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: Understand ratio concepts and use ratio reasoning to solve problems.

Analyze proportional relationships and use them to solve real-world and mathematical problems.
problem_activity: Optional activity
In this activity students compute rates to decide which job applicant is working the fastest checking online comments. They compare rates and total number of comments checked, then see that using rates is the more useful information in this situation.
Launch
Keep students in the same groups of 2.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.
Person 1 worked for 210 minutes and checked a total of 50,000 comments.
Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes.
Person 3 worked for 120 minutes, at a rate represented by
\(c = 331t\)
,
where
\(c\)
is the number of comments checked and
\(t\)
is the time in minutes.
Person 4 worked for 150 minutes, at a rate represented by
\(t = \left( \frac{3}{800} \right) c\)
.
Order the people from greatest to least in terms of total number of comments checked.
Order the people from greatest to least in terms of how fast they checked the comments.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Write equations for each job applicant that allow you to easily decide who is working the fastest.
Make a table that allows you to easily compare how many comments the four job applicants can check.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Ask students which job applicant should get the job and why. If time permits, consider using MLR 1 (Stronger and Clearer Each Time).
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to prepare students for the whole-class discussion. At the appropriate time, invite students to create a visual display showing which job applicant should get the job and why.  Allow students time to quietly circulate and analyze the selections and justifications in at least 2 other displays in the room. Give students quiet think time to consider what is the same and what is different and whether or not they agree. Next, ask students to find a partner to discuss what they noticed. Listen for and amplify observations that highlight advantages and disadvantages to each method of determining the top job applicant. This will help students identify situation when comparing rates is more effective than the sum of quantities.
Design Principle(s): Optimize output (for justification); Cultivate conversation


correct_option_index: 1