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6th Grade – Unit 1 – Prime Time (23 days) Things to Emphasize: GCF, LCM, and prime factorization Prime and composite numbers Distributive Property and factoring Order of Operations Standards: Materials/Technology: Quick Glance: Additional Resources: Mathshell - LCM and GCF Evidence of Learning: Unit Readiness Assessment 2 Check Ups 1 Partner Quiz 1 Unit Project 1 Unit Test 1 Unit Project 1 School Net Assessment Named: 6th Grade – Prime Time (Code: PA4QU3KY) Inv 1 (all): Building on Factors and Multiples Inv 2 (all): Common Multiples and Common Factors Inv 3 (all): Searching for Factor Strings Inv 4 (all): Linking Multiplication and Division Vocabulary: Coefficient Composite number Distributive Property Expanded form Factor Factor pair Factored form GCF LCM Order of Operations Prime factorization Prime number Product Quotient Sum Term 6.NS.2 – Fluently divide multi-digit numbers using the standard algorithm. 6.NS.4 – Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. 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. Identify parts of an expression using mathematical terms. Important Notes: Right before this unit, teach 6.NS.2 – they will need division to work on factors 6th Grade - Unit 2 – Comparing Bits and Pieces (25 days) Things to Emphasize: Relationship between fractions, percents, and decimals Ratios and rates – unit rate Benchmarks for percents Equivalence Negative numbers – opposites, absolute value Standards: Materials/Technology: Additional Resources: DPI - Lessons for Learning – Bake Sale Brownies DPI - Lessons for Learning – Paper Clip Comparisons Evidence of Learning: Important Notes: Unit Readiness Assessment This unit is laying the foundation for work with 2 Check Ups fractions, decimals, percents, 1 Partner Quiz and negative numbers; they 1 Unit Test are not expected to add, 1 Self Assessment subtract, multiply, or divide 1 School Net Assessment them in this unit, this will Named: 6th Grade – come in the next two units Comparing Bits and Pieces Quick Glance: Inv 1 (all): Making Comparisons Inv 2 (all): Connecting Ratios and Rates Inv 3 (all): Extending the Number Line Inv 4 (4.1, 4.2): Working with Percents Vocabulary: Absolute value Benchmarks Equivalent fractions Improper fractions Mixed number Opposites Percent Rate table Ratio Unit rate 6.RP.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b and use rate language in the context of a ratio relationship. 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. Make takes of equivalent ratios, solve unit rate problems, find percent of a quantity, use ratio reasoning to convert measurement units. 6.NS.5 – Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. 6.NS.6 – Understand a rational number as a point on the number line. 6.NS.7 – Understand ordering and absolute value of rational numbers. 6.EE.3 – Apply the properties of operations to generate equivalent expressions. 6.EE.6 – Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 6th Grade - Unit 3 – Let’s Be Rational (20 days) Things to Emphasize: Adding and subtracting fractions Multiplying fractions Dividing fractions Area models, visual fraction models, etc. to represent the operations Standards: Materials/Technology: Pinch Cards Quick Glance: Additional Resources: Evidence of Learning: Unit Readiness Assessment 2 Check Ups 1 Partner Quiz 1 Self Assessment 1 Unit Test 1 Unit Project 1 School Net Assessment Named: 6th Grade – Let’s Be Rational Inv 1 (all): Extending Addition and Subtraction of Fractions Inv 2 (all): Building on Multiplication with Fractions Inv 3 (all but 3.3): Dividing with Fractions Inv 4 (4.3): Wrapping Up the Operations Vocabulary: Algorithm Benchmark Number sentence Overestimate Reciprocal Underestimate 6.NS.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. 6.NS.2 – Fluently divide multi-digit numbers using the standard algorithm. 6.NS.4 – Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express. 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.6 – Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Important Notes: Allow students to represent these operations in multiple methods and acquire their own understanding of how to preform these operations before teaching them the algorithm 6th Grade - Unit 4 – Decimal Ops (23 days) Things to Emphasize: Adding and subtracting decimals Multiplying and dividing decimals Using percents in real life Standards: Materials/Technology: Quick Glance: Additional Resources: Evidence of Learning: Unit Readiness Assessment 2 Check Ups 1 Partner Quiz 1 Self Assessment 1 Unit Test 1 Unit Project 1 School Net Assessment Named: 6th Grade – Decimal Ops Inv 1 (all): Decimal Operations and Estimation Inv 2 (all): Adding and Subtracting Decimals Supplement: Multiplying and Dividing Decimals Inv 4 (all): Using Percents Vocabulary: Dividend Divisor Estimate Expanded form Factored form Percent Quotient Ratio Repeating decimal Terminating decimal Unit rate 6.RP.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b and use rate language in the context of a ratio relationship. 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems. Make takes of equivalent ratios, solve unit rate problems, find percent of a quantity, use ratio reasoning to convert measurement units. 6.NS.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. 6.NS.2 – Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3 – Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.EE.3 – Apply the properties of operations to generate equivalent expressions. 6.EE.5 – Understand solving an equation or inequality as a process of answering a question. Use substitution to determine if a number 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. Important Notes: Percents and decimals are one of the most applicable areas of math that our students will encounter on a regular basis – make sure students can work with benchmark percents and find tips, discounts, tax, etc. 6th Grade - Unit 5 – Variables and Patterns (26 days) Things to Emphasize: Relationship between variables, tables, and graphs Equivalent expressions Solving equations and inequalities Writing expressions and expressions and interpreting them Standards: Materials/Technology: Quick Glance: Additional Resources: DPI - Lessons for Learning – I’ll Race You? Evidence of Learning: Important Notes: Unit Readiness Assessment 2 Check Ups 1 Partner Quiz 1 Self Assessment 1 Unit Test 1 School Net Assessment Named: 6th Grade – Variables and Patterns Inv 1 (all): Variables, Tables, and Graphs Inv 2 (all): Analyzing Relationships Among Variables Inv 3 (all): Relating Variables with Equations Inv 4 (all): Expressions, Equations, and Inequalities Vocabulary: Average speed Coefficient Dependent Equation Equivalent Expression Independent Inequality Rate of change Solution Term Variable 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems (equivalent ratios and unit rate). 6.NS.8 – Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. 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.5 – Understand solving an equation or inequality as a process of answering a question. Use substitution to determine whether a given number makes it true. 6.EE.6 – Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 6.EE.7 – Solve real-world and mathematical problems by writing and solving equations in the form of x + p = q and px=q (no negatives). 6.EE.8 – Write an inequality of the form x>c or x<c to represent a constraint or condition in real-world or mathematical problem, has infinitely many solutions, and represent on number line. 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. 6th Grade - Unit 6 – Covering and Surrounding (23 days) Things to Emphasize: Area – discover and apply Volume – discover and apply Surface Area with nets Standards: Materials/Technology: Quick Glance: Additional Resources: DPI - Lessons for Learning – Block Part-y Evidence of Learning: Important Notes: Unit Readiness Assessment The formulas for area, volume, and surface area 2 Check Ups should be last, students need 1 Partner Quiz to develop where these comes 1 Self Assessment from, so when they forget the 1 Unit Test formula, they see the make up 1 Unit Project of the shape and can use their 1 School Net Assessment own understanding to get the Named: 6th Grade – answers Covering and Surrounding Inv 1 (all): Extending and Building on Area and Perimeter Inv 2 (all but 2.4): Measuring Triangles Inv 3 (all but 3.3): Measuring Parallelograms Inv 4 (all): Measuring Surface Area and Volume Vocabulary: Area Base Face Height Net Parallelogram Perimeter Polygon Rectangular prisms Surface Area Trapezoid Triangle Volume 6.NS.8 – Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. 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.6 – Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 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. 6.G.2 – Find the volume of right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and use this to show you can multiply to find volume. Apply the formulas V = lwh and V = bh to find volumes. 6.G.3 – Draw polygons in the coordinate plane given coordinates for the vertices, find lengths between points. 6.G.4 – Represent 3D figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. 6th Grade - Unit 7 – Data About Us (20 days) Things to Emphasize: Center: Mean and median Spread: IQR, range, MAD Box-and-whisker plots, histograms, line plots Standards: Materials/Technology: Additional Resources: DPI - Lessons for Learning – How MAD are you? DPI - Lessons for Learning – Shakespeare vs. Rowling Evidence of Learning: Important Notes: Unit Readiness Assessment Have a focus on scale when creating these 2 Check Ups representations of data 1 Partner Quiz 1 Self-Assessment 1 Unit Test 1 Unit Project 1 School Net Assessment Named: 6th Grade – Data About Us Quick Glance: Vocabulary: Box-and-whisker Inv 1 (all): What’s in a Name? Categorical data Organizing, Representing, Distribution and Describing Data Histogram IQR Supp: Using the Mean MAD Mean Inv 3 (all): What’s Your Median Favorite? Measuring Mode Variability Numerical data Outlier Inv 4 (4.1, 4.2): What Range Numbers Describe Us? Scale Variability 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 it’s center, spread, and overall shape. 6.SP.3 – Recognize that a measure of center for a numerical data set summarizes all o fits 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 (report # of observations, mean, median, IQR, MAD, variability and center)