Visual Fractions can be relevant in a variety of classroom settings. Kids can cycle through the explanations, do drills, or play games, then print report cards to show what they’ve accomplished. You can also introduce the whole class to the next concept using pre-made slides that cover each new fraction topic step by step. Accompanying printable worksheets (with separate answer keys) can be homework assignments. Small groups can use the design fractions tool to make word problems and represent their solutions with visuals. Or you could use any of these tools on an interactive whiteboard for whole-class or small-group demonstrations.Continue reading Show less
Visual Fractions is a website that offers a thorough introduction and review of all things fraction-related, including line and circle diagrams as well as interactive games to demonstrate identifying, renaming, comparing, and adding, subtracting, multiplying, and dividing with fractions. You can do drills (e.g., determine what fraction of a number line is shaded) or produce fraction demonstrations (e.g., create a circle diagram to represent 3/5 + 2/7). After playing games or completing drills, students can generate a report card that shows how many and what percentage of problems they got correct.Continue reading Show less
A now-retired math teacher created Visual Fractions in accordance with his philosophy that “fractions are better understood when seen.” Indeed, the visual models he presents have great potential for helping any student who's having trouble conceptualizing what 7/9 means or how to multiply mixed numbers. For each step in a student’s relationship with fractions, there are clear explanations and visual demonstrations (mostly using line and/or circle diagrams) to make the concept tangible.
Primitive but clever games drive the point home. They range from simple -- such as “Find Grampy,” who's hiding behind a hedge (aka, where is he on the number line?) -- to exploring the relationship between fractions and decimals by weighing animals in different combinations, to dabbling in ancient Egyptian payment methods to figure out how to divide three barley cakes evenly among five laborers. Visual Fractions is pretty bare bones and could benefit from a major design update, but it's well-organized and easy for teachers to navigate (kids new to fractions may need more guidance to find what they need on the site). It also lacks a sophisticated tracking system that could follow student learning as they progress through the site or adapt problems to address individual students’ areas of difficulty.Continue reading Show less
Key Standards Supported
Number And Operations—Fractions
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.