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Clarifications
Clarification 1: Instruction emphasizes conceptual understanding through the use of manipulatives visual models, number lines or equations.Clarification 2: Instruction includes the understanding that a decimal and fraction that are equivalent represent the same point on the number line and that fractions with denominators of 10 or powers of 10 may be called decimal fractions.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- NA
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to connect fractions to decimals. Students extend their understanding of fraction equivalence (MA.3.FR.2.2) to include decimal fractions with denominators of 10 or 100. The connection will continued in grade 6 (MA.6.NSO.3.5) and completed in grade 7 (MA.7.NSO.1.2).- Instruction should help students understand that decimals are another way to write fractions. The place value system developed for whole numbers extends to fractional parts represented as decimals. The concept of one whole used in fractions is extended to models of decimals. It is important that students make connections between fractions and decimals in models.
- Instruction should provide visual fraction models of tenths and hundredths, number lines, and equations so that students can express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
- Students reinforce understanding that the names for decimals match their fraction equivalents (e.g., seven tenths, 7 tenths, 0.7, , seventy hundredths, 70 hundredths, 0.70 and are all equivalent).
- This benchmark is a connection point to the metric system and will be explored in MA.4.M.1.2.
Common Misconceptions or Errors
- Students often confuse decimals such as 6 tenths and 6 hundredths. Students should use models and explain their reasoning to develop their understanding of the connections between fractions and decimals.
- Some students may not understand that fractions and decimals are different presentations of the same thing. Number lines and other visual models will help students gain a better understanding of this concept.
Strategies to Support Tiered Instruction
- Instruction includes building fractions and their decimal equivalents using base ten blocks.
- For example, students build “two-tenths” and “twenty hundredths” with base ten blocks while using vocabulary that will help students see the decimal connection as well. Students realize that the numbers have the same value.
Instructional Tasks
Instructional Task 1 (MTR.6.1)
Read the following numbers and use the benchmark fractions to place them on the number line.- a. 0.8
- b. 0.32
- c. 0.6
- d. 0.17
Instructional Items
Instructional Item 1
A value is shown.- a. 0.25
- b. 2.05
- c. 2.5
- d. 25.100
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Educational Games
Formative Assessments
Lesson Plans
Original Student Tutorials
Problem-Solving Tasks
Tutorials
STEM Lessons - Model Eliciting Activity
Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies. Students will use multiplication and division of whole numbers to plan for how many packages to order.
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.
This lesson asks students to recommend which cookie the owners of The Cookie Jar should add to their menu. Before they make their decision, the students have to convert decimal notation and fractions with denominators 10 and 100 to fractions with like denominators. Then they will be able to see exactly how many people voted for each cookie and they can factor in that information along with additional cookie facts to make their final recommendation.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this MEA, students will convert fractions into decimals and then compare the decimals to decide which donut a donut shop should add to their menu.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.
MFAS Formative Assessments
Students are asked to use benchmark decimals to place four fractions on a number line.
Students are asked to use benchmark fractions to place four decimals on a number line.
Original Student Tutorials Mathematics - Grades K-5
Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.
Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.
Student Resources
Original Student Tutorials
Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.
Type: Original Student Tutorial
Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.
Type: Original Student Tutorial
Educational Games
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!
Type: Educational Game
Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.
Type: Educational Game
Problem-Solving Tasks
The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.
Type: Problem-Solving Task
The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.
Type: Problem-Solving Task
The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.
Type: Problem-Solving Task
Tutorials
In this Khan Academy video decimals are written and spoken in words.
Type: Tutorial
The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.
Type: Tutorial
The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.
Type: Tutorial
This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.
Type: Problem-Solving Task
The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.
Type: Problem-Solving Task
The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.
Type: Problem-Solving Task
Tutorial
This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.
Type: Tutorial
