Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals.

The resources here offer support in explaining the concepts underpinning addition and subtraction of fractions and decimals — the concepts of equivalent fractions and decimal place values. The resources also include demonstrations of addition and subtraction and opportunities for practice. Whenever possible, we selected sites that visually or interactively engage the learner.

We begin with resources emphasizing fractions. Please scroll down the page to find decimal resources.

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Fractions

Visual Fractions http://www.visualfractions.com/

An exceptional tutorial on fractions, including step-by-step, illustrated explanations of addition and subtraction. Both circle and line models help students visualize the operations with like and unlike denominators. Interactive problems allow students to use these visual models as they figure the numerical answers. MSP full record

Equivalent fractions finder http://www.shodor.org/interactivate/activities/EquivFractionFinder/

To add or subtract fractions with unlike denominators, students must thoroughly understand how to find equivalent fractions. Here users are shown a fraction displayed in an area model and on a number line. They must visually represent two unique fractions that are equivalent to the given fraction. The fractional value is shown on a number line after the students check to see if their fraction is correct. MSP full record

Adding Fractions http://nlvm.usu.edu/en/nav/frames_asid_106_g_3_t_1.html

Students must do the usual exercise of finding equivalent fractions with common denominators, but here the fractions are represented visually as portions of a square. Once the computer checks that the fractions are correct, the students can drag the representations into a third box and enter the sum of the fractions. This is a learning experience! There are other activities on fractions as well, all worth checking out. (From National Library of Virtual Manipulatives — MSP full record)

The Fractionator http://syzygy.virtualave.net/webwork/OL_Text/tfractionator.htm

Created by math teacher Jeff LeMieux, the Fractionator offers online and offline tools to help students understand fractions. The online tools use unit squares to model two fractions to be added (or subtracted) and then create equivalent fraction models; with this visual aid, students complete the operation. They can request a new problem for each exercise or enter the two fractions themselves. Also provided are links to printable materials, such as overhead transparencies and student worksheets. MSP full record

Who Wants Pizza? A Fun Way to Learn about Fractions http://math.rice.edu/~lanius/fractions/index.html

Here are six lessons on the definition of a fraction, equivalent fractions, addition of fractions, and multiplication of fractions. Although too brief for a first introduction to fractions, the lessons can engage students in review or in extra practice. Students can respond online to get immediate feedback, or they can work the examples on grid paper. (From Mathematics Lessons that are Fun! Fun! Fun! — MSP full record)

Soccer Shootout http://www.funbrain.com/fractop/index.html

Practice time! Students can practice the addition and subtraction of fractions at levels of difficulty ranging from Easy to Super Brain. Students play against the computer and are provided with a full solution when a wrong answer is entered. MSP full record

Decimals

Builder Ted http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html

This interactive game deals with place value in decimals, necessary to understanding addition and subtraction. In the game scenario, students help Builder Ted by placing numbered bricks on a ladder in numerical order. At the first level of difficulty, all numbers are positive, but the two higher levels include negative numbers as well. If a number is placed incorrectly, all the bricks immediately fall and the player begins again. Tips for students are available as well as an explanation of the key ideas underlying the game. MSP full record

Place Value http://www.mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm

Here is another exercise preliminary to decimal addition and subtraction. The user can type in any number, such as 3601.076, or let the computer choose a number. As the student passes the mouse over each digit in the number, the place value is shown. Also, how to say the number is given, plus a short exercise asking the student to identify the digit in, say, the thousandth position. (From Math FROG — MSP full record)

Base blocks decimals http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html

With this virtual manipulative, students can explore the meaning of place value and grouping as they add and subtract decimals. Base blocks consist of individual "units," "longs," "flats," and "blocks" (ten of each set for base 10). The blocks can represent negative as well as positive numbers with one to four decimal places and in five different bases. Students exchange and group the blocks as needed to solve the problem. Problems can be presented to or created by the students. All material is available in Spanish and French as well as English, including instructions for using the manipulative, information about bases and place value, and suggested questions for classroom use. MSP full record

Decimals http://www.aaamath.com/dec.html

This site offers bare-bones explanations of decimal topics and interactive practice. In the long list of topics are adding and subtracting decimals as well as adding and subtracting money. The computer sets the problem and gives immediate feedback to the student’s response. The bottom of each lesson page contains timed exercises. MSP full record

NCTM. (2006). Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author

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Copyright March 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.