Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the State of Texas Assessments of Academic Readiness (STAAR) for Grade 6

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1 Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the State of Texas Assessments of Academic Readiness (STAAR) for Grade 6 Number, Operation, 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 Introduction to simplifying a fraction 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; Writing a signed number for a real-world situation 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 or subtraction of fractions with the same denominator Fractional part of a circle use addition and subtraction to solve problems involving fractions and decimals; 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 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 Addition with money Decimal addition Subtraction of aligned decimals Subtraction with money Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 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 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 Estimating a decimal sum or difference Double bar graphs 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 Patterns, Relationships, and Algebraic Thinking. ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/10

3 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 between percentages and decimals Converting a percentage to a fraction Converting a fraction to a percentage use ratios to make predictions in proportional situations. Introduction to expectation 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 Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Time unit conversion with whole number values Translating a sentence into a one-step equation Function tables with one-step rules Function tables with two-step rules Describing data patterns 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 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 Acute, obtuse, and right triangles Sum of the angle measures of a triangle Finding an angle measure for a triangle with an extended side Sum of the angle measures of a quadrilateral 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 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; Estimates and exact answers Circumference of a circle 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 Finding the radius or the diameter of a circle given its circumference Perimeter involving rectangles and circles Volume of a rectangular prism 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: Volume of a solid made of unit cubes Similar polygons Indirect measurement Choosing a measuring tool Choosing customary measurement units Reading a positive temperature from a thermometer Measuring length to the nearest inch Measuring length to the nearest quarter or half inch Choosing metric measurement units Measuring length to the nearest centimeter Measuring length to the nearest millimeter Time unit conversion with whole number values Introduction to adding time 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. Conversions involving measurements in feet and inches 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 Time unit conversion with whole number values Probability and Statistics. 6.9.A: 6.9.B: 6.10.A: TD = Teacher Directed 6.9: The student uses experimental and theoretical probability to make predictions. 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 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/10

6 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; 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 Using back-to-back stem-and-leaf plots to compare data sets sketch circle graphs to display data; and Angle measures in circle graphs solve problems by collecting, organizing, displaying, and interpreting data. Histograms for numerical data Bar graphs for non-numerical data Line plots Interpreting tally tables Interpreting pictograph tables Interpreting bar graphs Double bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Venn diagrams with two sets Venn diagrams with three sets Interpreting the graphs of two functions Underlying Processes and Mathematical Tools 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 using addition or subtraction Word problem on quotient and remainder Word problem using division Basic word problem using multiplication or division Word problem with multiple operations Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Distinguishing between area and perimeter Indirect measurement Conversions involving measurements in feet and inches Customary unit conversion with whole number values Customary unit conversion with whole number values, two-step conversion Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Time unit conversion with whole number values Introduction to adding time 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: Adding time Introduction to elapsed time Elapsed time Interpreting bar graphs Double bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Finding unit rates Introduction to the counting principle Introduction to probability of an event Probability of an event Writing a signed number for a real-world situation Describing data patterns 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 using division Word problem with multiple operations Filling in missing operations to make an equation Greatest common factor Least common multiple Word problem with common multiples Fractional part of a circle Ordering decimals 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 Perimeter involving rectangles and circles Indirect measurement Interpreting bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Finding unit rates Introduction to the counting principle 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 Word problem using division Basic word problem using multiplication or division Word problem with multiple operations Filling in missing operations to make an equation Greatest common factor Least common multiple Word problem with common multiples Finding the next terms of a simple sequence Fractional part of a circle ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/10

8 6.11.D: Ordering decimals Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Perimeter of a piecewise rectangular figure Distinguishing between area and perimeter Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Finding simple patterns in shapes Indirect measurement Customary unit conversion with whole number values Customary unit conversion with whole number values, two-step conversion Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Time unit conversion with whole number values Adding time Introduction to elapsed time Elapsed time Interpreting bar graphs Double bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Finding unit rates Introduction to the counting principle Probability of an event Function tables with one-step rules select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Addition of large numbers Subtraction and regrouping with zeros Word problem using addition or subtraction Multiplication by 10, 100, and 1000 Multiplication with trailing zeros: Problem type 1 Multiplication with trailing zeros: Problem type 2 Multiplication of large numbers Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Word problem on quotient and remainder Quotient and remainder: Problem type 3 Word problem using division Basic word problem using multiplication or division Word problem with multiple operations Rounding to tens or hundreds Rounding to hundreds or thousands Rounding to thousands, ten thousands, or hundred thousands Estimating a sum Estimating a difference Estimating a product Estimating a quotient Order of operations: Problem type 1 Order of operations: Problem type 2 Understanding equivalent fractions ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/10

9 6.12.A: Addition or subtraction of fractions with the same denominator Addition or subtraction of fractions with different denominators Writing a decimal and a fraction for a shaded region Rounding decimals Addition of aligned decimals Decimal addition Estimating a decimal sum or difference Measuring an angle with the protractor Sum of the angle measures of a triangle Perimeter of a piecewise rectangular figure Perimeter and area on a grid Distinguishing between area and perimeter Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Estimates and exact answers Drawing lines of symmetry Choosing customary measurement units Measuring length to the nearest quarter or half inch Choosing metric measurement units Measuring length to the nearest centimeter Measuring length to the nearest millimeter Adding time Introduction to elapsed time Elapsed time Double bar graphs Finding the percent of a grid that is shaded 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 Quotient and remainder: Problem type 2 Factors Prime numbers Prime factorization Greatest common factor Least common multiple Word problem with common multiples Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property Introduction to fractions Understanding equivalent fractions Writing a mixed number and an improper fraction for a shaded region Writing a decimal and a fraction for a shaded region Tenths and hundredths decimal place value Decimal place value Rounding decimals Acute, obtuse, and right angles Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Sum of the angle measures of a triangle ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/10

10 6.13.A: 6.13.B: Finding an angle measure for a triangle with an extended side Identifying parallelograms, rectangles, and squares Classifying quadrilaterals Distinguishing between area and perimeter Introduction to circle: diameter, radius, and chord Circumference of a circle Vertices, edges, and faces of a solid Drawing lines of symmetry Finding the percent of a grid that is shaded Writing a signed number for a real-world situation 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 Translating a sentence into a simple inequality Graphing a linear inequality on the number line Reading a point in quadrant 1 Plotting a point in quadrant : 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 Finding simple patterns in shapes Describing data patterns Writing a function rule given a table of ordered pairs: One-step rules validate his/her conclusions using mathematical properties and relationships. Factors Prime factorization Greatest common factor Least common multiple Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property Ordering fractions with same denominator Ordering fractions with same numerator Ordering fractions Introduction to ordering decimals Ordering decimals Ordering fractions and decimals Converting a decimal to a fraction: Basic Converting a fraction with a denominator of 10, 100, or 1000 to a decimal Converting a decimal to a mixed number 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 Venn diagrams with two sets Venn diagrams with three sets ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/10

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

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