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

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.

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.

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

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

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.

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.

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

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

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.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Narrative
The purpose of this activity is to use the standard algorithm to add multi-digit numbers, taking care to compose a new unit and record it accurately. They also analyze common errors and critique the given reasoning when composing a new unit (MP3).
Required Materials
Materials to Gather
Grid paper
Launch
Groups of 2
“Complete the first 2 problem and then talk to your partner about any patterns you notice.”
Activity
3 minutes: independent work time
2 minutes: partner discussion
Share and record responses.
If needed, use the expanded form to help students make connections between the way composing a larger unit is recorded when using the standard algorithm and what is happening in each place. In the bottom line of the example here, we see 10 in the ones place and 100 in the tens place. Both partial sums do not match the assigned values of their places.
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3–4 minutes: independent work time for the last problem.
Student Facing
Find the value of each sum.
a
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b
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c
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d
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Use the expanded form of both 8,299 and 1,111 to check the value you found for the last sum.
Each computation shown has at least one error. Find the errors and show the correct calculation.
a
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b
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c
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d
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Student Response
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Advancing Student Thinking
Students may need support identifying errors in the last problem. Consider asking: “How might subtraction be used to help identify the error?”
Activity Synthesis
Ask students to share the errors they identified in the last set of questions.
“What are some common errors when adding large numbers?”


correct_option_index: 8