Content Updates: Math Special Edition (July 2019)
We’re excited to share that we recently made significant enhancements to our core math classes!
One consequence of adding this new content is that it will impact Mastery percentages. When we add new content and remove old content, your Mastery percentage will change, since the overall number of skills available will change (for example, instead of mastering 90 out of 100 skills, you'll now have mastered 90 out of 110, which would reduce your percentage from 90% to 82%).
As always, don’t worry: this doesn’t affect Mastery points. Below you can find detailed information on what specifically was changed so you can better understand the new course content.
Table of Contents
Grades 35 (Including EngageNY)
What's Changed
Grade 5 Math
Algebra 1 & Algebra 2
What's Changed
Math 13, Precalculus, Prealgebra, Basic Geometry, and Arithmetic
What's Changed
Grades 35 (Including EngageNY)
What's Changed
 New and revised materials by our inhouse content experts reflect the depth, breadth, and rigor of CCSS, and reflect the best of how we've seen educators supporting mathematical practices and ongrade mathematical reasoning in their classes.
 Better scaffolding. New exercises and improvements to existing exercises support struggling students in mastering challenging material.
 More conceptual items. Exercises focusing on conceptual rigor make sure students understand why math makes sense before formalizing strategies into procedures. Includes an emphasis on helping students tie together multiple representations of mathematical concepts.
 Improved focus/spiral review. The major work of each grade will spiral across the year ensuring students have many opportunities to engage with the most important concepts.
 Smaller units. More manageable goals increase student motivation. Shorter units also allow teachers to assign precisely what their students are studying.
 Strong foundations. Each grade will begin with a place value unit to lay a strong foundation.
Grade 3 Math
Changes to Video Content in Grade 3 Math
New Videos  Removed Videos 
Equal groups  Estimating adding and subtracting 3digit numbers 
Introduction to multiplication  Subtracting in your head (no regrouping) 
Multiplication as repeated addition  The idea of division 
Multiplication on the number line  2step estimation problem: marbles 
Multiplication in real world contexts  Measuring area with partial unit squares 
Commutative property of multiplication  Rounding to nearest 10 
Distributive property when multiplying  Rounding to nearest 100 
Rounding to the nearest 10 on the number line  
Rounding to the nearest 100 on the number line  
Estimating when adding multidigit numbers  
Estimating when subtracting large numbers  
Subtraction by breaking apart  
Methods for subtracting 3digit numbers  
Missing number for 3digit subtraction within 1000  
Three digit addition word problems  
Three digit subtraction word problems  
Division as equal groups  
Visualizing division with arrays  
Division in context  
Using associate property to simplify multiplication  
Order of operations (2step expressions)  
2step estimation word problems  
Setting up 2step word problems  
Recognizing number patterns  
Patterns with multiplying even and odd numbers  
Patterns in hundreds chart 
Changes to Exercise Content in Grade 3 Math
New Exercises  Removed Exercises 
Equal groups  Letters and symbols in multiplication and division equations 
Understand equal groups as multiplication  Find area with partial unit squares 
Multiply using groups of objects  Measure to find area 
Understand multiplication with arrays  Measure to find perimeter 
Multiplication in contexts  
Represent the commutative property of multiplication  
Understand the commutative property of multiplication  
Multiply by 2 and 4  
Multiply by 10  
Multiply by 5 and 10  
Multiply by 3 and 6  
Visualize distributive property  
Select strategies for adding within 1000  
Estimate to subtract multidigit whole numbers  
Break apart 3digit subtraction problems  
Subtract on a number line  
Select strategies for subtracting within 1000  
Add and subtract within 1000 word problems  
Division with arrays  
Division in contexts  
Relate multiplication and division equations  
Fact families  
Fractions in contexts  
Relate number lines to fraction bars  
Fractions greater than 1 on the number line  
Compare fractions on the number line  
Equivalent fractions  
Understand associative property of multiplication


Use associative property to multiply 2digit numbers by 1digit


2step expressions  
Patterns in hundreds chart  
Classify quadrilaterals  
Understand area  
Area of rectangles with partial arrays  
Find perimeter when a side length is missing  
Area and perimeter situations  
Area and perimeter word problems 
Changes to Article Content in Grade 3 Math
Removed Articles 
Intro to multiplication 
Intro to division 
Intro to commutative property of multiplication 
Intro to associative property of multiplication 
Intro to distributive property 
Commutative property of multiplication review 
Associative property of multiplication review 
Distributive property review 
Grade 4 Math
Changes to Video Content in Grade 4 Math
New Videos  Removed Videos 
Place value tables  Multiplying with distributive property 
Writing numbers in words and standard form  Multiplying 2digit by 1digit 
Comparing with multiplication  Multiplying: 2digit by 1digit (regrouping) 
Estimating with multiplication  Multiplying 4digit by 1digit (regrouping) 
Estimating 2digit multiplication  Comparing with multiplication 
Writing decimals and fractions greater than 1 shown on grids  Comparing with multiplication: age 
Writing decimals and fractions shown on number lines  Canceling zeros when dividing 
Relating decimals and fractions in words  Long division: 280÷5 
Ordering fractions  
Writing decimal numbers shown in grids  
Comparing decimals 2  
Comparing place values  
Writing a number in standard form  
Rounding whole numbers to nearest ten 
Changes to Exercise Content in Grade 4 Math
New Exercises  Removed Exercises 
Place value tables  Cancel zeros when dividing 
Understand multiplying by a multiple of 10, 100, and 1000  Zeros in the dividend (no remainders) 
Multiply 2digits by 1digit with area models  Zeros in the quotient (no remainders) 
Multiply 3 and 4digits by 1digit with distributive property  Equivalent fractions and different wholes 
Estimate products (1digit times 2, 3, and 4digit)  Order fractions 
Multiply using partial products  Compare fractions and mixed numbers 
Estimate products (2digit numbers)  Draw rays, lines, & line segments 
Multiply with partial products (2digit numbers)  Draw right, acute, and obtuse angles 
Estimate to divide by 1digit numbers  Draw lines of symmetry and symmetrical figures 
Create division equations with area models  Whole number place value challenge 
Estimate quotients (3 and 4digit divided by 1digit)  
Identify factors  
Identify multiples  
Prime and composite numbers  
Patterns with shapes  
Equivalent fractions (number lines)  
Compare fractions using benchmark  
Compare fractions word problems  
Decompose fractions visually  
Graph data on line plots (through 1/8 of a unit)  
Multiply fractions and whole numbers on the number line  
Multiply mixed numbers and whole numbers  
Write decimals and fractions shown on number lines  
Write decimals and fractions greater than 1 shown on number lines


Relate decimals and fractions in words  
Write common fractions as decimals  
Order decimals and fractions in different forms  
Classify triangles by both sides and angles  
Types of angles by measure  
Estimate angle measures  
Area and perimeter situations 
Changes to Article Content in Grade 4 Math
Removed Articles 
Comparing fractions review 
Factors and multiples review 
Whole number place value review 
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Grade 5 Math
Changes to Video Content in Grade 5 Math
New Videos  Removed Videos 
Place value with decimals  Intro to multiplying decimals 
Thousandths on the number line  Multiplying decimals: place value 
Expressing decimals in multiple forms  Dividing whole numbers to get a decimal 
Visual understanding of regrouping decimals  Multidigit division strategies for decimals 
Regrouping with decimals  Strategies for dividing by tenths 
Ordering decimals  Intro to multiplying 2 fractions 
Ordering decimals through thousandths  Decimal place value 
Comparing decimals in different representations  Convert decimal from expanded form to standard form 
Multiplying and dividing by 10, 100, 1000  Ordering decimals 1 
Multiplying and dividing decimals by 10  Ordering decimals 2 
Multiplying and dividing decimals by 10, 100, 1000  Multiplying a decimal by a power of 10 
Introduction to powers of 10  Dividing a decimal by a power of 10 
Multiplying and dividing by powers of 10  Dividing a decimal by a power of 10: pattern 
Regrouping whole numbers: 675  
Regrouping whole numbers: 76,830  
Regrouping whole numbers: 430  
Regrouping with decimals: 86.93  
Regrouping with decimals: 0.25  
Adding units of volume  
Plotting corners of a rectangle 
Changes to Exercise Content in Grade 5 Math
New Exercises  Removed Exercises 
Decimals on the number line: thousandths  Divide decimals like 16.8÷40 by factoring out a 10 
Decimals in written and expanded form  Divide whole numbers like 80÷200 to get a decimal 
Write common fractions as decimals  Divide decimals like 1.32÷0.12 
Estimate to add and subtract fractions with different denominators  Understanding moving the decimal 
Multiply by 1digit numbers with standard algorithm  Shapes on the coordinate plane 
Represent fraction multiplication with visuals  Identify points on a line 
Relate fraction division to fraction multiplication  
Fraction and whole number division in contexts  
Estimating with multiplying decimals and whole numbers  
Multiply whole numbers by 0.1 and 0.01  
Multiply whole numbers and decimals  
Represent decimal multiplication with grids and area models  
Understand multiplying decimals  
Multiply decimals (up to 4digit factors)  
Divide whole numbers by decimals visually  
Volume with unit cubes  
Volume as area of base times height  
Understanding decomposing figures to find volume  
Convert units of time  
Convert units word problems (metrics)  
Convert units word problems (US customary)  
Graph data on line plots (through 1/8 of a unit) 
Changes to Article Content in Grade 5 Math
New Articles 
Dividing decimals 
Multiplying fractions review 
Convert units guided word problems (US customary) 
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EngageNY 3rd Grade Math
Changes to Video Content in EngageNY 3rd Grade
New Videos  Removed Videos 
Equal groups  Subtracting in your head (no regrouping) 
Introduction to multiplication  The idea of division 
Multiplication as repeated addition  2step estimation problem: marbles 
Multiplication in real world contexts  Measuring area with partial unit squares 
Commutative property of multiplication  Rounding to nearest 10 
Distributive property when multiplying  Rounding to nearest 100 
Rounding to the nearest 10 on the number line  
Rounding to the nearest 100 on the number line  
Estimating when adding multidigit numbers  
Estimating when subtracting large numbers  
Subtraction by breaking apart  
Methods for subtracting 3digit numbers  
Missing number for 3digit subtraction within 1000  
Three digit addition word problems  
Three digit subtraction word problems  
Division as equal groups  
Visualizing division with arrays  
Division in context  
Using associate property to simplify multiplication  
Order of operations (2step expressions)  
2step estimation word problems  
Setting up 2step word problems  
Patterns with multiplying even and odd numbers 
Changes to Exercise Content in EngageNY 3rd Grade
New Exercises  Removed Exercises 
Equal groups  Letters and symbols in multiplication and division equations 
Understand equal groups as multiplication  Find area with partial unit squares 
Multiply using groups of objects  Measure to find area 
Understand multiplication with arrays  Measure to find perimeter 
Multiplication in contexts  
Represent the commutative property of multiplication  
Understand the commutative property of multiplication  
Multiply by 2 and 4  
Multiply by 10  
Multiply by 5 and 10  
Multiply by 3 and 6  
Visualize distributive property  
Select strategies for adding within 1000  
Estimate to subtract multidigit whole numbers  
Break apart 3digit subtraction problems  
Subtract on a number line  
Select strategies for subtracting within 1000  
Add and subtract within 1000 word problems  
Division with arrays  
Division in contexts  
Relate multiplication and division equations  
Fact families  
Fractions in contexts  
Relate number lines to fraction bars  
Fractions greater than 1 on the number line  
Compare fractions on the number line  
Equivalent fractions  
Understand associative property of multiplication  
Use associative property to multiply 2digit numbers by 1digit  
2step expressions  
Classify quadrilaterals  
Understand area  
Area of rectangles with partial arrays  
Find perimeter when a side length is missing  
Area and perimeter situations  
Area and perimeter word problems 
Changes to Article Content in EngageNY 3rd Grade
Removed Articles

Intro to multiplication

Intro to division 
Intro to commutative property of multiplication

Intro to associative property of multiplication

Intro to distributive property

Commutative property of multiplication review

Associative property of multiplication review

Distributive property review

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EngageNY 4th Grade Math
Changes to Video Content in EngageNY 4th Grade
New Videos  Removed Videos 
Place value tables  Multiplying with distributive property 
Writing numbers in words and standard form  Multiplying 2digit by 1digit 
Comparing with multiplication  Multiplying: 2digit by 1digit (regrouping) 
Estimating with multiplication  Multiplying 4digit by 1digit (regrouping) 
Estimating 2digit multiplication  Comparing with multiplication 
Writing decimals and fractions greater than 1 shown on grids  Comparing with multiplication: age 
Writing decimals and fractions shown on number lines  Canceling zeros when dividing 
Relating decimals and fractions in words  Long division: 280÷5 
Ordering fractions  
Writing decimal numbers shown in grids  
Comparing decimals 2  
Comparing place values  
Writing a number in standard form  
Rounding whole numbers to nearest ten 
Changes to Exercise Content in EngageNY 4th Grade
New Exercises  Removed Exercises 
Place value tables  Cancel zeros when dividing 
Understand multiplying by a multiple of 10, 100, and 1000  Zeros in the dividend (no remainders) 
Multiply 2digits by 1digit with area models  Zeros in the quotient (no remainders) 
Multiply 3 and 4digits by 1digit with distributive property  Equivalent fractions and different wholes 
Estimate products (1digit times 2, 3, and 4digit)  Order fractions 
Multiply using partial products  Compare fractions and mixed numbers 
Estimate products (2digit numbers)  Draw rays, lines, & line segments 
Multiply with partial products (2digit numbers)  Draw right, acute, and obtuse angles 
Estimate to divide by 1digit numbers  Draw lines of symmetry and symmetrical figures 
Create division equations with area models  Whole number place value challenge 
Estimate quotients (3 and 4digit divided by 1digit)  
Identify factors  
Identify multiples  
Prime and composite numbers  
Patterns with shapes  
Equivalent fractions (number lines)  
Compare fractions using benchmark  
Compare fractions word problems  
Decompose fractions visually  
Graph data on line plots (through 1/8 of a unit)  
Multiply fractions and whole numbers on the number line  
Multiply mixed numbers and whole numbers  
Write decimals and fractions shown on number lines  
Write decimals and fractions greater than 1 shown on number lines


Relate decimals and fractions in words  
Write common fractions as decimals  
Order decimals and fractions in different forms  
Classify triangles by both sides and angles  
Types of angles by measure  
Estimate angle measures  
Area and perimeter situations 
Changes to Article Content in EngageNY 4th Grade
Removed Articles 
Comparing fractions review 
Factors and multiples review 
Whole number place value review 
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EngageNY 5th Grade Math
Changes to Video Content in EngageNY 5th Grade
New Videos  Removed Videos 
Place value with decimals  Intro to multiplying decimals 
Thousandths on the number line  Multiplying decimals: place value 
Expressing decimals in multiple forms  Dividing whole numbers to get a decimal 
Visual understanding of regrouping decimals  Multidigit division strategies for decimals 
Regrouping with decimals  Strategies for dividing by tenths 
Ordering decimals  Intro to multiplying 2 fractions 
Ordering decimals through thousandths  Decimal place value 
Comparing decimals in different representations  Convert decimal from expanded form to standard form 
Multiplying and dividing by 10, 100, 1000  Ordering decimals 1 
Multiplying and dividing decimals by 10  Ordering decimals 2 
Multiplying and dividing decimals by 10, 100, 1000  Multiplying a decimal by a power of 10 
Introduction to powers of 10  Dividing a decimal by a power of 10 
Multiplying and dividing by powers of 10  Dividing a decimal by a power of 10: pattern 
Adding units of volume  
Plotting corners of a rectangle 
Changes to Exercise Content in EngageNY 5th Grade
New Exercises  Removed Exercises 
Decimals on the number line: thousandths  Divide decimals like 16.8÷40 by factoring out a 10 
Decimals in written and expanded form  Divide whole numbers like 80÷200 to get a decimal 
Write common fractions as decimals  Divide decimals like 1.32÷0.12 
Estimate to add and subtract fractions with different denominators  Understanding moving the decimal 
Multiply by 1digit numbers with standard algorithm  Shapes on the coordinate plane 
Represent fraction multiplication with visuals  Identify points on a line 
Relate fraction division to fraction multiplication  
Fraction and whole number division in contexts  
Estimating with multiplying decimals and whole numbers  
Multiply whole numbers by 0.1 and 0.01  
Multiply whole numbers and decimals  
Represent decimal multiplication with grids and area models  
Understand multiplying decimals  
Multiply decimals (up to 4digit factors)  
Divide whole numbers by decimals visually  
Volume with unit cubes  
Volume as area of base times height  
Understanding decomposing figures to find volume  
Convert units of time  
Convert units word problems (metrics)  
Convert units word problems (US customary)  
Graph data on line plots (through 1/8 of a unit) 
Changes to Article Content in EngageNY 5th Grade
Removed Articles

Dividing decimals

Multiplying fractions review

Convert units guided word problems (US customary)

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Algebra 1 & Algebra 2
What's Changed
 Informed by the new High School Coherence Map launched in March 2019 by Student Achievement Partners.
 Updated scope and sequence. Easier to find content aligned to your Algebra 1 course without visiting other courses.
 Dozens of new videos, exercises, and practice items in Algebra 1 and Algebra 2
 More intuitive, with visual hints to support learners.
 Better scaffolding. New exercises and improvements to existing exercises support struggling students in mastering challenging material.
 More conceptual items. Exercises focusing on conceptual rigor make sure students understand why math makes sense before formalizing strategies into procedures.
 Revised introductory unit for Algebra 1, quickly refreshing a student’s knowledge of algebra prerequisites  great for summer review, or to kickstart classes on day 1 with a review session.
Algebra 1
Changes to Video Content in Algebra 1
New Videos  Removed Videos 
Graphing a line given point and slope  Evaluating expressions with variables: temperature 
Calculating slope from tables  Evaluating expressions with variables: cubes 
Slope, xintercept, yintercept meaning in context  Evaluating expressions with variables: exponents 
Slope and intercept meaning in context  Writing basic expressions with variables 
Slope and intercept meaning from a table  Writing expressions with variables 
Finding slope and intercepts from tables  Writing expressions with variables & parentheses 
Slope and yintercept from equation  Dependent & independent variables 
Constructing linear equations from context  Dependent & independent variables: graphing 
Constructing linear equations from context  Dependent & independent variables: equation 
Clarifying standard form rules  Interpreting linear expressions: diamonds 
Setting up a system of equations from context example (pet weights)  Interpreting linear expressions: flowers 
Setting up a system of linear equations example (weight and price)  Variables, expressions, & equations 
Interpreting points in context of graphs of systems  Testing solutions to equations 
Elimination strategies  Same thing to both sides of equations 
Evaluating discrete functions  Representing a relationship with an equation 
Determining whether values are in domain of function  Dividing both sides of an equation 
Examples finding the domain of functions  Onestep equations intuition 
Intro to inverse functions  Onestep addition & subtraction equations 
Inputs & outputs of inverse functions  Onestep subtraction equations 
Graphing the inverse of a linear function 
Onestep addition & subtraction equations: fractions & decimals

Finding inverse functions: linear  Onestep division equations 
Linear vs. exponential growth: from data  Onestep multiplication equations 
Linear vs. exponential growth: from data (example 2) 
Onestep multiplication & division equations: fractions & decimals

Intro to twostep equations  
Twostep equations intuition  
Worked example: twostep equations  
Twostep equation word problem: computers  
Twostep equation word problem: garden  
Twostep equation word problem: oranges  
Sums of consecutive integers  
Sum of integers challenge  
Linear equation word problem: saline  
Linear equation word problem: sugary drinks  
Testing solutions to inequalities  
Plotting inequalities  
Plotting an inequality example  
Inequalities word problems  
Onestep inequalities examples  
Onestep inequalities: 5c ≤ 15  
Onestep inequality word problem  
Twostep inequalities  
Twostep inequality word problem: apples  
Twostep inequality word problem: R&B  
Slope (more examples)  
Slopeintercept form problems  
Domain of a radical function  
Worked example: domain of algebraic functions  
Worked example: average rate of change from equation  
Average rate of change word problem: equation  
Linear equations word problems: earnings  
Linear equations word problems: volcano  
Linear graphs word problems  
Linear graphs word problem: cats  
Linear equations word problem: marbles  
Linear equations word problem: file transfer  
Comparing linear functions: equation vs. graph  
Comparing linear functions: table vs. graph  
Comparing linear functions: table vs. graph  
Comparing linear functions word problem: climb  
Comparing linear functions word problem: walk  
Comparing linear functions word problem: work  
Linear functions word problem: pool  
Linear functions word problem: iceberg  
Linear functions word problem: paint  
Linear models word problem: book  
Linear models word problem: marbles  
Manipulating expressions using structure  
Manipulating expressions using structure (example 2)  
Intro to rational exponents  
Rewriting roots as rational exponents  
Exponential equation with rational answer  
Simplifying quotient of powers (rational exponents)  
Simplifying mixed radical and exponential expressions  
Evaluating fractional exponents  
Evaluating fractional exponents: negative unitfraction  
Evaluating fractional exponents: fractional base  
Evaluating quotient of fractional exponents  
Evaluating mixed radicals and exponents  
Simplifying higherindex roots  
Simplifying cube root expressions  
Simplifying cube root expressions (two variables)  
Simplifying higherindex root expressions  
Exponential growth & decay word problems  
The parts of polynomial expressions  
Evaluating polynomials  
Simplifying polynomials  
Adding polynomials  
Subtracting polynomials  
Polynomial subtraction  
Adding & subtracting multiple polynomials  
Adding polynomials: two variables  
Subtracting polynomials: two variables  
Subtracting polynomials: two variables  
Finding an error in polynomial subtraction  
Polynomials review  
Multiplying monomials  
Multiplying monomials to find area: two variables  
Multiplying monomials to find area  
Multiplying monomials challenge  
Multiplying monomials by polynomials: area model  
Multiplying monomials by polynomials  
Multiplying monomials by polynomials challenge  
Multiplying binomials by polynomials  
Multiplying binomials by polynomials: area model  
Multiplying binomials by polynomials challenge  
Special products of binomials: two variables  
More examples of special products  
Polynomial multiplication word problem  
Polynomial word problem: rectangle and circle area  
Polynomial word problem: total value of bills  
Polynomial word problem: area of a window  
Monomial factorization  
Worked example: finding the missing monomial factor  
Worked example: finding missing monomial side in area model


Greatest common factor of monomials  
Factoring binomials: common factor  
Factoring polynomials: common factor  
Factoring polynomials: common factor area model  
Factoring polynomials: common binomial factor  
Worked example: evaluating expressions using structure  
Worked example: evaluating expressions using structure (more examples)


Factoring twovariable quadratics  
Factoring twovariable quadratics: rearranging  
Factoring twovariable quadratics: grouping  
Factoring difference of squares: missing values  
Factoring perfect squares: common factor  
Factoring perfect squares: 4th degree polynomial  
Factoring difference of squares: two variables  
Factoring difference of squares: two variables (example 2)


Using the quadratic formula  
Worked example: quadratic formula 
Changes to Exercise Content in Algebra 1
New Exercises  Removed Exercises 
Graphing from slope  Evaluating expressions with variables word problems 
Slope in a table  Writing basic expressions with variables 
Using slope and intercepts in context  Writing expressions with variables 
Relating linear contexts to graph features  Independent versus dependent variables 
Creating systems in context  Tables from equations with 2 variables 
Interpret points relative to a system  Match equations to coordinates on a line 
Combining equations 
Relationships between quantities in equations and graphs

Elimination strategies  Interpreting linear expressions 
Identifying values in the domain  Testing solutions to equations 
Evaluate inverse functions  Onestep addition & subtraction equations 
Find inverse functions 
Onestep addition & subtraction equations: fractions & decimals

Writing functions with exponential decay  Onestep multiplication & division equations 
Connecting exponential graphs with contexts 
Onestep multiplication & division equations: fractions & decimals

Linear vs. exponential growth: from data  Twostep equations 
Multiply monomials by polynomials (basic): area model  Twostep equations word problems 
Multiply perfect squares of binomials  Sums of consecutive integers 
GCF factoring introduction  Testing solutions to inequalities 
Interpret a quadratic graph  Plotting inequalities 
Factoring quadratics with a common factor  Inequalities word problems 
Onestep inequalities  
Twostep inequalities  
Twostep inequality word problems  
Average rate of change  
Compare linear functions  
Comparing linear functions word problems  
Linear models word problems  
Equivalent systems of equations  
Manipulate expressions using structure  
Linear systems of equations capstone  
4th & 5th roots  
Unitfraction exponents  
Fractional exponents  
Rational exponents challenge  
Properties of exponents (rational exponents)  
Properties of exponents challenge (rational exponents)  
Evaluate radical expressions challenge  
Warmup: exponential vs. linear growth  
Add polynomials (intro)  
Subtract polynomials (intro)  
Add & subtract polynomials  
Add & subtract polynomials: two variables (intro)  
Add & subtract polynomials: two variables  
Add & subtract polynomials: find the error  
Multiply monomials intro  
Multiply monomials  
Multiply monomials by polynomials: area model  
Multiply monomials by polynomials  
Multiply monomials by polynomials challenge  
Warmup: multiplying binomials intro  
Multiply binomials by polynomials  
Special products of binomials  
Factors & divisibility  
Factor monomials  
Greatest common factor of monomials  
Factor polynomials: common factor  
Evaluate expressions using structure  
Warmup: factoring quadratics intro  
Factor polynomials: quadratic methods  
Factor polynomials: quadratic methods (challenge)  
Factor polynomials: special product forms  
Factoring polynomials challenge  
Warmup: graphing quadratics in factored form  
Warmup: graphing quadratics in vertex form  
Warmup: Features of quadratic functions 
Changes to Article Content in Algebra 1
New Articles  Removed Articles 
Intro to inverse functions  Evaluating expressions with variables word problems 
Higher order roots  Writing basic expressions with variables 
Warmup: exponential vs. linear growth  Intro to equations 
Warmup: Multiplying binomials  Onestep addition & subtraction equations 
Onestep multiplication & division equations  
Twostep equations review  
Adding and subtracting polynomials review  
Adding and subtracting polynomials with two variables review


Multiplying monomials review  
Multiplying monomials by polynomials review  
Multiplying binomials review  
Multiplying binomials by polynomials review  
Factoring monomials  
Greatest common factor of monomials  
Factoring polynomials by taking a common factor  
Factoring by common factor review 
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Algebra 2
Changes to Video Content in Algebra 2
New Videos  Removed Videos 
Polynomials intro  Adding functions 
The parts of polynomial expressions  Subtracting functions 
Finding average rate of change of polynomials  Multiplying functions 
Sign of average rate of change of polynomial  Dividing functions 
Adding polynomials  Intro to composing functions 
Subtracting polynomials  Evaluating composite functions 
Polynomial subtraction  Evaluating composite functions: using tables 
Multiplying monomials  Evaluating composite functions: using graphs 
Multiplying monomials by polynomials: area model  Finding composite functions 
Multiplying monomials by polynomials  Evaluating composite functions (advanced) 
Multiplying binomials by polynomials: area model  Modeling with composite functions 
Polynomial special products: difference of squares  Modeling with composite functions (example 2) 
Polynomial special products: perfect square  Reflecting & compressing functions 
Introduction to factoring higher degree polynomials  Intro to inverse functions 
Introduction to factoring higher degree monomials  Inputs & outputs of inverse functions 
Monomial factorization  Graphing the inverse of a linear function 
Worked example: finding the missing monomial factor  Finding inverse functions: linear 
Worked example: finding missing monomial side in area model  Finding inverse functions: quadratic 
Greatest common factor of monomials  Finding inverse functions: quadratic (example 2) 
Factoring binomials: common factor  Finding inverse functions: radical 
Factoring polynomials: common factor  Verifying inverse functions by composition 
Factoring polynomials: common factor area model 
Verifying inverse functions by composition: not inverse

Factoring higher degree polynomials  Determining if a function is invertible 
Factoring perfect squares: common factor 
Restricting domains of functions to make them invertible

Identifying quadratic patterns  Adding & subtracting multiple polynomials 
Factorization with substitution  Subtracting polynomials: two variables 
Polynomial identities introduction  More examples of special products 
Describing numerical relationships with polynomial identities  Dividing polynomials: long division 
Geometric series introduction  Intro to polynomial synthetic division 
Geometric series word problems: swing  Dividing polynomials: synthetic division 
Geometric series word problems: hike  Why synthetic division works 
Dividing quadratics by linear expressions (no remainders) 
Dividing polynomials with remainders: monomial divisors (example 2)

Dividing quadratics by linear expressions with remainders  Dividing polynomials with remainders 
Dividing quadratics by linear expressions with remainders: missing xterm  Intro to the Binomial Theorem 
Dividing polynomials by linear expressions  Pascal's triangle and binomial expansion 
Dividing polynomials by linear expressions: missing term  Expanding binomials 
Factoring using polynomial division  Expanding binomials w/o Pascal's triangle 
Factoring using polynomial division: missing term  Binomial expansion & combinatorics 
Remainder theorem examples  Pascal's triangle & combinatorics 
Intro to rational exponents  Binomial expansion & combinatorics (old) 
Rewriting roots as rational exponents  Factoring quadratics as (x+a)(x+b) (example 2) 
Exponential equation with rational answer 
More examples of factoring quadratics as (x+a)(x+b)

Simplifying quotient of powers (rational exponents)  Intro to grouping 
Simplifying mixed radical and exponential expressions  Factoring quadratics by grouping 
Evaluating fractional exponents  Factoring quadratics: common factor + grouping 
Evaluating fractional exponents: negative unitfraction 
Factoring quadratics: negative common factor + grouping

Evaluating fractional exponents: fractional base  Factoring twovariable quadratics 
Evaluating quotient of fractional exponents  Factoring twovariable quadratics: rearranging 
Evaluating mixed radicals and exponents  Factoring twovariable quadratics: grouping 
Trig word problem: length of day (phase shift) 
Factoring difference of squares: leading coefficient ≠ 1

Factoring perfect squares: negative common factor


Factoring perfect squares  
Factoring difference of squares: two variables (example 2)


Factoring higherdegree polynomials  
Factoring sum of cubes  
Factoring difference of cubes  
Complex numbers & sum of squares factorization  
Factoring sum of squares  
The Fundamental theorem of Algebra  
Quadratics & the Fundamental Theorem of Algebra


Number of possible real roots of a polynomial  
Finding zeros of polynomials (1 of 2)  
Finding zeros of polynomials (2 of 2)  
Finding zeros of polynomials (example 2)  
End behavior of functions & their graphs  
Solving squareroot equations (basic)  
Domain of a radical function  
Graphs of squareroot functions  
Squareroot functions & their graphs  
Simplifying rational expressions (old video)  
Least common multiple  
Least common multiple: repeating factors  
Nested fractions  
Equations with one rational expression (advanced)


Intro to direct & inverse variation  
Recognizing direct & inverse variation  
Recognizing direct & inverse variation: table  
Inverse variation word problem: string vibration  
Constructing exponential models (old example)  
Linear vs. exponential growth: from data  
Linear vs. exponential growth: from data (example 2)


Comparing growth of exponential & quadratic models


Exponential function graph  
Graphs of exponential functions (old example)  
Graphs of logarithmic functions  
Logarithmic scale (with Vi Hart)  
Logarithmic scale  
Richter scale  
Benford's law (with Vi Hart, 1 of 2)  
Benford's law (with Vi Hart, 2 of 2)  
Sine & cosine identities: symmetry  
Tangent identities: symmetry  
Sine & cosine identities: periodicity  
Tangent identities: periodicity  
Interpreting equations graphically  
Interpreting equations graphically (example 2)  
Solving equations graphically (1 of 2)  
Solving equations graphically (2 of 2)  
Quadratic systems: graphical solution  
Quadratic systems: algebraic solution  
Quadratic systems: both variables are squared  
Comparing functions: xintercepts  
Comparing functions: shared features  
Comparing maximum points of quadratic functions  
Sequences intro  
Intro to arithmetic sequences  
Explicit formulas for arithmetic sequences  
Sequences word problem: growth pattern  
Summation notation  
Arithmetic series intro  
Arithmetic series formula  
Worked example: arithmetic series (sigma notation)


Worked example: arithmetic series (sum expression)


Worked example: arithmetic series (recursive formula)


Proof of finite arithmetic series formula  
Intro to geometric sequences  
Explicit & recursive formulas for geometric sequences


Converting recursive & explicit forms of geometric sequences


Geometric series intro  
Geometric series with sigma notation  
Worked example: finite geometric series (sigma notation)


Finite geometric series word problem: social media


Finite geometric series word problem: mortgage  
Intro to conic sections  
Graphing circles from features  
Features of a circle from its graph  
Features of a circle from its standard equation  
Graphing a circle from its standard equation  
Writing standard equation of a circle  
Features of a circle from its expanded equation  
Intro to focus & directrix  
Equation of a parabola from focus & directrix  
Focus & directrix of a parabola from equation 
Changes to Exercise Content in Algebra 2
New Exercises  Removed Exercises 
Polynomials intro  Evaluate composite functions 
Average rate of change  Evaluate composite functions: graphs & tables 
Subtract polynomials (intro)  Find composite functions 
Add & subtract polynomials  Model with composite functions 
Multiply monomials intro  Evaluate inverse functions 
Multiply monomials by polynomials: area model  Find inverse functions 
Multiply monomials by polynomials  Verify inverse functions 
Multiply binomials by polynomials: area model  Determine if a function is invertible 
Polynomial special products: difference of squares 
Restrict domains of functions to make them invertible

Factor monomials  Graphically add & subtract complex numbers 
Greatest common factor of monomials  Add & subtract polynomials: two variables (intro) 
Factor polynomials: common factor 
Divide polynomials with remainders: monomial divisors

Factor higher degree polynomials  Divide polynomials with remainders 
Identify quadratic patterns  Expand binomials 
Factorization with substitution  Factoring quadratics intro 
Geometric series formula  Factor quadratics by grouping 
Divide polynomials by x (no remainders)  Factor polynomials: quadratic methods 
Divide polynomials by x (with remainders) 
Factor polynomials: quadratic methods (challenge)

Divide quadratics by linear expressions (no remainders)  Difference of squares intro 
Divide quadratics by linear expressions (with remainders)  Difference of squares 
Factor using polynomial division  Perfect squares 
Remainder theorem and factors  Factor polynomials: complex numbers 
Zeros of polynomials (multiplicity)  Zeros of polynomials challenge problems 
Unitfraction exponents  Least common multiple 
Fractional exponents  Nested fractions 
Rational exponents challenge 
Equations with one rational expression (advanced)

Properties of exponents (rational exponents)  Recognize direct & inverse variation 
Properties of exponents challenge (rational exponents)  Analyzing structure with rational expressions 
Evaluate radical expressions challenge  Linear vs. exponential growth: from data 
Reflect functions  Interpret equations graphically 
Scale functions vertically  Solve equations graphically 
Scale functions horizontally  Compare features of functions 
Find inverses of rational functions  Extend arithmetic sequences 
Quadratic systems  Use arithmetic sequence formulas 
Solving equations graphically: intro  Recursive formulas for arithmetic sequences 
Solving equations graphically: graphing calculator  Explicit formulas for arithmetic sequences 
Solving equations graphically: word problems  Summation notation intro 
Unit circle  Arithmetic series 
Unit circle (with radians)  Extend geometric sequences 
Graph sinusoidal functions: phase shift 
Extend geometric sequences: negatives & fractions

Modeling with sinusoidal functions: phase shift  Use geometric sequence formulas 
Explicit formulas for geometric sequences  
Recursive formulas for geometric sequences  
Sequences word problems  
Finite geometric series  
Graph a circle from its features  
Features of a circle from its graph  
Features of a circle from its standard equation  
Graph a circle from its standard equation  
Write standard equation of a circle  
Features of a circle from its expanded equation  
Graph a circle from its expanded equation  
Equation of a parabola from focus & directrix 
Changes to Article Content in Algebra 2
New Articles  Removed Articles 
Adding and subtracting polynomials review  Intro to combining functions 
Multiplying monomials by polynomials review  Adding and subtracting functions 
Multiplying binomials by polynomials review  Multiplying and dividing functions 
Factoring monomials  Intro to composing functions 
Greatest common factor of monomials  Composing functions 
Factoring polynomials by taking a common factor  Intro to inverse functions 
Finding inverse functions  
Verifying inverse functions by composition  
Intro to invertible functions  
Solving equations graphically  
Intro to arithmetic sequences  
Intro to arithmetic sequence formulas  
Recursive formulas for arithmetic sequences  
Explicit formulas for arithmetic sequences  
Converting recursive & explicit forms of arithmetic sequences


Arithmetic series  
Arithmetic series worksheet  
Circle equation review  
Parabola focus & directrix review 
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Math 13, Precalculus, Prealgebra, Basic Geometry, and Arithmetic
What's Changed
Although these courses weren't specifically updated, they did see some content added and removed because of their relationship to courses that were given major enhancements.
Math 1
Changes to Video Content in Math 1
New Videos  Removed Videos 
What is a variable?  Simplifying higherindex root expressions 
Intro to combining like terms  Simplifying cube root expressions (two variables) 
Simplifying expressions  Simplifying cube root expressions 
Why aren't we using the multiplication sign?  Slope (more examples) 
Why all the letters in algebra?  Slopeintercept form problems 
Combining like terms challenge problem  Exponential growth & decay word problems 
Evaluating an expression with one variable  Simplifying higherindex roots 
Number of solutions to a system of equations  Linear equations word problems: earnings 
The beauty of algebra  Domain of a radical function 
Abstractness  Linear graphs word problems 
Origins of algebra  Comparing linear functions word problem: work 
Intro to the coordinate plane  Comparing linear functions: equation vs. graph 
Why dividing by zero is undefined  Linear models word problem: book 
The problem with dividing zero by zero  Linear functions word problem: iceberg 
Undefined & indeterminate expressions  Average rate of change word problem: equation 
Setting up a system of equations from context example (pet weights)  Linear functions word problem: paint 
Examples finding the domain of functions  Worked example: domain of algebraic functions 
Simplifying expressions with rational numbers  Linear equations word problem: file transfer 
Interpreting points in context of graphs of systems 
Worked example: average rate of change from equation

Slope, xintercept, yintercept meaning in context  Linear functions word problem: pool 
Evaluating discrete functions  Comparing linear functions: table vs. graph 
Setting up a system of linear equations example (weight and price)  Comparing linear functions word problem: climb 
Constructing linear equations from context  Linear equations word problems: volcano 
Equivalent expressions  Linear models word problem: marbles 
Elimination strategies  Linear graphs word problem: cats 
Graphing a line given point and slope  Performing dilations 
Determining whether values are in domain of function  Comparing linear functions word problem: walk 
Evaluating expressions with two variables: fractions & decimals  Manipulating expressions using structure 
Calculating slope from tables 
Manipulating expressions using structure (example 2)

Slope and intercept meaning in context  Linear equations word problem: marbles 
Slope and yintercept from equation  Comparing linear functions: table vs. graph 
Slope and intercept meaning from a table  
Clarifying standard form rules  
Evaluating expressions with two variables  
Finding slope and intercepts from tables 
Changes to Exercise Content in Math 1
New Exercises  Removed Exercises 
Evaluating expressions with multiple variables  Find angles in triangles 
Evaluating expressions with one variable  Linear systems of equations capstone 
Combining like terms with negative coefficients  Manipulate expressions using structure 
Combining like terms with negative coefficients & distribution  4th & 5th roots 
Graphing from slope  Warmup: exponential vs. linear growth 
Combining like terms with rational coefficients  Comparing linear functions word problems 
Using slope and intercepts in context  Linear models word problems 
Writing functions with exponential decay  Equivalent systems of equations 
Slope in a table  Compare linear functions 
Interpret points relative to a system  
Elimination strategies  
Identifying values in the domain  
Creating systems in context  
Relating linear contexts to graph features  
Evaluating expressions with multiple variables: fractions & decimals


Equivalent expressions  
Combining equations  
Connecting exponential graphs with contexts 
Changes to Article Content in Math 1
New Articles 
Evaluating expressions with one variable 
Evaluating expressions with two variables: fractions & decimals

Evaluating expressions with two variables 
Warmup: exponential vs. linear growth 
Higher order roots 
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Math 2
Changes to Video Content in Math 2
Removed Videos

Worked example: evaluating expressions using structure

Worked example: evaluating expressions using structure (more examples)

Evaluating polynomials 
Simplifying polynomials 
Multiplying monomials to find area 
Dividing polynomials: long division 
Worked example: quadratic formula 
More examples of special products 
Multiplying monomials to find area: two variables

Polynomial word problem: total value of bills 
Adding & subtracting multiple polynomials 
Polynomial word problem: area of a window 
Polynomial multiplication word problem 
Factoring twovariable quadratics: grouping 
Factoring difference of squares: two variables (example 2)

Using the quadratic formula 
Polynomial word problem: rectangle and circle area

Special products of binomials: two variables 
Intro to polynomial synthetic division 
Why synthetic division works 
Dividing polynomials: synthetic division 
Multiplying monomials challenge 
Comparing growth of exponential & quadratic models

Constructing exponential models (old example) 
Factoring twovariable quadratics: rearranging 
Factoring polynomials: common binomial factor 
Factoring twovariable quadratics 
Multiplying binomials by polynomials challenge 
Factoring difference of squares: missing values 
Multiplying monomials by polynomials challenge

Changes to Exercise Content in Math 2
New Exercises  Removed Exercises 
Interpret a quadratic graph  Evaluate expressions using structure 
Multiply monomials by polynomials (basic): area model  Factor polynomials: quadratic methods 
Multiply perfect squares of binomials 
Factor polynomials: quadratic methods (challenge)

Factoring quadratics with a common factor  Warmup: graphing quadratics in vertex form 
GCF factoring introduction  Multiply monomials 
Warmup: Features of quadratic functions  
Multiply monomials by polynomials challenge  
Warmup: multiplying binomials intro  
Warmup: graphing quadratics in factored form  
Warmup: factoring quadratics intro  
Factors & divisibility  
Factoring polynomials challenge 
Changes to Article Content in Math 2
New Articles  Removed Articles 
Warmup: Multiplying binomials  Multiplying monomials review 
Factoring by common factor review  
Multiplying binomials review 
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Math 3
Changes to Video Content in Math 3
New Videos  Removed Videos 
Trig word problem: length of day (phase shift)  Recognizing direct & inverse variation: table 
Polynomial special products: difference of squares 
Equation with two rational expressions (old example)

Factoring using polynomial division  Inverse variation word problem: string vibration 
Dividing quadratics by linear expressions with remainders: missing xterm 
Equation with two rational expressions (old example 3)

Polynomial identities introduction  Simplifying rational expressions (old video) 
Factoring using polynomial division: missing term  Factoring sum of cubes 
Remainder theorem examples  Logarithmic scale (with Vi Hart) 
Geometric series introduction  Benford's law (with Vi Hart, 2 of 2) 
Introduction to factoring higher degree monomials  Benford's law (with Vi Hart, 1 of 2) 
Sign of average rate of change of polynomial  Logarithmic scale 
Identifying quadratic patterns  Richter scale 
Dividing polynomials by linear expressions  Graphs of squareroot functions 
Finding average rate of change of polynomials  Binomial expansion & combinatorics (old) 
Geometric series word problems: swing  Finding inverse functions: quadratic 
Describing numerical relationships with polynomial identities  Finding inverse functions: quadratic (example 2) 
Factoring higher degree polynomials  Solving squareroot equations (basic) 
Introduction to factoring higher degree polynomials  Quadratic systems: graphical solution 
Polynomial special products: perfect square  Quadratic systems: algebraic solution 
Factorization with substitution 
Equation with two rational expressions (old example 2)

Dividing quadratics by linear expressions (no remainders) 
Equations with one rational expression (advanced)

Geometric series word problems: hike  Dividing functions 
Dividing polynomials by linear expressions: missing term  Multiplying functions 
Dividing quadratics by linear expressions with remainders  Subtracting functions 
Domain of a radical function  
Adding functions  
Factoring difference of cubes  
Intro to direct & inverse variation  
Recognizing direct & inverse variation  
Quadratic systems: both variables are squared  
Finding zeros of polynomials (example 2)  
Finding zeros of polynomials (2 of 2)  
Least common multiple  
Factoring higherdegree polynomials  
Comparing functions: xintercepts  
Graphs of logarithmic functions  
End behavior of functions & their graphs  
Finding inverse functions: radical  
Graphs of exponential functions (old example)  
Reflecting & compressing functions  
Nested fractions  
Least common multiple: repeating factors  
Comparing functions: shared features  
Squareroot functions & their graphs  
Finding zeros of polynomials (1 of 2) 
Changes to Exercise Content in Math 3
New Exercises  Removed Exercises 
Multiply binomials by polynomials: area model  Least common multiple 
Scale functions horizontally  Recognize direct & inverse variation 
Geometric series formula  Analyzing structure with rational expressions 
Graph sinusoidal functions: phase shift 
Equations with one rational expression (advanced)

Divide quadratics by linear expressions (no remainders)  Nested fractions 
Divide quadratics by linear expressions (with remainders)  Zeros of polynomials challenge problems 
Solving equations graphically: intro  Compare features of functions 
Reflect functions  
Scale functions vertically  
Divide polynomials by x (no remainders)  
Polynomial special products: difference of squares


Identify quadratic patterns  
Remainder theorem and factors  
Zeros of polynomials (multiplicity)  
Solving equations graphically: word problems  
Factor higher degree polynomials  
Modeling with sinusoidal functions: phase shift  
Find inverses of rational functions  
Unit circle (with radians)  
Solving equations graphically: graphing calculator


Quadratic systems  
Factorization with substitution  
Factor using polynomial division  
Unit circle  
Divide polynomials by x (with remainders) 
Changes to Article Content in Math 3
Removed Articles 
Adding and subtracting functions 
Multiplying and dividing functions 
Finding inverse functions 
Intro to combining functions 
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Precalculus
Changes to Video Content in Precalculus
New Videos  Removed Videos 
Geometric series introduction  Challenging complex numbers problem (1 of 3) 
Geometric series word problems: swing  Challenging complex numbers problem (2 of 3) 
Geometric series word problems: hike  Challenging complex numbers problem (3 of 3) 
Challenging complex numbers problem: complex determinant

Changes to Exercise Content in Precalculus
New Exercises 
Geometric series formula 
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Prealgebra
Changes to Video Content in Prealgebra
New Videos 
Commutative property of multiplication 
Distributive property when multiplying 
Rounding to the nearest 10 on the number line 
Rounding to the nearest 100 on the number line 
Using associate property to simplify multiplication 
Order of operations (2step expressions) 
2step estimation word problems 
Setting up 2step word problems 
Place value tables 
Writing numbers in words and standard form 
Writing decimals and fractions greater than 1 shown on grids

Writing decimals and fractions shown on number lines 
Relating decimals and fractions in words 
Place value with decimals 
Thousandths on the number line 
Expressing decimals in multiple forms 
Visual understanding of regrouping decimals 
Regrouping with decimals 
Ordering decimals 
Ordering decimals through thousandths 
Comparing decimals in different representations 
Multiplying and dividing decimals by 10 
Multiplying and dividing decimals by 10, 100, 1000 
Introduction to powers of 10 
Multiplying and dividing by powers of 10 
Changes to Exercise Content in Prealgebra
New Exercises 
Represent the commutative property of multiplication 
Understand the commutative property of multiplication 
Visualize distributive property 
Fractions in contexts 
Relate number lines to fraction bars 
Fractions greater than 1 on the number line 
Compare fractions on the number line 
Equivalent fractions 
Understand associative property of multiplication 
Use associative property to multiply 2digit numbers by 1digit

2step expressions 
Place value tables 
Understand multiplying by a multiple of 10, 100, and 1000

Identify factors 
Identify multiples 
Prime and composite numbers 
Equivalent fractions (number lines) 
Compare fractions using benchmark 
Compare fractions word problems 
Decompose fractions visually 
Multiply fractions and whole numbers on the number line

Multiply mixed numbers and whole numbers 
Write decimals and fractions shown on number lines 
Write decimals and fractions greater than 1 shown on number lines

Relate decimals and fractions in words 
Write common fractions as decimals 
Order decimals and fractions in different forms 
Decimals on the number line: thousandths 
Decimals in written and expanded form 
Write common fractions as decimals 
Estimate to add and subtract fractions with different denominators

Estimating with multiplying decimals and whole numbers

Multiply whole numbers by 0.1 and 0.01 
Multiply whole numbers and decimals 
Represent decimal multiplication with grids and area models

Understand multiplying decimals 
Multiply decimals (up to 4digit factors) 
Divide whole numbers by decimals visually 
Changes to Article Content in Prealgebra
Removed Articles 
Intro to commutative property of multiplication 
Intro to associative property of multiplication 
Intro to distributive property 
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Basic Geometry
Changes to Video Content in Basic Geometry
Removed Videos 
Plotting corners of a rectangle 
Measuring area with partial unit squares 
Changes to Exercise Content in Basic Geometry
New Exercises  Removed Exercises 
Volume with unit cubes  Draw rays, lines, & line segments 
Volume as area of base times height  Draw right, acute, and obtuse angles 
Understanding decomposing figures to find volume  Draw lines of symmetry and symmetrical figures 
Classify triangles by both sides and angles  Find area with partial unit squares 
Types of angles by measure  
Estimate angle measures  
Area and perimeter situations  
Classify quadrilaterals  
Understand area  
Area of rectangles with partial arrays  
Find perimeter when a side length is missing


Area and perimeter situations  
Area and perimeter word problems 
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Arithmetic
Changes to Video Content in Arithmetic
New Videos 
Equal groups 
Introduction to multiplication 
Multiplication as repeated addition 
Multiplication on the number line 
Multiplication in real world contexts 
Estimating when subtracting large numbers 
Subtraction by breaking apart 
Methods for subtracting 3digit numbers 
Missing number for 3digit subtraction within 1000

Three digit addition word problems 
Three digit subtraction word problems 
Visualizing division with arrays 
Division in context 
Writing decimals and fractions greater than 1 shown on grids

Writing decimals and fractions shown on number lines

Relating decimals and fractions in words 
Place value with decimals 
Thousandths on the number line 
Expressing decimals in multiple forms 
Visual understanding of regrouping decimals 
Regrouping with decimals 
Ordering decimals 
Ordering decimals through thousandths 
Comparing decimals in different representations

Multiplying and dividing by 10, 100, 1000 
Multiplying and dividing decimals by 10 
Multiplying and dividing decimals by 10, 100, 1000

Changes to Exercise Content in Arithmetic
New Exercises 
Equal groups 
Understand equal groups as multiplication 
Multiply using groups of objects 
Understand multiplication with arrays 
Multiplication in contexts 
Select strategies for adding within 1000 
Break apart 3digit subtraction problems 
Subtract on a number line 
Select strategies for subtracting within 1000 
Add and subtract within 1000 word problems 
Division with arrays 
Division in contexts 
Fractions in contexts 
Relate number lines to fraction bars 
Fractions greater than 1 on the number line 
Compare fractions on the number line 
Equivalent fractions 
Understand multiplying by a multiple of 10, 100, and 1000

Multiply 2digits by 1digit with area models 
Multiply 3 and 4digits by 1digit with distributive property

Multiply using partial products 
Multiply with partial products (2digit numbers)

Create division equations with area models 
Equivalent fractions (number lines) 
Compare fractions using benchmark 
Compare fractions word problems 
Decompose fractions visually 
Multiply fractions and whole numbers on the number line

Multiply mixed numbers and whole numbers 
Write decimals and fractions shown on number lines

Write decimals and fractions greater than 1 shown on number lines

Relate decimals and fractions in words 
Write common fractions as decimals 
Order decimals and fractions in different forms

Decimals on the number line: thousandths 
Decimals in written and expanded form 
Write common fractions as decimals 
Multiply by 1digit numbers with standard algorithm

Represent fraction multiplication with visuals 
Relate fraction division to fraction multiplication

Fraction and whole number division in contexts

Multiply whole numbers by 0.1 and 0.01 
Multiply whole numbers and decimals 
Represent decimal multiplication with grids and area models

Understand multiplying decimals 
Multiply decimals (up to 4digit factors) 
Divide whole numbers by decimals visually 
Changes to Article Content in Arithmetic
Removed Articles 
Intro to multiplication 
Intro to division 