options: Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Solve systems of equations.

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

Write expressions in equivalent forms to solve problems.

Use properties of operations to generate equivalent expressions.

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

Create equations that describe numbers or relationships

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

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

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

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

Use the four operations with whole numbers to solve problems.

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

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

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

Rewrite rational expressions.

Understand the relationship between zeros and factors of polynomials.

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

Analyze patterns and relationships.

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 describe the structure of an array by identifying the number of columns, the number of objects in each column, and the total number of objects. They learn that the columns of an array go up and down. Students begin to reason about how they can use the structure of the array to find the total number of objects without counting by 1.
This activity uses
MLR8 Discussion Supports. Advances: speaking, conversing
Representation: Develop Language and Symbols. S
upport understanding of the rows and columns by inviting students to act it out. For example, use students to create the first array (3 rows of 2). Discuss the students who create the rows. Now switch to talking about columns (2 columns of 3). Discuss the difference in which students create the columns.
Supports accessibility for: Visual-Spatial Processing, Organization
Required Materials
Materials to Gather
Counters
Launch
Groups of 2
Give students counters.
“Use your counters to make an array with 3 rows with 4 in each row. Make sure the counters in each row line up with the counters in the other rows.”
Display counters in an array as shown:
[IMG]
“Arrays are made up of rows, but they also have columns that go up and down. How many columns are in this array?” (4)
30 seconds: quiet think time
Share responses.
“How many counters are in each column of the array you made?” (3)
30 seconds: quiet think time
Share responses.
Activity
“Now you will look at a few arrays to decide how many columns they have, how many in each column, and find the total number of counters. Then you will make arrays using counters and answer a few questions.”
MLR8 Discussion Supports
Display sentence frames to support students when they describe the structure of the array:
“There are _____ columns in the array.”
“There are _____ counters in each column.”
“There are _____ counters in all.”
8 minutes: partner work time
Student Facing
[IMG]
How many columns are in this array?
How many counters are in each column?
How many counters are there in all?
[IMG]
How many columns are in this array?
How many counters are in each column?
How many counters are there in all?
Use 10 counters to make 2 columns with the same number in each column.
How many counters are in each column?
How many rows are in the array?
How could you count these counters without counting by ones?
Use 15 counters to make 3 columns with the same number in each column.
How many counters are in each column?
How many rows are in the array?
How many counters are in each row?
How could you count these counters without counting by ones?
Student Response
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Activity Synthesis
Display student work for an array with 10 counters.
“Describe _____’s array.” (It has 10 counters, it has 2 columns and 5 counters in each column. It has 5 rows with 2 counters in each row.)
“How can we prove there are 10 counters in this array?” (We can skip count by 2. We can add
\(2 + 2 + 2 + 2 + 2\)
. We can add
\(5 + 5\)
.)


correct_option_index: 7