CHAPTER 1
"How Many Wholes?"
A Math Game of Fractions: Instructions for CIRCLES
For 1-4 Players
1. Pull a domino from the bag. Don't peek! This domino shows the denominator. Return the piece to the bag.
• Note: for this game, the denominators will always be the part of the domino with the dots.
2. Spin the spinner (or roll a six sided die) to find the numerator.
3. Write the fraction you have made. Writing the fraction is an optional step, depending upon the student's ability.
• For example: You pull a domino with a blank at the top and 4 dots on the bottom. This is " /4". Spin the spinner (or roll the die) to find the numerator. You get a 6. The fraction is 6/4.
4. Show the fraction with the colored fraction pieces. Remember that "One Whole" is the purple circle. Keep track on a sheet of paper by using tally marks of How Many Wholes you have made in that turn. After each turn, return the fraction pieces to the bag.
• For the example above, take 6 of the V pieces. Put them together to make as many wholes as you can. The fraction 6/4 makes one and a half circles or one whole. The left-overs do not count towards your next whole.
5. The person with the most wholes (or who comes closest to making a whole) after three rounds, wins. If there is a tie, play a tie breaking round.
Notes:
• Variation: The left-overs DO count towards your next whole. Use them and other left-overs to make a whole but remember, the denominators MUST MATCH.
• Exploration Only: Put the fraction pieces in the bag just for students to have practice making a variety of wholes (without pulling a denominator or spinning a numerator), just free to explore the concepts of fractions to wholes using the manipulatives).
Preparing to Play
To play this game:
1. Copies of Pre-Test
2. Copies of Instructions
3. Cut out the following materials:
a. Domino Pieces (6)
b. Spinner
c. Colored Fraction Pieces (126):
• 6: Purple circles (One whole circle)
• 6: Blue circles (twelve pieces of one half of a circle)
• 6: Orange circles (eighteen pieces of one third of a circle)
• 6: Green circles (twenty-four pieces of one fourth of a circle)
• 6: Yellow circles (thirty pieces of one fifth of a circle)
• 6: Red circles (thirty-six pieces of one sixth of a circle)
4. Copies of Post-Test
Notes:
• Bags/containers for dominoes or fractions not included
• Laminate all parts for long life of the game
Enjoy-
From Leslie
A note from the Author:
Using "How Many Wholes?" in your class room will promote the following State Standards. Pre and Post Assessments are also included. A percentage of 80 will show mastery of the concepts.
State of Ohio Academic Content Standards: Math
GRADE THREE
NUMBER AND OPERATIONS — FRACTIONS
• Develop understanding of fractions as numbers.
Standard #1. 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.
Standard #3. Explain equivalence of fractions in special cases, and 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, e.g., ½ = 2/4, 4/6 = 2/3. 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 = 3/1; recognize that 6/1 = 6; locate 4/4 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.
GEOMETRY
• Reason with shapes and their attributes
Standard #2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as V of the area of the shape.
MEASUREMENT AND DATA
• Represent and interpret data
Standard #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.
GRADE FOUR
NUMBER AND OPERATIONS — FRACTIONS
• Extend understanding of fraction equivalence and ordering.
Standard #1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Standard #3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. 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. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
MEASUREMENT AND DATA
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
Standard #2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
• Represent and interpret data
Standard #4. Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
