Grade 6 Math

PA Core Mathematics Standards
Module 1 

• CC.2.1.6.E.4 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of numbers to the system of rational numbers.
  • M06.A-N.3.1.1 Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).
  • M06.A-N.3.1.2 Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3; 0 is its own opposite).
  • M06.A-N.3.2.1 Write, interpret, and explain statements of order for rational numbers in real-world contexts.
  • M06.A-N.3.2.2 Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation.

Module 2 

• CC.2.1.6.E.4 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of numbers to the system of rational numbers. 
  • M06.A-N.3.1.3 Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.
  • M06.A-N.3.2.1 Write, interpret, and explain statements of order for rational numbers in real-world contexts.
  • M06.A-N.3.2.2 Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation.
• CC.2.1.6.E.3 Students acquire the knowledge and skills needed to: Develop and/or apply number theory concepts to find common factors and multiples.
  • M06.A-N.2.2.1 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.
  • M06.A-N.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.
  • A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.

Module 3

• CC.2.1.6.E.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  • M06.A-N.1.1.1 Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions.
  • M06.A-N.2.1.1 Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.
• ​​CC.2.1.6.E.3 Students acquire the knowledge and skills needed to: Develop and/or apply number theory concepts to find common factors and multiples.
  • M06.A-N.2.2.1 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.
  • M06.A-N.2.2.2 Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

Module 4 

• CC.2.1.6.E.2 Students acquire the knowledge and skills needed to: Identify and choose appropriate processes to compute fluently with multi-digit numbers.

• Positive integers/rational numbers represent quantities greater than zero; negative integers/rational numbers represent quantities less than zero.
• Position of numbers on a number line: negative on the left/down from zero, positive on the right/up from zero.
• The farther right/up a number is, the greater it is. The farther left/down a number is, the smaller it is. Use this to compare and order numbers.
• Every integer/rational number has an opposite, and these opposites are equidistant from zero on the number line. 
• Zero is its own opposite.
• Absolute value represents the distance between a number and zero on the number line, regardless of direction.
• Absolute value is used in real-life situations, such as magnitude, calculating the distance between two points, or determining the temperature difference.
• Inequality symbols (<,>) represent the relative positions of numbers on the number line.
• A number line has evenly scaled tick marks.
• Rational numbers include fractions and decimals (positive and negative), and can be graphed on both horizontal and vertical number lines.
• GCF and LCM can be used to rewrite fractions with common denominators to compare and perform fraction operations.
• Numbers need to be converted to the same form to compare and order them. 
• Dividing fractions involves flipping (finding the reciprocal of) the second fraction and multiplying.
• A mixed number can be written as an improper fraction.
• When adding or subtracting decimals, you must align the place values and decimal points.
• When multiplying decimals using the standard algorithm, you must count the total number of decimal places in the factors to correctly place the decimal point in the product.
• The standard algorithm for long division.
• When there is a decimal in the divisor, the decimal point must be moved the same number of places in the dividend and the divisor before dividing.
• When dividing, remainders can be rounded, converted to a fraction, or ignored based on the real-world context of a problem.

• The number system includes both positive and negative rational numbers (fractions, decimals, and integers), and these can be represented on a number line. 
• Rational numbers can be used to describe and make sense of real-world situations such as values like debt, temperature, elevation, and more.
• Absolute value represents the distance a rational number is from zero on the number line, and can be interpreted as the size or magnitude of a quantity in real-world situations.
• Numbers have factors and multiples, which are useful for comparing and solving numerical relationship problems.
• The concept of multiplication and division can be extended to include dividing fractions and mixed numbers, allowing students to understand how these operations work with parts of a whole and how they relate to real-world situations.
• The ability to select and apply appropriate strategies and operations for computing with multi-digit whole numbers and decimals is essential for ensuring accuracy and efficiency in solving mathematical and real-world problems.

Module 1

• Use positive and negative integers and zero to represent real-world quantities.
• Graph positive and negative integers on a number line.
• Understand the relationship between integers and their opposites. 
• Use number lines to compare and order integers.
• Write, interpret, and explain statements of order for integers in real-world contexts. 
• Interpret statements of inequality as statements about the relative position of two numbers on a number-line diagram.
• Identify absolute value as the distance from 0 on a number line.
• Interpret absolute value as magnitude.
• Distinguish comparisons of absolute value from comparisons of order.
• Find and use absolute value in real-world situations.

Module 2

• Graph rational numbers on vertical and horizontal number lines.
• Compare rational numbers using a number line.
• Interpret inequality statements using a number line.
• Compare rational numbers using the GCF and LCM.
• Use strategies to order rational numbers. 
• Explain how to order positive and negative rational numbers in real-world contexts. 

Module 3

• Divide fractions, including mixed numbers, by multiplying by the reciprocal. (including fractions with like and unlike denominators) 
• Apply understanding of fraction operations to solve real-world and mathematical word problems with accuracy.
• Use LCM and GCF to add, subtract, multiply, and divide fractions.

Module 4

• Add and subtract multi-digit decimals.
• Multiply multi-digit decimals with the standard algorithm.
• Divide multi-digit whole numbers using the standard algorithm.
• Estimate the quotients of multi-digit division.
• Divide multi-digit decimals up to the thousandths using the standard algorithm.
• Interpret remainders in real-world contexts. 
• Solve real-world problems involving operations with multi-digit decimals.

• How can we represent and compare positive and negative numbers on a number line, and how does their position help us understand and describe their values and relationships in real-world situations?
• How does absolute value help us solve real-world problems by showing how far a number is from zero, regardless of direction?
• How can we use visual models and numerical strategies to divide fractions and mixed numbers, and how does this apply to real-world problems?
• What steps can we take to perform operations with decimals and whole numbers accurately, and how do we apply these skills to solve real-world problems?
   

• L1.1    How can I graph positive and negative integers and determine how to find their opposites?
• L1.2    How can I order integers from least to greatest and use inequalities to compare integers?
• L1.3    How can I find and use absolute value and magnitude to describe real-world situations?
• L2.1    How can I graph rational numbers on number lines and determine how to find absolute values and opposites?
• L2.2    How can I compare positive and negative rational numbers using a number line?    
• L2.3    How can I find and use the GCF and LCM to solve problems?
• L2.4    How can I order positive and negative rational numbers of different forms?
• L3.1    How can I divide fractions with like denominators with and without models?
• L3.2    How can I divide two fractions with unlike denominators using several methods?
• L3.3    How can I find the quotient of a mixed number or fraction and a mixed number, fraction, or whole number?
• L3.4    How can I divide mixed numbers and fractions to solve problems?
• L3.5    How can I use the LCM and GCF to add, subtract, multiply, and divide fractions?
• L4.1    How can I add and subtract multi-digit decimals to the thousandths with or without a model?
• L4.2    How can I multiply multi-digit decimals, up to thousandths?    
• L4.3    How can I divide multi-digit whole numbers by multi-digit numbers with or without remainders?
• L4.4    How can I divide a multi-digit decimal by a decimal to the hundredths place?
• L4.5    How can I determine which operation is needed to solve real-world problems with multi-digit decimals?

• Into Math Modules 1-4
• Number lines (-20 to 20)
• Fraction strips
• Centimeter grid paper
• Decimal models
• IXL skill plan
• Reflex Math
   

•  absolute value
• inequality
• integers
• negative number
• opposites
• positive number
• common denominator
• Distributive Property
• factor
• greatest common factor
• least common multiple
• rational number
• denominator
• dividend
• divisor
• expression
• numerator
• quotient
• rectangle
• simplify
• multiplicative inverse
• reciprocal
• equivalent
• remainder

1. Are You Ready?
2. Module 1: Test Form A
3. Module 2: Test Form A
4. Module 3: Test Form A
5. Module 4: Test Form A
6. Reteach & Reassess with Test Form B as needed
    

PA Core Mathematics Standards
Module 5 

• CC.2.1.6.D.1 Students acquire the knowledge and skills needed to: Understand ratio concepts and use ratio reasoning to solve problems.
  • M06.A-R.1.1.1 Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities.
  • M06.A-R.1.1.2 Find the unit rate a/b associated with a ratio a:b (with b ≠ 0) and use rate language in the context of a ratio relationship.
  • M06.A-R.1.1.3 Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.
  • M06.A-R.1.1.4 Solve unit rate problems, including those involving unit pricing and constant speed.

Module 6 

• CC.2.1.6.D.1 Students acquire the knowledge and skills needed to: Understand ratio concepts and use ratio reasoning to solve problems.

Module 7

• CC.2.1.6.D.1 Students acquire the knowledge and skills needed to: Understand ratio concepts and use ratio reasoning to solve problems.
  • M06.A-R.1.1.5 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part, and the percentage.
     

Module 5

• Equivalent fractions can be determined by multiplying the numerator and denominator by the same number.
• Equivalent fractions can be determined by dividing the numerator and denominator by the same factor.
• GCF and LCM can be used to rewrite fractions with common denominators for the purpose of comparing.
• Visual models can be used to compare fractions.
• The greatest common factor (GCF) of two integers is the largest number that divides evenly into both numbers.
• The least common multiple (LCM) of two or more integers is the smallest number that is a multiple of all the given numbers.
• Analyzing number relationships involves identifying patterns, comparing values, and understanding how numbers are connected through operations, factors, and multiples.
• Ordered pairs on a coordinate plane are plotted by locating the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis.
• Each point on a coordinate plane represents a relationship between two values.

Module 6

• How to measure angles using a protractor.
• A circle graph shows how a whole is divided into parts.
• A circle is 360°, and degrees can be used to represent part of a whole. 
• Identify and write equivalent ratios.
• Determine if two ratios form a proportion.
• Ratios compare two quantities and are used to describe relationships between parts or a part and a whole.
• Measurement units/conversions within different systems (length, volume, weight/mass).

Module 7

• A fraction can be converted to a decimal by dividing the numerator by the denominator.
• A fraction’s denominator can be used to determine whether a decimal will terminate or repeat.
• A decimal can be converted to a fraction using a denominator of 10 or 100.
• A fraction with a denominator of 10 can be expressed as an equivalent fraction with a denominator of 100.
• A ratio can be expressed in three different ways: a decimal, a fraction, and a percent.
• A percent is a rate per 100.

• Ratios and rates describe how two quantities relate to each other, allowing us to compare, scale, and analyze relationships in both mathematical contexts and real-world situations.
• The ability to recognize, express, and explain ratios and rates is essential for solving problems that require comparing quantities and understanding proportional relationships.
• Circle graphs represent parts of a whole using ratios or percentages, and interpreting or creating them requires proportional reasoning and an understanding of fractional relationships.
• Ratio reasoning can be extended to multiply and divide quantities with units, helping solve both mathematical and real-life problems by manipulating measurements logically and accurately.
• Understanding and applying equivalent ratios is essential for converting between different units of measurement, whether within the same system or across systems (e.g., inches to feet, or ounces to pounds).

Module 5

• Understand and use ratios.
• Use ratio and rate reasoning to solve problems.
• Make tables of equivalent ratios with whole-number measurements.
• Find missing values in tables.
• Plot pairs of values on a coordinate plane.
• Calculate or identify the unit rate from data presented in a table or graph.
• Learn the difference between ratios and rates.
• Examine rates expressed in tables and double number lines.
• Compare rates to see if they are equivalent.
• Find unit rates.
• Use unit rates to solve real-world problems.
• Use ratio and rate reasoning to solve real-world problems
• Solve unit rate problems, including unit pricing and constant speed.

Module 6

• Use ratio reasoning with measurement.
• Use ratio reasoning to make circle graphs.
• Use ratio reasoning to analyze circle graphs.
• Use ratio reasoning to convert measurement units.
• Use ratio reasoning to solve real-world problems involving measurement conversions.
• Use ratio reasoning to convert measurement units and manipulate units when multiplying or dividing quantities.
• Use ratio reasoning to solve real-world and mathematical problems.

Module 7

• Find a percent of a quantity as a rate per 100.
• Use a 10 x 10 grid to model percent.
• Use equivalent ratios to solve problems. 
• Use multiplication to find the percent of a quantity.
• Use bar diagrams to find the percent of a quantity.
• Use a double number line to visualize ratios expressed as equivalent percents.

• How can we use different representations—like tables, graphs, and double number lines—to understand and solve problems involving ratios and rates?
• What strategies can we use to solve problems when measurements or data are given in different forms or units?
• How can we use ratios, fractions, and decimals to understand and solve percent problems in everyday situations?
   

• L5.1     How can I write a ratio in three different ways, given a diagram or description?
• L5.2    How can I use a table or graph to find equivalent ratios and use the ratios to solve problems?
• L5.3    How can I compare ratios and rates using a table or a double number line?
• L5.4    How can I find and use unit rates to solve problems?
• L5.5    How can I find and use equivalent ratios using a table, model, or double number line to solve a real-world problem?
• L6.1    How can I use reasoning about equivalent ratios to make and interpret a circle graph?
• L6.2    How can I write and use equivalent fractions or conversion factors to convert units within a measurement system?
• L6.3    How can I write and use equivalent rates or conversion factors to convert units between measurement systems?
• L7.1    How can I convert ratios to percents by applying one strategy?
• L7.2    How can I write a percent as a fraction or a decimal and use multiplication to find the percent of a number?
• L7.3    How can I write a percent as a fraction or a decimal and use a variety of strategies to solve real-world
• problems?
   

• Into Math Modules 5-7
• Two-color counters
• Number lines (blank, -10 to 10) (Teacher Resource Masters)
• Compass
• Protractor
• Fraction circles (Teacher Resource Masters)
• Centimeter grid paper (Teacher Resource Masters)
• Decimal models (Teacher Resource Masters)
• IXL skill plan
• Reflex Math
   

• equivalent ratios
• rate
• ratio
• unit rate
• circle graph
• conversion factor
• percent

• Are You Ready?
• Module 5: Test Form A
• Module 6: Test Form A
• Module 7: Test Form A
• Reteach & Reassess with Test Form B as needed
   

PA Core Mathematics Standards
Module 8 

• CC.2.2.6.B.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of arithmetic to algebraic expressions.
  • M06.B-E.1.1.1 Write and evaluate numerical expressions involving whole-number exponents.
  • M06.B-E.1.1.2 Write algebraic expressions from verbal descriptions.
  • M06.B-E.1.1.3 Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity).
  • M06.B-E.1.1.4 Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems.
  • M06.B-E.2.1.2 Write algebraic expressions to represent real-world or mathematical problems.
• CC.2.2.6.B.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of arithmetic to algebraic expressions.
  • M06.B-E.1.1.5 Apply the properties of operations to generate equivalent expressions.

Module 9 

• CC.2.2.6.B.2 Students acquire the knowledge and skills needed to: Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems.
  • M06.B-E.2.1.1 Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • M06.B-E.2.1.3 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 non-negative rational numbers.
  • M06.B-E.2.1.4 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines.
  • M06.B-E.2.1.1 Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • M06.B-E.2.1.3 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 non-negative rational numbers.

Module 10

• CC.2.2.6.B.3 Students acquire the knowledge and skills needed to: Represent and analyze quantitative relationships between dependent and independent variables.
  • M06.B-E.3.1.1 Write an equation to express the relationship between the dependent and independent variables.
  • M06.B-E.3.1.2 Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation.

Module 8

• The order of operations ensures expressions are evaluated correctly and consistently, following the standard sequence: parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right). 
• Numerical expressions can be created from written statements.
• Written statements can be generated from numerical expressions.
• Terms are separated by a plus or a minus sign.
• An expression is a combination of numbers, symbols, and/or variables.
• Multiplication is used when there is a number in front of a variable.
• When a number is outside parentheses, it can be distributed to the terms within the parentheses.

Module 9

• To evaluate for a variable, substitute the value for the variable and simplify.
• A rational number is a point on the number line.
• Numerical expressions use only numbers, while algebraic expressions contain one or more variables.
• The value of an algebraic expression can be determined by substituting a value for the variable.
• Number lines can be used to compare and order rational numbers.
• The meaning of the greater than and less than symbols when placed between two numbers.
• The key parts of an expression can include a coefficient, constant, variable, term, exponent, and operations.
• Combining like terms can simplify an expression.
• An exponent is the number that indicates how many times the base is used as a factor.

Module 10

• The difference between additive and multiplicative numerical patterns given in a table or graph.
• Additive and multiplicative numerical patterns can be used to complete a table or graph.
• Identify and locate ordered pairs of whole numbers in the first quadrant.

• Exponents are a way to represent repeated multiplication of a number and can be used to write and evaluate numerical expressions and equations more efficiently.
• Expressions and equations are made up of different parts—including terms, coefficients, variables, and operations—and each part plays a specific role in the expression's meaning.
• Variables can stand in for unknown or changing numbers, allowing us to write and evaluate expressions that model real-world and mathematical situations.
• Equations and inequalities can model real-world situations and help us solve problems involving unknown values.
• We can evaluate the correctness of a solution by substituting numbers into equations or inequalities and checking if they make the statement true.
• Relationships between two variables can be represented using tables, graphs, and equations, and each representation helps us understand the relationship in a different way.
• By analyzing patterns in tables and graphs, we can make predictions, identify trends, and solve real-world problems using mathematical reasoning.

Module 8

• Write numerical expressions with whole-number exponents.
• Evaluate numerical expressions with whole-number exponents.
• Identify parts of an expression using mathematical terms.
• Write expressions with numbers and letters standing for numbers.
• Use variables to represent numbers and write expressions to solve problems.
• Evaluate expressions at specific values of their variables.
• Perform arithmetic operations using the order of operations.
• Apply the properties of operations to generate equivalent expressions.

Module 9

• Check the correctness of inequalities by trying various numbers as solutions.
• Learn how to represent real-world situations with an equation of the form x + p = q and px = q in which p, q, and x are non-negative rational numbers.
• Evaluate potential solutions for simple equations.
• Represent and solve real-world and mathematical problems with an equation in the form of px = q and xp = q in which p, q, and x are non-negative rational numbers.
• Evaluate solutions for multiplication and division equations.
• Represent and solve real-world and mathematical problems with one-step equations involving non-negative rational numbers.
• Evaluate solutions for one-step equations.
• Use variables and equations to determine angle relationships. 
• Write inequalities based on real-world situations.
• Graph inequalities on a number line.
• Check the correctness by trying various numbers as solutions.

Module 10

• Represent an equation with tables and graphs.
• Use unit rates to solve real-world problems.
• Represent a relationship between two variables using an equation.
• Understand how to write an equation from a table or graph.
• Use equations from tables and graphs to solve problems.

• Why is it important to understand and apply mathematical rules when interpreting, comparing, and creating expressions?
• What strategies can we use to write, solve, and graph equations and inequalities with unknown values?
• How can we represent relationships between quantities using tables, equations, and graphs?

• L8.1    How can I write and evaluate numerical expressions involving whole-number exponents?
• L8.2    How can I write and evaluate numerical expressions using the order of operations?
• L8.3    How can I use variables to write an algebraic expression to represent a real-world problem?
• L8.4    How can I interpret and evaluate algebraic expressions using the order of operations?
• L8.5    How can I use the properties of operations to determine if two expressions are equivalent and to generate equivalent algebraic expressions?
• L9.1    How can I write and solve equations that model real-world situations involving all four operations?
• L9.2    How can I write and solve equations using addition and subtraction to represent real-world situations involving an unknown?
• L9.3    How can I write and solve equations using multiplication and division to represent real-world situations involving an unknown?
• L9.4    How can I write and graph equations to solve a variety of real-world situations involving addition, subtraction, multiplication, or division?
• L9.5    How can I write and graph the solution of an inequality to represent a condition in a real-world or mathematical problem?
• L10.1    How can I represent a situation using a table, equation, or graph?
• L10.2    How can I identify the dependent and independent variables, write equations to represent a real-world situation, and use the equations to solve problems?
• L10.3    How can I identify patterns in tables and graphs, and use the patterns to write equations to represent real-world situations?

• Into Math Modules 8-10
• Centimeter grid paper 
• Algebra tiles
• Base-ten materials
• Equation mat
• Number lines (fractions, decimals, and percents)
• Grid of Quadrant I
• IXL skill plan
• Reflex Math

• algebraic expression
• base
• coefficient
• constant
• equivalent expression
• evaluate
• exponent
• like terms
• numerical expression
• term
• variable
• addition property of equality
• constraint
• division property of equality
• equation
• inequality
• multiplication property of equality
• solution of equation
• solution of inequality
• subtraction property of equality
• dependent variable
• independent variable

• Are You Ready?
• Module 8: Test Form A
• Module 9: Test Form A
• Module 10: Test Form A
•  Reteach & Reassess with Test Form B as needed
   

PA Core Mathematics Standards
Module 11 

• CC.2.1.6.E.4 Apply and extend previous understandings of numbers to the system of rational numbers.
  • M06.A-N.3.1.3 Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane.
  • M06.C-G.1.1.4 Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided.
  • M06.A-N.3.2.3 Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Module 12 

• CC.2.2.6.B.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of arithmetic to algebraic expressions.
  • M06.B-E.1.1.4 Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems.
  • M06.C-G.1.1.1 Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided.
  • M06.C-G.1.1.2 Determine the area of irregular or compound polygons.

Module 13

• CC.2.2.6.B.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of arithmetic to algebraic expressions.
  • M06.B-E.1.1.4 Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems.
• CC.2.3.6.A.1 Students acquire the knowledge and skills needed to: Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.
  • M06.C-G.1.1.3 Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided.
  • M06.C-G.1.1.5 Represent three-dimensional figures using nets made of rectangles and triangles.
  • M06.C-G.1.1.6 Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided.

Module 11

• An ordered pair is two numbers in the form (x, y) and is used to locate a point on a coordinate plane.
• The classification of a quadrilateral, a parallelogram, rectangle, and square.
• Plot points of an ordered pair on the coordinate plane by first locating the x-coordinate along the horizontal axis, then the y-coordinate along the vertical axis, and mark the point where these two values intersect.
• The absolute value is the distance from a number to zero on a number line.
• The distance between two numbers on a number line is the absolute value of the difference between the two numbers—that is, subtract the smaller number from the larger number.

Module 12

• Ability to identify and label sides, bases, and heights of 2-D shapes.
• Recognition of right angles (90 degrees) and parallel sides.
• Area is the amount of space inside a 2-D shape.
• The formula for the area of a parallelogram.
• Properties of triangles and quadrilaterals.
• Composite figures are shapes made up of 2 or more geometric figures (parallelograms, triangles, trapezoids) and can be decomposed.

Module 13

• Recognize volume as an attribute of solid figures.
• The area of polygons is determined by applying the appropriate mathematical formulas for each shape.
• Recognize volume as the number of cubic units needed to fill a given space.
• A solid figure is a three-dimensional figure.
• Volume is measured in cubic units.

• Polygons can be represented and analyzed on the coordinate plane by using ordered pairs to define their vertices. 
• Polygons can be represented and analyzed on the coordinate plane by plotting their vertices in all four quadrants, which supports finding lengths/distances, perimeter, and area.
• Area formulas are tools that represent mathematical relationships and can be used to solve real-world and abstract problems involving space and measurement.
• The area of composite and irregular figures can be found by decomposing them into simpler shapes (such as parallelograms, triangles, and trapezoids), applying appropriate formulas, and combining the results.
• Surface area measures the total area of all the faces of a solid, and can be found by calculating the areas of the individual faces represented in the net.
• Volume measures the amount of space inside a three-dimensional object, and formulas for volume provide a way to quantify this space for right rectangular prisms and other solids.
• Formulas for surface area and volume are connected to real-world contexts, allowing us to model and solve problems involving packaging, storage, and construction.

Module 11

• Identify the four quadrants of the coordinate plane.
• Write rational ordered pairs to represent points on the coordinate plane.
• Plot points on the coordinate plane.
• Graph polygons on the coordinate plane given coordinates for the vertices.
• Find and position pairs of integers on a coordinate plane to complete polygons.
• Find the distance between two points on the coordinate plane that share a first or second coordinate, with and without a coordinate plane.
• Plot and reflect points on the coordinate plane.
• Solve real-world problems involving distance using points on a coordinate plane.
• Draw polygons on the coordinate plane.
• Find the length of a side joining points with the same second coordinate.
• Solve real-world and mathematical problems by finding the distances between the points to find the perimeter and area of polygons.

Module 12

• Derive the formula for the area of a parallelogram.
• Apply the formula for the area of parallelograms to solve mathematical and real-world problems.
• Evaluate expressions resulting from the area formula of a parallelogram at specific values of the variables. 
• Find the area of right triangles and other triangles.
• Solve real-world problems by writing and solving equations and using arithmetic operations.
• Evaluate expressions resulting from the area formula of a triangle at specific values of its variables.
• Learn to find the area of trapezoids.
• Use the area formulas for trapezoids to solve real-world problems.
• Evaluate expressions resulting from the area formula of a trapezoid at specific values of their variables.
• Apply strategies to find the areas of composite figures.
• Apply the area formulas for trapezoids, triangles, and parallelograms.

Module 13

• Learn how to construct and interpret the net of a solid object, such as a prism or pyramid.
• Use nets to calculate the surface area of the solid objects they represent.
• Learn how to derive and apply the formula for the volume of a right rectangular prism.
• Use the formula for the volume of a right rectangular prism to solve a variety of real-world problems.
• Evaluate volume expressions arising from volume formulas used in real-world problems.
• Learn how to apply the formula for the volume of a right rectangular prism to solve various real-world problems.
• Write equations using the formula for the volume of right rectangular prisms, and solve for the unknown variable.
• Evaluate volume expressions arising from volume formulas used in real-world problems.

• How can we use the coordinate plane to represent, analyze, and solve problems involving geometric figures, distances, and real-world applications?
• How can we use area formulas and geometric reasoning to find the area of various shapes—including triangles, parallelograms, trapezoids, and composite figures—and solve real-world problems?
• How can understanding and using nets and formulas help us find the surface area and volume of rectangular and triangular prisms and pyramids?
   

• L11.1    How can I identify and graph rational number ordered pairs in all four quadrants on a coordinate plane?
• L11.2    How can I graph the given vertices of a figure and determine the coordinates of an unknown vertex to complete the figure, given the classification of the polygon?
• L11.3    How can I find the distance between two points with the same x- or y-coordinate across quadrants and use a scale in real-world problems to find actual distances?
• L11.4    How can I find the perimeter and area of polygons in the coordinate plane?
• L12.1    How can I understand the area formula for a parallelogram and use it to find area or to find unknown dimensions given the area?
• L12.2    How can I use the area formula for a triangle given either the base and height, or the area and the height, or the base?
• L12.3    How can I use the area formula for a trapezoid given the lengths of its bases and its height?
• L12.4    How can I find the area of any composite figure?
• L13.1    How can I make and use nets to find the surface area of rectangular and triangular prisms and pyramids?
• L13.2    How can I find the volume of a rectangular prism using the formula V = lwh or V = Bh?
• L13.3    How can I use the formula V = lwh to find the volume or an unknown dimension of a rectangular prism.
   

• Into Math Modules 11-13
• Coordinate Plane
• Grid of Quadrant I
• Centimeter grid paper 
• Geoboard
• Tangram pattern
• Ruler 
• Rectangular prism net
• Centimeter cubes
• IXL skill plan
• Reflex Math
   

• coordinate plane
• ordered pair
• origin
• polygon
• quadrant
• vertex
• x-axis
• y-axis
• composite figure
• diagonal
• trapezoid
• reflection
• net
• pyramid
• surface area

• Are You Ready? 
• Module 11: Test Form A
• Module 12: Test Form A
• Module 13: Test Form A
• Reteach & Reassess with Test Form B as needed
   

PA Core Mathematics Standards
Module 14 

• CC.2.4.6.B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.
• M06.D-S.1.1.4 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Module 15 

• CC.2.4.6.B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.
• M06.D-S.1.1.2 Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation).

Module 16

• CC.2.4.6.B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.
• M06.D-S.1.1.3 Describe any overall pattern and any deviations from the overall pattern with reference to the context in which the data were gathered.
• M06.D-S.1.1.1 Display numerical data in plots on a number line, including line plots, histograms, and box-and-whisker plots.
• M06.D-S.1.1.2 Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation).
• M06.D-S.1.1.4 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
   

Module 14

• Various types of questions can be asked to collect data (e.g., yes/no vs. open-ended).
• A dataset is a collection of related numbers or information.
• Recognize different attributes and characteristics in a data set.
• A line plot displays a data set of measurements that shows frequency. Each data point is one observation.
• Read and analyze visual representations of data to identify similarities, differences, trends or patterns (e.g., peak, spread, skewness).

Module 15

• Data can be collected and organized into a line plot to visually display data for analysis of clusters, gaps, and trends.
• The median is calculated by listing data from least to greatest and identifying the middle value.
• The mean is calculated by dividing the sum of items in a set of data by the number of items in the set.
• The mode is determined by identifying the number or numbers that occur most frequently.

Module 16

• Absolute value and opposites help determine the distance between data points.
• Absolute value is the distance of a number from zero on a number line
• The terms cluster, gap, peak and symmetry can be used to explain the overall shape of the data in a distribution. 
• The mean represents the center or average of the data points.
• Mean, median, and mode are measures of center.
• Mean absolute deviation (MAD), range, and interquartile range (IQR) are measures of spread.
• The presence of an outlier in a data set can determine the usefulness of the mean.
• Data can be collected and organized into a histogram to visually display ranges of data.
• When there are two middle values in a data set, the median is determined by finding the average of the middle values.
• A measure of center for a numerical data set summarizes all of its values with a single number.

• Statistical questions are designed to gather data that varies and require data collection and analysis to answer meaningfully.
• Different types of data displays—dot plots, histograms, frequency tables—provide varied ways to organize, summarize, and visualize numerical data.
• Interpreting and comparing these displays helps us understand and communicate what the data tell us.
• The mean, median, and mode are different ways to summarize a data set with a single value that represents its center.
• Choosing the best measure of center depends on the data’s context and characteristics, including the presence of outliers.
• Measures of center and variability (like mean, median, range, interquartile range, and mean absolute deviation) summarize key features of a data set and describe its overall pattern.
• Data displays such as dot plots, histograms, and box plots visually show the shape, spread, and important characteristics of data, helping us interpret and compare data sets.
• Understanding the relationship between data patterns, measures of center and variability, and the shape of the distribution enables us to draw meaningful conclusions about the data.

Module 14 

• Distinguish statistical questions from other types of questions.
• Identify the attributes of a data set.
• Describe the nature of an attribute, including how it is measured and its units of measurement.
• Report the number of observations.
• Construct a dot plot to display a set of numerical data.
• Interpret a dot plot to identify properties of a data set.
• Construct a histogram and a frequency table to display a data set.
• Interpret the information presented in a histogram or frequency table.
• Compare a histogram and frequency table to other data displays, such as dot plots.

Module 15

• Calculate and interpret the meaning of the mean of a data set.
• Relate the mean to the concepts of fair share and balance point.
• Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
• Summarize numerical data sets in relation to their context.
• Identify outliers in a data set.
• Determine whether the mean, median, or mode is the most appropriate measure of center for a data set.

Module 16

• Describe overall patterns in data and deviations from patterns.
• Relate the choice of measures of center to the shape of the data distribution.
• Draw conclusions about data sets from data displays.
• Find the median of a data set.
• Find the lower and upper quartiles of a data set.
• Display numerical data in box plots.
• Understand how a box plot displays both the distribution and range of a data set.
• Compute the mean absolute deviation of the data sets.
• Use mean absolute deviations to describe patterns in data.
• Calculate which data values fall within the mean absolute deviation and which data values fall outside the mean absolute deviation.
• Compute range, interquartile range, and mean absolute deviation.
• Use measures of variability to describe data sets.
• Draw conclusions about data sets using measures of variability and measures of center.
• Learn to identify an appropriate data display based on a table of data.
• Draw conclusions using measures of center and variability and the shape of the data distribution.
• Identify features of a data set by inspection of dot plots, box plots, and histograms, including symmetry, spread, the existence of gaps, range, and interquartile range. 

• How can I collect, organize, and represent data to answer statistical questions and understand patterns in the data?
• How can I use measures of center to summarize data and decide which measure best represents a data set?
• How can I analyze and describe data using measures of shape, center, and variability to draw meaningful conclusions?
   

• L14.1    How can I identify statistical questions, describe the nature of attributes under investigation, and report the number of observations?
• L14.2    How can I construct and analyze a dot plot?
• L14.3    How can I determine an appropriate interval for the data and construct a frequency table or histogram?
• L15.1    How can I find both the fair share and the balance point of a data set using a model or a number line?
• L15.2    How can I find and interpret the mean, median, and mode of a set of data?
• L15.3    How can I find the mean, median, and mode for a given data set and determine the best measure of center to describe the data set?
• L16.1    How can I describe data distribution by their shapes?
• L16.2    How can I draw and interpret box plots?
• L16.3    How can I find the mean absolute deviation of a data set?
• L16.4    How can I find and use range, IQR, and MAD to summarize a data set?
• L16.5    How can I describe the shape, distribution, and range of a data set, and use the shape, measures of center, or variability to draw conclusions about the data?

• Into Math Modules 14-16
• Centimeter grid paper
• Geoboard
• Tangram pattern
• Ruler
• Rectangular prism net
• Centimeter cubes
• Number lines
• Two-color counters
• IXL skill plan
• Reflex Math
   

• data
• dot plot
• frequency
• frequency table
• histogram
• statistical question
• average 
• mean
• measure of center
• median
• mode
• outlier
• box plot
• interquartile range (IQR)
• lower quartile
• mean absolute deviation (MAD)
• measure of variability
• range
• upper quartile

• Are You Ready? (3)
• Module 14: Test Form A
• Module 15: Test Form A
• Module 16: Test Form A
• Reteach & Reassess with Test Form B as needed