In this unit, students will identify that a digit has value due to its position in a number. Students will compose and decompose whole numbers to identify the value of each position. In addition, students will estimate to a given place value by rounding and will compare numbers using place value. Students will identify that the same number can be composed in multiple ways, and that changing the way a number is expressed does not change the numbers’ value. Students apply their understanding of place value and the properties of addition and subtraction to the standard algorithms for both operations as they work toward fluency by the end of the school year. Students will add and subtract within 1,000,000. Strategies such as decomposing numbers and partial sum are acceptable methods, but students are expected to be fluent with the standard algorithms by the end of the year school year, with an understanding of why and how the algorithms work.
Key Concepts:
 Digits in numbers represent ten times what they represent in the place to the right.
 The same quantity can be named and represented in multiple ways, and changing representations or names does not change a number's value.
 We can use our understanding of place value to round numbers.
 A real number is either equal to, less than, or greater than another real number. We can compare numbers using place value, and record comparisons using <, >, and =.
 The meaning of addition does not change depending on how we perform it. The meaning of subtraction does not change depending on how we perform it.
Prior Knowledge Needed:
 Use place value understanding to round whole numbers to the nearest 10 or 100; 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; Use parentheses to signify grouping and ungrouping; (Grade 3, Unit 3; 3.NBT.A.1, 3.NBT.A.2)
 Multiply onedigit whole numbers by multiples of 10 in the range 1090 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations; (Grade 3, Unit 8; 3. NBT.A.3)
Units on the Horizon:
 Solve measurement problems using the four operations (Grade 4, Unit 8)
 Problem solving with whole numbers (Grade 4, Unit 14)
 Expanding understanding of place value to decimals (Grade 5, Unit 4)
Lessons

Lesson objective: Understand that a number multiplied by ten will result in a product that is ten times the value of the original number. Students bring prior knowledge of fluently adding and subtracting within 1,000 using strategies based on place valu...

Lesson objective: Compare the values of a digits and fluently multiply by 10. This lesson helps to build fluency with place value. Students may use Base 10 blocks, digit cards and/or a place value chart as these materials highlight the visual representa...

Lesson objective: Understand that numbers can be represented in various ways and still be equivalent. Students bring prior knowledge of using parentheses to signify grouping and ungrouping Grade 3 (3.NBT.1). This prior knowledge is extended to include d...

Lesson objective: Represent numbers in expanded notation, base ten numerals, number names, and base 10 representation. This lesson helps to build fluency in recognizing and writing different representations of the same number. This work develops student...

Lesson objective: Understand that numbers have different values when rounded to different places. Students bring prior knowledge of rounding whole numbers to the nearest 10 or 100 from Grade 3 (3.NBT.A1). This prior knowledge is extended rounding number...

Lesson objective: Round whole numbers to multiple places. This lesson helps to build fluency with rounding. A number line is used because it offers a visual and establishes benchmark numbers and midpoint within a range of numbers based on place value. T...

Lesson objective: Apply rounding to approximate a total. This lesson provides an opportunity for students to apply their knowledge and understanding of rounding to a reallife situation. Students are asked to round three numbers and add the results to g...

Lesson objective: Extend understanding of comparing numbers using symbols to indicate comparison betwen numbers (greater than, less than, and equal to). Students bring prior knowledge of comparing numbers using place value to the hundreds from grade 3 (...

Lesson objective: Use place value to compare the value of a multidigit number to another multidigit number. This lesson helps to build fluency with comparing numbers using place value. A comparison place value chart is used here because it highlights ...

Lesson objective: Understand the role of place value in the standard algorithm for addition. Students bring prior knowledge of addition strategies from 3.NBT.A.2. This prior knowledge is extended to addition of whole numbers within 1,000,000 as students...

Lesson objective: Fluently add multidigit whole numbers using the standard algorithm. This lesson helps to build procedural skill with the standard algorithm for addition. The vertical arrangement of addends is used here because it supports the concept...

Lesson objective: Understand the role of place value in the standard algorithm for subtraction. Students bring prior knowledge of subtraction strategies from 3.NBT.A.2. This prior knowledge is extended to subtraction of whole numbers within 1,000,000 as...

Lesson objective: Fluently subtract multidigit whole numbers using the standard algorithm. This lesson helps to build procedural skill with the standard algorithm for subtraction. Baseten blocks and place value charts are used here because they illust...

Lesson objective: Determine whether addition or subtraction is required to solve a word problem. Then apply the standard algorithms. This lesson provides an opportunity for students to apply their knowledge and understanding of the standard algorithms f...