# Grade 6: Correlated to AGS Basic Math Skills

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1 Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and factors Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in owing ) AGS Basic Math Skills: Chapter 13: Lessons 1-9, 12, Interpret the absolute value as the distance of the number from zero on a number line, and find the absolute value of real numbers. AGS Basic Math Skills: Chapter 13: Lesson Compare and represent on a number line: positive and negative integers, fractions, decimals (to hundredths), and mixed numbers. AGS Basic Math Skills: Chapter 3: Lessons1-6; Chapter 4: Lessons 1-3; Chapter 13: Lessons 1-3, Convert between any two of these representations of numbers: fractions, decimals, and percents, without the use of a calculator. AGS Basic Math Skills: Chapter 3: Lessons 2-6; Chapter 4: Lesson 9, 10; Chapter 6: Lessons 2, Recognize decimal equivalents for commonly used fractions without the use of a calculator. AGS Basic Math Skills: Chapter 4: Lessons 9, Use models to represent ratios. AGS Basic Math Skills: Chapter 5: Lesson 1; Chapter 8: Lesson 8; Chapter 12: Lesson Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). AGS Basic Math Skills: Chapter 2: Lessons 8, 9; Chapter 3: Lessons 7, 12, 14, 15 1

2 (Indiana Academic Standards for M athematics: Grade 6, Cont. ) Grade 6: Standard 2 Computation Students solve problems involving addition, subtraction, multiplication, and division of integers. They solve problems involving fractions, decimals, ratios, proportions, and percentages Add and subtract positive and negative numbers. AGS Basic Math Skills: Chapter 13: Lessons 2-4, 6, Multiply and divide positive and negative integers. AGS Basic Math Skills: Chapter 13: Lessons 5, 7, Multiply and divide decimals. AGS Basic Math Skills: Chapter 4: Lessons 6, 8; Chapter 5: Lesson 4; Chapter 6: Lessons 5, 7, 9-11; Chapter 8: Lessons 5, 6, 8, 10; Chapter 10: Lessons Explain how to multiply and divide positive fractions and perform the calculations. AGS Basic Math Skills: Chapter 3: Lessons 7-10; Chapter 12: Lessons Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. AGS Basic Math Skills: Chapter 3: Lessons 7-15; Chapter 12: Lessons Interpret and use ratios to show the relative sizes of two quantities. Use the notations: a/b, a to b, a:b. AGS Basic Math Skills: Chapter 5: Lesson 1; Chapter 8: Lesson 8; Chapter 12: Lessons 1, Understand proportions and use them to solve problems. AGS Basic Math Skills: Chapter 5: Lessons 2-4; Chapter 6: Lesson 8; Chapter 12: Lessons Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. AGS Basic Math Skills: Chapter 6: Lessons Use estimation to decide whether answers are reasonable in decimal problems. AGS Basic Math Skills: Chapter 4: Lessons 3-8, 11 2

3 (Indiana Academic Standards for M athematics: Grade 6, Standard 2, C ont.) Use mental arithmetic to add or subtract simple fractions and decimals. AGS Basic Math Skills: Mental arithmetic skills can be encouraged in exercises throughout Chapter 3: Fractions, Chapter 4: Decimals, and Chapter 6: Percents. Grade 6: Standard 3 Algebra and Functions Students write verbal expressions and sentences as algebraic expressions and equations. They evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. They investigate geometric relationships and describe them algebraically Write and solve one-step linear equations and inequalities in one variable and check the answers. AGS Basic Math Skills: Chapter 13: Lessons 10, 11, Write and use formulas with up to three variables to solve problems. AGS Basic Math Skills: Chapter 5: Lessons 3, 4; Chapter 6: Lessons 4-8; Chapter 8: Lesson 5; Chapter 9: Lessons 7-11; Chapter 10: Lessons 1-3; Chapter 12: Lessons 1-3; Chapter 13: Lessons 8, Interpret and evaluate mathematical expressions that use grouping symbols such as parentheses. AGS Basic Math Skills: Chapter 13: Lessons 2, 3, Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. AGS Basic Math Skills: Chapter 13: Lesson Use variables in expressions describing geometric quantities Apply the correct order of operations and properties of real numbers (e.g., identity, inverse, commutative, associative, and distributive properties) to evaluate numerical expressions. Justify each step in the process. AGS Basic Math Skills: Chapter 1: Lesson 9; Chapter 3: Lesson 10; Chapter 13: Lesson 6; Supplementary Problems: Whole Numbers J 3

4 (Indiana Academic Standards for M athematics: Grade 6, Standard 3, C ont.) Identify and graph ordered pairs in the four quadrants of the coordinate plane. AGS Basic Math Skills: Chapter 13: Lesson Solve problems involving linear functions with integer values. Write the equation and graph the resulting ordered pairs of integers on a grid. AGS Basic Math Skills: Chapter 13: Lesson Investigate how a change in one variable relates to a change in a second variable. Grade 6: Standard 4 Geometry Students identify, describe, and classify the properties of plane and solid geometric shapes and the relationships between them Identify and draw vertical, adjacent, complementary, and supplementary angles and describe these angle relationships. AGS Basic Math Skills: Chapter 7: Lesson Use the properties of complementary, supplementary, and vertical angles to solve problems involving an unknown angle. Justify solutions. AGS Basic Math Skills: Chapter 7: Lesson Draw quadrilater als and triangles from given information about them. AGS Basic Math Skills: Chapter 7: Lesson 4; Chapter 9: Lessons 8, Understand that the sum of the interior angles of any triangle is 180 and that the sum of the interior angles of any quadrilateral in 360. Use this information to solve problems. AGS Basic Math Skills: Chapter 7: Lesson Identify and draw two-dimensional shapes that are similar. AGS Basic Math Skills: Chapter 7: Lesson Draw the translation (slide) and reflection (flip) of shapes. 4

5 (Indiana Academic Standards for M athematics: Grade 6, Standard 4, C ont.) Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids. AGS Basic Math Skills: Chapter 7: Lesson 5; Chapter 8: Lessons 6, 8, 10; Chapter 9: Lessons 10, 11 Grade 6: Standard 5 Measurement Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems. They calculate with temperature and money, and choose appropriate units of measure in other areas Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles. AGS Basic Math Skills: Chapter 7: Lesson 3; Chapter 8: Lessons 1-10; Chapter 9: Lessons Understand and use larger units for measuring length by comparing miles to yards and kilometers to meters. AGS Basic Math Skills: Chapter 8: Lessons 1, 3, 4; Chapter 9: Lesson Understand and use larger units for measuring area by comparing acres and square miles to square yards and square kilometers to square meters. AGS Basic Math Skills: Chapter 8: Lesson 5; Chapter 9: Lessons Understand the concept of the constant p as the ratio of the circumference to the diameter of a circle. Develop and use the formulas for the circumference and area of a circle. AGS Basic Math Skills: Chapter 10: Lessons Know common estimates of p (3.14, 22/7) and use these values to estimate and calculate the circumference and the area of circles. Compare with actual measurements. AGS Basic Math Skills: Chapter 10: Lessons Understand the concept of significant figures and round answers to an appropriate number of significant figures. AGS Basic Math Skills: Chapter 4: Lesson 3; Chapter 10: Lessons 1-3 5

6 (Indiana Academic Standards for M athematics: Grade 6, Standard 5, C ont.) Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area of these objects Use strategies to find the surface area and volume of right prisms and cylinders using appropriate units. AGS Basic Math Skills: Chapter 8: Lessons 6-8; Chapter 9: Lessons 10, 11; Chapter 10: Lesson Use a formula to convert temperatures between Celsius and Fahrenheit Add, subtr act, multiply, and divide with money in decimal notation. AGS Basic Math Skills: Chapter 4: Lessons 4-6, 8; Chapter 6: Lessons 6-14 Grade 6: Standard 6 Data Analysis and Probability Students compute and analyze statistical measures for data sets. They determine theoretical and experimental probabilities and use them to make predictions about events Organize and display single-variable data in appropriate graphs and stem-and-leaf plots, and explain which types of graphs are appropriate for various data sets. AGS Basic Math Skills: Chapter 11: Lessons Make frequency tables for numerical data, grouping the data in different ways to investigate how different groupings describe the data. Understand and find relative and cumulative frequency for a data set. Use histograms of the data and of the relative frequency distribution, and a broken line graph for cumulative frequency Compare the mean, median, and mode for a set of data and explain which measure is most appropriate in a given context. AGS Basic Math Skills: Chapter 11: Lesson Show all possible outcomes for compound events in an organized way and find the theoretical probability of each outcome. 6

7 (Indiana Academic Standards for M athematics: Grade 6, Standard 6, C ont.) Use data to estimate the probability of future events Understand and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable. Grade 6: Standard 7 Problem Solving Students make decisions about how to approach problems and communicate their ideas Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. AGS Basic Math Skills: Problem analysis is emphasized in a variety of ways throughout, including in-text examples, practice Exercises in each lesson, Problem Solving exercises in many lessons, Application exercises following each chapter, and many additional teaching suggestions in the ancillary materials. A wide variety of strategies are used, including those suggested in the standard Make and justify mathematical conjectures based on a general description of a mathematical question or problem Decide when and how to break a problem into simpler parts. AGS Basic Math Skills: In exercises and problem-solving sections throughout, students must often break more complex problems into smaller, simpler parts. See, for example, Chapter 3: Lessons 12, 14; Chapter 4: Lessons 9, 10; Chapter 5: Lesson 4; Chapter 6: Lessons

8 (Indiana Academic Standards for M athematics: Grade 6, Standard 7, C ont.) Students use strategies, skills, and concepts in finding and communicating solutions to problems Apply strategies and results from simpler problems to more complex problems. AGS Basic Math Skills teaches basic concepts of mathematics and introduces algebra concepts in a step-by-step approach. The text is organized into twelve discrete chapters, each of which begins with simpler, more familiar math concepts and then expands to more in-depth or difficult concepts Express the solution clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work. AGS Basic Math Skills: Students are given frequent opportunities to apply acquired terminology and notation in Exercises, Problem Solving sections, and Applications. Class discussion as well as assigned work in both student text and teacher s edition sidebar material encourages verbal wor k in addition to symbolic work Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. AGS Basic Math Skills: Chapter 1: Lessons 2, 5; Chapter 4: Lessons 3, 8; Chapter 6: Lesson 3; Chapter 8: Lesson 3; Chapter 11: Lessons 1, 2, Select and apply appropriate methods for estimating results of rational-number computations. AGS Basic Math Skills: Chapter 4: Lessons 3, 8, Use graphing to estimate solutions and check the estimates with analytic approaches Make precise calculations and check the validity of the results in the context of the problem. AGS Basic Math Skills: Most exercises, problem solving exercises, and applications throughout require precise calculations. In addition to checking their own work, students can find answers to odd-numbered problems at the back of the text. 8

9 (Indiana Academic Standards for M athematics: Grade 6, Standard 7, C ont.) Students determine when a solution is complete and reasonable, and move beyond a particular problem by generalizing to other situations Decide whether a solution is reasonable in the context of the original situation. AGS Basic Math Skills: Exercises, Problem Solving activities, and Application activities provide many opportunities for students to analyze reasonableness throughout Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems. AGS Basic Math Skills: Short lessons with lots of examples illustrate and teach each new skill. Rules are highlighted for quick reference, and math terms are bold-faced and defined throughout. Students are able to see rules and procedures applied to given problems, and then are given further related problems to solve themselves. 9

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