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Georgia Standards of Excellence Frameworks
GSE Third Grade
Unit 5: Representing and Comparing Fractions
TABLE OF CONTENTS
Standards for Mathematical Practice 3
Content Standards 4
Big Ideas 5
Essential Questions 6
Concepts & Skills to Maintain 7
Strategies for Teaching and Learning 7
Selected Terms and Symbols 8
· Exploring Fractions 13
· Candy Crush 18
· Comparing Fractions 23
· Strategies For Comparing Fractions 28
· Cupcake Party 33
· Using Fraction Strips to Explore the Number Line 40
· I Like to Move It! Move It!! 45
· Pattern Blocks Revisited-Exploring Fractions Further with Pattern Blocks 51
· Party Tray 56
· Make a Hexagon Game 64
· Pizzas Made to Order 69
· Graphing Fractions 74
· Inch by Inch 78
· Measuring to ½ and ¼ Inch 81
· Trash Can Basketball 87
· The Fraction Story Game 91
***Please note that all changes made to the standards will appear in red bold type. Additional changes will appear in green.
In this unit, students will:
· Develop an understanding of fractions, beginning with unit fractions.
· View fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole.
· Understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one.
· Solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
· Recognize that the numerator is the top number (term) of a fraction and that it represents the number of equal-sized parts of a set or whole; recognize that the denominator is the bottom number (term) of a fraction and that it represents the total number of equal-sized parts or the total number of objects of the set
· Explain the concept that the larger the denominator, the smaller the size of the piece
· Compare common fractions with like denominators and tell why one fraction is greater than, less than, or equal to the other
· Represent halves, thirds, fourths, sixths, and eighths using various fraction models.
STANDARDS FOR MATHEMATICAL PRACTICE (SMP)
This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.
Students are expected to:
1. Make sense of problems and persevere in solving them. Students make sense of problems involving fractions.
2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning by connecting fraction models of shapes with the written form of fractions.
3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding fractions by creating or drawing fractional models to prove answers.
4. Model with mathematics. Students use fraction strips to find equivalent fractions.
5. Use appropriate tools strategically. Students use tiles and drawings to solve the value of a fraction of a set.
6. Attend to precision. Students use vocabulary such as numerator, denominator, and fractions with increasing precision to discuss their reasoning.
7. Look for and make use of structure. Students compare unit fraction models with various denominators to reason that as the denominator increases, the size of the unit fraction decreases.
8. Look for and express regularity in repeated reasoning. Students will manipulate tiles to find the value of a fraction of a set. This will lead to the relationship between fractions and division.
***Mathematical Practices 1 and 6 should be evident in EVERY lesson***
Develop understanding of fractions as numbers
MGSE3.NF.1 Understand a fraction as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction as the quantity formed by a parts of size . For example, means there are three parts, so = + + .
MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size . Recognize that a unit fraction is located whole unit from 0 on the number line.
b. Represent a non-unit fraction on a number line diagram by marking off a lengths of (unit fractions) from 0. Recognize that the resulting interval has size and that its endpoint locates the non-unit fraction on the number line.
MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, e.g., . Explain why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = (3 wholes is equal to six halves); recognize that = 3; locate and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning
about their size. Recognize that comparisons are valid only when the two fractions refer
to the same whole. Record the results of comparisons with the symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model
MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
MGSE3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview.
In first grade and second grades, students discuss partitioning and equal shares. Students will have partitioned circles and rectangles into two, three, and four equal shares. This is the first time students are understanding/representing fractions through the use of a number line, and developing deep understanding of fractional parts, sizes, and relationships between fractions. This is a foundational building block of fractions, which will be extended in future grades. Students should have ample experiences using the words, halves, thirds, fourths, and quarters, and the phrases half of, third of, fourth of, and quarter of. Students should also work with the idea of the whole, which is composed of two halves, four fourths or four quarters, etc.
How can you and a friend share equally (partition) this piece of paper so that you both have the same amount of paper to paint a picture?
· Fractional parts are equal shares of a whole or a whole set.
· The more equal sized pieces that form a whole, the smaller the pieces of the whole become.
· When the numerator and denominator are the same number, the fraction equals one whole.
· When the wholes are the same size, the smaller the denominator, the larger the pieces.
· The fraction name (half, third, etc) indicates the number of equal parts in the whole.
· How are fractions used in problem-solving situations?
· How can I compare fractions?
· What are the important features of a unit fraction?
· What relationships can I discover about fractions?
CONCEPTS/SKILLS TO MAINTAIN
Third-grade students will have prior knowledge/experience related to the concepts and skills identified in this unit.
· In first grade, students are expected to partition circles and rectangles into two or four equal shares, and use the words, halves, half of, a fourth of, and quarter of.
· In second grade, students are expected to partition circles and rectangles into two, three, or four equal shares, and use the words, halves, thirds, half of, a third of, fourth of, quarter of.
· Students should also understand that decomposing into more equal shares equals smaller shares, and that equal shares of identical wholes need not have the same shape.