addition and subtraction to length.

Describe and compare measurable attributes.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Measure lengths indirectly and by iterating length units.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Represent and interpret data.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Work with time and money.

Convert like measurement units within a given measurement system.

Measure and estimate lengths in standard units.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Classify objects and count the number of objects in each category.

Geometric measurement: understand concepts of angle and measure angles.

Tell and write time.
problem_activity: Narrative
The purpose of this activity is for students draw their own picture graphs to represent given data. Each student receives a data table to use. After drawing their own graphs, they share their graph with a partner and receive feedback on what is clear and what they could improve. As students represent the data and share their graphs with others, they notice and describe the features of picture graphs that make it easy for others to understand (MP3, MP6). While students are making their graphs, monitor for any features that many students leave out (for example, titles or category labels) to emphasize when sharing in the synthesis.
The data tables will be used again in the next activity.
This activity uses
MLR8 Discussion Supports
. Advances: reading, writing, and conversing.
Required Materials
Materials to Copy
Data Tables
Picture and Bar Graph Template
Required Preparation
Each student needs 1 data table from the blackline master. Each student in a group of 2 may receive different data tables.
Launch
Groups of 2
Display “2nd Graders’ Favorite Sports” graph.
“What can you learn about 2nd graders’ favorite sports from this graph?”
“What are some features of this graph that help us understand the data?”
Share responses.
Highlight the important features (title, labels, and pictures or symbols).
Activity
"Now you are going to create your own picture graph."
Give each student 1 data table and a graph template from the blackline master.
“Write the number of the data table on your page.”
“This graph uses smiley faces, but you may choose something different when you make your graph."
"Think about what picture you are going to use, then represent the data shown in your table in a picture graph.”
10 minutes: independent work time
Monitor for students who use symbols that are easy to draw.
“Switch graphs with your partner.”
“Tell your partner 1 thing you think they did really well and 1 thing you still have a question about.”
MLR8 Discussion Supports
Display sentence frames.
“You did _____ really well in your graph.”
“Why did you . . . ?”
“Can you say more about . . . ?”
5 minutes: partner work time
Student Facing
A group of 2nd graders were asked, “What is your favorite sport?” Their responses are shown in this picture graph.
[IMG]
Represent the data shown in your table in a picture graph.
Table # _______
Student Response
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Activity Synthesis
Display graphs of previously selected students.
“What is same about these graphs? What is different?”
1 minute: quiet think time
1
–
2 minutes: partner discussion
Share responses.
Consider asking selected students:
“Why did you choose that symbol?”
"What other features did you add to your graph to help others' understand it?"


correct_option_index: 6