Middle School Math Course 3 Correlation of the ALEKS course Middle School Math Course 3 to the Texas Essential Knowledge and Skills (TEKS) for Mathematics Grade 8 (2012) (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: 1.A: apply mathematics to problems arising in everyday life, society, and the workplace; Word problem with addition or subtraction of whole numbers Word problem with division of whole numbers and rounding Word problem with multiplication or division of whole numbers Word problem with common multiples Writing ratios for real-world situations Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with powers of ten U.S. Customary unit conversion with mixed number values: One-step conversion U.S. Customary unit conversion with mixed number values: Two-step conversion Metric conversion with decimal values: Two-step problem Word problem on unit rates associated with ratios of whole numbers: Decimal answers Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Finding the sale price without a calculator given the original price and percent discount Finding simple interest without a calculator Computing a percentage from a table of values Making a reasonable inference based on proportion statistics Solving a fraction word problem using a linear equation of the form Ax = B Solving a fraction word problem using a linear equation with the variable on both sides Mean and median of a data set Choosing the best measure to describe data Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area 1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; Word problem with addition or subtraction of whole numbers Word problem with division of whole numbers and rounding ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/10
Word problem with multiplication or division of whole numbers Introduction to order of operations Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Word problem with common multiples Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with powers of ten U.S. Customary unit conversion with whole number values: Two-step conversion U.S. Customary unit conversion with mixed number values: One-step conversion U.S. Customary unit conversion with mixed number values: Two-step conversion Metric conversion with decimal values: Two-step problem Adding time Elapsed time Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Finding the sale price without a calculator given the original price and percent discount Finding simple interest without a calculator Computing a percentage from a table of values Solving a fraction word problem using a linear equation of the form Ax = B Solving a fraction word problem using a linear equation with the variable on both sides Writing an equation and drawing its graph to model a real-world situation: Advanced Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Sides of polygons having the same perimeter Perimeter of a piecewise rectangular figure Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area Area of a piecewise rectangular figure 1.C: select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; Rounding to tens or hundreds Rounding to thousands, ten thousands, or hundred thousands Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient Divisibility rules for 2, 5, and 10 Divisibility rules for 3 and 9 Factors Prime numbers Prime factorization Greatest common factor of 2 numbers Least common multiple of 2 numbers Word problem with common multiples Reading the temperature from a thermometer Introduction to fractions Understanding equivalent fractions Ordering fractions with the same denominator ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/10
Ordering fractions with the same numerator Using a common denominator to order fractions Fractional part of a circle Writing a mixed number and an improper fraction for a shaded region Multiplication of a decimal by a power of ten Division of a decimal by a power of ten Measuring length to the nearest quarter or half inch Adding measurements in feet and inches Finding the percentage of a grid that is shaded Finding a percentage of a whole number without a calculator: Basic Writing a ratio as a percentage without a calculator Finding the sale price without a calculator given the original price and percent discount Finding simple interest without a calculator Probabilities involving two dice Ordering numbers with positive exponents Least common multiple of two monomials Greatest common factor of two multivariate monomials Factoring a quadratic with leading coefficient 1 Finding the next terms of a sequence with whole numbers Finding a specified term of an arithmetic sequence given the common difference and first term Finding a specified term of a geometric sequence given the common ratio and first term Arithmetic and geometric sequences: Identifying and writing an explicit rule Distance between two points in the plane Measuring an angle with the protractor Drawing an angle with the protractor Word problem involving the area between two rectangles Volume of a rectangular prism made of unit cubes Side views of a solid made of cubes Surface area involving prisms or cylinders Similar solids: Problem type 1 Using a translated point to find coordinates of other translated points Finding the coordinates of three points reflected over an axis 1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; Expanded form Ordering large numbers Introduction to fractions Writing ratios for real-world situations Understanding equivalent fractions Fractional position on a number line Plotting fractions on a number line Ordering fractions with the same denominator Ordering fractions with the same numerator Using a common denominator to order fractions Ordering decimals Ordering fractions and decimals Writing an improper fraction as a mixed number Writing a mixed number as an improper fraction Finding the percentage of a grid that is shaded Converting between percentages and decimals ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/10
Converting a percentage to a fraction in simplest form Converting a fraction to a percentage: Denominator of 20, 25, or 50 Writing a ratio as a percentage without a calculator Computing a percentage from a table of values Making a reasonable inference based on proportion statistics Interpreting a circle graph or pie chart Identifying numbers as integers or non-integers Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property Constructing a histogram for numerical data Constructing a bar graph for non-numerical data Interpreting a bar graph Interpreting a double bar graph Constructing a line plot Interpreting a line graph Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Constructing a box-and-whisker plot Writing a function rule given a table of ordered pairs: One-step rules Reading a point in the coordinate plane Choosing a graph to fit a narrative : Advanced Writing an equation and drawing its graph to model a real-world situation: Advanced Area of quadrilaterals in the coordinate plane Indirect measurement Dilating a figure 1.E: create and use representations to organize, record, and communicate mathematical ideas; Plotting integers on a number line Plotting fractions on a number line Plotting rational numbers on a number line Graphing a linear inequality on the number line Constructing a histogram for numerical data Constructing a bar graph for non-numerical data Constructing a line plot Function tables with two-step rules Plotting a point in the coordinate plane 1.F: analyze mathematical relationships to connect and communicate mathematical ideas; and Writing a function rule given a table of ordered pairs: Two-step rules 1.G: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. Expanded form Numeral translation: Problem type 1 Numeral translation: Problem type 2 Writing ratios for real-world situations Making a reasonable inference based on proportion statistics ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/10
Translating a sentence into a one-step equation Translating a sentence by using an inequality symbol (2) Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to: 2.A: extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; Identifying numbers as integers or non-integers Identifying numbers as rational or irrational 2.B: approximate the value of an irrational number, including π, and square roots of numbers less than 225, and locate that rational number approximation on a number line; Plotting rational numbers on a number line 2.C: convert between standard decimal notation and scientific notation; and Scientific notation with positive exponent Scientific notation with negative exponent 2.D: order a set of real numbers arising from mathematical and real-world contexts. Ordering fractions with the same denominator Ordering fractions with the same numerator Using a common denominator to order fractions Ordering decimals Ordering fractions and decimals (3) Proportionality. The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to: = Teacher Directed 3.A: generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation; Similar polygons Similar right triangles 3.B: compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/10
Identifying similar or congruent shapes on a grid Dilating a figure 3.C: use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation. (4) Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to: = Teacher Directed 4.A: use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line; 4.B: graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and Writing an equation and drawing its graph to model a real-world situation: Advanced 4.C: use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems. Finding slope given the graph of a line on a grid Finding slope given two points on the line (5) Proportionality. The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to: = Teacher Directed 5.A: represent linear proportional situations with tables, graphs, and equations in the form of y = kx; Writing a function rule given a table of ordered pairs: One-step rules 5.B: represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b 0; Writing a function rule given a table of ordered pairs: Two-step rules Writing an equation and drawing its graph to model a real-world situation: Advanced ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/10
5.C: contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; 5.D: use a trend line that approximates the linear relationship between bivariate sets of data to make predictions; Scatter plots and correlation 5.E: solve problems involving direct variation; Solving a fraction word problem using a linear equation of the form Ax = B 5.F: distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b 0; 5.G: Identify functions using sets of ordered pairs, tables, mappings, and graphs; 5.H: identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and 5.I: write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations. Writing an equation and drawing its graph to model a real-world situation: Advanced (6) Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: 6.A: describe the volume formula V = Bh of a cylinder in terms of its base area and its height; Volume of a cylinder 6.B: model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and Volume of a cylinder Volume of a cone: Exact answers in terms of pi 6.C: use models and diagrams to explain the Pythagorean theorem. Pythagorean Theorem ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/10
(7) Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: 7.A: solve problems involving the volume of cylinders, cones, and spheres; Volume of a cylinder Volume of a cone: Exact answers in terms of pi Volume of a sphere Word problem involving the rate of filling or emptying a cylinder 7.B: use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders; Surface area of a cube or a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Surface area of a triangular prism Surface area of a cylinder: Exact answers in terms of pi Surface area involving prisms or cylinders 7.C: use the Pythagorean Theorem and its converse to solve problems; and Pythagorean Theorem 7.D: determine the distance between two points on a coordinate plane using the Pythagorean Theorem. Distance between two points in the plane (8) Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to: = Teacher Directed 8.A: write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; Solving a fraction word problem using a linear equation with the variable on both sides 8.B: write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants; 8.C: model and solve one-variable equations with variables on both sides of the equal ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/10
sign that represent mathematical and real-world problems using rational number coefficients and constants; and Solving a fraction word problem using a linear equation with the variable on both sides 8.D: use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (9) Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. Determining whether given points lie on one, both, or neither of 2 lines given equations Graphically solving a system of linear equations (10) Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to: = Teacher Directed 10.A: generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; Identifying congruent shapes on a grid 10.B: differentiate between transformations that preserve congruence and those that do not; Translating a polygon Reflecting a polygon over a vertical or horizontal line Rotating a figure about the origin Dilating a figure 10.C: explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90, 180, 270, and 360 as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and Translating a polygon Reflecting a polygon over a vertical or horizontal line ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/10
Rotating a figure about the origin Dilating a figure 10.D: model the effect on linear and area measurements of dilated two-dimensional shapes. (11) Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to: = Teacher Directed 11.A: construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; Scatter plots and correlation Sketching the line of best fit 11.B: determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points; and 11.C: simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/10