GCF, LCM, and Prime Factorization

GCF, LCM, and Prime Factorization

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:
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.
Materials/Technology: / Additional Resources:
  • Mathshell - LCM and GCF

Quick Glance:
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
/ 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)
/ 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:
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.
Materials/Technology: / Additional Resources:
  • DPI - Lessons for Learning – Bake Sale Brownies
  • DPI - Lessons for Learning – Paper Clip Comparisons

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
/ Evidence of Learning:
  • Unit Readiness Assessment
  • 2 Check Ups
  • 1 Partner Quiz
  • 1 Unit Test
  • 1 Self Assessment
  • 1 School Net Assessment - Named: 6th Grade – Comparing Bits and Pieces
/ Important Notes:
  • This unit is laying the foundation for work with fractions, decimals, percents, and negative numbers; they are not expected to add, subtract, multiply, or divide them in this unit, this will come in the next two units

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:
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.
Materials/Technology:
  • Pinch Cards
/ Additional Resources:
Quick Glance:
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
/ 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
/ 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:
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.
Materials/Technology: / Additional Resources:
Quick Glance:
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
/ 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
/ 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:
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 andpx=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.
Materials/Technology: / Additional Resources:
  • DPI - Lessons for Learning – I’ll Race You?

Quick Glance:
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
/ Evidence of Learning:
  • 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
/ Important Notes:
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:
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.
Materials/Technology: / Additional Resources:
  • DPI - Lessons for Learning – Block Part-y

Quick Glance:
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
/ 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 – Covering and Surrounding
/ Important Notes:
  • The formulas for area, volume, and surface area should be last, students need to develop where these comes from, so when they forget the formula, they see the make up of the shape and can use their own understanding to get the answers

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:
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)
Materials/Technology: / Additional Resources:
  • DPI - Lessons for Learning – How MAD are you?
  • DPI - Lessons for Learning – Shakespeare vs. Rowling

Quick Glance:
Inv 1 (all): What’s in a Name? Organizing, Representing, and Describing Data
Supp: Using the Mean
Inv 3 (all): What’s Your Favorite? Measuring Variability
Inv 4 (4.1, 4.2): What Numbers Describe Us? / Vocabulary:
  • Box-and-whisker
  • Categorical data
  • Distribution
  • Histogram
  • IQR
  • MAD
  • Mean
  • Median
  • Mode
  • Numerical data
  • Outlier
  • Range
  • Scale
  • Variability
/ 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 – Data About Us
/ Important Notes:
  • Have a focus on scale when creating these representations of data

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