Number and Operations—Fractions

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

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Resource | Resource Type Grade Level | Rating |
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This webpage for math students and their teachers offers a searchable archive of questions and answers about fractions and decimals at the elementary level. Equivalent fractions, common denominators, all four operations, fraction and decimal conversions, and other topics are included. | Community Grade Level: 3, 4, 5 | |

This Technology Problem of the Week (tPoW) challenges students to pop a balloon by exercising their command of fractions and estimation visually. The Java simulation shows a two-dimensional balloon and presents its original diameter; prompts you for a scaling fraction; and calculates the scaled diameter. The goal: to scale the balloon up (inflate) or down (deflate) so that it fits through a gap while still remaining wide enough to pop on two nails set just slightly narrower apart than the width of the gap. Scale up too much, and the balloon will fail to pass through the gap all together; scale down too much, and although the balloon will pass through the gap, it will fail to pop on the nails. Solve and explain your solution; download hints and answer checks. Also available in Spanish. Free registration is required. | Experiment/Lab Activity, Game, Interactive Media Grade Level: 5, 6+ | |

This tutorial provides students with experience using three types of distance scales on regional maps of North America. An introduction shows how to make use of the bar scale, the statement of equivalence, and the representative fraction (ratio) to determine distance between two locations. Printable instructions and two sets of interactive exercises are provided. | Activity, Interactive Media, Tutorial Grade Level: 5, 6+ | |

This FAQ page from the Teacher2Teacher service at The Math Forum @ Drexel contains many suggestions for learning about fractions. It includes ideas contributed by T2T Associates and teacher participants. There are links to Ask Dr. Math resources, children's literature connections, and outside websites with related resources. | Instructional Strategy, Reference Materials, Community Grade Level: 3, 4, 5, 6+ | |

This interactive applet provides a visual model of fraction multiplication using rectangular arrays. The applet offers both a demonstration/exploration mode ("show me") and a practice mode ("test me") in which students arrange the rectangle to display a given multiplication problem. Teaching ideas and applet instructions are available through the links at the top of the page. | Activity Grade Level: 4, 5, 6+ | |

The authors of this website have identified 8 common misconceptions that lead to errors in mathematics (and promise to add more as time permits). Topics include: Rounding Numbers, Multiplication can Increase or Decrease a Number, Multiplying Decimals, Decimals and their Equivalent Fractions, Dividing Whole Numbers by Fractions, Adding with Negative Numbers, Calculations with Negative Numbers, and Calculations with Hundreds and Thousands. Each misconception is described in a pdf document which explains how the misconception arises, the rationale for the correct concept, and exercises aimed at reinforcing the correction. | Problem Set, Tutorial Grade Level: 4, 5, 6+ | |

Students use these virtual fraction bars to model fractional addition, subtraction, multiplication (of fractions by whole numbers), and division on a number line. Students can create bars in positive or negative fractional lengths; align, stack, or remove bars; and change the number line marks in increments between 1/2 and 1/15. Applet instructions and teaching ideas are included in the links at the top of the page. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This problem, based on the story of Goldilocks and the Three Bears, provides a context for children to apply ratio and proportion concepts as well as fraction computation skills. Using the given size relationships among the bears, solvers determine the sizes of various objects in the bears' house. The Teachers' Notes page offers suggestions for implementation, key questions, ideas for extension and support, a printable pdf of the problem, and links to related problems. | Activity Grade Level: 4, 5, 6+ | |

Twenty-eight lesson plans make up this research-based fourth- through sixth-grade fraction and decimal curriculum, covering through addition and subtraction of decimals, and multiplication and division of fractions. It includes a teacher guide with theoretical framework and instructions and templates for making manipulatives, as well as suggestions for using the lessons with English-language learners (ELL). The Rational Number Project is an NSF-funded multi-university research project. | Lesson Plans Grade Level: 4, 5, 6+ | |

This collection of lessons, interactive Flash exercises and teacher utilities supports the learning of fraction concepts using side-by-side symbolic and pictorial representations. The lessons cover identifying, comparing, renaming and operating with fractions using circle and number line models. The Fraction Maker feature allows a teacher to create visual models to illustrate those same topics with fractions chosen by the user. The site includes student games and worksheets as well as suggestions and resources for the teacher. | Activity, Game, Interactive Media, Tutorial Grade Level: 3, 4, 5, 6+ |