Math / 3rd Grade / Unit 1: Rounding, Addition, and Subtraction
Students estimate quantities using rounding and develop fluency with the standard algorithm of addition and subtraction. Students focus on the precision of their calculations, and use them to solve real-world problems.
Math
Unit 1
3rd Grade
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In the first unit of 3rd grade, students will build on their understanding of the structure of the place value system from 2nd grade (MP.7) to estimate values by rounding them (3.NBT.1) and develop fluency with the standard algorithm of addition and subtraction (3.NBT.2). Throughout the unit, students attend to the precision of their calculations (MP.6) and use them to solve real-world problems (MP.4).
In 2nd grade, students developed an understanding of the structure of the base-ten system as based in repeated bundling in groups of 10. With this deepened understanding of the place value system, students "add and subtract within 1000, with composing and decomposing, and they understand and explain the reasoning of the processes they use" (NBT Progressions, p. 8). These processes and strategies include concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (2.NBT.7). As such, at the end of 2nd grade, students are able to add and subtract within 1,000 using a variety of strategies including algorithms, but are not yet fluent with them.
Because all students are not yet fluent with place value strategies, Unit 1 starts off by reinforcing some of the place value understanding that students learned in 2nd grade. Students use this sense of magnitude and the idea of benchmark numbers to first place numbers on number lines of various endpoints and intervals, and next use those number lines as a model to help them round two-digit numbers to the tens place as well as three-digit numbers to the hundreds and tens place (3.NBT.1). Next, students focus on developing their fluency with the addition and subtraction algorithms up to 1,000, making connections to the place value understandings and other models they learned in 2nd grade (3.NBT.2). Last, the unit culminates in a synthesis of all learning thus far in the unit, in which students solve one- and two-step word problems involving addition and subtraction and use rounding to assess the reasonableness of their answer (3.OA.8), connecting the NBT and OA domains. These skills are developed further and built upon in subsequent units in which students estimate and solve two-step word problems that also involve multiplication and division.
This builds toward an even deeper understanding of the place value system that students learn in 4th Grade Math. In 4th grade, students learn about multiplicative comparison, i.e., a value being x times as many as another value. Thus, students’ understanding of the place value system is more precisely refined as "a digit in one place represents ten times what it represents in the place to its right" (4.NBT.1, emphasis ours). Further, students learn to round any multi-digit number to any place. They also use the standard algorithm to solve addition and subtraction problems to the new place values they encounter at this grade level, namely, to one million. While the majority of the content learned in this unit is additional cluster content, they are deeply important skills necessary to be proficient with the major work of the grade with 3.OA.8, as well as a foundation for rounding and the standard algorithms used to any place value learned in 4th grade (4.NBT.1—4) and depended on for many grade levels after that.
Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)
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The following assessments accompany Unit 1.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Pre-Unit Student Self-Assessment
Have students complete the Mid-Unit Assessment after lesson 7.
Use the resources below to assess student understanding of the unit content and action plan for future units.
Post-Unit Assessment
Post-Unit Assessment Answer Key
Post-Unit Student Self-Assessment
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Suggestions for how to prepare to teach this unit
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
Example: Represent 342 with base ten blocks.
Standard algorithm for subtraction
Example: A grocery store sells 172 red apples and 86 green apples. How many apples did the grocery store sell?
The central mathematical concepts that students will come to understand in this unit
Terms and notation that students learn or use in the unit
algorithm
approximate/approximation
approximately equal sign, $${\approx}$$
digit
estimate/estimation
place
reasonable
round
value
To see all the vocabulary for Unit 1, view our 3rd Grade Vocabulary Glossary.
The materials, representations, and tools teachers and students will need for this unit
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
Topic A: Foundations of Place Value
Use counting, place value understanding, and addition/subtraction of ones and tens to complete a partially filled-in number grid.
3.NBT.A.1 3.NBT.A.2
Represent three-digit numbers using concrete manipulatives and drawings, including cases with more than 9 of any unit.
Locate three-digit numbers on a number line and explain their placement.
3.NBT.A.1
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Topic B: Rounding to the Nearest Ten and Hundred
Define estimation and its purpose. Round two-digit numbers to the nearest ten using a number line.
Round three-digit numbers to the nearest hundred using a number line.
Round three-digit numbers to the nearest ten using a number line.
Round multi-digit numbers to any place in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate.
Topic C: Addition and Subtraction Within 1,000
Add numbers with up to one composition within 1,000.
3.NBT.A.2
Add numbers with multiple compositions within 1,000.
Solve one-step word problems involving addition, using rounding to assess the reasonableness of answers.
3.NBT.A.1 3.NBT.A.2 3.OA.D.8
Subtract numbers with up to one decomposition within 1,000.
Subtract numbers with multiple decompositions within 1,000.
Solve one-step word problems involving subtraction, using rounding to assess the reasonableness of answers.
Solve one- and two-step word problems involving addition and subtraction, using rounding to assess the reasonableness of answers.
Key
Major Cluster
Supporting Cluster
Additional Cluster
The content standards covered in this unit
3.NBT.A.1 — Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.A.2 — Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Standards covered in previous units or grades that are important background for the current unit
2.MD.B.6 — Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.
2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
2.NBT.A.2 — Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.A.3 — Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
2.NBT.B.5 — Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
2.NBT.B.7 — Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.B.8 — Mentally add 10 or 100 to a given number 100—900, and mentally subtract 10 or 100 from a given number 100—900.
2.NBT.B.9 — Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.
2.OA.A.1 — Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Standards in future grades or units that connect to the content in this unit
4.NBT.A.3 — Use place value understanding to round multi-digit whole numbers to any place.
4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Multiplication and Division, Part 1
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