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: Apply and extend previous understandings of numbers to the system of rational numbers.

Use complex numbers in polynomial identities and equations.

Extend the properties of exponents to rational exponents.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Represent and model with vector quantities.

Reason quantitatively and use units to solve problems.

Perform operations on matrices and use matrices in applications.

Perform arithmetic operations with complex numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Use properties of rational and irrational numbers.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations on vectors.

Represent complex numbers and their operations on the complex plane.
problem_activity: Activity
It is common to use positive numbers to represent credit and negative numbers to represent debts on a bill. This task introduces students to this convention and asks them to solve addition and subtraction questions in that context. Note that whether a number should be positive or negative is often a choice, which means one must be very clear about explaining the interpretation of a signed number in a particular context (MP6).
For the second question, monitor for students who find the amount each week and sum those, and students who sum the value of the electricity used and the value of the electricity generated separately, and then find the sum of those.
Launch
Arrange students in groups of 2. Give students 4 minutes of quiet work time followed by partner discussion. Follow with a whole-class discussion.
Representation: Access for Perception.
Read Han’s electricity bill situation aloud. Students who both listen to and read the information will benefit from extra processing time. Check in with students to see if they have any questions about the context of the situation.
Supports accessibility for: Language
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, read the problem with the goal of comprehending the situation (e.g., This problem is about a house with solar panels that generate energy.). In the second read, ask students to analyze the mathematical quantities (e.g., used
$
83.56 worth of electricity, generated
$
6.75 worth of electricity, current charges are
$
83.56, Solar Credit is -
$
6.75 and the amount due is
$
74.81). In the third read, ask students to brainstorm possible strategies to answer the questions. This helps students connect the language in the word problem and the reasoning needed to solve the problem, while still keeping the intended level of cognitive demand in the task.
Design Principle(s): Support sense-making​
Student Facing
Han's family got a solar panel. Each month they get a credit to their account for the electricity that is generated by the solar panel. The credit they receive varies based on how sunny it is.
[IMG]
| Current charges:                         $                        83.56                         Solar Credit: -                         $                        6.75                         Amount due:                         $                        76.81 |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
Here is their electricity bill from January.
In January they used
$
83.56 worth of electricity and generated
$
6.75 worth of electricity.
In July they were traveling away from home and only used
$
19.24 worth of electricity. Their solar panel generated
$
22.75 worth of electricity. What was their amount due in July?
The table shows the value of the electricity they used and the value of the electricity they generated each week for a month. What amount is due for this month?
|        | used (                               $                              ) | generated (                               $                              ) |
|--------|-----------------------------------------------------------------------|----------------------------------------------------------------------------|
| week 1 |                                                                       |                                                                            |
| week 2 |                                                                       |                                                                            |
| week 3 |                                                                       |                                                                            |
| week 4 |                                                                       |                                                                            |
What is the difference between the value of the electricity generated in week 1 and week 2? Between week 2 and week 3?
Student Response
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Student Facing
Are you ready for more?
While most rooms in any building are all at the same level of air pressure, hospitals make use of "positive pressure rooms" and "negative pressure rooms."  What do you think it means to have negative pressure in this setting?  What could be some uses of these rooms?
Student Response
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Activity Synthesis
Ask one or more students to share their answer to the first question and resolve any discrepancies.
Ask selected students to share their reasoning for the second questions. Discuss the relative merits of different approaches to solving the problem.
Finish by going over the solution to the third question. Point out that the bill will reflect a negative number in the amount due section, but we can interpret this to mean that the family receives a credit, and it will be applied to their next bill.


correct_option_index: 3