few_shots: Example:
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.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Represent and solve equations and inequalities graphically.

Analyze patterns and relationships.

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

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

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

Solve equations and inequalities in one variable.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Multiply and divide within 100.

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

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

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

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

Solve systems of equations.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

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

Write expressions in equivalent forms to solve problems.
problem_activity: Activity
In this activity, students get a chance to practice applying their skills in representing situations symbolically, and finding and interpreting solutions.
The structure of a row game supports students to check their thinking because their partners should get the same answer to different questions. When students’ answers disagree, they must make sense of each other’s questions and thinking to figure out whose answer is correct.
The practice prepares students to solve equations and solve for one variable in terms of another in their Algebra 1 lessons.
Monitor for students:
calculating some specific values before generating an equation
analyzing the quantities and relationships in the text
looking for and using mathematical structures, such as
\(ax + by\)
or
\(mx + b\)
Launch
Students will work independently to complete their designated column, and will work with their partners in the event that an answer is different from what their partners got.
Student Facing
Partner A completes only column A, and partner B completes only column B. Your answers for each problem should match. Work on one problem at a time, and check whether your answer matches your partner’s before moving on. If you don’t get the same answer, work together to find your mistake.
Column A:
Lin’s teacher has a daughter that is
\(\frac13\)
of his age. Write an expression to represent the daughter’s age. Let
\(z\)
represent the teacher’s age, in years.
Han wants to save
$
40. He hasn’t met his goal yet. Write an expression to represent how far Han is from his goal, in dollars. Let
\(q\)
represent the amount of money, in dollars, he’s saved so far.
Priya has some money to spend at a fair. It costs
$
6 to get in and
$
0.50 per ride ticket. Write an expression to represent how much Priya spends at the fair, in dollars. Let
\(x\)
represent the number of ride tickets Priya buys.
Diego is inviting some friends over to watch movies. He is buying popcorn and peanuts. Popcorn costs 6 cents per ounce and peanuts cost 17 cents per ounce. Write an expression to represent the total cost of peanuts and popcorn, in cents. Let
\(j\)
represent how many ounces of popcorn Diego buys and
\(k\)
represent how many ounces of peanuts he buys.
Column B:
Jada leaves the beach with some seashells. One out of every three of the shells turns out to contain a hermit crab. Write an expression to represent the number of hermit crabs Jada found. Let
\(z\)
represent the total number of seashells she collected.
Tyler started the school year with 40 pencils, but he’s lost some. Write an expression to represent how many pencils Tyler has left. Let
\(q\)
represent the number of pencils he’s lost so far.
When Clare bought her plant, it was 6 inches tall. Each week, it’s been growing
\(\frac12\)
of an inch. Write an expression to represent how tall Clare’s plant is, in inches. Let
\(x\)
represent the number of weeks since Clare bought her plant.
Mai is packing care packages. She is putting in boxes of granola bars that weigh 6 ounces each and paperback books that weigh 17 ounces each. Write an expression to represent the total weight of a care package, in ounces. Let
\(j\)
represent the number of boxes of granola bars and
\(k\)
represent the number of books.
Student Response
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Activity Synthesis
The goal of this discussion is for students to name and clarify strategies they have for writing algebraic expressions to describe given situations.
Strategies students might have include:
calculating some specific values before generating an expression
analyzing the quantities and relationships in the text
looking for and using mathematical structures, such as
\(ax + by\)
or
\(mx + b\)
Call on previously identified students to share their strategies for writing expressions, and support students to share insights or tips that will help other students. Possible questions for discussion include:
Why did you do calculations with some specific numbers first? How did that help you?
How did you record your calculations? What patterns did you notice?
When you read the situation, how many times did you read it?
What did you notice the first time you read the situation?
What did you notice when you looked at it again?
How did you decide what operations to use in your expression?
What made you think that your final expression would look like
\(mx + b\)
(or whatever structure is appropriate)?


correct_option_index: 11