Math: Grade 6 Unit: Data About Us: Statistics Suggested Length: 5-6 weeks

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1 Reporting Category: Data and Analysis Math: Grade 6 Unit: Data About Us: Statistics Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Idea: Collecting, organizing displaying and analyzing data helps us make informed decisions about people and the world around us. Essential Question: How is data collected, analyzed, and displayed to be useful for informed decision- making? M6.E Analyze data and/or answer questions pertaining to data represented in frequency tables, double bar graphs, line plots. M6.E Display data in frequency tables, bar graphs or line plots using a title, appropriate scale, labels and a key when needed. Understand and use the process of data investigation: posing questions, collecting and analyzing data distributions, and making interpretations to answer questions. Develop strategies for comparing distributions of data. Represent distributions of data using line plots, bar graphs, stem and leaf plots and coordinate graphs. bar graph categorical data coordinate graph distribution line plot mean median measures of center mode numerical data outlier range stem and leaf plot survey table x-axis y-axis Data About Us textbook Launch -Pre-assessment Explore -Investigation -Group Activity Summarize -Post-assessment Quizzes Check Ups Self-Assessments Unit Test Unit Projects

2 M6.E Determine/calculate the mean, median, mode and/or range of displayed data (data can be displayed in a table or line plot use whole numbers only up to 2 digits). Compute the measures of central tendency: the mean, median, mode and range of the data. M6.E Choose the appropriate representation for a specific set of data (choices should be the same type of graph). Make informed decisions about which graph(s) and which measures of center (mean, median, mode) and range may be used to describe a distribution of data. Distinguish between categorical and numerical data and identify which graphs and statistics may be used to represent each kind of data.

3 Reporting Category: Numbers and Operations Math: Grade 6 Unit: Prime Time: Factors and Multiples Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Ideas: The important properties of whole numbers are directly related to properties of multiplication and division. The relationship between whole number properties and multiplication and division properties are useful for solving everyday problems. Essential Questions: How are the properties of whole numbers related to the properties of multiplication and division? How are properties of whole numbers used to solve everyday problems? M6.A Find the Greatest Common Factor (GCF) of two numbers (through 50) and/or use the GCF to simplify fractions. M6.A Find the Least Common Multiple (LCM) of two numbers (through 50) and/or use the LCM to find the common denominator of two fractions. M6.A Use divisibility rules for 2, 3, 5 and/or 10 to draw conclusions and/or solve problems. Develop strategies for finding factors and multiples, and greatest common factors. Use rectangles to represent the factor pairs of numbers. Use factors and multiples to solve problems and to explain some numerical facts of everyday life. Understand the relationships among factors, multiples, divisors and products. Recognize and use properties of prime and composite numbers, even and odd numbers, and abundant number common factor common multiple composite number conjecture deficient number dimensions (whole number) divisor even number exponent (whole number) factor factor pair factorization greatest common factor (GCF) lowest common factor (LCM) multiple odd number perfect number prime factorization prime number proper factor square number Venn Diagram Prime Time textbook Launch -Pre-assessment Explore -Investigation -Group Activity Summarize -Post-assessment Quizzes Check Ups Self-Assessments Unit Test Unit Projects

4 square numbers. M6.A Solve problems involving operations (+, -, x, ) with whole numbers, Recognize and use the fact that every whole number can be written in exactly one way as a product of prime numbers. Develop a variety of strategies for solving problems --building models, making lists and tables, drawing diagrams and solving simpler problems.

5 Reporting Category: Numbers and Operations Math : Grade 6 Unit: Bits and Pieces I: Understanding Fractions, Decimals and Percents Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Ideas: Fractions, decimals, and percents are related and they are apart of the set of rational numbers. Rational numbers are an essential part of everyday life. Essential Questions: How are fractions decimals and percents related? How is this relationship useful in everyday life? M6.A Represent common percents as fractions and/or decimals (e.g., 25% = ¼ =.25) common percents are 1%, 10%, 25%, 50%, 75%, 100%. M6.A Convert between fractions and decimals and/or differentiate between a terminating decimal and a repeating decimal. M6.A Represent a number in exponential form (e.g., 10x10x10=10 3 ). M6.A Represent a mixed number as an improper fraction. Model situations involving fractions, decimals and percents. Move flexibly among fraction, decimals and percent representations. Understand and use equivalent fractions to reason about situations. Use benchmark fractions and whole numbers to help estimate the size of a number or sum. benchmark decimal denominator equivalent fraction fraction improper fraction mixed number numerator percent place value ratio rational number Bits and Pieces I textbook Launch -Pre-assessment Explore -Investigation -Group Activity Summarize -Post-assessment Quizzes Check Ups Self-Assessments Unit Test Unit Projects Develop and use benchmarks that relate different forms of rational numbers. Use context, physical models, drawings, patterns or estimation

6 top help reason about real life situations involving rational numbers. M6.A Compare and/or order whole numbers, mixed numbers, fractions and/or decimals (do not mix fractions and decimals decimals through thousandths). Compare and order fractions and decimals.

7 Reporting Category: Measurement; Geometry Math: Grade 6 Unit: Shapes and Designs: Two-Dimensional Geometry Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Idea : Displaying, analyzing, measuring, and reasoning about shapes are important features of our world Essential Questions: How do we display, analyze, measure and reason about shapes? Why is being able to display, analyze, measure and reason about shapes an important feature of our world? M6.C Identify, classify and/or compare polygons (up to ten sides.) M6.C Identify, describe and/or label parallel, perpendicular or intersecting lines. Understand some important properties of polygons and recognize polygonal shapes both in and out of the classroom Draw or sketch polygons with certain properties Find patterns that help determine angle sums of polygons Investigate the symmetries of a shape rotation or reflection Explore parallel lines and angles created by lines intersecting parallel lines acute angle angle angle sum central angle degree diagonal equilateral triangle exterior angle interior angle isosceles angle irregular polygon line of symmetry line segment midpoint obtuse angle parallel lines parallelogram perpendicular lines polygon quadrilateral ray rectangle reflection symmetry regular polygon rhombus right angle rotation symmetry scalene triangle square straight angle Shapes and Designs textbook Launch -Pre-assessment Explore -Investigation -Group Activity Summarize -Post-assessment Quizzes Check Ups Self-assessments Unit Test Project: Create your own design/picture

8 tiling transversal trapezoid vertex M6.B Measure angles using a protractor up to protractor must be drawn - one side of the angle to be measured should line up with the straight edge of the protractor. Use an angle ruler or protractor for making more accurate angle measurements Estimate the measure of any angle using reference to a right angle and other benchmark angles M6.C Identify and/or describe properties of all types of triangles (scalene, equilateral, isosceles, right, acute, obtuse). M6.C Identify and/or use the total number of degrees in a triangle, quadrilateral and/or circle. Explain the property of triangles that makes them useful as a stable structure for building Find that the sum of two side lengths of a triangle is greater than the third side length Find that the sum of three side lengths of a quadrilateral is greater than the fourth side length M6.B Define, label and/or Reason about and

9 identify right, straight, acute and obtuse angles. M6.C Identify, draw and/or label points, planes, lines, line segments, rays, angles and vertices. solve problems involving shapes Determine which polygons fit together to cover a flat surface and why

10 Reporting Category: Numbers and Operations Math: Grade 6 Unit: Bits and Pieces II: Using Fraction Operations Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Idea: Develop an understanding of and strategies for computations involving fractions. Essential Question: What strategies and skills are useful for students to be able to perform fractional computations? M6.A Solve problems involving operations (+, -, x, ) with whole numbers, decimals (through thousandths) and fractions (avoid complicated LCDs) - straight computation or word problems. Use benchmarks and other strategies to estimate the reasonableness of results of operations with fractions Use estimates and exact solutions to make decisions Solve problems using arithmetic operations on fractions algorithm benchmark denominator equivalent fractions fact family numerator reciprocal unit fraction Bits and Pieces II textbook Launch -Pre-assessment Explore -Investigation -Group Activity Summarize -Post-assessment Develop ways to model sums, differences, products, and quotients with areas, strips, and number lines Quizzes Check Ups Self-Assessments Unit Test Look for and generalize patterns in numbers Use knowledge of fractions and equivalence of fractions to develop

11 algorithms for adding, subtracting, multiplying and dividing fractions Recognize when addition, subtraction, multiplication, or division is the appropriate operation to solve a problem Write fact families to show the inverse relationship between addition and subtraction, and between multiplication and division

12 Reporting Category: Numbers and Operations Math: Grade 6 Unit: Bits and Pieces III: Computing with Decimals and Percents Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA Standards) Competencies Key Vocabulary Suggested activities/labs and assessments (formative & summative) Big Idea: Develop an understanding of and strategies for computations involving decimals. Essential Question: What strategies and skills are useful for students to be able to perform decimal computations? M6.A Use estimation to solve problems involving whole numbers and decimals (up to 2- digit divisors and 4 operations). M6.A Solve problems involving operations (+, -, x, ) with whole numbers, decimals (through thousandths) and fractions (avoid complicated LCDs) - straight computation or word problems. Build on knowledge about operations with fractions and whole numbers Develop and use benchmarks and other strategies to estimate the answers to computations with decimals Develop meaning or and algorithms for operations with decimals Use the relationship between decimals and fractions to develop and understand why decimal algorithms work dividend divisor powers of 10 quotient repeating decimal terminating decimal Suggested activities: Bits and Pieces III Investigations Launch -Pre-assessment Explore -Investigation Group Activity Summarize -Post-assessment Suggested assessments: Quizzes Check Ups Self-assessments Unit Test Use the place value interpretations of decimals to make sense of shortcut algorithms for

13 operations Generalize number patterns to help make sense of decimal operations Choose between addition, subtraction, multiplication, or division as an appropriate operation to use to solve a problem Understand that decimals are often associated with measurements in realworld situations Solve problems using operations with decimals Big Idea: Develop an understanding of and strategies for computations involving percents. Essential Question: What strategies and skills are useful for students to be able to perform computations involving percents? Use understanding of operations and the meaning of percents to solve percent problems of the form a% b equals c for any one of the variables a, b, or c