few_shots: Example:
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.
shot_info: fl_problem_000674

5
options: Perform arithmetic operations on polynomials.

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

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

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

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

Analyze patterns and relationships.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Use polynomial identities to solve problems.

Rewrite rational expressions.

Multiply and divide within 100.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Solve systems of equations.

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

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

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

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

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.

Work with addition and subtraction equations.

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

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Generate and analyze patterns.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Activity
The activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable, and choosing parameters of an equation that will result in its graph looking a certain way.
Launch
Arrange students in groups of 2. Give students two minutes of quiet work time on the first question, and ask them to check their answers with their partner before starting the second question. Call attention to the scale on the axes. Identify students who use the scale to select the parameters for their linear equation.
Student Facing
Evaluate each expression when
\(x\)
is -3.
\(x^2\)
\(\text-x^2\)
\(x^2+20\)
\(\text-x^2+20\)
For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share various equations that each graph could represent. Use different but equally correct equations to help students generalize. For example, either
\(y=x+15\)
or
\(y=x+12\)
makes sense for graph C, because it looks like
\(y=x\)
, and is shifted up by some number between 10 and 20. So we know that the equation this graph represents is in the form
\(y=x+b\)
, where
\(b\)
is positive, even though we can’t tell its exact value from the given information.


correct_option_index: 25