Deming Public Schools Mathematics Curriculum Applied Math

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1 Standard #1: NUMBER AND OPERATIONS: Students will understand numerical concepts and mathematical operations. Deming Public School EPSS: Ib, Id, II, IV, VI Career Readiness: 3, 5 Benchmark A. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Performance Standards 1. Compare and order using concrete or illustrated models: whole numbers (to millions) common fractions (halves, thirds, fourths, eighths) decimals (thousandths) 2. Demonstrate understanding of the magnitude of the value of numbers from thousandths to millions, including common fractions. 3. Represent place value using concrete or illustrated models up to one billion (1,000,000,000). 4. Interpret percents as part of a hundred (i.e., find decimal and percent equivalents for common fractions, explain how they represent the same value, and compute a given percent of a whole number). 5. Identify and represent on a number line decimals, fractions, and mixed numbers. 6. Identify prime and composite numbers to Compare and order rational numbers. 8. Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents). 9. Use appropriate representations of positive rational numbers in the context of real-life applications. 10. Identify greatest common factor and least common multiples for a set of whole numbers. 11. Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. 12. Determine the absolute value of rational numbers. 13. Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers. 14. Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems. 15. Read, write, and compare rational numbers in scientific notation (e.g., positive and negative powers of 10) with approximate numbers using scientific notation. 16. Simplify numerical expressions using order of operations. 17. Demonstrate the magnitude of rational numbers (e.g., trillions to millions).

2 B. Understand the meaning of operations and how they relate to one another. 1. Explain and perform whole number division and express remainders as a whole number or a fractional part as appropriate to the context of real-life problems. 2. Add and subtract decimals. 3. Add and subtract fractions and mixed numbers without regrouping and express answers in simplest form. 4. Find the factors and multiples of whole numbers. 5. Use arithmetic operations and inverse relationships to represent and solve real-world problems. 6. Identify and represent on a number line decimals, fractions, and mixed numbers. 7. Demonstrate proficiency with division, including one- and two-digit divisors. 8. Solve simple problems involving the addition and subtraction of fractions and mixed numbers. 9. Represent and use fractions and decimals in equivalent forms. 10. Calculate multiplication and division problems using contextual situations. 11. Factor a whole number into a product of its primes. 12. Demonstrate the relationship and equivalency among ratios and percents. 13. Use proportions to solve problems. 14. Explain and perform: whole number division and express remainders as decimals or appropriately in the context of the problem addition, subtraction, multiplication, and division with decimals addition and subtraction with integers addition, subtraction, and multiplication with fractions and mixed numerals 15. Determine the least common multiple and the greatest common divisor of whole numbers and use them to solve problems with fractions. 16. Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive rational numbers to whole-number powers. 17. Convert terminating decimals into reduced fractions. 18. Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest) 19. Add and subtract fractions with unlike denominators. 20. Multiply, divide, and simplify rational numbers by using exponent rules. 21. Understand the meaning of the absolute value of a number: interpret the absolute value as the distance of the number from zero on a number line determine the absolute value of real numbers.

3 C. Compute fluently and make reasonable estimates. 22. Simplify and evaluate positive rational numbers raised to positive whole number powers. 23. Solve addition, subtraction, multiplication, and division problems that use positive and negative integers and combinations of these operations. 24. Use real number properties (e.g., commutative, associative, distributive) to perform various computational procedures. 25. Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers 1. Add, subtract, multiply, and divide whole numbers. 2. Add and subtract decimals. 3. Use estimation strategies to verify the reasonableness of calculated results. 4. Explain how the estimation strategy impacts the result. 5. Relate the basic arithmetic operations to one another (e.g., multiplication and division are inverse operations). 6. Simplify numerical expressions using order of operations. 7. Recognize and explain the differences between exact and approximate values. 8. Estimate quantities involving rational numbers using various estimations. 9. Use estimates to check reasonableness of results and make predictions in situations involving rational numbers. 10. Determine if a problem situation calls for an exact or approximate answer and perform the appropriate computation. 11. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 12. Interpret and use ratios in different contexts. 13. Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving problems. 14. Use estimation to check reasonableness of results, and use this information to make predictions in situations involving rational numbers, pi, and simple algebraic equations. 15. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications 16. Calculate the percentage of increases and decreases of a quantity 17. Add and subtract fractions with unlike denominators. 18. Formulate algebraic expressions that include real numbers to describe and solve real-world problems. 19. Use a variety of computational methods to estimate quantities involving real numbers. 20. Estimate answers and use formulas to solve application problems involving surface area and volume.

4 Standard #2: Algebra: Students will understand algebraic concepts and applications. Deming Public School EPSS: Ib, II, IV, V, VI Career Readiness: 3, 5 Benchmark A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. Performance Standards 1. Solve problems involving proportional relationships. 2. Explain and use the relationships among ratios, proportions, and percents. 3. Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the same general pattern presented in different representations. 4. Simplify numerical expressions by applying properties of rational numbers, and justify the process used. 5. Solve problems involving rate, average speed, distance, and time. 1. Compute the value of the expression for specific numerical values of the variable. 2. Understand the differences between the symbols for less than, less than or equal to, greater than, and greater than or equal to. 3. Solve problems involving proportional relationships. 1. Use mathematical models to represent and explain mathematical concepts and procedures. 2. Understand and use mathematical models such as: the number line to model the relationship between rational numbers and rational number operations pictorial representation of addition and subtraction of rational numbers with regrouping manipulatives or pictures to model computational procedures graphs, tables, and charts to describe data diagrams or pictures to model problem situations 3. Demonstrate how a situation can be represented in more than one way. 4. Develop and use mathematical models to represent and justify mathematical relationships found in a variety of situations. 5. Create scale models and use them for dimensional drawings. 6. Generate different representations to model a specific numerical relationship given one representation of data (e.g., a table, a graph, an equation, a verbal description).

5 D. Analyze changes in various contexts. 1. Recognize and create patterns of change from everyday life using numerical or pictorial representations. 2. Solve problems that involve change using proportional relationships. 3. Use ratios to predict changes in proportional situations. 4. Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, and perimeter. 5. Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change. 6. Use appropriate problem-solving strategies (e.g., drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table or graph, working a simpler problem, writing an algebraic expression or working backward) to solve problems that involve change. 7. Solve multi-step problems that involve changes in rate, average speed, distance, and time.

6 District/National Standard #4: Measurement: Students will understand measurement systems and applications. Deming Public School EPSS: Ib, II, IV, V, VI Career Readiness: 3, 5 Benchmark A. Understand measurable attributes of objects and the units, systems, and processes of measurement. Performance Standards 1. Understand properties (e.g., length, area, weight, volume) and select the appropriate type of unit for measuring each using both U.S. customary and metric systems. 2. Select and use appropriate units and tools to measure according to the degree of accuracy required in a particular problem-solving situation. 3. Solve problems involving linear measurement, weight, and capacity (e.g., measuring to the nearest sixteenth of an inch or nearest millimeter; using ounces, milliliters, or pounds and kilograms) to the appropriate degree of accuracy. 4. Perform one-step conversions within a system of measurement (e.g., inches to feet, centimeters to meters). 5. Perform multi-step conversions of measurement units to equivalent units within a given system (e.g., 36 inches equals 3 feet or 1 yard) 6. Estimate measurement in both U.S. customary and metric units. 7. Choose appropriate units of measure and ratios to recognize new equivalences (e.g., 1 square yard equals 9 square feet) to solve problems. 8. Select and use the appropriate size and type of unit for a given measurement situation. 9. Compare masses, weights, capacities, geometric measures, times, and temperatures within measurement systems. 10. Approximate the relationship between standard and metric measurement systems (e.g., inches and centimeters, pounds and kilograms, quarts and liters). 11. Use measures expressed as rates and measures expressed as products to solve problems, check the units of the solutions, and analyze the reasonableness of the answer

7 B. Apply appropriate techniques, tools, and formulas to determine measurements. 1. Solve measurement problems using appropriate tools involving length, perimeter, weight, capacity, time, and temperature. 2. Select and use strategies to estimate measurements including length, distance, capacity, and time. 3. Apply strategies and use tools for estimating and measuring the perimeter of regular and irregular shapes. 4. Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time. 5. Select and justify the selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given situation. 6. Solve problems involving scale factors, ratios, and proportions. 7. Use estimation to solve problems. 8. Use proportional relationships in similar shapes to find missing measurements.

8 District/National Standard #5: Data Analysis and Probability: Students will understand how to formulate questions, analyze data, and determine probabilities. Deming Public School EPSS: Ib, Id, II, III, IV, V, VI Career Readiness: 2, 3, 4, 5 Benchmark A. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Performance Standards 1. Construct, read, analyze, and interpret tables, charts, graphs, and data plots. 2. Construct, interpret, and analyze data from graphical representations and draw simple conclusions using bar graphs, line graphs, circle graphs, frequency tables, and Venn diagrams. 3. Display, analyze, compare, and interpret different data sets, including data sets of different sizes. 4. Organize, read, and display numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including correct titles, labels, and intervals or categories including: bar, line, and circle graphs pictorial displays charts and tables 5. Formulate questions and identify data to be collected to correctly answer a question. 6. Use statistical representations to analyze data. 7. Draw and compare different graphical representations of the same data. 8. Use mean, median, mode, and range to describe data. 9. Sketch circle graphs to display data. 10. Solve problems by collecting, organizing, displaying and interpreting data.