options: Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

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

Create equations that describe numbers or relationships

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

Rewrite rational expressions.

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

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

Work with radicals and integer exponents.

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

Generate and analyze patterns.

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

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

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

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

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

Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.
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.
[IMG]
Rule 2: Start at 0. Keep adding 6.
[IMG]
Set B
Rule 1: Start at 4. Keep adding 3.
[IMG]
Rule 2: Start at 9. Keep adding 6.
[IMG]
Set C
Rule 1: Start at 0. Keep adding 5.
[IMG]
Rule 2: Start at 0. Keep adding 3.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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: 31