August 19, 2009

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This resource guide provides links to exemplary resources and insight on how to teach mathematics and science concepts at the middle school level. The guides provide information on the needed content knowledge, science and mathematical pedagogical knowledge, exemplary lessons and activities, career information, and correlations to national mathematics and science standards.

- Mathematics > General

- Grade 3
- Grade 4
- Grade 5

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September 16, 2009

This resource received a 3* rating because it is part of the larger resource, Math Focal Points: Grade 5, which received a rating of 3-Exemplary in the Curriki Review System. You can learn more about this larger resource by reading its review and comments.

Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with standard procedures for adding and subtracting fractions and decimals. They make reasonable estimates of fraction and decimal sums and differences. Students add and subtract fractions and decimals to solve problems, including problems involving measurement (NCTM, 2006, p.17).

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.

**Fractions**

Visual Fractions 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.

Equivalent fractions finder 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.

Adding Fractions 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.

The Fractionator 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.

Who Wants Pizza? A Fun Way to Learn about Fractions 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.

Soccer Shootout 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.

**Decimals**

Builder Ted 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.

Place Value 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.

Base blocks decimals 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.

Decimals 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.

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