options: Represent and solve equations and inequalities graphically.

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

Gain familiarity with factors and multiples.

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

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Analyze patterns and relationships.

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

Rewrite rational expressions.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

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

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

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

Interpret the structure of expressions.

Add and subtract within 20.

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

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

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

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

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Generate and analyze patterns.
problem_activity: Narrative
In this activity, students analyze three different ways to subtract. They see that taking away is one way to find the difference, but that you can also count on or use known addition facts. Students further solidify their understanding that addition and subtraction are related, which sets the groundwork for a later activity when students solve subtraction problems within 10.
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.
Activity
Read the task statement.
“First you will work on your own. Think about what each student means and be ready to explain your thinking in a way that others will understand.”
5 minutes: independent work time
4 minutes: partner discussion
Monitor for students who can use the 10-frame with six red counters to explain the relationship between
\(10 - 6\)
and
\(6 + \boxed{\phantom3} = 10\)
.
Student Facing
Mai, Diego, and Noah find the value of
\(10 - 6\)
.
Diego says, “I can take away.”
[IMG]
What does Diego mean?
Be ready to explain your thinking in a way that others will understand.
Mai says, “I can count on.”
[IMG]
What does Mai mean?
Be ready to explain your thinking in a way that others will understand.
Noah says, “I can use what I know about
\(6 + 4\)
to help me.”
What does Noah mean?
Be ready to explain your thinking in a way that others will understand.
Student Response
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Activity Synthesis
Invite previously identified students to share.
“Who can restate what _____ just showed us?” (Diego subtracted by taking away 6 counters one at a time and saw that there were 4 counters left. Mai subtracted by thinking about addition. She counted on from 6 until she got to 10 and noticed she counted up 4. Noah knows his sums of 10. He knows 10 can be made by 6 and 4, so
\(10 - 6 = 4\)
.)
“Which method do you like best?” (I know my sums to 10 so I would use that. I like counting on because I like to add more than take away.)


correct_option_index: 19

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