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.
Table of Contents
Grades 3-5 (Including EngageNY)
What's Changed
Grade 5 Math
Algebra 1 & Algebra 2
What's Changed
Math 1-3, Precalculus, Prealgebra, Basic Geometry, and Arithmetic
What's Changed
Grades 3-5 (Including EngageNY)
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.
Grade 3 Math
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 |
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 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 |
top^
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 | 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^
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 | 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^
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 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^
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 | 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)
|
top^
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, x-intercept, y-intercept 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 y-intercept 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 | One-step equations intuition |
| Intro to inverse functions | One-step addition & subtraction equations |
| Inputs & outputs of inverse functions | One-step subtraction equations |
| Graphing the inverse of a linear function |
One-step addition & subtraction equations: fractions & decimals
|
| Finding inverse functions: linear | One-step division equations |
| Linear vs. exponential growth: from data | One-step multiplication equations |
| Linear vs. exponential growth: from data (example 2) |
One-step multiplication & division equations: fractions & decimals
|
| Intro to two-step equations | |
| Two-step equations intuition | |
| Worked example: two-step equations | |
| Two-step equation word problem: computers | |
| Two-step equation word problem: garden | |
| Two-step 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 | |
| One-step inequalities examples | |
| One-step inequalities: -5c ≤ 15 | |
| One-step inequality word problem | |
| Two-step inequalities | |
| Two-step inequality word problem: apples | |
| Two-step inequality word problem: R&B | |
| Slope (more examples) | |
| Slope-intercept 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 unit-fraction | |
| Evaluating fractional exponents: fractional base | |
| Evaluating quotient of fractional exponents | |
| Evaluating mixed radicals and exponents | |
| Simplifying higher-index roots | |
| Simplifying cube root expressions | |
| Simplifying cube root expressions (two variables) | |
| Simplifying higher-index 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 two-variable quadratics | |
| Factoring two-variable quadratics: rearranging | |
| Factoring two-variable 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 | One-step addition & subtraction equations |
| Find inverse functions |
One-step addition & subtraction equations: fractions & decimals
|
| Writing functions with exponential decay | One-step multiplication & division equations |
| Connecting exponential graphs with contexts |
One-step multiplication & division equations: fractions & decimals
|
| Linear vs. exponential growth: from data | Two-step equations |
| Multiply monomials by polynomials (basic): area model | Two-step 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 |
| One-step inequalities | |
| Two-step inequalities | |
| Two-step 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 | |
| Unit-fraction 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 | 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 |
top^
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 x-term | 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 unit-fraction |
Factoring quadratics: negative common factor + grouping
|
| Evaluating fractional exponents: fractional base | Factoring two-variable quadratics |
| Evaluating quotient of fractional exponents | Factoring two-variable quadratics: rearranging |
| Evaluating mixed radicals and exponents | Factoring two-variable 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 higher-degree 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 square-root equations (basic) | |
| Domain of a radical function | |
| Graphs of square-root functions | |
| Square-root 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: x-intercepts | |
| 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 |
| Unit-fraction 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 |
top^
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 |
top^
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 |
top^
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 x-term |
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 square-root 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 square-root 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 higher-degree polynomials | |
| Comparing functions: x-intercepts | |
| 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 | |
| Square-root 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 |
top^
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 |
top^
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 |
top^
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 |
top^
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 |