Course: RPC 6th Grade Math Procedures

Course Description

Math PCD is one of two math classes taken daily by 6th graders at Roxbury Prep. It focuses on conceptual and computational work, preparing students for the word problems, data analysis, and other topics they cover in their Math Problem Solving class. Many files in these lessons contain comments about instruction, as well as in-class notes written on a SMART Board. PLEASE NOTE: I have some uploading and updating to do, so please send me a message if you are interested in units or lessons that appear incomplete!

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Curriculum

41 lessons 1 Whole Numbers
Whole number computation, number theory, and early algebra work
- Lessons
- First Day - Class Systems
  Students will be able to perform Math PCD class systems.
  
  Students will be able to identify place values.
- Expanded Form, Whole #s
  Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation.
- Whole Number Forms (St, W, Ex)
  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.
  Students will be able to complete and score Mad Minute drills.
- Comparing Whole Numbers
  Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents.
- Whole Number Lines
  Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.
- Whole Number Lines 2
  Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.
- Counting by Increments
  Students will be able to count by whole number increments.
- Rounding Whole Numbers
  Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.
- Rounding, non-routine
- Addition
  Students will be able to define and perform addition, using appropriate terminology.
- Subtraction
  Students will be able to define subtraction terms and use appropriate subtraction phrases.
- Subtraction with Regrouping
  Students will be able to subtract whole numbers by regrouping.
- Math Writing Workshop
  Students will be able to write explanations using appropriate math vocabulary.
- Multiplication
  Students will be able to define multiplication terms and quickly estimate products.
- Quick Multiplication
  Students will be able to estimate products by quickly multiplying multiples of 10.
- Multiplication, Partial Products 1
  Students will be able to multiply whole numbers with two or more digits by using partial products.
- Multiplication, Partial Products 2
  Students will be able to multiply whole numbers with two or more digits by using partial products.
- Estimation in Multiplication
  Students will be able to estimate answers to multiplication problems.
- Division
  Students will be able to define division and use correct phrases for division problems.
- Long Division 1
  Students will be able to divide by a 1-to-3-digit divisor to get a 1-to-3-digit quotient.
- Long Division 2
  Students will be able to divide by a 1-to-3-digit divisor to get a 1-to-3-digit quotient.
- Multiples and Long Division
  Students will be able to use multiples as an aid in long division problems.
- Exponentials
  Students will be able to evaluate exponentials with whole-number bases and exponents.
- Least Common Multiples
  Students will be able to find the least common multiple for a given pair or set of numbers.
- Factors
  Students will be able to define factors. Students will be able to find the common factors of numbers.
- Divisibility by 2, 5, and 10
  Students will be able to state and apply divisibility rules for 2, 5, and 10.
- Prime and Composite Numbers - Factor Game
  Students will be able to distinguish prime and composite numbers using the factor game.
- Divisibility by 3, 9
  Students will be able to state and apply divisibility rules for 3, and 9.
- Prime and Composite Classification
  Students will be able to classify numbers as prime or composite.
- Prime Factorization
  Students will be able to write the prime factorization of a number.
- Prime Factorization with Exponentials
  Students will be able to write the prime factorization of a number using exponentials.
  Students will be able to use divisibility rules to begin factor trees.
- Common Factors and Divisibility Rules
  Students will be able to find common factors using diagrams and divisibility rules.
- Greatest Common Factor
  Students will be able to find the greatest common factor of two numbers.
- Order of Operations 1
  Students will be able to evaluate expressions with multiple operations.
- Order of Operations 2
  Students will be able to evaluate expressions with multiple operations and exponentials.
- Order of Operations 3
  Students will be able to evaluate expressions with multiple operations.
- Order of Operations 4, Make 24
  Students will be able to evaluate expressions with multiple operations.
- Variables
  Students will be able to define variables and evaluate expressions that contain variables.
- Variables, Day 2
- Algebraic Expressions
- Solving for Unknowns
25 lessons 2 Decimals
Decimal concepts, place value, and computation
- Lessons
- Introduction to Fractions
- Fraction Word Form
- Mixed Numbers and Improper Fractions
- Mixed Numbers and Improper Fractions, Day 2
- Fractional Number Lines
- Introduction to Decimals
  Students will be able to show decimal amounts.
- Decimal Increments
  Students will be able to count by decimal increments.
- Decimal Number Forms
  Students will be able to read and write decimals to the thousandths place.
- Decimal Expanded Form
  Students will be able to write decimals in expanded form.
- Decimals on Number Lines
  Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.
- Comparing Decimals
  Students will be able to compare and order decimals.
- Decimal Addition and Subtraction
  Students will be able to master adding, subtracting, and ordering decimals.
- Decimal Addition/Subtraction Mastery
  Students will be able to show mastery of decimal addition and subtraction.
- Multiplying Decimals 1
  Students will be able to multiply decimals by whole numbers.
- Multiplying Decimals 2
  Students will be able to multiply whole numbers and decimals by decimals.
- Multiplication and Magnitude
  Students will be able to describe the effects of multiplying by decimals greater than and less than 1 whole.
- Rounding Decimals 1
  Students will be able to round numbers to decimal places.
- Rounding Decimals 2
  Students will be able to round numbers to decimal places.
- Decimal Dividends
  Students will be able to divide by whole numbers, writing quotients as decimals.
- Decimal Quotients
  Students will be able to use decimal quotients as an alternative to remainders.
- Decimal Division Review
  Students will be able to estimate quotients in decimal division problems.
- Powers of Ten and Expanded Form
- Decimal Divisors
- Decimal Divisors, Day 2
- Powers of Ten and Expanded Form, Day 2
35 lessons 3 Fractions
Fraction concepts, comparison, and computation; conversions between fractions and decimals
- Lessons
- Fractions, 1st lesson
- Fraction Word Form
  Students will be able to write fractions in word form.
- Mixed Numbers, Improper Fractions
  Students will be able to convert between mixed numbers and improper fractions.
- Conversions of Fractional Forms
  Students will be able to convert between mixed numbers and improper fractions.
- Fractional Number Lines
  Students will be able to place and compare fractional forms on number lines.
- Equivalent Fractions
  Students will be able to find fractions equivalent to given fractions.
- Comparing Fractional Forms
  Students will be able to compare fractions and mixed numbers with like denominators.
- Comparing Fractions Using LCDs
  Students will be able to compare fractional forms with different denominators by finding a common denominator.
- Simplifying Fractions
  Students will be able to simplify fractions using common factors.
- Fractions of Groups
  Students will be able to create visual representations of fractions of groups.
- Fraction Drawings
  Students will be able to create visual representations of fractional amounts.
- Fraction Addition and Subtraction (like denominators)
  Students will be able to add and subtract fractions with like denominators. Students will be able to write answers as simplified mixed numbers.
- Fraction Addition and Subtraction (unlike denominators)
  Students will be able to add and subtract fractions with different denominators by using a common denominator.
- Mixed Number Addition and Subtraction
  Students will be able to add and subtract mixed numbers, using common denominators when necessary.
- Regrouping with Fraction Addition
  Students will be able to use regrouping when adding and subtracting mixed numbers.
- Subtracting Fractional Forms
  Students will be able to add and subtract all fractional forms.
- Subtracting Fractional Forms (Day 2)
  Students will be able to combine common denominators and regrouping when they subtract.
- Fractions of Wholes
  Students will be able to illustrate and describe examples of multiplication of a whole number and a fraction.
- Multiplying Fractions by Wholes
  Students will be able to multiply a fraction and a whole number.
- Fractions of Fractions
  Students will be able to illustrate and describe examples of multiplication of two fractions.
- Multiplying Fractions by Fractions
  Students will be able to multiply fractions by fractions and simplify products.
- Multiplying Fractions and Mixed Numbers
  Students will be able to multiply fractions by mixed numbers and simplify products.
- Fraction Dividends
  Students will use area models to divide fractions by whole numbers.
- Fraction Divisors
  Students will be able to illustrate and describe division by a fraction.
- Fraction Division
  Students will be able to relate division with fractional forms to multiplication.
- Division with Reciprocals
  Students will be able to divide with fractional forms, using a reciprocal.
- Decimals to Fractions
  Students will be able to convert decimals to fractions and mixed numbers and simplify them.
- Fractions to Decimals
- Fractions to Terminating Decimals
  Students will be able to convert fractions and mixed numbers to terminating decimals.
- Fractions to Repeating Decimals
  Students will convert fractions and mixed numbers to repeating decimals.
- More Repeating Decimals
  Students will convert fractions and mixed numbers to repeating decimals.
- Patterns in Repeating Decimals
  Students will be able identify patterns in the repetends of repeating decimals.
- Fraction/Decimal Benchmarks
  Students will be able to calculate and memorize common fraction/decimal equivalents.
- Using Fraction-Decimal Benchmarks
  Students will be able to use fraction and decimal benchmarks in solving problems.
- Comparing Fractions and Decimals
10 lessons 4 Percents
Percent concepts and computation; conversions between fractions, decimals, and percents
- Lessons
- Percents (1st lesson)
  Students will be able to define percents and use qualitative language related to percentage.
- Fractions to Percents
  Students will be able to convert fractions to percents.
- Fractions to Percents 2
  Students will be able to convert fractions to percents.
- Calculating Percentages
- Calculating Percentages, Day 2
- Comparing Statistics with Percentages
- Fractions to Percents 3
  Students will be able to convert fractions to percents.
- Comparing Parts of Wholes
  Students will be able to compare decimals, fractions, and percents of different amounts.
- F-D-P Comparison
  Students will be able to compare decimals, fractions, and percents of different amounts.
- F-D-P Ordering
  Students will be able to order fractions, decimals, and percents.
57 lessons 5 Geometry
A survey of 2D and 3D geometry topics
- Lessons
- Coordinate Plane
  Students will be able to identify parts of, and points in, the coordinate plane.
- Point-Line-Plane Introduction
  Students will be able to define, identify, and draw points, lines, planes, rays and segments.
- Geometry Notation
  Students will be able to use correct notation for representing lines, segments and rays.
- Parallel and Intersecting Lines
  Students will be able to define and identify intersection lines and parallel lines.
- Parallel and Intersecting Lines (day 2)
  Students will be able to define and identify intersection lines and parallel lines.
- Angles
  Students will be able to define, identify, and name angles.
- Measuring Angles
  Students will be able to measure angles using a protractor.
- Classifying Angles
  Students will be able to classify angles as acute, obtuse, right, or straight.
- Perpendicular and Oblique Lines
  Students will be able to define and identify perpendicular and oblique lines.
- Finding Angles
- Polygons
  Students will define and name polygons according to the number of sides and angles.
- Circles
  Students will be able to define circles. Students will be able to define, identify, and calculate the measures of diameters and radii.
- Circumference and Pi
  Students will be able to define the circumference of a circle and the number pi.
- Circle Dimensions
  Students will be able to practice calculating the radius, diameter, and circumference of a circle.
- Complementary Angles
  Students will be able to identify and calculate the measures of complementary angles.
- Supplementary Angles
  Students will be able to identify and calculate the measures of supplementary angles.
- Circle Algebra
  Students will be able to show the relationship between diameter and circumference using algebraic tools.
- Circle Area 1
  Students will be able to calculate the area of a circle.
- Circle Area 2
  Students will be able to calculate the area of a circle.
- Triangles
  Students will be able to distinguish components of triangles.
  Students will be able to enter answers on CPS RF pads.
- Triangle Angle Sum
  Students will be able to calcuate the size of a triangle's interior angle given the other two angles.
- Classifying Triangles by Angles
  Students will be able to classify triangles by their interior angles.
- Classifying Triangles by Sides
  Students will be able to classify triangles by the lengths of their sides.
- Classifying Triangles
  Students will be able to determine the various possible classifications of triangles.
- Polygon Angle Sum
- Polygon Angle Sum, Day 2
- Classifying Quadrilaterals, Day 1
  Students will be able to classify quadrilaterals by their properties.
- Classifying Quadrilaterals, Day 2
  Students will be able to classify quadrilaterals by their properties.
- Altitudes and Area
  Students will be able to identify altitudes of parallelograms and triangles as related to those shapes' area.
- Parallelogram Area
  Students will be able to find the areas of all types of parallelograms.
- Triangle Area 1
  Students will be able relate the area of a triangle to the area of a parallelogram.
- Triangle Area 2
  Students will be able to find the area of a triangle.
- Classifying Quadrilaterals, Continued
- Regular Polygons
- Kites
- Classifying Triangles (PowerPoint)
  Students will be able to complete PowerPoint slides with different classifications of triangles.
- Prism Nets
  Students will be able to define rectangular prisms. Students will be able to define cubes and draw their nets.
- Cube Nets
- Net Mastery
  Students will be able to create the net for a rectangular prism.
- Surface Area
  Students will be able to use nets to calculate the surface area of a rectangular prism.
- Surface Area 2
  Students will be able to calculate the surface area of a rectangular prism.
- Summarizing Geometry Notes
- Prism Volume 1
  Students will be able to define volume and find the volume of a rectangular prism.
- Prism Volume 2
  Students will be able to define volume and find the volume of a rectangular prism.
- Translations
  Students will be able to translate points and shapes in the coordinate plane.
- Reflections
  Students will be able to reflect a figure over a line.
- Line Symmetry
  Students will be able to define line symmetry and find the lines of symmetry in a figure.
- Rotational Symmetry
  Students will be able to define rotational symmetry and identify figures that have rotational symmetry.
- Symmetry Review
- Net Completion
- MCAS Review
  Students will be able to review MCAS material using a recent assessment.
- Prism Types
  Students will be able to define prisms and name types of prisms.
- Pyramids
  Students will be able to define and identify pyramids. Students will be able to count edges, vertices, and faces for prisms and pyramids.
- Graphing Prism Components
- Graphing Circle Measures
- Graphing Polygon Angle Measures
- Kite Area
21 lessons 6 Extensions and Review
- Lessons
- Mastery of the Order
  Students will be able to review and practice using the order of operations.
- Powers of Ten
  Students will be able to write the expanded form of a number using powers of ten.
- Decimal Divisors 1
  Students will be able to divide by decimal divisors.
- Decimal Divisors 2
  Students will be able to divide by decimal divisors.
- Polygon Angle Sum, Day 1
  Students will be able to find the sum of any polygon's angles.
- Polygon Angle Sum, Day 2
  Students will be able to graph and discuss algebraically the angle sums of various polygons
- Kites
  Students will be able to define kites and classify them with other quadrilaterals.
- Congruent Figures
  Students will will be able to identify congruent figures and explain their congruence.
- Line Systems and Angles
  Students will be able to find acute and obtuse angles in systems of lines.
- Writing Expressions for Given Conditions
  Students will be able to write expressions for numbers that match given conditions.
- Regular Polygons and Angles
  Students will be able to calculate the measures of the interior angles of regular polygons.
- Regular Polygons and Angles - Graphing
  Students will be able to calculate and graph the measures of the interior angles of regular polygons.
- Multiplying Integers 1
  Students will be able to multiply positive and negative numbers.
- Multiplying Integers 2
  Students will be able to multiply positive and negative numbers.
- Multiplying Integers 3
  Students will be able to practice multiplying positive and negative numbers.
- Homework Review
  Students will be able to review recent homework in preparation for their exam.
- Final Exam Answer Submission
  Students will be able to complete their comp exams and submit scores using their CPS pads.
- Tessellations
  Students will be able to define and create tessellations with quadrilaterals.
- PCD Competition
  Students will be able to earn points for their advisories in an in-class competition.
- PCD Final Comp Review and Correction
  Students will be able to review their final comps and assess their overall improvement for the year.
- Determining Mr. Armstrong's Age
  Students will be able to determine a particular number using clues about its properties.
2 lessons Assessments
- Lessons
- Quizzes
  Short assessments on specific topics.
- Tests
  Full-period unit or cumulative assessments
4 lessons Daily Activities
- Lessons
- Mad Minute
  Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500.
- Number of the Day
  Students will be able to write numerical expressions for given numbers, employing the order of operations and fitting given conditions.
- Make 24 Problem of the Day
- Decimal Race
  Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.