In this unit, students will further their understanding of the relationship between the values of the digits within a number. Students will understand that when they multiply or divide a number with a decimal by the power of 10, the digits shift place values. This unit deepens students’ understanding of reading and writing decimals, now including thousandths. Later work in the baseten system relies on the meaning and properties of operations as well as comparing decimals.
Key Concepts:
 In numbers, digits represent \({1 \over 10}\) of what they represent in the place to the left.
 When the place value extends to thousandths, the structure does not change.
 Multiplying a number by a given power of 10 shifts the position of its digits that many places to the left, and dividing a number by a power 10 shifts the position of its digits that many places to the right.
Prior Knowledge Needed:
 Recognize that in a multidigit whole number, a digit in a given place represents ten times as much as the digit in the place to its right. (Grade 4, Unit 4; 4.NBT.A.1)
 Use decimal notation for fractions with denominators 10 or 100. (Grade 4, Unit 4; 4.NBT.C.6 )
Units on the Horizon:
 Compare and round decimals (Grade 5, Unit 6: 5.NBT.A.3b, 5.NBT.A.4)
Lessons

Lesson objective: Understand that in numbers, digits represent 1/10 of what they represent in the place to the left. Students bring prior knowledge of the relationship between the digits within a multidigit number from 4.NBT.A.1 (that each place value ...

Lesson objective: Compare the values of digits in numbers. This lesson helps to build procedural skill with comparing the values of digits in numbers. Base ten blocks are used here because they allow for concrete representation of the concept. This work...

Lesson objective: Compare digit values by using their understanding of place value. This lesson provides an opportunity for students to apply their knowledge and understanding of the idea that the value of a digit in a given place is onetenth as much a...

Lesson objective: Understand that when the place value extends to thousandths, the structure does not change. Students bring prior knowledge of decimal notation from 4.NBT.C.6. This prior knowledge is extended to represent decimals to the thousandths in...

Lesson objective: Write decimal numbers in expanded form to compare the value of the digits. This lesson helps to build procedural skill with expanded form of a decimal number using decimals and fractions. The place value chart is used here because it v...

Lesson objective: Write decimal numbers in expanded notation, representing each digit’s value as a product of the digit itself and a decimal or fraction. This lesson helps to build procedural skill with expanded notation of a decimal number using decima...

Lesson objective: Solve place value problems by understanding the structure of place value does not change even when extended to the thousandths. This lesson provides an opportunity for students to apply their knowledge and understanding of thousandths ...

Lesson objective: Understand that multiplying a number by 10 or a power of ten shifts the position of a value's digits to the left. Students bring prior knowledge of relationship between the digits within a number from 5.NBT.A.1. This prior knowledge is...

Lesson objective: Multiply a value by 10 or a power of ten to shift the position of that value's digits to the left. This lesson helps to build procedural skill with multiplying a value by the powers of 10. Place value chart is used here because it high...

Lesson objective: Apply the knowledge of the pattern when multiplying a value by 10: When you multiply a number by 10, the digits of the number shift one place value to the left. When you multiply a value by a power of ten, the exponent indicates how ma...