options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
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: 2