options: Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

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

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

Gain familiarity with factors and multiples.

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

Interpret the structure of expressions.

Work with radicals and integer exponents.

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

Use the four operations with whole numbers to solve problems.

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

Use polynomial identities to solve problems.

Solve systems of equations.

Rewrite rational expressions.

Represent and solve equations and inequalities graphically.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.

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

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.
problem_activity: Narrative
The purpose of this activity is for students to solve problems about a locker game by using the ideas of factors and multiples and by observing patterns in the numbers. The situation offers many possible explorations, but the questions around which lockers are touched and by how many people are designed to elicit understandings about multiplication.
Discussion about which lockers will be open or closed or by whom will likely move students away from thinking about factors and multiples and should not be the focus. The final question challenges students who are ready for more to look for additional patterns and generalize their observations. It is not expected that all students complete it. Students who are ready may simulate opening and closing the lockers in different ways, such as:
using actual lockers, if available
using a printed set of squares labeled 1 through 20
using two color counters and 10-frames, if available
using the head and tail sides of coins
MLR7 Compare and Connect
. Synthesis: Invite groups to prepare a visual display that shows the strategy they used to determine which lockers will be open. Encourage students to include details that will help others interpret their thinking. For example, specific language, using different colors, shading, arrows, labels, notes, diagrams or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students, “Which students open or close locker 10? What about locker 20? What patterns do you notice about the number of factors for a locker number and whether it is open or closed?”
Advances: Representing, Conversing
Representation: Internalize Comprehension
. Support students in transferring their knowledge to a new context. Begin by asking, “Does this problem remind anyone of the concepts we have been studying?” Invite students to reference the vocabulary display, and continue to refer them to it throughout the lesson.
Supports accessibility for: Conceptual Processing, Language, Attention
Launch
Groups of 3–4
“Let’s solve some problems about a game you read about earlier, where students take turns opening and closing lockers.”
“Silently read and think about each question.”
1 minute: quiet think time
“Work in your group to answer each question. Consider the representations you created or saw earlier to help you think about the problems.”
Activity
15–20 minutes: group work time
Monitor for students who:
represent each contact with the lockers in a systematic way
represent the open and closed lockers in various ways
reason about factors and multiples and use the vocabulary in their explanations
Encourage students who use a pattern to answer the final question to share their explanation. Invite them to consider a situation with more lockers such as 50 or 100.
Student Facing
The 20 students in Tyler’s fourth-grade class are playing a game in a hallway with 20 lockers in a row.
Your goal is to find out which lockers will be touched as all 20 students take their turn touching lockers.
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Which locker numbers does the 3rd student touch?
Which locker numbers does the 5th student touch?
How many students touch locker 17? Explain or show how you know.
Which lockers are only touched by 2 students? Explain or show how you know.
Which lockers are touched by only 3 students? Explain or show how you know.
Which lockers are touched the most? Explain or show how you know.
If you have time: Which lockers are still open at the end of the game? Explain or show how you know.
Student Response
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Activity Synthesis
“Take a few minutes to share your answers with students in a different group.”
Invite students to share how they kept track of the number of touches for each locker.
See lesson synthesis.


correct_option_index: 6