options: Multiply and divide within 100.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

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

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

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

Add and subtract within 20.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Solve systems of equations.

Work with addition and subtraction equations.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

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

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

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

Interpret the structure of expressions.

Create equations that describe numbers or relationships

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

Work with radicals and integer exponents.

Rewrite rational expressions.

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

Use polynomial identities to solve problems.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.
problem_activity: Narrative
The purpose of this activity is for students to build arrays with physical objects and describe the arrays in terms of multiplication. Students focus on where equal groups can be seen in arrays. Students will write expressions and equations to represent arrays in future lessons. In the activity, students are asked to create different arrays with 24 cubes. It is not an expectation of grade 3 for students to find all the arrays for a given number.
When students notice that the rows or columns in an array have the same number of objects and relate this to equal groups, they look for and make use of structure (MP7).
Keep connecting cubes out for the cool-down.
MLR8 Discussion Supports.
Synthesis:
Create a visual display of the various arrays created by the students. As students discuss each array, annotate the display with the language used, such as “array”, “rows”, “columns”, and “equal groups”.
Advances: Speaking, Representing
Representation: Internalize Comprehension.
Synthesis: Invite students to identify what is important or most useful to pay attention to. Display the sentence frame, “The next time I arrange objects in an array, I will remember to . . . .“
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Memory
Required Materials
Materials to Gather
Connecting cubes
Required Preparation
Each group of 2 needs 60 cubes.
Launch
Groups of 2
Give each group of 2 students at least 60 connecting cubes.
Activity
7–10 minutes: partner work time
Monitor for students who relate the same number of objects in each row and column in an array to how multiplication expresses equal groups of objects.
Student Facing
Use cubes to make 6 groups of 5.
Arrange them into an array.
Explain or show how the array is related to equal groups.
Count out 20 cubes.
Arrange them into as many arrays as you can.
Explain or show how each array is related to equal groups.
Count out 24 cubes.
Arrange them into as many arrays as you can.
Explain or show how each array is related to equal groups.
Student Response
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Activity Synthesis
Have students share different arrays they made for the last problem.
“Why were you able to create different arrays with 24 objects?” (There are many ways to put 24 things into equal groups.)


correct_option_index: 33