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

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fl_problem_000674

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options: Understand independence and conditional probability and use them to interpret data.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Investigate chance processes and develop, use, and evaluate probability models.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Calculate expected values and use them to solve problems.

Use random sampling to draw inferences about a population.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Develop understanding of statistical variability.

Use probability to evaluate outcomes of decisions.

Interpret linear models.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.

Understand and evaluate random processes underlying statistical experiments.
problem_activity: In Class Launch
Use after Unit 3, Lesson 9
The US Department of Education does a survey of colleges every year. Students will use this data to test a conjecture they have about colleges. Tell students that these are some of the characteristics we have information on:
college ownership: public, private non-profit, or private for-profit
average SAT scores of admitted students
acceptance rate
number of enrolled students
average cost of attendance
median earnings 10 years after graduation
Task Statement 1 has four more categories (highest degree awarded, completion rate, percent of white students, and median ACT score), which can also be included in this discussion if students will be using that task statement.
Ask students to identify what type of data each of these is (for example, categorical, percent, mean, or count). Once all the types are identified, ask "Which of these characteristics might be related to each other? How are they related?" Write down each idea for all to see. Ask students why they think a pair of categories is related in the way they propose, to increase investment in finding the answer. However, students do not need to have well-supported reasons at this time.
If students are having trouble generating ideas, or they do not bring up a wide enough variety of ideas, introduce a few more. Here are some examples:
The more selective the college is, the higher the average SAT scores of the people who are accepted.
Private for-profit colleges cost more on average, but also have a wider range of costs, because they need to make money but also attract lots of students.
Public schools are larger than private schools.
Once enough ideas have been suggested, ask “If these relationships exist, how could we see them in the data? How could we present the data to show that they’re true?” Give students quiet think time and then invite them to share one of their ideas with a partner. Then ask students to share their ideas with the class. Ensure that a variety of ways of presenting data are discussed. Here are some examples:
The more selective the college is, the higher the average SAT scores of the people who are accepted: Make a scatter plot of admission rate vs. average SAT score.
Private for-profit colleges cost more on average, but also have a wider range of costs: Make a box-and-whisker plot of costs for each type of college.
Public schools are larger than private schools: Make a two-way frequency table of school ownership (public or private) vs school size (small, medium, and large, defined by ranges of numbers of enrolled students).
Teacher Instructions
The data provided is a spreadsheet of 200 schools, not all of which have information about each of the ten categories. Students will need access to technology such as Geogebra or Excel that will allow them to analyze and display the relationships that interest them.
If desired, the complete data set can be downloaded from the Department of Education website, and data can be curated in a different way. Different categories can be chosen based on the interests of the class, or the range of colleges can be narrowed down to those in the state. Historical data is also available. A few local colleges could be compared across time. If a customized data set is created, modify the launch accordingly.
Student-Facing Statement
Here are the characteristics of colleges that we have data about:
Choose two that might be related. What do you predict the relationship between them is?
college ownership: public, private non-profit, or private for-profit
average SAT score of admitted students
acceptance rate
number of enrolled students
average cost of attendance per year
median earnings 10 years after graduation
highest degree awarded
completion rate
percent of students who self-identify as white
median ACT score of admitted students
Take a look at the data in the spreadsheet. Before calculating, do some estimation based on the data. Can you tell if your hypothesis seems reasonable?
Use an appropriate display to summarize the data.
Analyze your graph or table and do any other calculations needed. Do your results confirm your prediction? If not, what do you think explains the results?
Here are some headlines. What analysis do you think the article describes? Give some examples of evidence that would support the headline or contradict it.
“Students from Selective Colleges Tend to Succeed”
“Isolation at Larger Colleges Leads to Higher Dropout Rates”
“High Cost of Private Colleges Not Outweighed by Lifetime Earnings”
Teacher Instructions
The data provided is a spreadsheet of 100 schools for which there is information about each of the six categories. Students will need access to technology such as Geogebra or Excel that will allow them to analyze and display the relationships that interest them.
If desired, the complete data set can be downloaded from the Department of Education website, and data can be curated in a different way. Different categories can be chosen based on the interests of the class, or the range of colleges can be narrowed down to those in the state. Historical data is also available. A few local colleges could be compared across time. If a customized data set is created, modify the launch accordingly.
Student-Facing Statement
Here are the characteristics of colleges that we have data about:
Choose two that might be related. What do you predict the relationship between them is?
college ownership: public, private non-profit, or private for-profit
average SAT score of admitted students
acceptance rate
number of enrolled students
average cost of attendance per year
median earnings 10 years after graduation
Take a look at the data in the spreadsheet. Before calculating, do some estimation based on the data. Can you tell if your hypothesis seems reasonable?
Use an appropriate display to summarize the data.
Analyze your graph or table and do any other calculations needed. Do your results confirm your prediction? If not, what do you think explains the results?
Here are some headlines. What analysis do you think the article describes? Give some examples of evidence that would support the headline or contradict it.
“Students from Selective Colleges Tend to Succeed”
“Isolation at Larger Colleges Leads to Higher Dropout Rates”
“High Cost of Private Colleges Not Outweighed by Lifetime Earnings”


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