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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

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

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Represent and solve problems involving multiplication and division.

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

Solve equations and inequalities in one variable.

Perform arithmetic operations on polynomials.

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

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Analyze patterns and relationships.

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

Work with radicals and integer exponents.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

Gain familiarity with factors and multiples.

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

Work with addition and subtraction equations.

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

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

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

Generate and analyze patterns.

Interpret the structure of expressions.

Use polynomial identities to solve problems.
problem_activity: Narrative
The purpose of this activity is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. In the activity synthesis, students share their solutions. As students share, record their drawings and solutions systematically, as shown:
1 cheese, 7 almond
2 cheese, 6 almond
3 cheese, 5 almond
4 cheese, 4 almond
5 cheese, 3 almond
6 cheese, 2 almond
7 cheese, 1 almond
Only record solutions that students find for the problem. Leave an empty space if a combination isn’t shared.
In the lesson synthesis, students discuss whether a solution of 3 dates stuffed with cheese and 5 dates stuffed with almonds is the same solution as 5 dates stuffed with cheese and 3 dates stuffed with almonds. The purpose of the question is for students to think about and discuss what decompositions of numbers mean in context (MP2, MP6). There is no correct answer to the question. Some students may determine that both solutions are the same because they both showed 5 and 3 while other students may determine that the solutions are different because there are different numbers of dates stuffed with cheese and dates stuffed with almonds (MP3).
Representation: Internalize Comprehension.
Synthesis: Reiterate the fact that in this problem there is more than one answer. Make a connection between the solutions that were found and that they all add up to the same total number of dates.
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to connecting cubes or 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
“What are we trying to figure out?” (How many of the dates were stuffed with cheese and how many of the dates were stuffed with almonds?)
30 seconds: quiet think time
1 minute: partner discussion
“Show your thinking using drawings, numbers, words, or objects.”
Activity
2 minutes: quiet work time
2 minutes: partner discussion
“Write an expression to show how many of the dates were stuffed with cheese and how many were stuffed with almonds.”
1 minute: independent work time
“As you walk around, look to see if you can find other ways to solve the story problem.”
5 minutes: gallery walk
Student Facing
Andre and his older brother have 8 dates.
They stuff some of the dates with cheese.
They stuff the rest of the dates with almonds.
How many of the dates did they stuff with cheese?
Then how many of the dates did they stuff with almonds?
Expression: _______________________________
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Student Response
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Activity Synthesis
Invite students to share their solution or solutions they found during the gallery walk. Record student solutions as explained in the activity narrative.
“What do you notice? What do you wonder?” (2 and 6 is there but not 6 and 2. When it’s 4 and 4, there are the same number of cheese dates and almond dates. The first numbers are getting bigger and the second numbers are getting smaller.)
“Are there any other ways that we can solve the problem? What makes you think that?”
Record each student solution with an equation.


correct_option_index: 9