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Generated on 9/16/2025 at 10:23 PM |
https://www.cpalms.org/PreviewIdea/Preview/1462
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.
This cluster includes the following benchmarks.
Visit the specific benchmark webpage to find related instructional resources.
- MAFS.4.NF.3.5 : Express a fraction with denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two fractions with
respective denominators 10 and 100. For example, express 3/10 as
30/100, and add 3/10 + 4/100 = 34/100.
- MAFS.4.NF.3.6 : Use decimal notation for fractions with denominators 10 or 100. For
example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate
0.62 on a number line diagram.
- MAFS.4.NF.3.7 : Compare two decimals to hundredths by reasoning about their size.
Recognize that comparisons are valid only when the two decimals
refer to the same whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions, e.g., by using a visual
model.
This cluster includes the following Access Points.
- MAFS.4.NF.3.AP.5a : Find the equivalent fraction with denominators that are multiples of 10.
- MAFS.4.NF.3.AP.6a : Identify the equivalent decimal form for a benchmark fraction.
- MAFS.4.NF.3.AP.6b : Match a fraction (with a denominator of 10 or 100) with its decimal equivalent (5/10 = 0.5).
- MAFS.4.NF.3.AP.6c : Read, write, or select decimals to the tenths place.
- MAFS.4.NF.3.AP.6d : Read, write, or select decimals to the hundredths place.
- MAFS.4.NF.3.AP.7a : Use =, <, or > to compare two decimals (decimals in multiples of .10).
- MAFS.4.NF.3.AP.7b : Compare two decimals expressed to the tenths place with a value of less than 1 using a visual model.
- MAFS.4.NF.3.AP.7c : Compare two decimals expressed to the hundredths place with a value of less than 1 using a visual model.
Vetted resources educators can use to teach the concepts and skills in this topic.
- Fractions at the Fair: Equivalent Tenths and Hundredths: Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.
- Return to Deciland: Locating Decimals on a Number Line: 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.
- Deci Land Escape: 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.
- Fraction Quiz: 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.
- Decimal and Fraction: This interactive Flash applet has students match fractions with their equivalent one- or two-place decimals. Students have a chance to correct errors until all matches are made.
- Using Models to Compare Decimals: Students are asked to compare decimals by drawing a visual model and record the comparison using the less than, greater than, or equal to symbol.
- Tenths and Hundredths: Students are asked if an equation involving the sum of two fractions is true or false. Then students are asked to find the sum of two fractions.
- Comparing Decimals in Context: Students are asked to compare two pairs of decimals in the context of word problems and to record a comparison using an inequality symbol.
- Adding Five Tenths: Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.
- Comparing Four Tenths: Students are asked to consider two grids with different sized wholes and determine if both models show four-tenths.
- Compare Decimals: Students are asked to compare four pairs of decimals using the less than, greater than, or equal to symbols.
- Using Benchmark Decimals on a Number Line: Students are asked to use benchmark decimals to place four fractions on a number line.
- Hundredths and Tenths: Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions.
- Fractions to Decimals: Students are given four fractions and asked to write each in decimal form.
- Seven Tenths: Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.
- Using Benchmark Fractions on a Number Line: Students are asked to use benchmark fractions to place four decimals on a number line.
- Decimals to Fractions: Students are given four decimals and asked to write each as a fraction.
- Cookies, Fractions and Decimals, Oh My!: 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
- Donuts and Decimals: 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
- Supermarket Sweep!: In this lesson, students will use a grocery store ad to select items for purchase, working within the constraint of making their purchases with a $50 gift card. After their initial plan, they have some emergency expenses that change the amount of the gift card unexpectedly, and they must alter their list and re-compute how much money would remain on their gift card after their planned purchases are made.
- Cell Phone Inquiry: Students will determine what cell phone would be the best phone for their teacher to purchase for science class. Factors to consider are price, touch screen, camera, voice command, weight and display size. Students will need to compare decimals to determine how to order and rank the phone brands.
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.
- Wondrous Water Parks: 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.
- Comparing and Ordering Decimals: In this cooperative learning activity, students will have five sets of decimal cards to sort and put in order - least to greatest. The lesson starts with a short whole group activity and then breaks off in to structured groups. The teacher is free to interact with each of the groups and monitor progress, participation, and understanding.
- Cookies and Treats: 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.
- Equivalency Detectives: Fractions and Decimals!: This is a lesson intended to reinforce students' ability to find equivalent fractions and decimals. The lesson requires prior essential vocabulary knowledge, and a basic understanding of converting fractions to decimals and decimals to fractions (tenths and hundredths).
- Fractions Undercover!: Students will correctly model and discover fractions and their decimal equivalents through the use of decimal grids and base ten blocks.
- Dynamic Decimals, Fractions and Money!: This lesson is a practice lesson for student’s knowledge on connecting decimals, money and fractions.
- Happy Hundredths (Lesson 2 of 2): In this lesson, students will work with math manipulatives to understand that it takes 100 hundredths of something to make one whole. They will use manipulatives with money (pennies and dollars), fractions (one hundredth pieces and one whole pieces), and base ten blocks (units and wholes) to show different values. They will express values with combinations of the given manipulatives and draw their solutions.
This lesson 2 of 2 in a unit on fraction and decimal concepts
- Playground Picks: In this Model Eliciting Activity, MEA, students will work in groups to determine a procedure for ranking playground equipment to help a school purchase new equipment for their playground. Students will compare fractions with like and unlike denominators and numerators, make decisions based on information given in a data table, and write a letter to the school providing evidence for their decisions.
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
- Terrific Tenths (Lesson 1 of 2): Students will work with math manipulatives to understand that it takes 10 tenths to make one whole. They will use manipulatives with money (dimes), fractions (one tenth pieces), and base ten blocks (rods) to show different values. They will use decimal notation to record these tenths.
This is lesson one in a two part lesson unit. Lesson two (HAPPY HUNDREDTHS) deals with hundredths.
- Adding Tenths and Hundredths: The purpose of this task is adding fractions with a focus on tenths and hundredths.
- How Many Tenths and Hundredths?: 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.
- Fraction Equivalence: Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.
- Expanded Fractions and Decimals: 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.
- Dimes and Pennies: The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.
- Using Place Value: Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.
- Adding Two Fractions with Denominators 10 and 100: The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .
- Comparing Two Decimals with a Visual Model: In this Khan Academy tutorial video two decimals are compared using grid diagrams.
- Decimals as Words: In this Khan Academy video decimals are written and spoken in words.
- Decimals and Fractions from Grid and Number-Line Representations: The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.
- Grid Representations of Decimals: The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.
- Visually Converting from Tenths to Hundredths: In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams.
- Introduction to Decimals: 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.
- Fraction Models: An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.