NCTM Principles and Standards. Fractions Meanings and Operations. Florida Standards. Developing Fraction Concepts and Number Sense.

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1 Fractions Meanings and Operations NCTM Principles and Standards What NCTM Content Strand includes Fractions? Grades PreK Number and Operation Understand and represent commonly used fractions, such as 1/, 1/, and 1/. NCTM Grades 5 Number and Operations Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers. Use models, benchmarks, and equivalent forms to judge the size of fractions. Recognize and generate equivalent forms of commonly used fractions, decimals, and percents. Explore numbers less than 0 by extending the number line and through familiar applications. Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students experience. Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals. Fraction Woes Florida Standards Florida Sunshine State Standards Florida Teacher Certification Examinations (FTCE) Elementary Education K 6 Competencies and Skills 0Education%0K6.pdf Developing Fraction Concepts and Number Sense Initial work with fractions should begin with natural activities children experience, ex. sharing. Represent fractions using words, a variety of models, diagrams and symbols and make connections among various representations. Manipulative models should be used throughout the middle years. Give other names for numbers and justify the procedures used to generate equivalent forms.

2 Vocabulary Vocabulary Fraction is derived from a Latin word meaning to break. A fraction is a number that expresses part of a group. a Fractions are written in the form b or a/b, where a and b are whole numbers, and the number b is not 0. We define a fraction bar to be a horizontal line that separates the numerator from the denominator. Some writers use the term vinculum for the horizontal fraction bar. Fibonacci used the Latin word virga for the horizontal fraction bar. The number a is called the numerator. The number b is called the denominator. The diagonal fraction bar (also called a solidus or virgule) was introduced because the horizontal fraction bar was difficult typographically, requiring three terraces of type. The numerator counts the parts and the denominator tells what sized parts are being counted. Fraction Representations Developing the Meaning of Half Fractions Models Region Model Cutting in half means that we show two parts that are the same amount. The Region Model should be learned before the model of the Parts of a Set The parts are the same size. The whole can be a region (an object to be shared or an area to be divided) When a figure has been cut in half, each part is half the shape. Story: Give Me Half by Stuart Murphy Equality of parts Early fraction work identifies fractional parts as all being congruent. Remember fractions do not have to be congruent to be the same part of the whole. Regular geometric regions are good fraction models Manipulative: Fraction Circles (textbook circles)

3 Part of a Set Model Measurement Model In fractional parts of a set, the whole becomes a given number of objects rather than a region. Any unit of length can be partitioned into fractional parts How many? is a whole number answer. Manipulatives Points on a number line Tape Ribbon Strips of Paper Fractions Bars Cuisenaire Rods How much? and What part? have fraction number answers. M & Ms Activity 0.html Each part must be equal in length Area Model A special case of the Region Model The parts must be equal in area, but not necessarily congruent. Fraction Fantasy Activity NCTM Navigating Through Geometry in Grades 5 pages Fraction Fantasy Activity Area Model Do the following models meet the criteria? Why or why not? Fraction Fantasy Activity Area Model Cut a model for the fraction one half from a 6 paper square in such a way that two congruent pieces result. Use another paper square and create a different model for one half that is not congruent to the model you created in the previous cut. Continue to cut out as many additional representations for one half as you can that are not congruent to any you have already created. Share the models you created to represent one half with your neighbor. Ratio Interpretation A fraction such as can also represent a ratio, which means that two elements of one set are present for every three elements of another set. The order of the words in the final question set the order or position of the numbers. What is the ratio of circles to squares?

4 Quotient Interpretation Fractions denote division of one set by the other. A fraction such as also represents division. Equivalent Fractions Equivalent Fractions are different fractions which name the same amount. Examples: The fractions are all equivalent fractions. We can test if two fractions are equivalent by cross multiplying their numerators and denominators. This is also called taking the cross product. Ordering Fractions Compare by representing fractions concretely and pictorially before symbolically. Relative Size of Fractions Improper Fractions Mixed Numbers Understanding Equivalent Fractions fractions can be expressed in different ways Equivalentequal value Multiplication Grid Renaming fractions Developing Fraction Computation Before beginning fraction computation students must: Understand fraction concepts Be able to compare fractions Develop number sense about fractions Recognize equivalence Understand the meaning of operations on whole numbers The multiplication table can also help show equivalent fractions. Fraction Addition Add + Add the numerators and keep the common denominator. Combine the two grey halves to make one whole. Adding Fraction an Alternate Method + 5 Cross multiply x 5 10 Cross multiply x 1 Add Multiply x 5 15 Answer: 15

5 Picture Pie Activity Picture Pie Activity This fish was created using two squares. Each square is folded along the diagonal to create a triangle. The triangle is folded in half, then in half again. Each square has 8 triangular regions. Cut the triangles out and create the fish. This fish uses 1 triangles. When compared to the original squares this fish represents Fraction Subtraction You have out of parts and take away one of the three parts. How many do you have left? Create a bird as shown by Ed Emberley using a half circle, a quarter of a circle, and two eighths of a circle Create additional fractional designs. You may choose to use a triangle, square or rectangle to create your designs. Fraction Multiplication X Draw two congruent rectangles and show each fraction. 1 Then draw a third rectangle congruent to the others and shade and of the rectangle as shown. When you subtract again you need common denominators. Then subtract the numerators and keep the common denominator. The part where the shading intersects shows the answer. Division of Fractions Partitive Division Steve had 6 apples. He decided to eat the same number of apples every day for days. How many apples did he eat each day? tells the number of groups (or parts) that are being made. Measurement Division Steve had 6 apples. He decided to eat apples every day. How many days could he eat apples? tells the size (or measure) of the equal groups that are being made. Fraction Games I Have, Who Has? Fraction Line Up That s One Whole Number A Zero Balance Spin a Fraction Fraction War Fraction Match Fraction Interaction Fraction Fracas Fraction Fixation Snappo

6 Fraction Stories Fraction Fun by David Adler Pizza Counting by Christina Dobson Piece Part Portion by Scott Gifford Fraction Action by Loreen Leedy Gator Pie by Louise Mathews Skittles Riddles Math by Barbara McGrath How Many Ways Can You Cut a Pie? by Jane Moncure Give Me Half by Stuart Murphy The Hershey s Milk Chocolate Fractions Book by Jerry Pallotta Apple Fractions by Jerry Pallotta Resources Fraction Bars Virtual Manipulative Visual Fractions Fraction Lessons NCTM Fun with Fractions Units interactive.html