This unit bundles student expectations that address representing and generating equivalent forms of fractions, decimals, and percents as well as solving real-world problems involving fractions, decimals, and percents. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace. The introduction to the grade level standards state, “While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology."
Prior to this Unit
In Grade 4, students determined if two given fractions were equivalent using a variety of methods. Additionally, in Grade 5 students added and subtracted positive rational numbers fluently, including problems involving mixed forms of rational numbers.
During this Unit
Students extend their mathematical foundations of equivalency within rational numbers, including percents. Concrete and pictorial models, including 10 by 10 grids, strip diagrams, and number lines are used to represent multiples of benchmark fractions and percents. Additionally, percents are represented with concrete and pictorial models, fractions, and decimals. Students continue their understanding of equivalency by generating and using equivalent forms of fractions, decimals, and percents to solve real-world problems, including those involving money. Percents less than or greater than 100%, including percents with fractional or decimal values such as 8.25% or are encompassed within this unit. Students apply their understandings of percents to solve real-world problems that involve finding the whole given a part and the percent, the part given the whole and a percent, and the percent given the part and the whole. Methods for solving real-world problem situations involving percents, such as the use of proportions or scale factors between ratios, are not included in this unit. Computations within this unit are restricted to operational capabilities from Grade 5 which include sums and differences with any positive rational numbers, products with factors limited to a whole number by a whole number, a decimal by a decimal, or a whole number by a fraction, and quotients limited to whole number dividends and divisors, a decimal dividend by a whole number divisor, or whole number and unit fraction dividends and divisors.
After this Unit
In Unit 02, students will further their understanding of equivalency by ordering whole numbers, positive and negative rational numbers, and integers. In Unit 03, students will add, subtract, multiply, and divide whole numbers, positive rational numbers, and integers. In Unit 05, students will examine percents again through the lens of proportional reasoning with ratios and rates. At that time, the proportion method and utilizing scale factors between ratios will be appropriate methods to solve real-world problem situations involving percent. In Grade 7, students will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
In Grade 6, generating equivalent forms of fractions, decimals, and percents is identified as STAAR Readiness Standard 6.4G. Representing percents with concrete models, fractions and decimals is STAAR Supporting Standard 6.4E. Representing benchmark fractions and percents with concrete and pictorial models and numbers, as well as using equivalent fractions, decimals, and percents to show equal parts of the same whole are identified as STAAR Supporting Standards 6.4F and 6.5C. All of these standards are subsumed under the Grade 6 STAAR Reporting Category 1: Numerical Representations and Relationships. Solving real-world problems involving percents is identified as STAAR Readiness Standard 6.5B and part of the Grade 6 STAAR Reporting Category 2: Computations and Algebraic Relationships. All of these standards are subsumed under the Grade 6 Texas Response to Curriculum Focal Points (TxRCFP): Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, IX. Communication and Representation, VIII. Problem Solving and Reasoning, and X. Connections.
According to Van de Walle, Bay-Williams, Lovin, and Karp (2013), “Physical models provide the main link between fractions, decimal, and percents. Students should develop an understanding of the percent equivalence of familiar fractions (halves, thirds, fourths, fifths, and eighths)” (p. 162). The essential understanding of percent is built on the concept of 100. “Students who understand that percent means parts out of one hundred and have a good pictorial representation of percent are more successful in solving percent problems than those who do not” (Reyes, Lindquist, Lambdin & Smith, 2012, p. 292). Additionally, as students initially begin to solve problems involving percents instruction should include “activities that center on direct translation of experiences involving 100” (p. 293). When determining equivalent forms of fractions, decimals, and percents, Van de Walle et al. (2013) suggests that rather than, “rush[ing] to develop rules or procedures for different types of problems – encourage students to notice patterns…Require student to use manipulatives, drawings, and contexts to explain their solutions” (p. 166).
Reyes, R. E., Lindquist, M., Lambdin, D. V., & Smith, N. L. (2012). Helping children learn mathematics. (10th ed.). Hoboken, NJ: Wiley.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., Bay-Williams, J., Lovin, L., & Karp, K., (2013). Teaching student-centered mathematics: Developmentally appropriate instruction for grades 6 - 8. Boston, MA: Pearson.