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.


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.


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.


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.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Work with equal groups of objects to gain foundations for multiplication.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand and apply properties of operations and the relationship between addition and subtraction.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

Multiply and divide within 100.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.

Understand the connections between proportional relationships, lines, and linear equations.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Understand solving equations as a process of reasoning and explain the reasoning.

Add and subtract within 20.

Understand properties of multiplication and the relationship between multiplication and division.

Solve systems of equations.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve equations and inequalities in one variable.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.
problem_activity: Narrative
The purpose of this activity is for students to practice division within 100 by playing a game called Race to 1. The goal of the game is to repeatedly divide numbers until they reach one.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community.
Supports accessibility for: Social-Emotional Functioning, Organization
Required Materials
Materials to Gather
Number cubes
Launch
Groups of 2
“Take a minute to read the directions for Race to 1.”
1 minute: quiet think time
“Let’s look at a sample game. Jada rolled a 3 on her first turn, then rolled 2 a few times afterwards. Talk with your partner about what her next move should be if she rolls 2 on her next turn.” (She should divide 4 or 6 by 2 because those moves get her really close to one.)
1 minute: partner discussion
Share responses.
Give each group a number cube.
Activity
“Play Race to 1 with your partner.”
10–15 minutes: partner work time
If students finish early, have them play again. Students can fill in the same numbers from the first game at the top of the columns of the second game or use the numbers 24, 36, 48, and 72 for a challenge.
Student Facing
Directions for Race to 1
On your first turn:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose one number from the top row of your table. Divide it by your divisor.
Write a division expression and record the quotient in the table. Your turn is done.
On all your other turns:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose either a quotient from one of your past turns or a new number from the top row of the table. Divide it by your divisor.
Write a division expression and record the quotient in the table.
The first player to get a quotient of 1 wins.
Sample Game
Jada rolled 3 on her first turn, then rolled 2 a few times afterwards.
|    start number     |     12      |     16      | 18 |     24      |
|---------------------|-------------|-------------|----|-------------|
| division expression | \(12\div3\) | \(16\div2\) |    | \(24\div2\) |
|      quotient       |      4      |      8      |    |     12      |
| division expression |             |             |    | \(12\div2\) |
|      quotient       |             |             |    |      6      |
| division expression |             |             |    |             |
|      quotient       |             |             |    |             |
Game 1
|    start number     | 12 | 16 | 18 | 24 |
|---------------------|----|----|----|----|
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
Game 2
|    start number     |   |   |   |   |
|---------------------|---|---|---|---|
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
Activity Synthesis
“How was having an efficient way to divide helpful as you played Race to 1?” (I had to decide which number I was going to divide, so it was helpful to be able to do it quickly. I had to divide a few times on each turn.)
“What was a helpful strategy as you played Race to 1?” (I had to think about which number I could divide by the number I rolled. I divided the smallest number by the largest divisor to try to get to the quotient to be as small as possible so I could get to 1 first.)


correct_option_index: 5