Wisconsin Technical College System HSED 5.09 - Math Course Outcome Summary Course Information Description Learners will apply math concepts in real-world context including financial literacy consumer applications. Course Competencies 1 Calculate with whole numbers you calculate quotients with single digit divisors you demonstrate mastery of multiplication facts from 0-12 you estimate reasonableness of answer you add multiple digit whole numbers with and without regrouping you subtract multiple digit whole numbers with and without regrouping you solve word problems using sums and differences, multiplication and division Add multiple digit whole numbers with and without regrouping Subtract multiple digit whole numbers with and without regrouping Round whole numbers to requested value Compare whole numbers using "less than", "greater than", and equals signs Solve word problems using sums and differences, multiplication and division Compute products Compute quotients without remainders 2 Calculate with fractions you write fractions from pictures and word you identify forms of fractions you reduce fractions you raise fractions to higher terms you determine the lowest common denominator you change improper fractions to whole numbers or mixed numbers you change mixed numbers to improper fractions Course Outcome Summary - Page 1 of 11
you determine what part one number is of another you add and subtract multiply and divide whole numbers, fractions, and mixed numbers you solve word problems using addition, subtraction, multiplication and division of fractions Identify fractions and their parts including: numerator, denominator, fraction bar, proper fractions, improper fractions and mixed numbers Write proper, improper and mixed number fractions from pictures and words Convert between improper fractions, whole numbers, and mixed numbers Reduce fractions Distinguish between common denominator and lowest common denominator Find the lowest common denominator of two or more fractions Convert fractions to higher terms Arrange fractions in ascending or descending order Demonstrate strategies for adding fractions Demonstrate strategies for subtracting fractions Explain how to use regrouping to subtract fractions Calculate subtraction of fractions using regrouping Explain how to cancel when multiplying fractions Calculate multiplication of fractions using canceling Identify the reciprocal of a fraction Demonstrate strategies for dividing fractions 3 Calculate with decimals you identify the place value of decimals by reading and writing decimals you convert whole numbers to decimal forms you compare decimals you round decimals to the specified place value you add, subtract, multiply and divide decimals and whole numbers you solve word problems using addition, subtraction, multiplication and division of decimals Identify place values of decimals Read decimals using proper terminology Express decimals in both word and numeric form Round decimals to a specified place value Arrange decimals in ascending or descending order Demonstrate strategies for adding and subtracting decimals Demonstrate strategies for multiplying decimals Demonstrate strategies for dividing decimals by whole numbers Demonstrate strategies for dividing decimals by decimals Demonstrate strategies for dividing whole numbers by decimals Demonstrate strategies to convert fractions to decimals Demonstrate strategies to convert decimals to fractions 4 Calculate with ratio and proportions Course Outcome Summary - Page 2 of 11
you write ratios and proportions you simplify ratios and proportions you compare ratios and proportions you solve problems using proportions and/or rations Define ratios and proportions Write ratios using the three different notations Write ratios for word problems using whole numbers Reduce ratios Identify equivalent ratios Convert written statements to ratios and reduce if necessary Define proportions Compare two sets of data using ratios to determine if they are proportional Solve numerical proportion and ration problems Set up proportions using word problems Solve multi-step problems using proportion Solve word problems using proportion you solve multi-step word problems using proportions 5 Calculate with percents you determine the value of percent you identify the percent, the whole, and the part you change decimals to percents you change percents to decimals you change fractions to percents you change percents to fractions you solve problems using percent you solve word problems using percent Define percent Convert between decimals and percents Convert between fractions and percents Identify the part, the whole, and the percent Solve for the part in a percent problem Solve for the whole in a percent problem Solve for the percent in a problem Demonstrate strategies for solving percent problems, such as using percent circles, proportions, and/or formulas 6 Calculate with integers Course Outcome Summary - Page 3 of 11
you define integers you add, subtract, multiply and divide integers you solve word problems using integers Define signed numbers by locating integers on a number line Demonstrate strategies for adding and subtracting signed numbers Demonstrate strategies for multiplying and dividing signed numbers Demonstrate strategies using absolute value Solve problems using signed numbers Put integers in order by value 7 Calculate with exponents you compute powers of numbers you compute square roots of perfect squares you compute roots of real numbers you solve word problems using roots Define exponents Identify the base and exponents in a mathematical expression Express the exponential form in a factored form Express the factored form in an exponential form 8 Calculate with rational numbers you simplify rational expressions you add/subtract and multiply/divide rational terms you solve rational equations you solve word problems using rational equations Define rational expressions Simplify rational expressions Determine lowest common denominator of rational expressions Convert terms of rational expressions to LCD Combine like terms of rational expressions Multiply rational expressions Divide rational expressions Determine lowest common denominator (LCD) of rational equation Solve rational equations Check answers for other means to obtain solutions Check solutions for reasonableness Course Outcome Summary - Page 4 of 11
9 Calculate using the order of operations you identify order of operations you apply order of operations you solve word problems applying order of operations you apply commutative property of addition and multiplication you apply associative property of addition and multiplication you solve word problems using the order of operations List the sequence of steps in the order of operations Solve problems using the order of operations Define the commutative and associative properties of addition and multiplication Apply the commutative and associative properties when solving problems Solve word problems using the order of operations 10 Calculate with radical numbers (square roots) you compute powers of numbers you compute square roots of perfect squares you solve word problems using square roots Define square roots and perfect squares Identify the square root symbol Memorize the square roots of common perfect squares up to 144 Perform square root operations on a calculator 11 Use calculators in problem solving you calculate whole numbers using a calculator you calculate fractions using a calculator you calculate decimals using a calculator you estimate reasonableness of answer you solve problems using calculators Perform calculations of whole numbers, signed numbers, roots, powers and percents using a calculator Perform calculations of fractions using a calculator Perform calculations of decimals using a calculator Solve problems using calculators Check resonableness of answers with a calculator Course Outcome Summary - Page 5 of 11
12 Use measurement tools you identify common measurement tools (ruler, cup, Fahrenheit and Celsius thermometers, etc) you read common measurements (whole, half, quarter) you use common measurement tools you solve word problems using measurement tools Recognize common measurements (whole, half, third, quarter, etc.) Use measurement tools to determine length, weight, time, and capacity (dry and liquid cup measurements, clock/stopwatch, scales) Solve word problems using measurement tools 13 Demonstrate use of measurement systems you identify units of length you identify units of weight you identify units of capacity you identify units of time you compare units of measurement you change larger units of measurement to smaller units of measurement (including within the Metric system and between Metric and US Customary Systems) you change smaller units of measurement to larger units of measurement (including within the Metric system and between Metric and US Customary Systems) you convert from one unit of measurement to another (proportion and/or dimensional analysis) you change mixed measurements to specific units of measurement you add and subtract measurements you multiply and divide measurements you solve word problems using measurement systems Identify units of length, weight, capacity, and time Compare units of measurement Select appropriate units of measure Convert between smaller and larger units of measurement (including within the Metric system and between Metric and US Customary Systems) Demonstrate strategies for solving measurement conversions using proportions and dimensional analysis Change mixed measurements to specific units of measure Calculate problems using U.S. Customary System measurement units Solve problems involving measurement Solve word problems involving measurement Identify measurement units within the Metric System 14 Use rectangular co-ordinate system (graphs) Course Outcome Summary - Page 6 of 11
you solve word problems using rectangular co-ordinate systems you identify parts and points of coordinate planes you find distance on a coordinate plane you create x/y tables of values you graph linear equations you solve linear equations using graphs you find slopes in intercepts you label solution using correct units you use level appropriate terminology you estimate reasonableness of answer Solve problems using visual data Identify the following terms related to a coordinate plane: origin, x-axis, y-axis, x- coordinate, y-coordinate, slope, intercept, ordered pair Graph ordered pairs on a coordinate plane Compute midpoint Create x/y tables Construct a graph of a linear equation Solve linear equations using graphs Find slopes Find intercepts Using the formula find distance on a coordinate plane Find slopes and intercepts using slope-intercept form 15 Interpret tables, charts and graphs you locate a point on a map you interpret tables you interpret bar, line and circle graphs you solve word problems involving visual data you organize information to construct tables and graphs you extract information from graphs to solve problems you solve word problems using tables and graphs Use coordinates to locate a point on a map Explain the components of visual data Interpret tables and bar, line, and circle graphs Solve problems using visual data Solve word problems involving visual data Describe how tables and graphs can be used to organize information Locate information and data in various kinds of tables and graphs Explain how to use tables and graphs to solve problems Create a table or graph from given information Course Outcome Summary - Page 7 of 11
Solve problems using visual data Compare the characteristics and uses of picture graphs, line graphs, bar graphs, and circle graphs 16 Analyze data using basic statistics you compute range you compute mean you compute median you determine mode you solve word problems involving basic statistical data Define range, mean, median, and mode Determine range, mean, median, and mode Solve word problems involving statistical data 17 Predict outcomes using probability you calculate probabilities you calculate odds you use probability to predict outcomes you solve problems using probability you solve word problems using probability you estimate reasonableness of answer Define probability, outcome, odds Calculate probability Calculate odds Use probability to predict outcomes Solve word problems using probability 18 Solve problems using geometric figures you identify common geometric formulas you identify angle relationships (parallel and perpendicular lines, vertical angles, supplementary, complementary, acute, obtuse, right, straight line and reflex angle) you identify plane and solid geometric figures you compute area, volume, perimeter, and circumference problems you solve area, volume, perimeter, and circumference word problems you solve triangle problems (similar, congruent, etc.) you use Pythagorean Theorem you solve problems using the Pythagorean Theorem Course Outcome Summary - Page 8 of 11
you solve 30-60 triangles you solve 45-45 triangles you calculate area of non-right triangles Define the following geometric terms: parallel lines, perpendicular lines, vertical angles, supplementary and complementary angles, acute angles, etc. Identify types of angles and lines Identify plane and solid geometric figures Compute perimeter and circumference problems Solve perimeter and circumference word problems Compute area problems Solve area word problems Define the following geometric terms: base angles, vertex, isosceles, equilateral, right, scalene, similar, and congruent triangles Identify different triangles and their respective parts Solve triangle problems using similarity and congruency Use Pythagorean Theorem to find length of any side of a right triangle Solve right triangle problems using Pythagorean Theorem Identify the properties of 30-60 triangles Solve problems involving 30-60 triangle Identify the properties of 45-45 triangles Solve problems involving 45-45 triangles 19 Simplify algebraic equations you simplify expressions using order of operations you solve linear equations you use number operations to simplify polynomial expressions (+, -, x, /, FOIL) COLLEGE BOUND ONLY you factor polynomials COLLEGE BOUND ONLY you solve literal equations COLLEGE BOUND ONLY Define the following algebraic terms: linear and literal equations, monomial, binomial, trinomial, polynomial Solve linear and literal equations Factor prime factor monomials Combine like terms Simplify algebraic expressions using the order of operations Solve equations with variables Formulate equations or inequalities into words Solve inequalities Write algebraic equations Solve problems using pre-algebra concepts Substitute values for variables in expressions and equations Evaluate expressions and equations with substituted values Solve word problems Define variables, expressions, equations, and inequalities Write expressions Course Outcome Summary - Page 9 of 11
Factor trinomials (COLLEGE BOUND ONLY) Perform multiplication of polynomials including the use of "FOIL" (COLLEGE BOUND ONLY) 20 Solve algebraic equations you simplify algebraic expression using the order of operations you substitute values for variables in expressions and equations you evaluate expressions and equations with substituted values you solve basic equations with variables you solve basic inequalities you write basic algebraic equations you use algebra to solve word problems you perform order of operations you identifiy the meaning for each algebraic variable Define variables, expressions, equations, and inequalities Write expressions Simplify algebraic expressions using the order of operations Formulate equations or inequalities into words Solve equations with variables Solve inequalities Write algebraic equations Solve problems using pre-algebra concepts Substitute values for variables in expressions and equations Evaluate expressions and equations with substituted values Solve word problems 21 Calculate with scientific notation (Expected for College Bound Students, Optional for others) you compute powers of real numbers you use number operations with powers of real numbers you write numbers in scientific notation you convert between scientific notation and numeric form you perform number operations with scientific notation you identify rules of significant digits you solve problems using rules of significant digits Define the following algebraic terms: real number, scientific notation, significant digits List the laws of exponents. Solve problems using the laws of exponents. Compute powers and roots of real numbers Perform number operations using powers and roots Write numbers in scientific notation Course Outcome Summary - Page 10 of 11
Perform number operations using scientific notation Convert between scientific notation and numeric form Identify rules of significant digits Use rules of significant digits to solve problems Course Outcome Summary - Page 11 of 11