Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6 Numbers Sense and Operations TD = Teacher Directed 6.N.1: Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten, e.g., 10 to 2nd power, 10 to the 5th power. Introduction to exponents Powers of 10: Positive exponent 6.N.2: Demonstrate an understanding of place value to billions and thousandths. Tenths and hundredths decimal place value Decimal place value 6.N.3: Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. Expanded form Expanded form with zeros Numeral translation: Problem type 2 Ordering decimals Introduction to ordering decimals 6.N.4: Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. Introduction to fractions Plotting fractions on a number line Fractional position on a number line 6.N.5: Identify and determine common equivalent fractions, mixed numbers, decimals, and percents. Understanding equivalent fractions Equivalent fractions Introduction to simplifying a fraction Simplifying a fraction Writing a mixed number and an improper fraction for a shaded region Writing an improper fraction as a mixed number Writing a mixed number as an improper fraction Converting a decimal to a fraction: Basic Converting a decimal to a fraction: Advanced Converting a fraction with a denominator of 10, 100, or 1000 to a decimal ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/9
Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a decimal to a mixed number Converting a mixed number to a decimal Converting between percentages and decimals Converting a percentage to a fraction Converting a fraction to a percentage 6.N.6: Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line. Plotting fractions on a number line Fractional position on a number line Plotting integers on a number line 6.N.7: Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents. Ordering fractions with same denominator Ordering fractions with same numerator Ordering fractions Ordering decimals Introduction to ordering decimals Ordering fractions and decimals 6.N.8: Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10-to the solution of problems. Divisibility rules for 2, 5, and 10 Divisibility rules for 3 and 9 Factors Prime numbers Prime factorization Greatest common factor Least common multiple 6.N.9: Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Word problem using addition or subtraction Using addition and multiplication to count the objects on a grid Word problem on quotient and remainder Word problem using division Basic word problem using multiplication or division Average of two numbers Fractional part of a circle Word problem with fractions Addition with money Subtraction with money Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/9
Percentage of a whole number Finding the sale price given the original price and percent discount Finding the percentage increase or decrease Simple interest 6.N.10: Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers. TD 6.N.11: Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ). Introduction to parentheses Introduction to order of operations Order of operations: Problem type 1 Order of operations: Problem type 2 6.N.12: Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. Fact families for addition and subtraction 6.N.13: Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. Addition of large numbers Subtraction with multiple regrouping steps Subtraction and regrouping with zeros Multiplication by 10, 100, and 1000 Multiplication with carry Introduction to multiplication of large numbers Multiplication with trailing zeros: Problem type 1 Multiplication with trailing zeros: Problem type 2 Multiplication of large numbers Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division involving quotients with intermediate zeros Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Addition of aligned decimals Decimal addition Subtraction of aligned decimals Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Decimal multiplication: Problem type 2 Division of a decimal by a power of ten Decimal division 6.N.14: Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. Introduction to simplifying a fraction Simplifying a fraction ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/9
Addition or subtraction of fractions with the same denominator Addition and subtraction of simple unit fractions Introduction to addition or subtraction of fractions with different denominators Addition or subtraction of fractions with different denominators Addition or subtraction of mixed numbers with same denominator Product of a unit fraction and a whole number Product of a fraction and a whole number Introduction to fraction multiplication Fraction multiplication Fraction division Division involving a whole number and a fraction Addition of mixed numbers with same denominator and carry Subtraction of mixed numbers with same denominator and borrowing Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 Mixed number multiplication: Problem type 2 Mixed number division 6.N.15: Add and subtract integers, with the exception of subtracting negative integers. Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 6.N.16: Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates. Estimating a sum Estimating a difference Estimating a product Estimating a quotient Patterns, Relations, and Algebra 6.P.1: Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13...; 3, 9, 27,... Finding the next terms of a simple sequence Writing a function rule given a table of ordered pairs: One-step rules 6.P.2: Replace variables with given values and evaluate/simplify, e.g., 2(x) + 3 when x = 4. Evaluating a simple algebraic expression: Problem type 1 Evaluating a simple algebraic expression: Problem type 2 Evaluating a simple algebraic expression: Problem type 3 Evaluating a linear expression in two variables Evaluating a quadratic expression in one variable 6.P.3: Use the properties of equality to solve problems, e.g., if + 7 = 13, then = 13-7, ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/9
therefore = 6; if 3 x = 15, then 1/3 x 3 x = 1/3 x 15, therefore = 5. Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Additive property of equality with integers Multiplicative property of equality with integers Solving simple equations with multiplication or division Multiplicative property of equality with whole numbers Solving a fraction word problem using a linear equation of the form Ax = B Using two steps to solve an equation with whole numbers 6.P.4: Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables. Writing a simple variable expression for a real-world situation Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Function tables with one-step rules Function tables with two-step rules Graphing whole number functions Graphing a line in quadrant 1 Graphing a line given its equation in slope-intercept form Graphing a vertical or horizontal line 6.P.5: Solve linear equations using concrete models, tables, graphs, and paper-pencil methods. Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Additive property of equality with integers Multiplicative property of equality with integers Solving simple equations with multiplication or division Multiplicative property of equality with whole numbers Solving a fraction word problem using a linear equation of the form Ax = B Using two steps to solve an equation with whole numbers 6.P.6: Produce and interpret graphs that represent the relationship between two variables in everyday situations. Interpreting line graphs Interpreting the graphs of two functions 6.P.7: Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. Writing a function rule given a table of ordered pairs: One-step rules Geometry 6.G.1: Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/9
rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles. Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Classifying quadrilaterals Identifying parallelograms, rectangles, and squares Classifying parallelograms 6.G.2: Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces. Vertices, edges, and faces of a solid 6.G.3: Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular. Identifying parallel and perpendicular lines 6.G.4: Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). Reading a point in the coordinate plane Plotting a point in the coordinate plane 6.G.5: Find the distance between two points on horizontal or vertical number lines. Computing distances on the number line 6.G.6: Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections. Introduction to translations Translation of a polygon Introduction to reflections Reflection of a polygon over a vertical or horizontal line Rotation of a figure about the origin Identifying transformations 6.G.7: Identify types of symmetry, including line and rotational. Drawing lines of symmetry 6.G.8: Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections. Identifying congruent shapes on a grid 6.G.9: Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings. Nets of solids Measurement ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/9
6.M.1: Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate. Sides of polygons having the same perimeter Distinguishing between area and perimeter Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area Perimeter of a piecewise rectangular figure Area of a piecewise rectangular figure 6.M.2: Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals. Measuring an angle with the protractor Drawing an angle with the protractor Acute, obtuse, and right angles Supplementary and complementary angles Corresponding and alternate angles Supplementary and vertical angles Constructing congruent angles Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Classifying quadrilaterals Identifying parallelograms, rectangles, and squares Classifying parallelograms 6.M.3: Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed. Word problem with powers of ten Similar polygons Indirect measurement Customary unit conversion with whole number values Customary unit conversion with whole number values, two-step conversion Customary unit conversion with mixed number values Customary unit conversion with mixed number values, two-step conversion Conversions involving measurements in feet and inches Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Metric conversion with decimal values, two-step conversion Time unit conversion with whole number values Word problem with clocks Finding unit rates Simple word problem on proportions Word problem on proportions: Problem type 1 6.M.4: Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes. Area of a triangle Area of a square or a rectangle Distinguishing between area and perimeter Areas of rectangles with the same perimeter Area of a piecewise rectangular figure ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/9
Area of a parallelogram Area of a trapezoid Area involving rectangles and triangles 6.M.5: Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, π = C/d), and use the concepts to solve problems. Introduction to circle: diameter, radius, and chord Circumference of a circle Finding the radius or the diameter of a circle given its circumference Circumference and area of a circle Perimeter involving rectangles and circles Area between two concentric circles Area involving rectangles and circles Area involving inscribed figures 6.M.6: Find volumes and surface areas of rectangular prisms. Volume of a rectangular prism Volume of a solid made of unit cubes Surface area of a cube or a rectangular prism Surface area of a solid made of unit cubes 6.M.7: Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles. Sum of the angle measures of a triangle Data Analysis, Statistics, and Probability 6.D.1: Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range. Mode of a data set Finding the mode and range of a data set Mean and median of a data set Mean of a data set Using back-to-back stem-and-leaf plots to compare data sets How changing a value affects the mean and median Finding the value for a new score that will yield a given mean 6.D.2: Construct and interpret stem-and-leaf plots, line plots, and circle graphs. Line plots Interpreting circle graphs or pie charts Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets 6.D.3: Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes. Introduction to the counting principle Counting principle ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/9
Tree diagrams 6.D.4: Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event. Outcomes and event probability Introduction to probability of an event Understanding likelihood Probability of an event ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/9