options: Generate and analyze patterns.

Perform arithmetic operations on polynomials.

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

Represent and solve problems involving multiplication and division.

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

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Multiply and divide within 100.

Create equations that describe numbers or relationships

Write expressions in equivalent forms to solve problems.

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

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

Solve systems of equations.

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

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

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

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Use polynomial identities to solve problems.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Rewrite rational expressions.

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Narrative
The purpose of this activity is for students to make sense of a questionless Put Together/Take Apart, Both Addends Unknown story problem. In this activity, students are asked to show what Lin’s apples could have looked like. The focus of this activity is for students to show the two groups of apples, rather than on answering specific questions about how many red apples and how many yellow apples Lin had. While students may notice that there is more than one possible solution to the story problem, that is not highlighted until the next lesson.
When students explain to a partner how they have represented the apples they reason abstractly and quantitatively (MP2).
MLR8 Discussion Supports.
Use multimodal examples to show the meaning of “some of” and “the rest of.” Use verbal descriptions along with gestures, drawings, or concrete objects to show the groupings.
Advances: Listening, Representing
Required Materials
Materials to Gather
Connecting cubes
Two-color counters
Launch
Groups of 2
Give students access to connecting cubes and two-color counters.
Read and display the task statement.
“Tell your partner what happened in the story.”
30 seconds: quiet think time
1 minute: partner discussion
Monitor for students who accurately retell the story. Choose at least one student to share with the class.
“Use objects or drawings to show what Lin’s apples could look like.”
Activity
3 minutes: independent work time
“Share how you showed Lin’s apples with your partner. Tell your partner how your objects or drawings show Lin’s apples.”
30 seconds: quiet think time
2 minutes: partner discussion
Monitor for students who use two-color counters to show 8 apples, some red and some yellow. Monitor for students who show different decompositions of 8, such as 5 and 3 and 4 and 4.
Student Facing
Lin picked 8 apples at the orchard.
Some of the apples were yellow.
The rest of the apples were red.
Student Response
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Activity Synthesis
Invite previously selected students to share.
As each student shares, ask:
“How many apples did Lin pick?”
“Where do you see the red apples that Lin picked?”
“Where do you see the yellow apples that Lin picked?”
“_____ used red and yellow counters to show Lin’s apples. What could I do if I wanted to draw a picture to show Lin’s apples?” (You could draw 4 red apples and 4 yellow apples. You could draw some circles. You could write r for red and y for yellow.)


correct_option_index: 20