# Place Value, Rounding, Addition, and Subtraction

Students learn to compare numbers, round to any place value, work towards fluency with the standard algorithms for adding and subtracting, and solve multi-step word problems involving addition and subtraction.

## Unit Summary

In the first unit for Grade 4, students extend their work with whole numbers and use this generalized understanding of the place value system in the context of comparing numbers, rounding them, and adding and subtracting them.

Students understanding of the base ten system begins as early as Kindergarten, when students learn to decompose teen numbers as ten ones and some ones (K.NBT.1). This understanding continues to develop in Grade 1, when students learn that ten is a unit and therefore decompose teen numbers into one ten (as opposed to ten ones) and some ones and learn that the decade numbers can be referred to as some tens (1.NBT.1). Students also start to compare two-digit numbers (1.NBT.2) and add and subtract within 100 based on place value (1.NBT.3—5). In second grade, students generalize the place value system even further, understanding one hundred as a unit (2.NBT.1) and comparing, adding, and subtracting numbers within 1,000 (2.NBT.2—9). In Grade 3, place value (NBT)  standards are additional cluster content, but they still spend time fluently adding and subtracting within 1,000 and rounding three-digit numbers to the nearest 10 and 100 (3.NBT.1—2).

Thus, because students did not focus heavily on place value in Grade 3, Unit 1 begins with where things left off in Grade 2 of understanding numbers within 1,000. Students get a sense of the magnitude of each place value by visually representing the place values they are already familiar with and building from there. Once students have a visual and conceptual sense of the “ten times greater” property, they are able to articulate why a digit in any place represents 10 times as much as it represents in the place to its right (4.NBT.1). Next, students write multi-digit numbers in various forms and compare them (4.NBT.2). Comparison leads directly into rounding, where Grade 4 students learn to round to any place value (4.NBT.3). Next, students use the standard algorithms for addition and subtraction with multi-digit numbers (4.NBT.4) and apply their algorithmic knowledge to solve word problems. The unit culminates with multi-step word problems involving addition and subtraction, using a letter to represent the unknown quantity, then using rounding to assess the reasonableness of their answer (4.OA.3), allowing for students to connect content across different clusters and domains (4.NBT.A, 4.NBT.B, and 4.OA.B).

Throughout the unit, students will repeatedly look for and make use of structure, specifically the structure of the place value system (MP.7). Students develop an understanding that a digit in any place represents 10 times as much as it represents in the place to its right, then apply that understanding of structure to compare, round, and add and subtract multi-digit whole numbers.

In subsequent grade levels, students generalize their base ten understanding to decimals. While students do some work with tenths and hundredths later on in Grade 4 (4.NF.5—7), students in Grade 5 are able to extend the decimal system to many more place values, seeing that a digit represents $\frac{1}{10}$ of what it represents in the place to its left (5.NBT.1—3). Students subsequently round, compare, and operate on decimals as they did with numbers greater than one in Grade 4. Thus, this unit sets a precedent for a deep understanding of the number system that supports much of their mathematical knowledge later this year and in years to come.

Pacing: 22 instructional days (19 lessons, 2 flex days, 1 assessment day)

## Assessment

This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.

### Fishtank Plus

#### Expanded Assessment Package

Learn how to use these tools with our Guide to Assessments

## Unit Prep

### Essential Understandings

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• Our place value system is structured such that a digit in any place represents 10 times as much as it represents in the place to its right.
• “To read numerals between 1,000 and 1,000,000, students need to understand the role of commas. Each sequence of three digits made by commas is read as hundreds, tens, and ones, followed by the name of the appropriate base-thousand unit (thousand, million, billion, trillion, etc.)” (NBT Progression, p. 13).
• Comparing numbers written in standard form uses the understanding that 1 of any unit is greater than any amount of a smaller unit. Thus, the largest place values in each number contains the most relevant information when comparing numbers. If both numbers have the same number of largest units, the next largest place value should be attended to next, iteratively until one digit is larger than another in the same unit.
• The rounding process is based on knowing the number halfway between multiples of 10, 100, and so on. Rounding is a process for finding the multiple of 10, 100, etc., closest to a given number.
• The standard algorithm for addition and subtraction is based in the idea of needing to add like-units together, and regrouping them when those units exceed 10.
• Rounding numbers can help one to determine whether an answer is reasonable, based on whether the estimate is close to the computed answer or not.
• Making sense of problems and persevering to solve them is an important practice when solving word problems. Key words do not always indicate the correct operation.

### Vocabulary

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 ten thousand hundred thousand million

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### Intellectual Prep

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#### Intellectual Prep for All Units

• Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan.
• Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind.
• Take the unit assessment.

## Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

### Core Standards

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##### Number and Operations in Base Ten
• 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

• 4.NBT.A.2 — Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

• 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.

##### Operations and Algebraic Thinking
• 4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.

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• 2.MD.B.6

• 2.NBT.A.1

• 2.NBT.A.2

• 2.NBT.A.3

• 2.NBT.A.4

• 3.NBT.A.1

• 3.NBT.A.2

• 3.NBT.A.3

• 3.OA.D.8

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• 5.NBT.A.1

• 5.NBT.A.2

• 5.NBT.A.3

• 5.NBT.A.4

• 5.NBT.B.6

• 5.NBT.B.7

### Standards for Mathematical Practice

• 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.