options: Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

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

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Rewrite rational expressions.

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

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

Work with radicals and integer exponents.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Represent and solve problems involving multiplication and division.

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

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

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

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

Perform arithmetic operations on polynomials.

Add and subtract within 20.

Multiply and divide within 100.

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

Solve systems of equations.

Analyze patterns and relationships.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.
problem_activity: Narrative
The purpose of this activity is for students to visualize and make sense of the context of problems they will solve in the next activity. They will also consider representations that can be used to model the quantities and actions in the situation (MP4) and try creating them. Students will not have time to make a complete representation, so the focus is on making sense of the situation and persevering in finding effective representations (MP1).
Required Materials
Materials to Gather
Coins
Index cards
Paper
Two-color counters
Launch
Groups of 3 or 4
Display the image of the lockers.
“In your small group, discuss what you notice and wonder about the picture.”
1 minute: quiet think time
1 minute: group discussion
Share and record responses. If students are not familiar with lockers, explain that lockers are used to hold students’ coats, books, and backpacks in some schools.
Activity
Read the problem aloud to students.
“Take some time on your own to make sense of the problem. You may want to try to visualize it or reread the problem.”
2 minutes: quiet think time
Give students access to two-color counters, index cards, coins, and other materials that may be helpful to them.
“Based on what you know, create a representation of the problem.”
5 minutes: independent work time
Monitor for and select 3 different representations that:
represent lockers in different ways
show instances of contact with lockers (or of opening and closing)
show correspondence between each student and the lockers touched
Student Facing
The picture shows lockers in a school hallway.
The 20 students in Tyler’s fourth-grade class are playing a game in a hallway that is lined with 20 lockers in a row.
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The first student starts with the first locker and goes down the hallway and opens all the lockers.
The second student starts with the second locker and goes down the hallway and shuts every other locker.
The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
This process continues until all 20 students in the class have touched the lockers.
Create a representation to show what you understand about this problem. Consider:
How does your representation show lockers?
How does your representation keep track of students who touch lockers?
How does your representation show which lockers are open or closed?
Student Response
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Activity Synthesis
While discussing each representation, ask students:
“Where are the lockers in this representation?” (Numbers or pictures used to indicate lockers)
“How can we tell if a locker is open or closed in this representation?” (Symbols or colors used to indicate open or closed)
“How does this representation show which student is touching the lockers?” (Students and their actions listed in a table or a T-chart)
“In the next activity, you will answer questions about the game. You may use your representation or one shared by a classmate to help you think through the problems.”


correct_option_index: 30