Introduction This unit bundles student expectations that address sets and subsets of rational numbers, operations with rational numbers, and personal financial literacy standards regarding sales tax, income tax, financial assets and liabilities records, and net worth statements. 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 6, students classified whole numbers, integers, and rational numbers using a visual representation, such as a Venn diagram, to describe relationships between sets of numbers. Students performed all four operations with integers as well as multiplied and divided positive rational numbers fluently. This included whole numbers, decimals, fractions, and percents converted to equivalent decimals or fractions for multiplying or dividing. Grade 5 students defined income tax, payroll tax, sales tax, and property tax.
During this Unit Students use a visual representation to organize and display the relationship of the sets and subsets of rational numbers, which include counting (natural) numbers, whole numbers, integers, and rational numbers. Students also apply and extend operations with rational numbers to include negative fractions and decimals. Grade 7 students are expected to fluently add, subtract, multiply, and divide various forms of positive and negative rational numbers that include integers, decimals, fractions, and percents converted to equivalent decimals or fractions. Exposure to solving mathematical and real-world situations assists students in generalizing operations with positive and negative rational numbers, which builds fluency and reasonableness of solutions. Students also create and organize a financial assets and liabilities record, construct a net worth statement, calculate sales tax for a given purchase, and calculate income tax for earned wages.
After this Unit In Units 2 – 12, students will continuously apply rational number operations to solve problems with equations and inequalities, ratios and rates, similarity, probability, geometry, measurement, and statistical representations. In Grade 8, students will extend their knowledge of sets and subsets of numbers to describe relationships between sets of real numbers as well as solve problem situations involving real numbers
Additional Notes In Grade 7, describing relationships between sets of rational number is identified as STAAR Supporting Standard 7.2 and is subsumed under the Grade 7 STAAR Reporting Category 1: Probability and Numerical Representations. Using addition, subtraction, multiplication, and division to solve problems involving rational numbers is identified as STAAR Readiness Standard 7.3B while adding, subtracting, multiplying, and dividing rational numbers fluently is identified as STAAR Supporting Standard 7.3A. The two standards are included in the Grade 7 STAAR Reporting Category 2: Computations and Algebraic Relationships. All of these standards are a foundational block of the Grade 7 Texas Response to Curriculum Focal Points (TxRCFP): Developing fluency with rational numbers and operations to solve problems in a variety of contexts. Calculating sales tax and income tax, as well a financial assets and liabilities record and constructing a net worth statement are identified as STAAR Supporting Standards 7.13A and 7.13C. These two standards are included within the Grade 7 STAAR Reporting Category 4: Data Analysis and Personal Financial Literacy and the Grade 7 Focal Point: Financial Literacy (TxRCFP). This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections.
Research According to the National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics (2000), “In the middle grades, students should continue to refine their understandings of addition, subtraction, multiplication, and division as they use these operations with fractions, decimals, percents, and integers” (p. 218). Developing an understanding of operations of all rational numbers helps in solving linear equations. Students reference the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. (NCTM, 2006, p. 19) Based on findings from a report prepared for the U.S. Department of the Treasury, “In addition to knowledge and banking behavior, financial education also has the potential to influence student’s attitudes about savings and financial institutions” (Wiedrich, Collins, Rosen, & Rademacher, 2014, p. 25). Additionally, “Financial education in schools, even small amounts, does appear to increase financial knowledge and capability…[as well as] improved student attitudes towards savings and the usefulness of financial institutions” (p. 32).
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc. National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc. 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 Wiedrich, K., Collins, J., Rosen, L., & Rademacher, I. (2014). Financial education and account access among elementary students: findings from the assessing the financial capabilities outcomes youth pilot. Retrieved from http://opportunitytexas.org/images/stories/AFCO%20Youth%20Full%20Report%20Final.pdf |