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Mathematics Grade 6
Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (6.RP) Standard 6.RP.3
These games and activities help students investigate the relationship between fractions and decimals, focusing on equivalence.
Students should use models and other strategies to represent and study decimal numbers. Fractions and decimals both represent parts of a whole, and both can represent numbers greater than one. Learners need to investigate the relationship between fractions and decimals, focusing on equivalence. Any fraction can be rewritten as an equivalent decimal and any decimal can be rewritten as an equivalent fraction. Help them understand that a fraction such as 1⁄2 is equivalent to 5/10 and that is has a decimal representation of (0.5). After developing and understanding of equivalent fraction and decimal forms, students need to recall fluently the decimal equivalents for common fractions such as 1⁄4= 0.25, 1⁄2= 0.5 and 3⁄4= 0.75. For other fractions divide the numerator by the denominator. It is important for students to understand the traditional algorithm, but also be able to use a calculator to convert fractions to decimals. In addition, students can examine that some fractions are terminating decimals and others are not.
Decimals are part of our every day life. We see them in the amount of rainfall in weather reports, sports statistics (e.g. batting averages), and stock market reports. It is important to connect fractions to decimals by numerous conceptual experiences, rather than just memorizing the algorithm.
1. Develop a positive learning attitude toward mathematics.
6. Represent mathematical ideas in a variety of ways.
Invitation to Learn
Ask students if they have ever created new words by taking a word and rearranging its letters. Explain that they are going to do a similar activity only using numbers. Have the students cut three index cards in half the wide way. Then, have students label the card as follows: 7, 5, 4, 0, and a decimal point. Tell the students you are going to ask them to make numbers that will fit a specific rule. Remind students that each number and the decimal must be used for each problem. Have students work in small groups and discuss their findings and discoveries. Start giving rules such as: Build a number that is greater than 750, Build a number that is less than 5, Build a number that is between 70 and 70.5, etc.
Part One: Rolling For One
Play the game with the class using the following rules:
Part Two: Get the Hint?
The rules of the game are as follows:
a. Partner A will choose a secret number between 1-100.
b. Partner B will try to figure out what partner As secret number is by guessing a number.
c. Partner A will take partner Bs guess and divide it by the secret number.
d. Partner A records the decimal on the Record Sheet.
e. Partner B finds the decimal point and draws a box around the 3 numbers on the right side. Then, determines the approximate percentage of the decimal.
f. With your new information, make another guess.
g. Try to guess the secret number in less than 5 guesses.
Part Three: The Tile Company
1. Students need to determine the fraction, percent, and decimal form of each The Tile Center tiles.
2. Determine the cost of each tile.
3. Make a recommendation about which of existing tiles should continue to be manufactured (provide profit) and which should be eliminated and why.
4. Create six unique grid patterns that will make the company money. State the cost of each tile and the fraction, decimal, and percent shaded for each tile.
5. Finally suggest a new price that would make the tile company at least $0.05 profit per tile.
6. Write a one page letter to the President discussing #2, #3, #4, and #5.
Curriculum Extensions/Adaptations/ Integration
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA.
Teaching and learning mathematics is a complex, active, and social activity. The research on problem solving and mathematical reasoning clearly states the great need to create mathematically rich environments for students to deepen their understanding of mathematics. The instructional strategies chosen should match the varied learning needs of students. Effective instruction occurs when teachers choreograph the learning experience by carefully choosing select problems, standard- based materials, and conducting formal and informal assessments. The end goal is to empower students in problem solving by blending conceptual, procedural, and factual knowledge into a powerful learning package.
Van de Walle, J. A. (2001). Elementary and middle school mathematics: Teaching developmentally (4th ed.). New York: Addison Wesley Longman.
Van de Walle clearly states the importance of constructivism. Constructivism provides us with insights concerning how children learn mathematics and guides us to use instructional strategies that begin with children rather than ourselves (2001, p. 26). The whole learning process focuses on learning the concept, instead of the small pieces or procedural parts in the learning process. Effective teachers know their students strengths and weaknesses and plan instruction to challenge all learners to meet high standards. To do this, teachers must find ways to learn students prior mathematics knowledge and misunderstandings so that knowledge gaps can be addressed, inconsistencies resolved, and understanding deepened.