Objective 1 : The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

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1 Essential Mathematics (with QuickTables) Correlation of the ALEKS course Essential Mathematics to the Texas Assessment of Knowledge and Skills (TAKS) for Grade 6 Objective 1 : The student will demonstrate an understanding of numbers, operations, and quantitative reasoning. 6.1.A: 6.1.B: 6.1.C: 6.1.D: 6.1.E: 6.1.F: 6.1: The student represents and uses rational numbers in a variety of equivalent forms. compare and order non-negative rational numbers; Ordering fractions with same denominator Ordering fractions with same numerator Ordering fractions Introduction to ordering decimals Ordering decimals Ordering fractions and decimals generate equivalent forms of rational numbers including whole numbers, fractions, and decimals; Equivalent fractions Simplifying a fraction 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 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 use integers to represent real-life situations; Reading the temperature from a thermometer write prime factorizations using exponents; Prime factorization identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers; and Factors Greatest common factor identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers. Multiples: Problem type 1 Multiples: Problem type 2 Least common multiple Word problem with common multiples ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/10

2 6.2: The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. 6.2.A: 6.2.B: 6.2.C: 6.2.D: 6.2.E: model addition and subtraction situations involving fractions with objects, pictures, words, and numbers; Addition and subtraction of simple unit fractions Introduction to addition or subtraction of fractions with different denominators Fractional part of a circle Addition with money Subtraction with money use addition and subtraction to solve problems involving fractions and decimals; Addition or subtraction of fractions with the same denominator Addition or subtraction of fractions with different denominators Fractional part of a circle Addition or subtraction of mixed numbers with same denominator 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 Addition of aligned decimals Decimal addition Subtraction of aligned decimals Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Additive property of equality with decimals Additive property of equality with fractions and mixed numbers use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates; Word problem on quotient and remainder Word problem using division Basic word problem using multiplication or division Similar polygons Indirect measurement Finding unit rates estimate and round to approximate reasonable results and to solve problems where exact answers are not required; and Estimating a sum Estimating a difference Estimating a product Estimating a quotient Double bar graphs Estimating a square root use order of operations to simplify whole number expressions (without exponents) in problem solving situations. Introduction to parentheses Introduction to order of operations Order of operations: Problem type 1 Order of operations: Problem type 2 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/10

3 Objective 2 : The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning. 6.3.A: 6.3.B: 6.3.C: 6.4.A: 6.4.B: 6.5.A: TD = Teacher Directed 6.3: The student solves problems involving direct proportional relationships. use ratios to describe proportional situations; Similar polygons Indirect measurement represent ratios and percents with concrete models, fractions, and decimals; and Introduction to ratios Finding the percent of a grid that is shaded Converting a percentage to a fraction Converting a fraction to a percentage use ratios to make predictions in proportional situations. 6.4: The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area; and Finding the next terms of a simple sequence Customary unit conversion with whole number values Customary unit conversion with whole number values, two-step conversion Translating a sentence into a one-step equation Writing a function rule given a table of ordered pairs: One-step rules use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc. TD 6.5: The student uses letters to represent an unknown in an equation. formulate equations from problem situations described by linear relationships. Translating a sentence into a one-step equation Objective 3 : The student will demonstrate an understanding of geometry and spatial reasoning. ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/10

4 6.6: The student uses geometric vocabulary to describe angles, polygons, and circles. 6.6.A: 6.6.B: 6.6.C: 6.7.A: use angle measurements to classify angles as acute, obtuse, or right; Acute, obtuse, and right angles identify relationships involving angles in triangles and quadrilaterals; and Scalene, isosceles, and equilateral triangles Sum of the angle measures of a triangle Finding an angle measure for a triangle with an extended side Identifying parallelograms, rectangles, and squares Classifying quadrilaterals describe the relationship between radius, diameter, and circumference of a circle. Introduction to circle: diameter, radius, and chord Circumference of a circle 6.7: The student uses coordinate geometry to identify location in two dimensions. locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Reading a point in quadrant 1 Plotting a point in quadrant 1 Objective 4 : The student will demonstrate an understanding of the concepts and uses of measurement. 6.8.A: 6.8.B: 6.8: The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. estimate measurements (including circumference) and evaluate reasonableness of results; Measuring length to the nearest inch Measuring length to the nearest quarter or half inch select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; Area of a triangle Perimeter of a square or a rectangle Perimeter of a polygon Sides of polygons having the same perimeter Perimeter of a piecewise rectangular figure Area of a square or a rectangle Distinguishing between area and perimeter 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 Area of a parallelogram Area of a trapezoid Area involving rectangles and triangles Circumference of a circle ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/10

5 6.8.C: 6.8.D: Finding the radius or the diameter of a circle given its circumference Perimeter involving rectangles and circles Volume of a rectangular prism Volume of a solid made of unit cubes Surface area of a solid made of unit cubes Measuring length to the nearest inch Measuring length to the nearest quarter or half inch Adding time Introduction to elapsed time Elapsed time Reading the temperature from a thermometer measure angles; and Measuring an angle with the protractor convert measures within the same measurement system (customary and metric) based on relationships between units. 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 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 Objective 5 : The student will demonstrate an understanding of probability and statistics. TD = Teacher Directed ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/10

6 6.9: The student uses experimental and theoretical probability to make predictions. 6.9.A: 6.9.B: 6.10.A: construct sample spaces using lists and tree diagrams; and Tree diagrams find the probabilities of a simple event and its complement and describe the relationship between the two. Introduction to probability of an event Probability of an event 6.10: The student uses statistical representations to analyze data. select and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot; TD 6.10.B: 6.10.C: 6.10.D: identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data; Average of two numbers Mode of a data set Finding the mode and range of a data set Mean of a data set Mean and median of a data set sketch circle graphs to display data; and TD solve problems by collecting, organizing, displaying, and interpreting data. Histograms for numerical data Line plots Interpreting bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Computing a percentage from a table of values Venn diagrams with two sets Venn diagrams with three sets Interpreting the graphs of two functions Objective 6 : The student will demonstrate an understanding of the mathematical processes and tools used in problem solving A: 6.11: The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; Word problem with fractions Word problem with one decimal operation: Problem type 1 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/10

7 6.11.B: 6.11.C: 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 Time unit conversion with whole number values Adding time Introduction to elapsed time Elapsed time Histograms for numerical data Bar graphs for non-numerical data Interpreting bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Box-and-whisker plots Finding the value for a new score that will yield a given mean Finding unit rates Finding the sale price given the original price and percent discount Finding the percentage increase or decrease Simple interest Counting principle Word problem involving combinations Probability of an event Probability of independent events Probability of dependent events Solving a fraction word problem using a linear equation of the form Ax = B use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Perimeter involving rectangles and circles Converting between metric and customary unit systems Interpreting bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Box-and-whisker plots Finding the value for a new score that will yield a given mean Finding unit rates Finding the sale price given the original price and percent discount Finding the percentage increase or decrease Simple interest Solving a fraction word problem using a linear equation of the form Ax = B select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and Basic word problem using multiplication or division ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/10

8 6.12.A: Word problem with fractions 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 Computing distances on the number line 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 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 Converting between metric and customary unit systems Time unit conversion with whole number values Adding time Introduction to elapsed time Elapsed time Word problem with clocks Histograms for numerical data Bar graphs for non-numerical data Interpreting bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Box-and-whisker plots Finding the value for a new score that will yield a given mean Finding unit rates Finding the sale price given the original price and percent discount Finding the percentage increase or decrease Simple interest Counting principle Word problem involving permutations Word problem involving combinations Probability of an event Probability of independent events Probability of dependent events Solving a fraction word problem using a linear equation of the form Ax = B 6.12: The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and Numeral translation: Problem type 1 Numeral translation: Problem type 2 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Factors ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/10

9 6.13.A: 6.13.B: Prime numbers Prime factorization Greatest common factor Least common multiple Word problem with common multiples Introduction to fractions Tenths and hundredths decimal place value Decimal place value Rounding decimals Acute, obtuse, and right angles Supplementary and complementary angles Corresponding and alternate angles Supplementary and vertical angles Constructing congruent angles Constructing an angle bisector Constructing the perpendicular bisector of a line segment Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Sum of the angle measures of a triangle Finding an angle measure for a triangle with an extended side Identifying parallelograms, rectangles, and squares Classifying quadrilaterals Introduction to circle: diameter, radius, and chord Circumference of a circle Vertices, edges, and faces of a solid Drawing lines of symmetry Integers and rational numbers Properties of addition Translating a sentence into a simple inequality Graphing a linear inequality on the number line 6.13: The student uses logical reasoning to make conjectures and verify conclusions. make conjectures from patterns or sets of examples and nonexamples; and Finding the next terms of a simple sequence Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Integers and rational numbers Writing a function rule given a table of ordered pairs: One-step rules validate his/her conclusions using mathematical properties and relationships. Prime factorization Greatest common factor Least common multiple Ordering fractions and decimals Supplementary and complementary angles Corresponding and alternate angles Supplementary and vertical angles Constructing congruent angles Constructing an angle bisector Finding an angle measure for a triangle with an extended side Identifying parallelograms, rectangles, and squares Classifying quadrilaterals Similar polygons ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/10

10 Solving a proportion of the form x/a = b/c Plotting rational numbers on a number line Integers and rational numbers Distributive property: Whole number coefficients Combining like terms: Integer coefficients Properties of addition 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 Solving simple equations with multiplication or division Multiplicative property of equality with whole numbers Multiplicative property of equality with integers Solving a fraction word problem using a linear equation of the form Ax = B ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/10

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