## Common Core State Standards for Mathematics

Grade(s) 5 resources related to the following standard:
Number and Operations—Fractions
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5. Interpret multiplication as scaling (resizing), by:
1. 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.
2. 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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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
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
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
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
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
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+