options: Generate and analyze patterns.

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

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

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Solve systems of equations.

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

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Multiply and divide within 100.

Work with radicals and integer exponents.

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

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

Rewrite rational expressions.

Work with addition and subtraction equations.

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.

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

Interpret the structure of expressions.

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

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Narrative
The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rearrange would be helpful in this activity.
MLR8 Discussion Supports.
To support partner discussion, display the following sentence frames: “This array matches the diagram because . . .”, and “This array shows multiplication because . . . .”
Advances: Conversing, Representing
Required Materials
Materials to Gather
Connecting cubes or counters
Launch
Groups of 2
Give students access to connecting cubes or counters.
Activity
“Work independently to draw a way that the first group of dots in problem 1 could be arranged into an array.”
2 minutes: independent work time
“Discuss how you arranged your dots and how the array is related to multiplication with your partner.”
1 minute: partner discussion
“How did you rearrange the dots to make an array?” (Since there were 3 in each group, I put 3 dots in each row. I saw 2 groups of 6, so I made 2 rows of 6.)
Consider asking:
“Did anyone create a different array?”
“Now you are going to make as many arrays as you can from 16 dots.”
2–3 minutes: independent work time
“Share how you rearranged the dots into arrays with your partner. See if together you can come up with any other arrays.”
3–5 minutes: partner work time
Student Facing
Draw 1 way the dots could be rearranged into an array.
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Explain or show how the array is related to multiplication.
Draw ways that the dots could be arranged into arrays. Draw as many ways as you can.
[IMG]
Explain or show how each array is related to multiplication.
Student Response
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Activity Synthesis
“What kinds of equal groups did you make from 16 dots? How can you see the equal groups in the arrays you made?” (I can make 2 groups of 8. I drew it as 2 rows of 8 dots.)


correct_option_index: 4