options: Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

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

Interpret the structure of expressions.

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

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

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

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

Multiply and divide within 100.

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

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

Represent and solve problems involving 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.

Represent and solve equations and inequalities graphically.

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

Rewrite rational expressions.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Narrative
The purpose of this activity is for students to solve two-step problems without the scaffold of having the first step explicitly stated. Students solve in a way that makes sense to them and might use diagrams to help them make sense of the story. In the synthesis, the tape diagram is highlighted.
MLR7 Compare and Connect.
Synthesis: Invite group to prepare a visual display that shows the strategy they used to solve the story problems. Encourage students to include details that will help others interpret their thinking. For example, using labels, notes, diagrams, or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students, “What did the representations have in common?”, “How were they different?” and “Did anyone solve the problem the same way, but would explain it differently?”
Advances: Representing, Conversing
Launch
Groups of 2
“With a partner, choose a problem from the first activity to solve. Discuss how the diagram can help you think about the problem.”
4 minutes: partner work time
Activity
“Now you will be solving a few money problems on your own.”
“Use a diagram if it helps you make sense of the story.”
10 minutes: independent work time
Monitor for students who use a diagram to represent and solve the problem about Tyler, Andre, and Noah.
Student Facing
For each problem, show your thinking. Write your final answer using the \$. Use a diagram if it helps.
Mai has \$27, Elena has \$48, and Jada has \$16. How much money do they have altogether?
Tyler has \$45, Andre has \$36, and Noah has \$28. How much less money does Tyler have than Andre and Noah combined?
Lin has \$19. Together, Lin and Han have \$45. Then Han gets \$17 more. How much money does Han have now?
Student Response
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Advancing Student Thinking
If students want to represent the story with a diagram or equation but need support to start, consider asking:
“What is the story about? How could you break the problem into smaller parts?”
“How could you use a diagram or equation to represent the smaller parts?”
Activity Synthesis
Invite previously identified students to share the diagram for comparing Tyler's money to Andre's and Noah's money.
“How does this diagram represent the story?” (It shows Tyler's amount and then the combined amount of Andre and Noah. I can see that Tyler has less than Andre and Noah and that I need to add Andre's amount and Noah's amount and then subtract Tyler's amount from that.)


correct_option_index: 27