few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. 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.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Work with radicals and integer exponents.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

Add and subtract within 20.

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

Gain familiarity with factors and multiples.

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

Represent and solve equations and inequalities graphically.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

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

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

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

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

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

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

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

Rewrite rational expressions.

Interpret the structure of expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Narrative
The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression
\(4\times6\)
. Feel free to adjust this expression to better fit the number of students in your class.
Launch
Groups of 2
Display
\(4\times6\)
“Work together as a class to use your bodies to create an array for this multiplication expression.”
If the number of students does not exactly match the product, ask extra students to monitor the array and be prepared to explain where they see parts of the expression in the array.
3–5 minutes: whole-class work time
Activity
“Work with your partner to draw an array for each multiplication expression. Be ready to share connections you notice between the multiplication expressions and arrays.”
2–3 minutes: partner work time
Student Facing
Draw an array for each multiplication expression. Be prepared to share your reasoning.
\(2\times3\)
\(5\times2\)
\(4\times4\)
Student Response
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Advancing Student Thinking
If students draw equal groups that are not arrays, consider asking:
“How did you use the expression to create your drawing?”
“How could we rearrange your drawing into an array?”
Activity Synthesis
Share an array or two for each expression.
“What connections did you and your partner see between the multiplication expressions and arrays?” (The factors tell us how many things are in each row and column. For
\(2\times3\)
, we drew an array with 2 columns that have 3 things in each column. For
\(2\times3\)
, we drew an array with 2 rows that have 3 things in each row.)


correct_option_index: 2