MathMammoth Grade 6. Supplemental Curriculum: Learning Goals/Performance Objectives:

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Marvin Bradford
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1 MathMammoth Grade 6 Class Description: In sixth grade, students encounter the beginnings of algebra, learning about algebraic expressions, one-variable equations and inequalities, integers, and ratios. We also review and deepen the students' understanding of rational numbers: both fractions and decimals are studied in depth, while percent is a new topic for 6th grade. In geometry, students learn to compute the area of various polygons, and also calculate volume and surface area of various solids. The last major area of study is statistics, where students learn to summarize and describe distributions using both measures of center and variability. Learning Materials: Main Curriculum Math Mammoth Light Blue Student Worktexts 6A, 6B, Answer Key book, Cumulative Review& Test book. (*PEARL Recommends using the printed workbook version. It can be purchased at Amazon.com. Alternatively, you could purchase the download, but be aware that you will need to print all the worktext pages yourself. Downloads & CDs are available at MathMammoth.com.) Supplemental Curriculum: Learning Goals/Performance Objectives: 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers 6.EE.3 Apply the properties of operations to generate equivalent expressions. 6.EE.4 Identify when two expressions are equivalent. 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c orx < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems

2 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5 Summarize numerical data sets in relation to their context. 6.SP.5 Summarize numerical data sets in relation to their context Learning Activities: The student will complete these activities, following the timeline below. The student will complete Worktexts 6A and 6B, and supplement learning with the review workbook and online math websites. There is a summative test after each chapter. SEPTEMBER-Chapter 1: Review of the Basic Operations Warm Up: Mental Math 6.EE.7 Review of the Four Operations 1 6.NS.2 Review of the Four Operations 2 6.NS.2 6.NS.3 6.RP.3 Powers and Exponents 20 6.EE.1 Place Value 6.EE.1 Rounding and Estimating Lessons in Problem Solving 6.NS.3 Chapter 1 Review 6.EE.1 6.NS.2 6.NS.3 CHAPTER 1 TEST Chapter 2: Expressions and Equations Terminology for the Four Operations 6.EE.2 6.EE.7 The Order of Operations 6.EE.1 6.EE.2 Multiplying and Dividing in Parts 6.EE.3 OCTOBER-(Chapter 2: continued) Expressions 6.EE.1 6.EE.2 6.EE.4 Writing and Simplifying Expressions 1 6.EE.1 6.EE.2 6.EE.4 Length and Perimeter 6.EE.2 6.EE.3 More on Writing and Simplifying Expressions 6.EE.2 6.EE.3 6.EE.4 Writing and Simplifying Expressions 2: 6.EE.1 6.EE.2 6.EE.4 Area 6.EE.2 6.EE.3 The Distributive Property 6.EE.3 Equations 6.EE.2 6.EE.5 6.EE.7 More Equations 6.EE.3 6.EE.7 Inequalities 6.EE.8 Using Two Variables 6.EE.9 Mixed Review 6.NS.2 6.EE.1 6.EE.2 Chapter 2 Review 6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.5 6.EE.6 CHAPTER 2 TEST NOVEMBER-Chapter 3: Decimals Place Value with Decimals Comparing Decimals Add and Subtract Decimals 6.NS.3 6.EE.2 Rounding Decimals 5.NBT.4 Review: Multiply and Divide Decimals Mentally Review: Multiply Decimals by Decimals 6.NS.3 6.EE.2 6.EE.7 Review: Long Division with Decimals 6.NS.3

3 Problem Solving with Decimals 6.RP.3 6.NS.3 Fractions and Decimals 7.NS.2.d Multiply and Divide by Powers of Ten 6.NS.3 Review: Divide Decimals by Decimals 6.NS.3 6.EE.7 Divide Decimals by Decimals 2 6.NS.3 6.EE.2 6.EE.7 DECEMBER-( Chapter 3:comtinued) Convert Customary Measuring Units Convert Metric Measuring Units 125 Convert Between Customary and Metric Mixed Review 6.NS.2 6.EE.2 6.EE.3 6.EE.5 6.EE.8 Chapter 3 Review 6.NS.3 6.EE.1 6.EE.2 6.EE.7 CHAPTER 3 TEST Chapter 4: Ratios Ratios and Rates 6.RP.1 6.RP.3 Unit Rates 6.RP.2 6.RP.3 Using Equivalent Rates. 6.RP.3 6.EE.9 JANUARY-Chapter 4continued) Ratio Problems and Bar Models 1 6.RP.3 Ratio Problems and Bar Models 2 6.RP.3 Aspect Ratio 6.RP.3 Using Rates to Convert Measuring Units 6.RP.3 Mixed Review 6.NS.3 6.EE.1 6.EE.2 6.EE.9 Chapter 4 Review 6.RP.1 6.RP.2 6.RP.3 CHAPTER 4 TEST Chapter 5: Percent Percent What Percentage...? Percentage of a Number (Mental Math) 6.RP.3 Percentage of a Number: Using Decimals 6.RP.3 Discounts Practice with Percent 6.RP.3 Finding the Total When the Percent Is Known 6.RP.3 Mixed Review 6.NS.2 6.NS.3 6.EE.2 6.EE.3 6.EE.7 6.RP.3 Review: Percent 6.RP.3 CHAPTER 5 TEST FEBRUARY-Chapter 6: Prime Factorization, GCF, and LCM. The Sieve of Eratosthenes and Prime Factorization Using Factoring When Simplifying Fractions The Greatest Common Factor (GCF) 6.NS.4 Factoring Sums 6.NS.4 The Least Common Multiple (LCM) 6.NS.4 Mixed Review 6.NS.3 6.RP.3 6.EE.1 6.EE.2 6.EE.3 6.EE.5 Chapter 6 Review 6.NS.4 CHAPTER 6 TEST Chapter 7: Fractions Review: Add and Subtract Fractions and Mixed Numbers 6.EE.2 5.NF.1 5.NF.2 Add and Subtract Fractions: More Practice 5.NF.1 Review: Multiplying Fractions 1 5.NF.4 5.NF.6 Review: Multiplying Fractions 2 5.NF.4 5.NF.6 Dividing Fractions: Reciprocal Numbers 6.NS.1

4 Divide Fractions 6.NS.1. MARCH-(Chapter 7 continued) Problem Solving with Fractions 1 6.NS.1 Problem Solving with Fractions 2 6.NS.1 6.RP.3 Mixed Review 6.RP.3 6.NS.3 6.NS.4 6.EE.2 Fractions Review 6.NS.1 CHAPTER 7 TEST Chapter 8: Integers Integers 6.NS.5 6.NS.6 6.NS.7 Coordinate Grid 6.NS.8 Coordinate Grid Practice 6.NS.7 6.NS.8 6.G.3 Addition and Subtraction as Movements 7.NS.1 Adding Integers: Counters 7.NS.1 Subtracting a Negative Integer 7.NS.1 Add and Subtract Roundup 7.NS.1 Graphing 6.NS.8 6.EE.2 6.EE.9 Mixed Review 6.EE.7 6.RP.3 6.NS.1 Integers Review 6.NS.5 6.NS.6 6.NS.7 6.NS.8 6.G.3 CHAPTER 8 TEST APRIL-Chapter 9: Geometry Quadrilaterals Review 5.G.4 Drawing Problems Area of Right Triangles 6.G.1 Area of Parallelograms 6.G.1 Area of Triangles 6.G.1 Area of Polygons 6.G.1 Polygons in the Coordinate Grid 6.NS.8 6.G.3 Area and Perimeter Problems 6.G.1 6.RP.3 Nets and Surface Area 1 6.G.4 Nets and Surface Area 2 6.G.4 Converting Between Area Units 6.G.1 MAY/JUNE-Chapter 9 continued) Volume of a Rectangular Prism with Fractional Side Lengths 6.G.2 Volume Problems 6.G.2 Mixed Review 6.NS.1 6.NS.3 6.RP.1 6.RP.2 6.RP.3 6.EE.7 6.EE.9 6.G.1 6.G.3 Geometry Review 6.G.1 6.G.2 6.G.4 CHAPTER 9 TEST Chapter 10: Statistics Understanding Distributions 6.SP.1 6.SP.2 6.SP.4 6.SP.5 Mean, Median, and Mode 6.SP.3 6.SP.4 6.SP.5 Using Mean, Median, and Mode 6.SP.3 6.SP.4 6.SP.5 Measures of Variation 6.SP.3 6.SP.4 6.SP.5 Making Histograms 6.SP.4 6.SP.5 Boxplots 16.SP.4 Stem-and-Leaf-Plots 6.SP.4 6.SP.5 Mixed Review 6.NS.1 6.NS.4 6.NS.7 6.G.1 6.G.3 6.EE.3 6.EE.7 Statistics Review 6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5 CHAPTER 10 TEST

5 Progress Criteria/Methods of Evaluation: For successful completion of this course, the student will complete at least 70% of the lessons/goals, at a minimum of 70% accuracy. See timeline above.

Unit Title Key Concepts Vocabulary CCS

Unit Title Key Concepts Vocabulary CCS Unit 1 Writing and Evaluating s Unit 2 Writing and Solving Equations s and Equations Write numerical expressions Evaluate numerical expressions Write algebraic expressions