options: Rewrite rational expressions.

Create equations that describe numbers or relationships

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

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

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

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

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

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

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving multiplication and division.

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

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

Add and subtract within 20.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Work with radicals and integer exponents.

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

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

Interpret the structure of expressions.
problem_activity: Narrative
The purpose of this activity is for students to learn about
prime numbers
and
composite numbers
. Students are given a set of cards with rectangles on them. They sort the rectangles by area and then attempt to draw an additional rectangle for each category. They notice that some areas can be represented by more than one rectangle and some areas can only be represented by one rectangle.
During the synthesis, highlight that the side lengths of each rectangle represent one factor pair (each pair of side lengths should be used only once), and that the area of each rectangle represents a multiple of each side length. Students learn that a number with only one factor pair—1 and the number itself—is a prime number, and a number with more than one factor pair is a composite number.
Here is an image of the cards for reference.
[IMG]
MLR8 Discussion Supports
. Invite students to take turns selecting a rectangle, and explaining how they should sort it to their partner. Display the following sentence frames: “This rectangle belongs with _____ , because . . .” Encourage students to challenge each other when they disagree.
Advances: Conversing, Representing
Engagement: Develop Effort and Persistence.
Chunk this task into manageable parts to support organizational skills in problem solving. Some students may benefit from explicit guidance for how to begin. For example, before sorting, students can find the area of each rectangle.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Organization
Required Materials
Materials to Gather
Grid paper
Inch tiles
Materials to Copy
Card Sort: Area
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Give each group a set of cards from the blackline master.
“Sort the cards into categories in any way that makes sense to you.”
2 minutes: partner work time
Ask students to share ways in which they sorted.
Activity
“If you did not already, sort the rectangles by their area.”
3–5 minutes: partner work time
Ask students to check their work with another group to make sure the cards in each category match.
“Now, create at least one rectangle to add to each category in your card sort.”
3–5 minutes: partner work time
Observe the rectangles students add to each category. Monitor for students who notice that no new rectangles could be drawn for the area of 7 square units.
Student Facing
Your teacher will give you a set of cards to sort.
Sort the cards by area. Record your sorting results. Be prepared to explain your choices.
For each group of sorted cards, think of at least one more rectangle. Name its length and width. Be prepared to explain your reasoning.
[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
Select 2–3 students to share the rectangles they added to each category.
“Why were you able to create more rectangles for some areas and not others?” (Some of the numbers had more factor pairs. For some numbers, there was only one possible factor pair.)
Revoice student reasoning. “Only one rectangle can be made for the area of 7. Numbers like this are called
prime numbers
. Prime numbers have only one factor pair: 1 and itself.”
“Numbers like 15 that have more than one factor pair are called
composite numbers
.”
“What other composite numbers did you work with? How do you know they are composite?” (Twenty-four is a composite number because I can make 2 rows of 12 or 4 rows of 6. Eighteen is composite because it has factor pairs of 2 and 9 and 3 and 6.)


correct_option_index: 25