options: Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

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

Reason about and solve one-variable equations and inequalities.

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

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Analyze patterns and relationships.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

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

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

Write expressions in equivalent forms to solve problems.

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

Write and interpret numerical expressions.

Add and subtract within 20.

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

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

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Understand and apply properties of operations and the relationship between addition and subtraction.
problem_activity: Narrative
The purpose of this activity is for students to practice generating two different patterns from two different rules and observe and quantify relationships between corresponding terms. Both sets of rules generate patterns that have the same relationships between corresponding terms. Each of Priya’s terms is 3 times greater than each of Jada’s corresponding terms and each of Jada’s terms is
\(\frac{1}{3}\)
of Priya’s corresponding terms.
When students find and explain patterns related rules and relationships, they look for and express regularity in repeated reasoning (MP8).
Launch
Groups of 2
“You and your partner will each complete some problems about patterns independently. After you’re done, discuss your work with your partner.”
Activity
5 minutes: independent work time
3 minutes: partner discussion
“Look back at your work and make any revisions based on what you learned from discussing with your partner.”
1–2 minutes: independent work time
Monitor for students who:
revise their thinking based on partner discussion
use multiplication expressions to represent the relationships between the patterns
Student Facing
Partner A
Use each rule to create a pattern.
Jada’s rule: Start at 0. Keep adding 2.
[IMG]
Priya’s rule: Start at 0. Keep adding 6.
[IMG]
If the patterns continue:
What number will be in Priya’s pattern when Jada’s pattern has 34? Explain or show your reasoning.
What number will be in Jada’s pattern when Priya’s pattern has 120? Explain or show your reasoning.
What relationships do you notice between the numbers in Priya's pattern and the numbers in Jada's pattern?
Partner B
Use each rule to create a pattern.
Jada’s rule: Start at 0. Keep adding 3.
[IMG]
Priya’s rule: Start at 0. Keep adding 9.
[IMG]
If the patterns continue,
What number will be in Priya’s pattern when Jada’s pattern has 54? Explain or show your reasoning.
What number will be in Jada’s pattern when Priya’s pattern has 198? Explain or show your reasoning.
What relationships do you notice between the numbers in Priya’s pattern and the numbers in Jada’s pattern?
Student Response
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Activity Synthesis
Ask previously identified students to share their thinking.
Display completed patterns from both sets of rules.
“How are the patterns from the pairs of rules the same? How are they different?” (Some of the numbers are in all four patterns. Some numbers aren’t in any pattern like 5 and 11. In both sets of rules, Priya’s numbers are 3 times greater than Jada’s numbers and Jada’s numbers are
\(\frac{1}{3}\)
Priya’s numbers.)
“How would you describe the relationship between Priya's pattern and Jada's pattern?” (Priya's numbers are all 3 times as much as Jada's corresponding numbers.)
“What can I multiply the numbers in Priya’s pattern by to get the corresponding numbers in Jada’s pattern?” (
\(\frac{1}{3}\)
, each number in Jada's pattern is
\(\frac{1}{3}\)
the corresponding number in Priya's pattern.)


correct_option_index: 15