options: Understand the relationship between zeros and factors of polynomials.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Rewrite rational expressions.

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

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Solve systems of equations.

Gain familiarity with factors and multiples.

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

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

Analyze patterns and relationships.

Work with addition and subtraction equations.

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

Reason about and solve one-variable equations and inequalities.

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

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

Use polynomial identities to solve problems.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

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

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Narrative
The purpose of this activity is for students to practice interpreting relationships between patterns generated from two different rules. Students may need to generate patterns beyond the boxes provided. Encourage them to continue the pattern as needed. Students may describe the patterns and relationships in different, but accurate ways. Encourage them to notice as many relationships as they can and describe the relationships in whatever way makes sense to them. This is the first time students see two patterns where the numbers in one pattern are not multiples of the numbers in the other pattern.
This activity uses
MLR7 Compare and Connect
. Advances: Representing, Conversing.
Launch
Groups of 2
Activity
5 minutes: independent work time
2 minutes: partner discussion
MLR7 Compare and Connect
“Create a visual display that shows your thinking about the relationships between each set of patterns. Include details such as notes, diagrams, and drawings to help others understand your thinking.”
2–5 minutes: independent or group work
3–5 minutes: gallery walk
Student Facing
Complete the patterns for each set of rules.
What are some relationships between the patterns for each set of rules? Be prepared to explain your thinking.
Set A
Rule 1: Start at 0. Keep adding 3.
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Rule 2: Start at 0. Keep adding 6.
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Set B
Rule 1: Start at 4. Keep adding 3.
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Rule 2: Start at 9. Keep adding 6.
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Set C
Rule 1: Start at 0. Keep adding 5.
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Rule 2: Start at 0. Keep adding 3.
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Student Response
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Activity Synthesis
“What is the same and what is different in the way we represented the relationships between the patterns?” (Some of us used numbers and symbols, some of us wrote sentences.)
30 seconds: quiet think time
1 minute: partner discussion
“What is the same and what is different about Set A and Set B?” (They both add the same amount, but one set starts at 0. Set B has a lot more odd numbers in it. In set A, each number in rule 2 is double the number in rule 1, but in set B, each number in rule 2 is 1 more than double the number in rule 1.)
“For which pair of rules was it most challenging to notice and describe relationships?” (Set B because there was no multiple that worked to get from one pattern to the other. Set C because there weren’t doubles or halves.)


correct_option_index: 16