Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. (Major Cluster)Archived

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

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.

Type: Educational Game

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Students are asked to compare two pairs of decimals in the context of word problems and to record a comparison using an inequality symbol.

Type: Formative Assessment

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.

Type: Formative Assessment

Students are asked to consider two grids with different sized wholes and determine if both models show four-tenths.

Type: Formative Assessment

Students are asked to compare four pairs of decimals using the less than, greater than, or equal to symbols.

Type: Formative Assessment

Students are asked to use benchmark decimals to place four fractions on a number line.

Type: Formative Assessment

Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions.

Type: Formative Assessment

Students are given four fractions and asked to write each in decimal form.

Type: Formative Assessment

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.

Type: Formative Assessment

Students are asked to use benchmark fractions to place four decimals on a number line.

Type: Formative Assessment

Students are given four decimals and asked to write each as a fraction.

Type: Formative Assessment

This is a Model Eliciting Activity (MEA) activity which requires the students to convert fractions to decimals, order the decimals, and then design a process for ranking the classrooms from quantitative and qualitative data and then re-test their procedure on a new set of data. Ultimately, the students have to write a letter explaining and supporting the step-by-step process they used.

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.

Type: Lesson Plan

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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers, fractions, decimals and percent by using different mathematical operations. The students will be asked to assist an ice cream shop owner, who is planning a promotional program "Flavor of the Month," to rank the ice cream flavors based on the data provided. Students will need to read a data table, rank the flavors, convert the fraction amount to a percent and decimal and per serving costs to a decimal as well. A twist is added to the problem when one of the flavors is too expensive to make because of seasonal availability but two new flavors are added to be calculated. An additional twist is given by adding an adult survey to the second data table. The students will need to recalculate the new percent and decimals for the additional flavors.

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.

Type: Lesson Plan

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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Students will help Amazing Alice Cookies choose the perfect chocolate chip brand to use for their cookies. Students will be given data in the form of fractions and decimals. Fourth grade students will compare decimals and order and compare fractions. Students will write a letter describing their procedure to the client.

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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).

Type: Lesson Plan

Students will correctly model and discover fractions and their decimal equivalents through the use of decimal grids and base ten blocks.

Type: Lesson Plan

This lesson is a practice lesson for student’s knowledge on connecting decimals, money and fractions. 

Type: Lesson Plan

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

Type: Lesson Plan

In this open-ended real world problem, 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 need to find like denominators, make decisions based on a data table, and write a letter to the school providing evidence for their decisions. Students will need to trade off between the cost of the equipment, its safety rating and student opinions.

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

Type: Original Student 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.

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

The purpose of this task is adding fractions with a focus on tenths and hundredths. 

Type: Problem-Solving Task

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

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.

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

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.

Type: Problem-Solving Task

The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .

Type: Tutorial

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

Type: Tutorial

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

In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams.

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

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.

Type: Virtual Manipulative