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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

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

Interpret the structure of expressions.

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

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

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

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

Multiply and divide within 100.

Rewrite rational expressions.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

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

Use properties of operations to generate equivalent expressions.

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

Add and subtract within 20.

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

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

Analyze patterns and relationships.

Write and interpret numerical expressions.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

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

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.
problem_activity: Narrative
In this optional activity, students investigate patterns in multiples of 15 and analyze and describe features of the digits in the tens and ones place. The activity also prompts them to consider why those features exist and to predict whether a given number could be a multiple of 15. The goal here is not to elicit clear justifications, but rather to encourage students to use their understanding of place value and numbers in base-ten to reason more generally about patterns in numerical patterns.
This activity uses
MLR5 Co-craft Questions
. Advances: writing, reading, representing
Launch
Groups of 2
MLR5 Co-Craft Questions
Display only the opening sentence and list of numbers, without revealing the question(s).
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“What do these questions have in common? How are they different?”
Reveal the task (students open books), and invite additional connections.
“Let’s see what patterns we can find when we count by 15.”
Activity
“Take a few quiet minutes to work on the activity. Afterwards, discuss your responses with your partner.”
5 minutes: independent work time
5 minutes: partner discussion
Monitor for:
the different patterns students notice
the different ways they explain the patterns
the ways students reason about whether 250 could be a number being called out
Student Facing
Elena counted by 15 and recorded the numbers she counted:
15
30
45
60
75
90
Write the next four numbers she’d record if she kept going.
What patterns do you see? Describe as many as you can.
Choose one pattern that you noticed and explain why you think it happens.
Could 250 be a number that Elena calls out if she continued to count by 15? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
To answer the last question, students may try to count up by 15 and see if they would reach 250. Encourage students to see if any of the patterns they noticed could help them answer the question.
Activity Synthesis
Invite students to share the patterns they noticed and their explanations for the patterns. Record them for all to see.
Select other students to share their explanation on whether 250 could be a number that Elena calls said. Highlight explanations that make use of the structure in the numbers.


correct_option_index: 27