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Standard 1 : Understand the place value of multi-digit numbers with decimals to the thousandths place.
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MA.5.NSO.1.1 : Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.
  • MA.5.NSO.1.2 : Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form.
  • MA.5.NSO.1.3 : Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.
  • MA.5.NSO.1.4 : Plot, order and compare multi-digit numbers with decimals up to the thousandths.
  • MA.5.NSO.1.5 : Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number.
Cluster Information
Number:
MA.5.NSO.1
Title:
Understand the place value of multi-digit numbers with decimals to the thousandths place.
Type:
Standard
Subject:
Mathematics (B.E.S.T.)
Grade:
5
Strand
Number Sense and Operations
Cluster Access Points

This cluster includes the following Access Points.

  • MA.5.NSO.1.AP.1 : Explore how the value of a digit in a multi-digit number with decimals to the hundredths changes if the digit moves one place to the left. Multi-digit numbers not to exceed 9.99.
  • MA.5.NSO.1.AP.2 : Read and generate multi-digit numbers with decimals to the hundredths using standard form and expanded form. Multi-digit numbers not to exceed 9.99.
  • MA.5.NSO.1.AP.3 : Compose and decompose multi-digit numbers with decimals to the hundredths. Demonstrate each composition or decomposition with objects, drawings, expressions or equations. Multi-digit numbers not to exceed 9.99.
  • MA.5.NSO.1.AP.4 : Plot, order and compare multi-digit numbers with decimals up to the hundredths. Multi-digit numbers not to exceed 9.99.
  • MA.5.NSO.1.AP.5 : 5 Round multi-digit numbers with decimals to the tenths to the nearest whole number (e.g., 1.7 rounds to 2); and numbers with decimals to the hundredths to the nearest tenth (e.g., 2.36 rounds to 2.4). Multi-digit numbers not to exceed 9.99.
Cluster Resources

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

Original Student Tutorials
  • 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.

  • 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 Game
  • 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
  • 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.

  • 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.

  • 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.

  • 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
  • Blessings in a Bag!!: In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities.  Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money.  Additionally, they will be asked to compare multi-digit numbers to the thousandths.

  • To Oregon by Wagon: Students work in teams to plan the contents of a covered wagon for a family relocating from Missouri to Oregon. Students must calculate the weight and cost of the wagon by adding, subtracting, and multiplying with decimals.

  • Beach on a Budget: In this Model Eliciting Activity, MEA, students work in teams to determine which store the client should use to buy beach equipment for a new beach rental business, after considering quality, replacement efficiency, and estimating the total price. 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. 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

  • 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: In this Model Eliciting Activity, MEA, the students' will determine the best canteen for an outdoor hiking company.

    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

  • 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?: In this Model Eliciting Activity, MEA, students help a 5th grader to decide which cell phone she will ask for as a 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.

  • Building a Better Baseball Team: In this Model Eliciting Activity, MEA, students will be comparing fractions and comparing decimal numbers 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.

  • 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.

  • 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.

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