5.NBT.1 - About the Math, Learning Targets, and Rigor

Grade 5 Place Value and Decimals

5.NBT.1

About the Math

Full Standard

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**5th Grade Students Learning 5th Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

**4th Grade Students Learning 5th Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

Learning Targets

Explain the value of each digit as ten times the value of the digit to its right (including decimals)
Explain the value of each digit as one-tenth of the value of the digit to its left (including decimals)
Describe patterns found in place value (i.e. 70,000 is ten times 7,000; 7,000 is ten times 700; b/c 10 x 10 is 100, 70,000 must be 100 times 700; conversely 700 is 1/100 of 70,000 using the same logic).
Demonstrate place value understanding by working flexibly with numbers (i.e. what is a number between 5,000 and 5,500 with an odd number in the hundreds place, etc.)

About the Math

Our number system is the Hindu-Arabic system. This means that the digits used are 0 - 9. The position of the digit in a number defines its value.This is a base-ten system. In a base-ten system, the place value is 10 times as great as the place value immediately to its right and 1/10 as great as the place value to the immediately left. In the number 12,486 the 2 is in the thousands place and has a value of 2000. In the number 45,268, the two is in the hundreds place and has a value of 200. Numbers can be written in several ways.

Explain the value of each digit as ten times the value of the digit to its right (including decimals)

7,000 is ten times 700, which is ten times 70, which is ten times 7. This understanding must be more robust than simply adding zeroes or moving decimal points. Students should be able to represent this with models and explain the relationships.

Explain the value of each digit as one-tenth of the value of the digit to its left (including decimals)

7 is one-tenth of 70, which is one-tenth of 700, which is one-tenth of 7,000. The relationship between place values is different when we consider place values to the immediate left. Again, one can divide or remove zeroes to explain this relationship. However, students should also be able to explain this with place value models including base ten models and place value charts.

Describe patterns found in place value (i.e. 70,000 is ten times 7,000; 7,000 is ten times 700; b/c 10 x 10 is 100, 70,000 must be 100 times 700; conversely 700 is 1/100 of 70,000 using the same logic).

Students will apply this understanding in a variety of ways as their mathematics careers progress. Connections to conversions are an explicit way to connect in grade 5.

Demonstrate place value understanding by working flexibly with numbers (i.e. what is a number between 5,000 and 5,500 with an odd number in the hundreds place, etc.)

Students should understand attributes about numbers beyond simple place value. Students should represent numbers in varied ways including those listed below and should be able to decompose beyond expanded form. Students should show understanding of magnitude and how these numbers compare to real-world contexts. For example, 850 is a large number if it is the number of students in an elementary school but a small number of people if it is the size of city. Another example is considering when milliions are used to quantify something (i.e. distance in space, money, number of cells).

Standard Form: 4,582,591

Expanded Form: 4,000,000 + 500,000 + 80,000 + 2,000 + 500 + 90 +1.

Word Form: Four million, five hundred, eighty-two thousand, five-hundred-ninety-one.

Essential vocabulary for this standard includes place value, place value names ( ones, tens, hundreds, tenths, hundredths , etc), and digit.

Progression of Standard within Grade 5

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Explain the value of each digit as ten times the value of the digit to its right (including decimals) Explain the value of each digit as one-tenth of the value of the digit to its left (including decimals) Describe patterns found in place value (i.e. 70,000 is ten times 7,000; 7,000 is ten times 700; b/c 10 x 10 is 100. 70,000 must be 100 times 700; conversely 700 is 1/100 of 70,000 using the same logic).

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 4	Grade 6
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 (4.NBT.1) Decimal equivalents of fractions (n/10, n/100) (4.NF.5) Write and read decimals (4.NF.6) Compare two decimals to hundredths (4.NF.7)	Write/evaluate numerical expression with exponents (6.EE.1)

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Provide students with ten 10 x 10 grid from the resources page. In groups, students should create one model that shows 1 whole, 1 tenth, 1 hundredth, and 1 thousandth. Explain to students that the grids can be taped together but each of the place values need to be represented in a different color. Have students share their models with other groups and compare how each model represents 1 whole, 1/10, 1/100, and 1/1,000.
How is the value of 6 different in 496 and 9.64?
How are .7, 7, 70 related?
Why is 35 x 10 = 350? Draw pictures and/or use number sentences to illustrate your explanation.
Explain why 6 ÷ 10 = .6. Draw pictures and or use number sentences to illustrate your explanation.
Jesse puts 10 jellybeans on a scale and the scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Why?
How are 24 and .24 alike and different?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 8 • Decimals

Explain the Value of Digits in Relation to Adjacent Digits:

Additional Tasks

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

Kipton's Scale Links to an external site. (Illustrative Mathematics)
Tenths and Hundredths Links to an external site. (Illustrative Mathematics)
Which number is it? Links to an external site.(Illustrative Mathematics)
Millions and Billions of People Links to an external site. (Illustrative Mathematics)
Meaning of Place Value Links to an external site. (MSDE Lesson)
Every Breath You Take Links to an external site.(NCTM Illuminations, lesson)
Understand the Place Value System Links to an external site. (MSDE Full Unit)
What Can I Buy in the Newspaper Download What Can I Buy in the Newspaper
(Utah Core Academy Lesson)
Patterns R Us Links to an external site., pgs. 55-60 (Georgia Dept. Of Education)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	3-5	What Comes Next?, Activity 2.8, & Page 48 Calculator Decimal Counting, Activity 7.3, Page 187
Number SENSE	4 -6	221 - 223 'Where's the Point?'
Math In Practice Teaching Fifth-Grade Mathematics	5	Module 1

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Place Value Memory Download Place Value Memory
(HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Assessment

Learning Targets

rubric

Explain the value of each digit as ten times the value of the digit to its right (including decimals)
Explain the value of each digit as one-tenth of the value of the digit to its left (including decimals)
Describe patterns found in place value (i.e. 70,000 is ten times more than 7,000; 7,000 is ten times more than 700; b/c 10 x 10 is 100, 70,000 must be 100 times more than 700; conversely 700 is 1/100 of 70,000 using the same logic).

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.