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# Content Updates: Math Special Edition (July 2019)

Updated

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.

Algebra 1

Algebra 2

Math 1

Math 2

Math 3

Precalculus

Prealgebra

Basic Geometry

Arithmetic

### What's Changed

• New and revised materials by our in-house content experts reflect the depth, breadth, and rigor of CCSS, and reflect the best of how we've seen educators supporting mathematical practices and on-grade 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.

### Changes to Video Content in Grade 3 Math

 New Videos Removed Videos Equal groups Estimating adding and subtracting 3-digit numbers Introduction to multiplication Subtracting in your head (no regrouping) Multiplication as repeated addition The idea of division Multiplication on the number line 2-step 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 multi-digit numbers Estimating when subtracting large numbers Subtraction by breaking apart Methods for subtracting 3-digit numbers Missing number for 3-digit 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 (2-step expressions) 2-step estimation word problems Setting up 2-step 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 multi-digit whole numbers Break apart 3-digit 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 2-digit numbers by 1-digit 2-step 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

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### 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 2-digit by 1-digit Comparing with multiplication Multiplying: 2-digit by 1-digit (regrouping) Estimating with multiplication Multiplying 4-digit by 1-digit (regrouping) Estimating 2-digit 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 2-digits by 1-digit with area models Zeros in the quotient (no remainders) Multiply 3- and 4-digits by 1-digit with distributive property Equivalent fractions and different wholes Estimate products (1-digit times 2, 3, and 4-digit) Order fractions Multiply using partial products Compare fractions and mixed numbers Estimate products (2-digit numbers) Draw rays, lines, & line segments Multiply with partial products (2-digit numbers) Draw right, acute, and obtuse angles Estimate to divide by 1-digit numbers Draw lines of symmetry and symmetrical figures Create division equations with area models Whole number place value challenge Estimate quotients (3- and 4-digit divided by 1-digit) 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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### 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 Multi-digit 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 1-digit 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 4-digit 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)

## top^

### 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 2-step 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 multi-digit numbers Estimating when subtracting large numbers Subtraction by breaking apart Methods for subtracting 3-digit numbers Missing number for 3-digit 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 (2-step expressions) 2-step estimation word problems Setting up 2-step 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 multi-digit whole numbers Break apart 3-digit 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 2-digit numbers by 1-digit 2-step 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

## top^

### 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 2-digit by 1-digit Comparing with multiplication Multiplying: 2-digit by 1-digit (regrouping) Estimating with multiplication Multiplying 4-digit by 1-digit (regrouping) Estimating 2-digit 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 2-digits by 1-digit with area models Zeros in the quotient (no remainders) Multiply 3- and 4-digits by 1-digit with distributive property Equivalent fractions and different wholes Estimate products (1-digit times 2, 3, and 4-digit) Order fractions Multiply using partial products Compare fractions and mixed numbers Estimate products (2-digit numbers) Draw rays, lines, & line segments Multiply with partial products (2-digit numbers) Draw right, acute, and obtuse angles Estimate to divide by 1-digit numbers Draw lines of symmetry and symmetrical  figures Create division equations with area models Whole number place value challenge Estimate quotients (3- and 4-digit divided by 1-digit) 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

## top^

### 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 Multi-digit 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 1-digit 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 4-digit 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)

# 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 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 One-step addition & subtraction equations One-step multiplication & division equations Two-step 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

## Algebra 2

### 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

# Math 1-3, 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 higher-index 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? Slope-intercept form problems Combining like terms challenge problem Exponential growth & decay word problems Evaluating an expression with one variable Simplifying higher-index roots Number of solutions to a system of equations Linear equations word problems: earnings The beauty of algebra Domain of a radical function Abstract-ness 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, x-intercept, y-intercept 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 y-intercept 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

## 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 two-variable 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 two-variable quadratics: rearranging Factoring polynomials: common binomial factor Factoring two-variable 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

## Math 3

### 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

## 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

## 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 (2-step expressions) 2-step estimation word problems Setting up 2-step 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 2-digit numbers by 1-digit 2-step 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 4-digit 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

## 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

## 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 3-digit numbers Missing number for 3-digit 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 3-digit 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 2-digits by 1-digit with area models Multiply 3- and 4-digits by 1-digit with distributive property Multiply using partial products Multiply with partial products (2-digit 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 1-digit 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 4-digit factors) Divide whole numbers by decimals visually

### Changes to Article Content in Arithmetic

 Removed Articles Intro to multiplication Intro to division