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

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

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

Add and subtract within 20.

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

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

Multiply and divide within 100.

Generate and analyze patterns.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

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

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

Represent and solve equations and inequalities graphically.

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

Write expressions in equivalent forms to solve problems.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

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

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

Interpret the structure of expressions.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

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

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. Students may see equal groups in the rows or the columns of the array. Recording the equations for each way of seeing the groups is an opportunity to reinforce the commutative property.
When students use different ways to group dots within the same array to find the total number of dots they look for and make use of structure (MP7).
Launch
Groups of 2
“How many do you see? How do you see them?”
Flash the image.
30 seconds: quiet think time
Activity
Display the image.
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Repeat for each image.
Student Facing
How many do you see? How do you see them?
[IMG]
[IMG]
[IMG]
Student Response
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Activity Synthesis
“How did the arrays allow us to find the number of dots in different ways?” (We were able to look at the number of dots in each row and think about how many rows there were. I counted the number in each column and multiplied it by the number of columns.)
As students share, record equations to match their thinking.
Consider asking: “How do the equations change if we think about the rows as the groups or the columns as the groups?” (For the image with 12 dots, if we think about the rows as the groups, we write
\(4 \times 3 = 12\)
, but if we think about the columns as the groups, we write
\(3 \times 4 = 12\)
. The order of the factors is reversed, but the product stays the same.)


correct_option_index: 2