Standard 1 : Understand the place value system. (Major Cluster) (Archived)



This document was generated on CPALMS - www.cpalms.org


Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information

Number: MAFS.5.NBT.1
Title: Understand the place value system. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 5
Domain-Subdomain: Number and Operations in Base Ten

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.5.NBT.1.1:

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.


MAFS.5.NBT.1.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
MAFS.5.NBT.1.3: Read, write, and compare decimals to thousandths.
  1. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
  2. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
MAFS.5.NBT.1.4: Use place value understanding to round decimals to any place.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.5.NBT.1.AP.3a: Read, write, or select a decimal to the hundredths place.
MAFS.5.NBT.1.AP.3b: Compare two decimals to the hundredths place, whose values are less than 1.
MAFS.5.NBT.1.AP.4a: Round decimals to the next whole number.
MAFS.5.NBT.1.AP.4b: Round decimals to the tenths place.
MAFS.5.NBT.1.AP.4c: Round decimals to the hundredths place.
MAFS.5.NBT.1.AP.1a: Compare the value of a number when it is represented in different place values of two three-digit numbers.
MAFS.5.NBT.1.AP.2a: Identify what an exponent represents (e.g., 10³= 10X10X10).
MAFS.5.NBT.1.AP.2b: Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorials

Name Description
Rounding Race:

Explore rounding decimals through the thousandths place as you help Tyrese the Turtle train to race the hare in this interactive tutorial.

Fishing for Decimals: Comparing Decimals:

Help out at the fishing tournament while comparing decimals through the thousandths place in this interactive tutorial.

Base Ten and Exponents:

Explore base 10 and exponents in this baseball-themed, interactive tutorial. 

Cracking the Decimal Code:

By the end of this tutorial, you will be able to read and write decimals to the thousandths using base-ten numerals, number names, and expanded form.

Educational Games

Name Description
Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Formative Assessments

Name Description
Decimals in Expanded Form:

Students are asked to write numbers involving decimals in both standard form (as base ten numerals) and expanded form.

Comparing Decimals:

In the context of two word problems students are asked to compare decimals using the less than, equal to, and greater than symbols.

Decimals in Number Name:

Students are asked to write the number name (word form) of a number when given the base-ten numeral (standard form).

Decimals in Word and Expanded Form:

Students compare pairs of decimals, one in word form to one in expanded form.

Rounding To The Nearest Whole Number:

Students are given four numbers and asked to round each to the nearest whole number and to explain their reasoning.

Rounding To The Thousandths Place:

Students are given four numbers and asked to round each to the nearest thousandth and to explain their reasoning.

 

Note: Three of the numbers are decimals to the ten-thousandths place and one number is to the hundred-thousandths place. If students are not ready for rounding larger decimals to the thousandths place, use an alternate MFAS task that rounds to the hundredths, tenths, or whole number.

Rounding To The Tenths Place:

Students are given four numbers and asked to round each to the nearest tenth and to explain their reasoning.

Shopping for Produce:

Students are asked to round numbers given in a context to the nearest hundredth.

 

Note: The decimals students are rounding in this task extend past the thousandths place. If students are not ready for rounding larger decimals to the hundredths place, use an alternate MFAS task that rounds to the hundredths, tenths, or whole number.

Writing and Reading Decimals:

Students are read aloud four numbers and are asked to write the numbers using decimal notation. Then students are shown a number containing a decimal and asked to read it aloud.

Using Whole Number Exponents:

Students are asked to explain what 10 to the third power means and to rewrite 1,000,000 and a product of 10 using exponents.

The Error:

Students are asked to analyze a problem in which a decimal number is multiplied by 10 to determine which of two answers is correct and discuss what happens when a decimal is divided by 10.

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

How Many Zeros?:

Students are asked to determine how many zeros are in the expansion of 10 to the sixth power.

The Odometer:

Given an odometer reading, students are asked to discuss the value of each digit and explain how a digit in one place represents 10 times as much as the same digit to its right, and one-tenth as much as the same digit to its left.

Dylan’s Baseball Card Collection:

Students are asked to find Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. of 500 and are assessed on the use of their knowledge of the base-ten number system.

Five-Tenths:

Students are asked to consider how much larger five is than five-tenths.

Walking to School:

Students are presented with two decimals in the context of a distance word problem and asked to tell how many times longer one distance is than the other.

Lesson Plans

Name Description
Just Right Goldilocks’ Café: Temperature:

This is lesson 1 of 3 in the Just Right Goldilocks’ Café unit. This lesson focuses on systematic investigation on getting a cup of coffee to be the “just right” temperature. Students will use temperature probes and code using ScratchX during their investigation.

 

Rounding Decimal Numbers - Lesson #3:

This is the final lesson in the Rounding Decimal Numbers Unit and will bring together the mathematical concepts in lesson 1 and 2. This lesson then bridges the computer science coding and mathematical thought process together as students dissect code that rounds decimal numbers as well as building their own code to make rounding an automated process.

Rounding Decimal Numbers - Lesson #1:

This is lesson 1 of 3 in the Rounding Decimal Numbers unit. This lesson connects decimal place value names with exponential powers of ten. Through the inquiry based lesson, students will discover that there is a mathematical pattern they can use when performing multiplication and division using the powers of ten on a multi-digit decimal number.

Rounding Decimal Numbers - Lesson #2:

This is lesson 2 of 3 in the Rounding Decimal Numbers unit. This lesson introduces Traditional Rounding method to determine an estimated value rounded to a specific place value. This lesson bridges the concepts of fractions to decimals and powers of ten as well expanded notation to rounding methods.

This lesson uses flowchart model to describe the method in which the rounding is performed. Rounded numbers are verified using a Scratch activity in this lesson.

The Coasta with the Mosta:

Students will create an exciting and thrilling roller coaster model. Students will use their knowledge of forces to build a model of a roller coaster using foam insulation and a marble.

What happens when you multiply by powers of 10?:

This lesson shows patterns when multiplying a whole number by powers of 10 through a hands-on conceptual approach that then leads into the procedure of multiplying numbers by a power of 10 and writing exponents using the base of 10.

This is intended to be an introductory lesson to the powers of ten in an exponent form. The concepts in this lesson will be a precursor to evaluating expressions using exponents and eventually scientific notation.

Wire We All Wet?:

A fire caused by faulty wiring set off a sprinkler system, which damaged a school. The school must be remodeled and the electrical wiring must be replaced. Students will decide which materials to use to as conductors and which to use as insulators in the new wiring.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Beach on a Budget:

Topic Overview:This 5th grade MEA asks students to work in teams to determine from which store they will buy beach equipment for a new beach rental business, after considering several criteria. After the students have created a proposal based on given data, a twist is added which may vary their results.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Solar Cooking:

This is a 5th grade MEA designed to have students compare different types of solar cookers based on temperature, cook time, dimensions, weight, and customer reviews.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Camping Supply Innovators MEA:

Help CSI determine the best canteen model to use by applying an understanding of comparing decimals.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Where's Your Place In the Kingdom of Decimals?:

This lesson has activities to review place value to the thousandths place. The teacher creates a kingdom of decimals in the classroom and opposing knights duel with their digits while reviewing the meaning of place value.

Which Cell Phone for Mia?:

This engaging MEA requires students to help a 5th grade student decide which cell phone she will ask her parents for as her birthday present. Students must use a chart to analyze information and make conclusions based upon their own ranking system within their cooperative group. They then must write a letter to the student justifying their conclusions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Understanding Place Value:

This lesson is designed to help students understand the 10 to 1 relationship among place value positions and the mathematical patterns when calculating place value.

Currency Craze!:

If I travel to Italy, can I buy a raspberry gelato with a $5.00 bill? Students will understand that other countries use currencies different from the United States, and that when visiting those countries, exchange rates are used to determine the value of the United States dollar (USD). This lesson integrates Mathematics with Social Studies as the students apply their knowledge of decimals and basic operations with their passports for a real-world application.

"Shift the Place, Shift the Value" - Understanding Adjacent Places in the Base-ten System:

In this lesson students will be challenged to discover the relationship between values of adjacent places in the base-ten system. After an introduction to the concept by the teacher, pairs of students will play a place value game with digit cards, then they will individually complete a written summative assessment.

X-treme Roller Coasters:

This MEA asks students to assist Ms. Joy Ride who is creating a virtual TV series about extreme roller coasters. They work together to determine which roller coaster is most extreme and should be featured in the first episode. Students are presented with research of five extreme roller coasters and they must use their math skills to convert units of measurements while learning about force and motion.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Which Sweets for the Bakery?:

This MEA gives students the opportunity to use real world data to rank proposed product lines from most likely to be profitable to least likely to be profitable. There are two sequential tasks; the second task adds a component of complexity to the original task. Students will apply multiplication and division skills in problem solving, write a procedure with grade-appropriate organization and conventions, and participate in group collaboration to complete this task.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

The Dazzling Painting Co.:

ResourceID: 49826

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Building a Better Baseball Team:

In this MEA activity, students will be comparing and contrasting whole and decimal numbers in order to recruit a baseball player(s).

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Estimating Decimal Products:

In this lesson, students will learn to estimate decimal products using different strategies to arrive at compatible numbers. They will learn that estimates will vary depending on the strategy chosen and that the closer the compatible numbers are to the actual factors, the closer the estimate will be to the exact answer. Students will also learn that estimation is used to solve problems that don't require exact answers and to check exact answers for reasonableness.

Seeking Patterns Using Base 10 and Powers of 10:

This lesson focuses on the exploration of patterns in the number of zeros of the product, when multiplying a number by powers of 10. It also uses whole-number exponents to denote powers of 10.

Patterns divided by a power of ten should be done in a subsequent lesson, once the students have the basic understanding of multiplying base ten by exponents.

Patterns using decimals should be done in a subsequent lesson, once the students have the basic understanding using whole numbers.

Intro to Multiplying Decimals by 10, 100, 1000:

In this lesson, students are introduced to multiplying decimals by 10, 100, and 1000, in which students begin by creatively solving word problems. Students will analyze the number sentences used to solve the word problems, looking for and recording patterns and discovering that each place value has a value ten times as much as the place to its right, which is why each time a number is multiplied by 10, the digits move one place to the left.

Getting Dry:

This MEA asks the students to compare hand drying products based on: initial cost, replacement cost and absorbency. Students will provide the "top choice" to the principal of the school and explain how they arrived at the solution. In the twist, students will be asked to consider the environmental impact of the products and reevaluate their conclusions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Decimals Have a Point!:

This 5E lesson provides a framework for students to manipulate and understand the relationships between decimal place values through the thousandths. Students will have the opportunity to work with a concrete model that they will then use in a pictorial representation. This lesson is designed to be spread over 2, 45-minute sessions.

Batting a Thousand(th):

This 5E lesson emphasizes the framework created in the lesson "Decimals Have a Point!" (ID: 30766) in which students learned to manipulate and understand the relationships between decimal place values through the thousandths. Students will have the opportunity to reference the pictorial model (see attached) to compare two decimals up to thousandths. This lesson is designed to be done in a 60 minute block.

Secret Number-Place Value Game:

Students will be able to use decimals through the thousandths place to name numbers between whole numbers through the use of number generators and critically thinking about where to place numbers on a place value chart.

Tacking on Decimals:

This lesson involves writing, reading and comparing decimals. It is a review of place value, and a Swat game at the end for skills practice.

The 20 Second Game:

This is a game students will love to play to improve their understanding of estimating decimal products and increase speed when finding these estimations. The game can be modified to practice estimating products of whole numbers, quotients of whole numbers, and quotients of decimals.

Vending Machine Snacks:

In this MEA, students are challenged to choose the snacks that will be in a vending machine in a school. Students will need to multiply and divide whole numbers and decimal numbers as well as compare fractions and decimal numbers. Students will work in groups to solve the problem and write a letter to the client explaining their thinking.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Perspectives Video: Teaching Idea

Name Description
Precision of Measurement:

Classroom activities that teach students precision of measurement.

Tutorials

Name Description
Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.  

Powers of 10: Patterns:

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, exponent and base, are introduced.

Comparing Two Decimals with a Visual Model:

In this Khan Academy tutorial video two decimals are compared using grid diagrams.

Comparing Two Decimals to Thousandths:

This Khan Academy tutorial video presents using place-value to compare two decimals expressed to thousandths.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Title Description
Rounding Race:

Explore rounding decimals through the thousandths place as you help Tyrese the Turtle train to race the hare in this interactive tutorial.

Fishing for Decimals: Comparing Decimals:

Help out at the fishing tournament while comparing decimals through the thousandths place in this interactive tutorial.

Base Ten and Exponents:

Explore base 10 and exponents in this baseball-themed, interactive tutorial. 

Cracking the Decimal Code:

By the end of this tutorial, you will be able to read and write decimals to the thousandths using base-ten numerals, number names, and expanded form.

Educational Games

Title Description
Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Tutorials

Title Description
Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.  

Powers of 10: Patterns:

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, exponent and base, are introduced.

Comparing Two Decimals with a Visual Model:

In this Khan Academy tutorial video two decimals are compared using grid diagrams.

Comparing Two Decimals to Thousandths:

This Khan Academy tutorial video presents using place-value to compare two decimals expressed to thousandths.