**Better Practice = Better Scores.**

**Our adaptive engine powered by machine learning continuously learns about each student, the questions are chosen to match the estimated ability level of the student, if student succeeds on a question, a more challenging question is presented next. If the student answers a question incorrectly, a less-challenging questions is presented, which helps them thoroughly master each skill.**

**Standard**

- Our standard plan is great for children who wants to access our member only practice tests and adaptive practice quizzes for CogAT, MAP Math & ELA, CCAT, NNAT, OLSAT, GATE, NYC GT Programs, ERB CTP 5, Iowa Assesssements, CPS Selective Enrollment, Texas GT Porgrams, Texas STAAR, GMAS, FSA, NC-EOG, Virgnia SOL, Math Olympiad, HSPT & PSAT 8/9 , but don’t need tutor personalization, guidance, or one-on-one tutoring. This is for independent practice.
- Adaptive Practice Quizzes for CogAT, CCAT, NNAT, OLSAT, InView, GATE, NYC GT Programs, MAP Math, ELA, GMAS, FSA, CMAS, EOG & SBAC
- 4000+ CogAT Practice Questions
- Canada CCAT (Use CogAT Practice questions, as both tests are similar)
- CPS Selective Enrollment (Use CogAT & MAP)
- NYC GT (Use OLSAT & NNAT)
- GATE (Use CogAT, OLSAT & NNAT)
- 2000+ OLSAT Practice Questions
- 2000+ NNAT Practice Questions
- 1000+ InView Practice Questions
- 2000 + MAP Practice Questions
- 2000 + Iowa Assessment Practice Questions
- 2000 + ERB CTP Practice Questions
- 2 Full Length ISEE Practice Tests + ERB Questions
- 5 Full Length Practice Tests for State Assessments.
~~Dedicated Coach~~~~Student Specific GT Test Prep~~~~Personalized practice tests aligned to your school curriculum.~~~~Weekly Skill Assessments~~~~Parent-Tutor progress discussions~~~~Homework Help~~

**Advanced Test Prep**

**Advanced Test Prep**- Our advanced test prep plan is great for children who benefit from a dedicated coach for CogAT, MAP Math & ELA, CCAT, NNAT, OLSAT, GATE, NYC GT Programs, ERB CTP 5, Iowa Assessments, CPS Selective Enrollment, Texas GT Programs, Texas STAAR, GMAS, FSA, NC-EOG, Virginia SOL, Math Olympiad, HSPT & PSAT 8/9. Your coach structure your study plan, tailor practice tests that matches your test prep & school curriculum.
- Adaptive Practice Quizzes for CogAT, CCAT, NNAT, OLSAT, InView, GATE, NYC GT Programs, MAP Math, ELA, GMAS, FSA, CMAS, EOG & SBAC
- 4000+ CogAT Practice Questions
- Canada CCAT (Use CogAT Practice questions, as both tests are similar)
- CPS Selective Enrollment (Use CogAT & MAP)
- NYC GT (Use OLSAT & NNAT)
- GATE (Use CogAT, OLSAT & NNAT)
- 2000+ OLSAT Practice Questions
- 2000+ NNAT Practice Questions
- 1000+ InView Practice Questions
- 2000 + MAP Practice Questions
- 2000 + Iowa Assessment Practice Questions
- 2000 + ERB CTP Practice Questions
- 2 Full Length ISEE Practice Tests + ERB Questions
- 5 Full Length Practice Tests for State Assessments.
- Dedicated Coach
- Student Specific GT Test Prep
- Personalized practice tests aligned to your school curriculum.
- Weekly Skill Assessments
~~Homework Help~~~~1 : 1 Private Tutoring~~

**Private Tutoring**

- Our Private Tutoring plan includes all of the
**Standard Plan**and also pairs your child with an US based expert tutor for one-on-one whiteboard tutoring sessions, homework help & test prep for CogAT, MAP Math & ELA, CCAT, NNAT, OLSAT, GATE, NYC GT Programs, ERB CTP 5, Iowa Assesssements, CPS Selective Enrollment, Texas GT Porgrams, Texas STAAR, GMAS, FSA, NC-EOG, Virgnia SOL, Math Olympiad, HSPT & PSAT 8/9. - 4000+ CogAT Practice Questions
- Canada CCAT (Use CogAT Practice questions, as both tests are similar)
- CPS Selective Enrollment (Use CogAT & MAP)
- NYC GT (Use OLSAT & NNAT)
- GATE (Use CogAT, OLSAT & NNAT)
- 2000+ OLSAT Practice Questions
- 2000+ NNAT Practice Questions
- 1000+ InView Practice Questions
- 2000 + MAP Practice Questions
- 2000 + Iowa Assessment Practice Questions
- 2000 + ERB CTP Practice Questions
- 2 Full Length ISEE Practice Tests + ERB Questions
- 5 Full Length Practice Tests for State Assessments.
- 4 Tutoring Sessions (55 Minutes each)
- US Based Tutors
- Flexible Morning & Evening Scheduling
- Dedicated Coach
- Student Specific GT Test Prep
- Personalized practice tests aligned to your school curriculum.
- Weekly Skill Assessments
- Parent-Tutor progress discussions
- Homework Help
- 1 : 1 Private Tutoring

**How Our Private Tutoring Works?**

## Aligned to Curriculum

Our personalized study plans are aligned to your child’s school curriculum. Our coaches work with students one-on-one to personalize private or public school curriculum for each child’s individual needs.

## United States based Tutors

Tutorified’s difference is our Math & English Language & Arts tutors are US based professional educators who hold tutoring certificate or mater’s degree. We find the best tutors, so you get best tutoring.

## Coaches Available 24 x 7

Our knowledgeable dedicated coaches are available to help 24/7, anytime to fit your schedule. Students should have access to personalized, learning support the moment they need it.

**Select your Membership Start Practicing Instantly !**

### Our 3 Step Approach

**Step 1 : Evaluation**

In our 1:1 Lesson & Private Tutoring plans, each student takes a comprehensive academic evaluation quiz which pin points strength and weakness.

**Step 2 : Study Plan**

Based on the results of the academic evaluation, our dedicated coaches develop a individualized study plan to meet each student’s needs.

**Step 3 : Communication**

We keep parents in the loop by sending out monthly one personalized student progress report via email.

**Are you concerned about what we teach to your child? Don’t be**!

Our guided mathematics video lessons are aligned to public & private school curriculum. We also prepare your child for private & public school state assessments, Iowa assessments, ERB-CTP, TerraNova, Gifted & Talented programs.

##### 2nd Grade

##### Adding & Subtracting Fluently within 20

• Add by making a ten.

• Add and subtract on a number line

• Subtract by finding the difference on a number line.

• Add and subtract using fact families.

##### Add & Subtract within 100 to solve one- and two-step word problems.

* Solve word problems by counting.

* Solve word problem with missing parts by drawing bar.

* Solve two-step problems by writing an equation.

* Solve two-step problems by making a model.

##### Working with equal groups to gain foundations for multiplication.

* Determine whether a group contains an even or odd number.

* Use the digit in the ones place to determine if a number is even or odd.

* Understanding arrays.

* Count objects by using an array.

##### Understand the Place Value

* Understand the value of a number.

* Combine tens, ones, and hundreds to create numbers.

* Draw a visual representation of a 3-digit number.

* Understand the value of digits using pictures.

##### Count within 1000; skip-count by 5s, 10s, and 100s.

* Identify number patterns by skip-counting with base ten blocks.

* Identify patterns when counting by 5.

* Identify patterns when counting by 10.

* Identify patterns when counting by 100.

##### Compare two three-digit numbers.

* Compare numbers using a number chart and counting sequence.

* Identify an equal number of ones, tens, and hundred.

* Represent a 2-digit number using a place value model.

* Show numbers in different ways by taking models apart.

##### Fluently add and subtract within 100

* Add within 100 on an open number line.

* Add within 100 using base ten blocks.

* Subtract numbers within 100 using an open number line.

* Subtract numbers within 100 using base ten blocks.

##### Add up to four two-digit numbers

* Add three 2-digit numbers by decomposing.

* Add three and four 2-digit numbers by making 10s.

* Add up to four 2-digit numbers using place value.

* Add up to four 2-digit numbers using the properties of addition

##### Add and subtract within 1000.

* Add within 1000 using a number line.

* Add within 1000 using base 10 blocks.

* Subtract three-digit numbers with a number line.

* Subtract within 1000 using base 10 blocks.

##### Mentally Add & Subtract 10 or 100

* Mentally add 10 or 100 visualizing base ten blocks.

* Mentally add or subtract 10 using a hundreds chart.

* Mentally subtract 10 or 100 using base ten blocks.

* Subtract using expanded notation.

##### Explain why addition and subtraction works.

* Choose appropriate strategies to explain.

* Explain addition using place value.

* Explain subtraction by decomposing numbers.

* Explain subtraction using place value.

##### Choose the appropriate measurement tool

* Measure using a ruler

* Measure with foot and yard-length units

* Measure with inch length-units

* Measure in centimeter and meter-length units

##### Relate addition and subtraction to length.

* Solve length word problems using a bar model.

* Solve length word problems using a ruler.

* Solve length word problems using color tiles.

* Find unknowns by creating number bonds.

##### Work with time and money.

* Tell time using the hour hand

* Tell time to the nearest 5 minutes using analog and digital

* Solve money word problems using base ten blocks

* Count money by drawing pictures

##### Represent and interpret data

Create a data table

Display data from a word problem on a line plot

Collect data by recording tally marks in a table

Solve compare problems using information from a picture graph

##### Reason with shapes and their attributes

Draw a triangle

Draw a quadrilateral

Draw a hexagon

Draw a pentagon

##### Identifying shapes and their attributes

Identify triangles,

Identity quadrilaterals,

Identity pentagons

Identify hexagons

##### Partition a rectangle into rows and columns

Partition a rectangle into columns

Partition a rectangle into rows

Partition rectangles using same-sized squares

Find the number of same-size squares in a rectangles

##### Partition circles and rectangles into shares

Count unit fractions

Partition a circle into equal shares

Compare equal shares from different wholes

Partition a circle into two, three, or four equal shares

##### 3rd Grade

##### Represent and solve problems involving multiplication & Division

* Represent equal groups using multiplication

* Solve multiplication problems by skip counting

* Understand division problems matching equations

* Solve division problems by subtracting equal groups

##### Use multiplication and division to solve word problems

* Understand multiplication problems using equal groups

* Solve word problems using the idea of equal groups

* Find the missing quotient in a division problem

* Solve division problems using properties of 1 and 0

##### Understand relationship between multiplication and division

* Understand the commutative property of multiplication in word

* Solve multiplication problems using distributive property

* Interpret division as an unknown factor problem using a bar

* Interpret division as an unknown factor problem using arrays

##### Multiplication and Division up to 100

* Understand division with 0 and 1

* Divide using fact families

* Multiply by combining known facts

* Solve multiplication problems using associative property

##### Identify and explain patterns in arithmetic

* Estimate solutions to two-step word problems

* Solve two-step problems using letters to represent unknowns

* Identify addition and subtraction patterns using a hundreds

* Find number patterns by using multiplication and division

##### Use place value understanding to round whole numbers

* Understand the value of a digit in a multi-digit number

* Find benchmark numbers using a number line

* Round to the nearest ten using base ten blocks

* Round to the nearest ten or hundred in real world situation

##### Fluently add and subtract within 1000

* Solve addition problems using partial sums

* Solve addition problems with numbers up to 1,000

* Solve subtraction problems using a number line

* Solve subtraction word problems by identifying key phrases

##### Multiply one-digit whole numbers by multiples of 10

* Multiply by multiples of 10 using number lines

* Multiply by multiples of 10 with base ten blocks

* Multiply by multiples of 10 by breaking apart the multiple

* Multiply by multiples of 10 using arrays

##### Understanding of fractions as numbers

* Understand fractions create mini-stories

* Count fractions to make 1 whole

* Represent fractions in different ways

* Solve fraction word problems using key words and pictures

##### Fraction on the number line

* Place fractions on a number line

* Plot a unit fraction on a number line

* Plot fractions greater than one on a number line

* identify a fraction as a point on a number line using area

##### Understand and generate equivalent fractions

* Identify equivalent fractions using fraction models

* Use a number line to generate equivalent fractions

* Generate equivalent fractions using fraction models

* Use area models to generate equivalent fractions

##### Express whole numbers as fractions & compare two fractions

* Express whole numbers as fractions

* Express fractions equivalent to 1 using a number line

* Compare unit fractions

* Recognize when comparisons are valid by reasoning

##### Tell and write time and solve word problems involving time

* Reading the exact minute on a clock

* Identifying the start time, change of time, and end time

* Solving elapsed time word problems to the nearest hour

* Solving elapsed time word problems to the nearest minute

##### Measure and estimate liquid volumes and solve word problems

* Find the volume of liquids

* Estimate the volume of a liquid

* Solve word problems about volume by adding and subtracting

* Solve multiplication and division word problems about volume

##### Solve problems involving mass of an object

* Find the mass of an object using a balance scale

* Measure mass in kilograms

* Solve mass and volume word problems using addition and subtraction

* Solve multiplication and division word problems about mass

##### Represent and interpret data

* Draw bars on a graph

* Label and title a graph

* Identify questions that can be answered using graphs

* Title and label graphs by looking at data collected

##### Solve one- and two-step problems using graphs

* One-step questions about a bar graph

* One-step questions about a picture graph

* Two-step questions about a picture graph

* Two-step story problems about a bar graph

##### Generate measurement data by measuring lengths using rulers

* Collect and display measurement data

* Collect and show data on a line plot

* Creating and reading a ruler to measure objects

* Measuring objects using whole, half, and quarter inches

##### Understand concepts of area measurement

* Cover the area of a shape using square unit

* Use equal square units to find the area

* Use grid paper to find the area

* Determine which unit of measurement to use to find the area

##### Measure areas by counting unit squares

* Determine which unit of measurement to use to find the area

* Find the area of a polygon using a key

* Find the area of a shape using a key to find the unit of measurement

* Find the area of a square or rectangle by counting unit square

##### Relate area to the operations of multiplication and addition

* Find area by counting square units

* Apply mathematical reasoning to a known area to find unknown

* Find area of a polygon using multiplication

* Find area using multiplication in real world problems

##### Find the area of a rectangle using side lengths

* Find the area of a rectangle by counting columns and rows

* Find the area of a rectangle by multiplying side lengths

* Find missing side lengths by drawing arrays

* Find the area of a rectangle using side lengths

##### Decompose area models & apply distributive property

* Decompose a rectangle

* Apply the distributive property using area models

* Use area models to represent the distributive property

* Find area by using multiplication

##### Find & recognize the perimeter

* Find perimeter with missing side lengths

* Find the perimeter of a polygon with more than 4 sides

* Use a chart to understand how rectangles

* Find the perimeter of a polygon in real world problems

##### Identify shapes in different categories

* Identify rectangles

* Identify rhombuses

* Identify squares

* Identifying trapezoids and parallelogram

##### Reason with shapes and their attributes

* Reason with shapes and their attributes

* Recognize shape attributes

* Identify a polygon by its attributes

* Sort quadrilaterals by their attributes

##### Partition shapes into parts, area of each part as a unit fraction

* Partition a shape into equal shares

* Count the unit fractions of one whole using fraction

* Describe a fraction as an equal share of a whole

* Write unit fractions as a number

##### 4th Grade

##### Interpret a multiplication equation as a comparison

* The commutative property

* Compare numbers using bar models

* See multiplication as a comparison using number sentences

##### Multiply to solve word problems involving multiplicative comparison,

* Solve word problems by drawing pictures

*Solve multiplicative comparison word problems by using a multiply

* Solve multiplicative comparison word problems by using bar model

* Solve multiplicative comparison word problems using multiplies

##### Divide to solve word problems involving multiplicative comparison

* Interpret the remainder of a division problem

* Solve multiplicative comparison word problems by using a div

* Solve division work problems using a variable

* Represent unknown numbers using symbols or letters

##### Solve multi-step word problems posed with whole numbers

Solve multi-step problems using multiple operations

Solve multi-step word problems by writing two equations

Solve multi-step word problems by drawing a picture

Solve multi-step word problems using estimation

##### Solve multi-step word problems posed with whole numbers

Solve multi-step problems using multiple operations

Solve multi-step word problems by writing two equations

Solve multi-step word problems by drawing a picture

Solve multi-step word problems using estimation

##### Find all factor pairs for a whole number in the range 1-100

* Find all factor pairs of a number using a chart

* Find all the factor pairs of a number using area models

* Find multiples by using a number line

##### Determine whether a given whole number in the range 1-100

* Determine multiples of a number using a table

* Determine multiples of a number using area models

* Determine if a number is prime or composite

* Use divisibility rules to determine if a number is a multiple

##### Generate a number or shape pattern that follows a given rule

Generate a pattern sequence using a chart

Extend a fraction pattern using a number line

Find missing elements in growing patterns

Using a table to find the rule for a geometric shape pattern

##### Place Value for Multi-Digit Numbers

* Model numbers using base ten blocks

* Understand relationships between digits and their place value

* Use a place value chart and arrow cards to understand larger number

##### Find and compare using place values

* Find place value using pictures

* Compare numbers using place values

* Creating numbers based on given conditions

* Write numbers in word form using place values

##### Read and write multi-digit whole numbers

* Read and write numbers with zeros

* Read and write numbers in numeric form

* Read and write numbers in expanded form

* Write numbers in word form using punctuation

##### Use place value to round multi-digit whole numbers to any place

Round numbers to a specified place on a number line

Round numbers to the leading digit using a number line

Round number in real-life situations

##### Fluently add and subtract multi-digit whole numbers

Add using the standard addition algorithm

Subtract using an open number line

Subtract using the standard subtraction algorithm

Answer one-step questions about a bar graph by drawing

##### Multiply four digits by a one-digit whole number, and multiply two two-digit numbers

Solve 1 by 1 digit multiplication problems using area model

Use an area model for multiplication of two-digit numbers

Solve 2 by 2 digit multiplication problems using partial

##### Find remainders with up to four-digit dividends

Report remainders as whole numbers by drawing pictures

Divide two-digit dividends using multiples

Report remainders as fractions

##### Recognize and generate equivalent fractions

Create equivalent fractions using an area model

Create equivalent fractions using a number line

Recognize equivalent fractions using area models

Recognize equivalent fractions using number lines

##### Compare two fractions with different numerators and denominators

Compare fractions using a set model

Compare fractions using an area model

Compare fractions with different denominators

Compare fractions with different numerators and denominators

##### Compare fractions to a benchmark fraction such as 1/4, 1/2 & 3/4

Compare fractions to the same whole

Compare fractions to the benchmark of 1/2

Compare fractions to the benchmark of 1/4

Compare fractions to the benchmark of 3/4

##### Compare fractions to a benchmark fractions

Compare fractions to a benchmark of one using number lines

Compare fractions to a benchmark of one using area models

Compare fractions to a benchmark of one half using number line

Compare fractions to a benchmark of one half using area model

##### Create common denominators or numerators

Understand the denominator

Create common denominators using number lines

Create common denominators using area models

Create common denominators finding the least common multiple

##### Represent fraction results of comparisons

Identify fractions as values between 0 and 1

Represent a fraction greater than one using area models

Use a number line to represent a fraction greater than one

##### Addition and subtraction of fractions as joining and separating parts

Add fractions with like denominators using a number line

Add fractions by joining parts

Decompose a fraction into a sum of fractions using an area model

Subtract fractions by separating parts

##### Decompose a fraction into a sum of fractions with the same denominator

Subtract fractions with like denominators using a number line

Subtract fractions with like denominators using an area model

Decompose fractions into unit fractions

##### Add mixed numbers with like denominators

Add mixed numbers using a number line

Add mixed numbers by creating equivalent fractions

Add fractions with like denominators from two different whole

Add mixed numbers using properties of operations

##### Subtract mixed numbers with like denominators

Subtract mixed numbers using a number line

Subtract mixed numbers by creating equivalent fractions

Subtract fractions with like denominators labeling sets

Subtract mixed numbers by finding equivalent fractions

##### Solve word problems involving addition and subtraction of fractions

Add fractions with like denominators using visual models

Add fractions with like denominators by decomposing

Subtract fractions with like denominators using a number line

Subtract fractions with like denominators by decomposing

##### Understand a fraction a/b as a multiple of 1/b

Multiply fractions by whole numbers using repeated addition

Represent a fraction as the sum of unit fractions using number line

Write a fraction to describe part of a set

Write fractions of a set

##### Understand a multiple of a/b as a multiple of 1/b

Use repeated addition for multiplication of fractions

Use a fraction model for multiplication of fractions and whole

Estimate products in multiplication of whole numbers and fraction

##### Solve word problems involving multiplication of a fraction by a whole number

Solve problems involving a fraction and a whole number

Solve problems involving multiplying a fraction and a whole number

Solve word problems involving multiplying a fraction by a whole Number

Solve word problems involving multiplying a fraction

##### Express a fraction with denominator 10 as an equivalent fraction with denominator 100

Use a number line to show how fractions with denominators 10

Generate equivalent fractions using a grid model

Add fractions with denominators 10 and 100

Add fractions with tenths and hundredths denominators

##### Use decimal notation for fractions with denominators 10 or 100

Convert fractions into decimals to the tenths place

Convert fractions into decimals to the hundredths place

Convert decimals to fractions to the hundredths place

##### Compare two decimals to hundredths by reasoning about their size

Compare two decimal lengths using a ruler

Compare two decimals to the hundredths place

Compare two decimals to the hundredths place using fraction

Compare two decimal dollar amounts using coin values

##### Measurement units within one system of units

Recognize common units of measurement

Determine the correct unit to use when measuring

Measure weight in U.S. customary units

Convert a larger unit into a smaller unit

##### Compare and convert units of length, weight and volume

Compare and convert metric units of weight

Compare and convert metric units of volume

Compare and convert metric units of length

Compare and convert customary units of weight

##### Solve word problems involving distances, time,volumes, mass and money

Solve problems involving distance

Solve problems involving mass

Solve problems involving money

Solve problems involving volume

Solve problems involving time

##### Apply the area and perimeter formulas for rectangles

Apply area and perimeter formulas

Find the perimeter of a rectangle

Find the area of a rectangle

Find a missing rectangle side length using formulas

##### Solve problems addition and subtraction of fractions by using line plots

Create a line plot with fractions of a unit like denominatorsom

Create a line plot with fractions of a unit unlike denominators

Solve word problems involving the addition of fractions

Solve word problems involving the subtraction of fractions

##### Understand concepts of angle measurement

Identify angles using angle characteristics

Measure full and half rotations

Measure quarter and three-quarter rotations

Solve real world problems involving angle measurement

##### Measure angles in whole-number degrees using a protractor

Introduction to protractors

Measure angles to the nearest 10 by reading a protractor

Measure angles to the nearest degree with protractor

Sketch angles that are not multiples of 10 degrees

##### Solve addition and subtraction problems to find unknown angles

Compose and decompose angles

Find unknown angles using diagrams

Find unknown angles using angle properties

Write an equation to solve for a missing angle meas

##### Draw Lines, Angles, and Shapes

Classify and draw various types of angles

Draw geometric figures using their characteristics

Draw parallel and perpendicular lines

Draw points, lines, and line segments

##### Identifying Lines, Angles, and Shapes

Identify angles by comparing them to square angles

Identify geometric figures by observing characteristics

Identify points, lines, line segments, and rays

Identify points, lines, rays and angles in a two-dimensional

##### Classify two-dimensional figures

Classify parallelograms by examining their angles and sides

Classify polygons by observing the presence or absence of perpendicular lines

Classify quadrilaterals by examining their sides

Classify two-dimensional figures by examining their properties

##### Recognize right triangles as a category, and identify right triangle

Identify angles by comparing them to square angles

Identify geometric figures by observing characteristics

Identify points, lines, line segments, and rays

Identify points, lines, rays and angles in a two-dimensional

##### Recognize a line of symmetry for a two-dimensional figure

Identify line symmetry in a geometric figure

Identify line symmetry in irregular polygons

Identify line symmetry in regular polygons

Recognize a line of symmetry by folding a two-dimensional figure

##### 5th Grade

##### Use parentheses, brackets, or braces in numerical expression

* Add parentheses to an expression to make it easier to solve

* Change the value of an expression by moving parentheses

* Determine if parentheses change the value of an expression

* Make equations with fractions or decimals true by adding

##### Write simple expressions that record calculations with numbers

* Write expressions to represent numerical situations

* Write a numerical expression to represent a verbal description

* Record a numerical expression as a written description

* Determine if a verbal description matches a numerical expressions

##### Use numerical expression to solve real world problems

* Describe relationships between expressions

* Compose a real world problem by interpreting a given numerical expression

* Represent a real world situation as a numerical expression

* Use expressions with parentheses to solve problems

##### Generate two numerical patterns & analyze patterns and relationships.

* Identify how patterns are related by making a chart

* Graph and compare patterns on a coordinate plane

* Identify numerical patterns by forming and graphing

* Identify patterns by sketching

##### Understand the place value system

* Understand the value of a digit using a place-value chart

* Use number lines to show decreases in place value

* Understand that the value of a digit in one place is 10 time

* Understand that a digit in one place is 1/10

##### Compare & recognize value of the digits

* Identify the value of a digit by looking at its place

* Compare the value of the digits in a decimal number

* Compare the value of the digits in a multi-digit whole number

* Recognize place value relationships by multiplying and divide

##### Explain patterns in the number of zeros of the product when multiplying

* Explain patterns in zeros when multiplying by a power of ten

* Multiply decimal numbers by a power of ten

* Multiply whole numbers and decimals by powers of ten

* Use whole number exponents to denote powers of ten

##### Explain patterns in the number of zeros of the product when dividing

* Understand how division by a power of ten causes decimal shifts

* Divide a whole number by a power of ten

* Divide whole numbers and decimals by powers of ten

* Write a value as a multiplication or division expression

##### Read and write decimals to thousandths using base-ten numerals

* Represent decimal values to the thousandths using base ten

* Read and write decimals to the thousandths using a place value

* Name decimals through the thousandths place

* Write decimals in expanded form

##### Compare two decimals to thousandths

* Compare decimals using base ten blocks

* Compare decimals using fractions

* Compare and order numbers written as fractions or decimals

* Compare and order numbers to the millions place

##### Use place value to round decimals to any place

* Round decimals to the nearest hundredth using a number line

* Round decimals to the nearest whole number using a number line.

* Round decimals to the nearest tenth

* Round decimals to the nearest hundredth

##### Fluently multiply multi-digit whole numbers using the standard algorithm

* Multiply multi-digit numbers using an area model

* Multiply multi-digit numbers using partial products

* Use partial products for multiplication

* Use the standard algorithm for multiplication

##### Four-digit dividends and two-digit divisors and explain by using rectangular array or area models

* Divide 4-digit dividends by 2-digit divisors by setting up

* Divide 4-digit dividends by 2-digit divisors by using a rectangular array

* Divide 4-digit dividends by 2-digit divisors by using expanded notation

* Divide decimals using knowledge of multiplication

##### Add and subtract decimals to hundredths, using concrete models or drawings

* Add decimals using a number line

* Subtract decimals using base-ten blocks

* Subtract decimals using a number line

* Estimate the addition and subtraction of decimals

##### Multiply and divide decimals to hundredths, using concrete models or drawings

* Multiply decimals by whole numbers by using an area model

* Multiply decimals to the hundredths by using fractions

* Divide decimals by using a number line

* Divide decimals using knowledge of multiplication

##### Add fractions with unlike denominators including mixed numbers

* Add fractions with different denominators using fraction bar

* Add fractions with unlike denominators by creating area model

* Add mixed numbers with unlike denominators using fraction base

* Add unlike fractions using equivalent fractions and the number

##### Subtract fractions with unlike denominators including mixed numbers

* Subtract fractions with different denominators using fraction

* Subtract fractions with unlike denominators by creating area

* Subtract unlike fractions using equivalent fractions

* Subtract mixed numbers with unlike denominators

##### Solve word problems involving addition and subtraction of fractions

* Write equations to solve word problems by determining key information

* Use a number line to solve word problems involving addition

* Solve word problems involving the addition and subtraction

* Solve word problems with subtraction of unlike denominators

##### Estimate answers to problems involving fractions

* Estimate answers to problems involving fractions using area model

* Estimate answers to problems involving fractions using number line

* Estimate the addition of fractions with unlike denominators

* Estimate mentally to assess the reasonableness of answers

##### Interpret a fraction as division of the numerator by the denominator

* Understand numerators and denominators

* Write fractions labeling important information

* Place improper fractions on a number line

* Express improper fractions as mixed numbers

##### Solve word problems involving multiplication & division of whole numbers

* Solve a division problem by writing a multiplication equation

* Solve division problems by partitioning the whole

* Solve word problems involving division of whole numbers

* Solve division story problems by representing the answers

##### Multiply a fraction or whole number by a fraction

* Multiply fractions by fractions using a sequence of operation

* Multiply a whole number by a fraction using area models

* Multiply by fractions using repeated addition

* Multiply fractions by fractions finding a part of a part

##### Find the area of a rectangle with fractional side lengths

* Find the area of a rectangle by multiplying a fraction

* Find the product of a fraction and a mixed number by using area models

* Find the product of a whole number and a fraction by using area models

* Multiply a whole number by a fraction using area models

##### Interpret multiplication as scaling by comparing & explaining

* Understand how numbers scale using multiplication

* Interpret multiplication as scaling using visual models

* Predict products by comparing factors

* Solve multiplication word problems by comparing the size of the product and factors

##### Solve real world problems involving multiplication of fractions and mixed numbers

* Multiply fractions by mixed numbers using visual representation

* Multiply a fraction by a whole number using visual representation

* Write equations to multiply fractions and mixed numbers

* Solve word problems with positive and negative fractions

##### Divide unit fractions by whole numbers and whole numbers by unit fractions

* Divide unit fractions by whole numbers by drawing a model

* Divide unit fractions by whole numbers by using the multiplication

* Divide a whole number by a unit fraction

* Divide by unit fractions using the number line

##### Solve real world problems involving division of unit fractions

* Solve word problems involving division of whole numbers

* Solve problems involving division of unit fractions by whole

* Solve word problems involving division of fractions by whole numbers

* Solve word problems involving division of whole numbers 1/2

##### Convert like measurement units within a given measurement system

* Select appropriate measurement conversions

* Solve multi-step word problems involving metric conversions

* Solve real world distance problems with unit conversions

* Solve real world mass problems with unit conversions

##### Make a line plot to display a data set of measurements

* Represent and interpret data

* Redistribute items equally using the information in a line

* Use the information from more than one line plot

* Solve multi-step word problem using information provided in line plot

##### Measurement: understand concepts of volume

* Understanding volume

* Describe cubic volume measures

* Find volume by counting cubes

* Find volume by counting cubes

##### Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft

* Compute volume using knowledge of addition and multiplication

* Count unit cubes in a rectangular prism

* Identify and label three-dimensional figures

* Multiply and divide to find volume using improvised units

##### Find the volume of a right rectangular prism & apply formulas V = l × w × h and V = b × h

* Recognize that volume is additive by finding the volume

* Use volume to understand the associative property

* Find the volume of complex rectangular prisms

* Use multiplication (V = l x w x h) to find the volume

##### Graph points on the coordinate plane to solve real-world and mathematical problems

* Plot points on a coordinate plane

* Use a model to identify parts of a coordinate plane

* Move a point and describe its location on a coordinate plane

* Determine the shortest distance between two points on a coordinate plane

##### Classify two-dimensional figures into categories based on their properties

* Analyze and compare triangles by their sides

* Identify attributes of polygons

* Classify and compare quadrilaterals

* Classify quadrilaterals by looking at multiple attributes

##### 6th Grade

##### Understand the concept of a ratio

* Identify part-to-part ratios using a diagram

* Identify part-to-total ratios using a diagram

* Identify all types of ratios using a diagram

* Understand the difference between fractions and ratios

##### Ratio relationship between two quantities

* Understand the importance of order in ratios

* Convert between part-to-part and part-to-total ratios by drawing a picture

* Understanding ratios and fractions by analyzing a picture

* Simplify ratios by finding patterns in a picture

##### Understand the concept of a unit rate

* Understand rates as a type of ratio

* Create unit rate using diagram

* Create unit rate using tape diagram

* Define unit rate using double number line

##### Make tables of equivalent ratios relating quantities

* Find missing values in ratio problems using a table

* Solve missing values in ratio problems using a double number line

* Solve missing values in ratio problems using multiplicative

* Graph ratios using a table

##### Use ratio and rate reasoning to solve real-world problems

* Solve rate problems using double number lines

* Solve rate problems using multiplicative reasoning

* Compare ratios using tables and percents

* Solve percent problems using a ratio table

##### Apply understanding of division to divide fractions by fractions.

* Use visual models for division of whole numbers by unit fraction

* Use models for division of fractions by fractions

* Divide fractions by fractions: using the common denominator

* Divide fractions by fractions: using the reciprocal

##### Apply understanding of multiplication fractions by fractions

* Divide mixed numbers: multiplying by the reciprocal

* Use bar models for multiplication of fractions by whole numbers

* Multiply fractions by fractions using area models

* Multiply fractions by fractions using an algorithm

##### Solve word problems involving division of fractions by fractions

* Solve word problems involving division of fractions by fraction

* Solve word problems involving division of fractions by whole numbers

* Solve word problems involving division of fractions by fractions using pictures

* Solve word problems involving division of mixed numbers and fractions

##### Fluently divide multi-digit numbers using the standard algorithm

* Divide 4-digit numbers by 2-digit numbers using long division

* Use double division to divide 4-digit numbers by 3-digit numbers

* Interpret and explain the long division algorithm

* Divide with three-digit divisors using the standard algorithm

##### Fluently add, subtract, multiply, and divide multi-digit decimals

* Multiply decimals

* Multiply multi-digit decimals using the standard algorithm

* Subtract multi-digit decimals using the standard algorithm

* Solve real-world problems with multi-digit decimals

##### Find the greatest common factor of two whole numbers

* Find the greatest common factor of two numbers

* Find the least common multiple of two numbers

* Find the GCF and LCM using prime factorization

* Find the GCF of two numbers using the distributive property

##### Understand positive and negative numbers

* Understand negative numbers using a number line

* Understanding positive and negative numbers using elevations

* Understanding positive and negative numbers with money

* Understanding positive and negative numbers with temperature

##### Recognize opposite signs of numbers

* Find opposite numbers on the number

* Locate positive rational numbers using a number line

* Understand the opposites of fractions by looking at a number

* Locate positive rational numbers using a number line

##### Understand & locate a point on coordinate plane

* Understand the coordinate plane as horizontal and vertical number lines

* Graph points on a coordinate plane

* Graph rational numbers on a coordinate plane

* Locate a point on the coordinate plane

##### Locate points are related by reflections across one or both axes

* Understand the coordinate plane as horizontal and vertical

* Reflect points over the x and y axes by using a coordinate plane

* Translate shapes across the x and y axes by using a coordinate plane

* Translate shapes across the x and y axes

##### Find and position integers and rational numbers

* Find the value of a number using its distance and direction

* Locate rational numbers using a number line

* Graph rational numbers on a coordinate plane

* Compare fractions using less than 12 or more than 12

##### Understand relationship & compare positive and negative numbers

* Understand the relationship between two numbers

* Understand the relationship between two negative numbers using a number line

* Compare two positive or negative numbers in real-world situation

* Compare more than two positive or negative numbers in real-world situations

##### Understand the absolute value of a rational number

* Find absolute value using a number line

* Use a number line to understand the relationship between rational numbers

* Understand how while the value of a negative number decreases

* Interpret absolute value in real-world situations

##### Solve real-world and mathematical problems by graphing points

* Use absolute value to find distances between points

* Find the distance between two points in different quadrants

* Graph and solve mathematical problems using a coordinate plane

* Graph and solve real-world problems using a coordinate plane

##### Write and evaluate numerical expressions involving whole-number exponents.

* Write numerical expressions involving whole-number exponents

* Evaluate numerical expressions by using whole-number exponents

* Write numerical expressions using area and volume models

* Write a numerical expression using exponents by interpreting a problem

##### Write & read algebraic expressions in which letters stand for numbers

* Write word problems as algebraic expressions

* Read and write algebraic expressions using parentheses

* Simplify addition and subtraction expressions combining

* Simplify multiplication and division expressions combining

##### Identify & evaluate algebraic expressions at specific values

* Evaluate algebraic expressions with exponents

* Evaluate one-step algebraic expressions by substitution

* Evaluate multiple step algebraic expressions by substitution

* Write and evaluate algebraic expressions using formulas

##### Apply properties of operations to produce equivalent expression

* Write equivalent expressions using the Additive Identity Property

* Write equivalent expressions using the Distributive Property of Multiplication

* Write equivalent expressions using the Additive Inverse Property

* Write equivalent expressions using the Multiplicative Inverse Property

##### Create and apply equivalent expression using diagrams

* Create an equivalent expression using the standard algorithm

* Create equivalent expressions using diagrams

* Apply the distributive property using diagrams

* Factor expressions using the distributive property and area models

##### Simplify & regroup algebraic expression

* Simplify algebraic expressions by combining like terms

* Simplify algebraic expressions by applying the distributive property

* Regroup with distributive property by using a visual model

* Simplify algebraic expressions by combining like terms and applying the distributive property

##### Read and write equivalent expressions with variables

* Read and write equivalent expressions with variables

* Write equivalent expressions by combining like terms

* Write equivalent expressions using visual area model

##### Understand solving an equation or inequality as a process of answering a question

* Understand equations using a bar model

* Distinguish between equalities and equations

* Understand that equations have one solution using a pan balance

* Understand that inequalities have more than one solution using a number line

##### Use variables to represent numbers and write expressions

* Understand how variables are used

* Write algebraic expressions using addition and subtraction

* Write an algebraic expression for a real-world scenario addition

* Write an algebraic expression for a real-world scenario multiply

##### Solve real-world and mathematical problems by writing and solving equations

* Solve algebraic equations involving addition and subtraction

* Solve addition and subtraction problems using 1-step equation

* Solve real-world problems using multiplication and division

* Write an algebraic equation from a real-world scenario

##### Write an inequality of the form

* Graph an inequality

* Compare inequalities

* Write and graph inequalities shopping

* Write and graph inequalities temperature

##### Analyze relationships between dependent and independent variables

* Identify variables and their relationship in a real-world situation

* Use a graph and a table to interpret independent and dependent variables

* Identify independent and dependent variables

* Relate independent and dependent variables using a function table

##### Find the area of right triangles, other triangles, and polygons

* Find the area of a parallelogram by decomposing.

* Find the area of a right triangle

* Find the area of a trapezoid by composing a parallelogram

* Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids

##### Find the volume of a right rectangular prism

* Find the volume of a rectangular prism: using unit cubes

* Find the volume of a fractional rectangular prism: using unit cubes

* Find the volume of a 3-dimensional figure composed of 2 rectangular prisms

* Find the volume of a rectangular prism by filling it with unit cubes

##### Draw polygons in the coordinate plane given coordinates for the vertices

* Draw polygons using given coordinates as vertices

* Find perimeter and area by finding the length of sides using coordinates

* Determine unknown ordered pairs using the characteristics of polygons

* Find distances on a map by comparing ordered pairs

##### Represent three-dimensional figures and use the nets to find the surface area

* Identify the parts of three-dimensional solids

* Represent three-dimensional figures with nets

* Analyze rectangular prisms to find congruent faces

* Analyze triangular prisms to find surface area

* Use congruent faces to find the surface area of rectangular prisms

##### Understand that a set of data collected

* Find the mean of a data set

* Use and find the range of a data set

* Describe the distribution of data using the mean absolute deviation

* Analyze the shape of a graph to describe the distribution of data

##### Recognize that a measure of center for a numerical data set

* Summarize the spread of data using range and mean absolute deviation

* Identify clusters, peaks and gaps in a dot plot

* Distinguish between measure of center and measure of variance

* Solve a real-world problem involving measures of center and variance

##### Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

* Construct a dot plot

* Describe a data set

* Choose the best graph for a data set using measures of center

* Describe attributes of a data set by analyzing line plots, histograms, and box plots

##### Summarize numerical data sets in relation to their context

* Summarize a data set using the mean, median, and mode

* Describe the spread of data by finding range, and mean absolute

* Describe patterns in data sets

* Choose the best measure of center and variability

##### 7th Grade

##### Compute unit rates associated with ratios of fractions

* Determine unit rates using a table

* Understand unit rates using fractional rates

* Find unit rates in situations involving fractions

* Find the best deal by comparing unit rates

##### Decide whether two quantities are in a proportional relationship

* Analyze a table to find proportional relationships

* Convert between currencies and find exchange rate

* Determine if two rates are equivalent by graphing

##### Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams

* Identify the constant of proportionality in graphs

* Identify the constant of proportionality from a diagram

* Identify the constant of proportionality by writing an equation in the form y=mx

* Identify rates from verbal descriptions

##### Represent proportional relationships by equations

* Write an equation that represents a proportional relationship

* Determine the best deal by comparing equations

* Write an equation that expresses the relationship between distance and time

* Write equations to represent the proportional relationship between amount of change

##### Explain what a point (x, y) on the graph of a proportional relationship

* Graph a proportional relationship using a table

* Describe the relationship between measures by examining

* Evaluate specific points on a graph of a proportional relationship

* Identify proportional relationships by examining the origin

##### Use proportional relationships to solve percent problems

* Understand percent problems

* Apply taxes, tips, and discounts using a proportion and scale

* Calculate percent increase and decrease in context

* Calculate percent of a number using a proportion model

##### Use proportional relationships solve multistep ratio & percent problems

* Solve for an unknown percentage

* Solve multi-step ratio and percent problems using proportion

* Solve multistep percent problems using proportions and equation

* Solve percent of a number problems using a proportion model

##### Represent addition and subtraction on a horizontal or vertical number line

* Determine the values of opposite numbers using a number line

* Understand the concept of additive inverse

* Determine which values combine to make 0

* Find the additive inverse using an equation

##### Describe situations in which opposite quantities combine to make 0

* Combine opposite quantities to make zero using a number line

* Create zero pairs using integer

* Combine opposite numbers on a number line

* Combine opposite rational numbers on a number line

##### Add integers with the same & different signs

* Add integers using a number line

* Add integers using color counters

* Add integers with the same sign

* Add integers with different signs

##### Interpret sums of rational numbers by describing real-world contexts.

* Add integers with the same sign using number lines

* Add rational numbers using algorithms and number lines

* Adding integers with opposite signs using an algorithm

* Solve word problems with rational numbers

##### Subtract Integers using number line & place value

* Subtract integers by adding the additive

* Subtract integers using integer

* Subtract integers using number lines

* Subtract decimals: using place value chart

##### Understand subtraction of rational numbers as adding the additive inverse

* Understand subtraction as adding the additive inverse

* Subtract integers by adding the additive inverse

* Find the distance between two points using absolute value

* Subtract rational numbers in real-world contexts

##### Apply properties of operations as strategies to add rational numbers

* Add mixed fractions using improper fractions

* Adding positive and negative integers on a number line

* Adding two positive or two negative integers on a number line

* Demonstrate the Commutative Property of Addition with a number

##### Apply properties of operations as strategies to subtract rational numbers

* Subtract mixed numbers regrouping

* Subtract integers using the take away definition of subtract

* Subtract integers using the difference definition of subtract

* Determine the distance between integers

##### Apply and extend previous understandings of multiplication and of fractions

* Multiply fractions less than one using rectangular models

* Multiply two positive or two negative integers on a number line

* Solve multiplication problems by using the distributive property

* Solve multiplication problems using the commutative and associative properties

##### Apply and extend previous understandings of division and of fractions

* Multiply to divide proper and improper fractions

* Rewrite division problems using the commutative property

* Rewrite problems with rational numbers using different properties of * Multiplication and division

Use the commutative property to solve division problems

##### Multiply positive and negative integers using distributive property

* Prove that a negative times a negative equals a positive

* Multiply positive and negative integers by noticing patterns

* Multiply positive and negative integers using the distributive property

* Multiply a negative by a negative using the distributive property

##### Understand that integers can be divided, provided that the divisor is not zero

* Use division concepts to understand where to put the negative sign in a fraction

* Understand dividing by zero

* Dividing with zero

* Divide positive and negative integers by observing patterns

##### Mulitply and determine the product of the two integers and describe in real world context

* Multiply a positive integer by a negative integer by thinking about equal groups

* Multiply a negative integer by a positive integer by thinking about equal groups

* Multiply a negative integer by a negative integer by thinking about equal groups

* Multiply integers using the money model

##### Interpret quotients of rational numbers by describing real-world contexts.

* Understand rational quotients

* Rewrite negative fractions

* Compare fraction and decimal division

##### Convert a rational number to a decimal using long division

* Understand relationship between fractions and decimals

* Convert fractions and mixed numbers to decimals

* Determine whether a fraction will convert to a repeating decimal

* Convert fractions to decimals using division

##### Solve real-world and mathematical problems involving rational numbers

* Use addition and subtraction to solve real-world problems involving fractions

* Use addition and division to solve real-world problems with rational numbers

* Simplify expressions with order of operations

##### Apply properties of operations as strategies and expand linear expressions

Add linear expressions by combining like terms

Expand linear expressions using the distributive property

Expand linear expressions with fractions using the distribution

Factor an expression

##### Apply properties of operations as strategies and simplify an expression

* Simplify an expression by distributing a negative

* Simplify an expression with a fraction by adding or subtract

* Simplify an expression with a fraction using the distributive

* Simplify expressions using distribution and combining

##### Understand that rewriting an expression in different forms

* Rewrite an expression by expanding it

* Write a percent decrease problem as a product of the original

* Write an expression to find the cost of a discounted item

* Write an expression to find the cost of an item with tax

##### Solve real-life and mathematical problems using numerical and algebraic expressions and equation

* Solve problems using a chart

* Solve multi-step problems by creating diagrams

* Describe a real-world situation with an equation

* Solve problems by writing and solving equations

##### Solve problems involving scale drawings of geometric figures

* Generate a scale drawing

* Generate a scale drawing using fraction and decimal scale factors

* Identify scale factors using rectangle side length

* Calculate distance on a map using a scale

##### Draw geometric shapes with given conditions.

* Draw geometric shapes given the length of sides

* Draw triangles using given angles

* Draw a polygon using more than one condition

* Determine if given measurements will allow you to create shape

##### Describe the two-dimensional figures that result from slicing three-dimensional figures

* Describe 2-dimensional cross sections of right rectangular prisms

* Describe 2-dimensional cross sections of right rectangular pyraminds

##### Know the formulas for the area and circumference of a circle

* Determine the measures of a circle

* Find the area of a circle

* Find the circumference of a circle

##### Use facts about supplementary, complementary, vertical, and adjacent angles

* Find angle measurements using complementary and supplementary angles

* Use vertical and adjacent angles to find unknown angles

* Write and solve equations using complementary and supplementary angle

* Write equations for problems using facts about angle relation

##### Solve real-world and mathematical problems involving area, volume and surface area

* Choose the appropriate measurement for solving a problem

* Find missing dimensions using the volume formula

* Find surface area of cubes and prisms by pulling them apart

* Find surface area of cubes and prisms using formulas

##### Understand random sample & representative samples

* Identify a random sample

* Identify a representative sample

* Generate a representative sample

* Understanding biased samples

##### Use data from a random sample to draw inferences about a population

* Make inferences about a population by analyzing random sample

* Use proportional reasoning to make estimates about a population

* Make estimates about a population using the mean of multiple

##### Informally assess two numerical data distributions with similar variability

* Compare two data sets by looking at their means and mean absolute deviations

* Compare two data sets by looking at their medians and ranges

* Use variability and measures of center to persuade

* Analyze deceptive advertising using measures of center

##### Draw informal comparative inferences about two populations

* Compare populations using mean

* Compare two populations using the median

* Compare two populations using mean absolute deviation

* Compare two populations using range and interquartile range

##### Understand probability of a chance event is a number between 0 and 1

* Calculate the probability of an event by creating a ratio

* Describe the probability of an event using a number line

* Calculate the probability of an event by making a sum of 1

##### Approximate the probability of a chance event by collecting data

* Find the experimental probability by creating a ratio

* Compare experimental and theoretical probability to interpret data

* Predict the frequency of an event using results from experiments

* Predict the frequency of an event using the theoretical probability

##### Develop a probability model and use it to find probabilities of events

* Analyze the probability of an event by assigning equal probability

* Find the probability of events with multiple possibilities

* Understand the law of large numbers by comparing experimental

##### Find probabilities of compound events using organized lists, tables, tree diagrams

* Analyze independent and dependent events

* Find the probability of a compound event by creating an organized list

* Find the probability of a compound event by creating a table

* Find the probability of a compound event by creating a tree

##### 8th Grade

##### Know that there are numbers that are not rational, and approximate them by rational numbers.

Understand and apply the definition of rational numbers

Convert repeating decimals into fractions

##### Know and apply the properties of integer exponents

* Apply a negative exponent using patterns and rules

* Apply a zero exponent using patterns and rules

* Apply exponents to negative bases

* Evaluate expressions involving exponents

##### Divide exponential expressions

* Divide exponential expressions

* Divide exponential expressions by noticing patterns

* Divide exponential expressions when exponent in denominator

##### Simplify equivalent expressions

* Simplify exponential multiplication expressions

* Simplify expressions with 0 and negative exponents

* Simplify expressions with negative exponents

##### Multiply exponential expressions & convert to scientific notation

* Multiply two or more exponential expressions

* Multiply numbers expressed in scientific notation

* Convert from standard to scientific notation

##### Use square root and cube root symbols to represent solutions to equations

* Simplify expressions involving square roots

* Understand the relationship between squaring and taking the square roots

* Use squares to find side length of a square

* Solve problems with inverse of squares and square roots

##### Write & compare small and large numbers in scientific notation

Write small numbers in scientific notation

Write large numbers in scientific notation

Compare small numbers using scientific notation

Compare large numbers using scientific notation

##### Perform operations with numbers expressed in scientific notation

* Multiply numbers in scientific notation

* Use scientific notation to estimate products

* Divide numbers in scientific notation

* Use scientific notation to estimate quotients

##### Graph proportional relationships, interpreting the unit rate as the slope of the graph

* Understand proportional relationships by relating graphs and equations

* Display all possibilities in a proportional relationship by graphing

* Find a unit rate using a graph

* Find a fractional unit rate using a graph

##### Use similar triangles to explain why the slope m is the same

* Find coordinates of points on a straight line

* Find the slope of a line on the coordinate plane

* Describe a line with a unique slope

* Describe positive and negative slopes

##### Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line

* Derive y=mx using similar triangles

* Derive y=mx+b using similar triangles

##### Solve linear equations with one solution, many solutions, or no solutions

* Understand a linear equation with one solution

* Understand a linear equation that has no solutions

* Solve equations with no solutions

* Solve equations with infinite solutions

##### Solve linear equations collecting like terms

* Solving linear equations with a variable on each side

* Solve equations with variables on both sides

* Solve linear equations by combining like terms

* Solving linear equations by choosing from among different techniques

##### Solve linear equations with rational number

Solving linear equations with decimal coefficient

Solve linear equations with fractional coefficients

Solve linear equations with rational numbers by using integers

Solve linear equations with rational numbers using decimal

Solve linear equations with rational numbers using fractions

Solve linear equations with rational numbers using mixed number

##### Understand that solutions to a system of two linear equations in two variables

* Determine whether two lines intersect

* Decide whether a point is a solution to a pair of linear equations

* Find the solution to a pair of linear equations by using tables

* Solve pairs of linear equations using patterns

##### Understand that solutions to a system of two linear equations in two variables

* Determine whether two lines intersect

* Decide whether a point is a solution to a pair of linear equations

* Find the solution to a pair of linear equations by using tables

* Solve pairs of linear equations using patterns

##### Solve systems of two linear equations in two variables and estimate solutions by graphing

* Solve systems of equations graphing

* Solve systems of equations using elimination

* Solve linear systems algebraically using visual models

* Solve systems of equations through trial and error

##### Understand & Identify a function

* Identify a function

* Identify function properties

* Identify a function from a graph

* Understand a function as a type of relation

##### The graph of a function is the set of ordered pairs

* Determine whether a graph is a function

* Define a function by looking at its parts

* Determine whether a set of ordered pairs represents a function

* Determine whether a set of points plotted on a graph is a function

##### Compare properties of two functions each represented in a different way

* Compare two functions by analyzing an equation and a graph

* Compare two functions by analyzing an equation and a table

* Compare two functions by analyzing an equation and a verbal description

##### Interpret the equation y = mx + b as defining a linear function

* Identify a linear function by analyzing characteristics of a linear fraction

* Analyze Tables of y = x and y = mx

* Analyze graphs and tables of y = mx + b

* Analyze graphs of y = x and y = mx

##### Construct a function to model a linear relationship between two quantities.

* Construct a linear function

* Construct linear functions from tables

* Create equation, table, and graph from a situation

* Construct a function by solving for unknown information

##### Determine the rate of change and initial value of the function

* Determine initial value in a linear relationship

* Determining the constant rate of change

* Determining the y-intercep

* Interpreting slope and y-intercept in context

##### Describe qualitatively the functional relationship between two quantities

* Compare two linear relations

* Describe function relationships using graphs

* Describe the rate of change on an interval using a graph

* Create a verbal description of a linear relation given a graph

##### Verify experimentally the properties of rotations, reflections, and translations

*Explore reflections by investigating their effects on line segment and angles

*Explore rotations by investigating their effects on line segment and angles

*Explore translations by investigating their effects on line segment and angles

*Identify what changes and what stays the same when sliding a parallelogram

##### Verify experimentally the properties of rotations, reflections, and translations

*Explore reflections by investigating their effects on line segment and angles

*Explore rotations by investigating their effects on line segment and angles

*Explore translations by investigating their effects on line segment and angles

*Identify what changes and what stays the same when sliding a parallelogram

##### Understand that a two-dimensional figure is congruent

* Identify congruent figures

* Recognize congruence by analyzing the sequence of steps

* Demonstrate congruence using a transformation sequence

* Assess congruence using transformation

##### Apply and assess congruence to rotation, reflections & transformations

* Apply properties of congruence to rotations

* Apply the properties of congruence to reflections

* Investigate translations

* Assess congruence using multiple transformations

##### Describe the effect of dilations, translations, rotations, and reflections

* Understand how reflections and rotations change coordinates

* Understand how translations change coordinates

* Analyze dilation of parallelograms

* Describe translations using coordinates

##### Use informal arguments to establish facts about the angle sum and exterior angle of triangles

* Prove two figures are similar after a dilation

* Determine similarity by comparing angles

* Relate angles and transversals

* Understand the properties of the interior angles of triangle

* Understand the relationship between exterior angles

##### Explain a proof of the Pythagorean Theorem and its converse.

* Identify properties of right triangles

* Apply the Area of Squares Proof to determine if a triangle

* Use the Area of Squares Proof to relate side lengths of a right triangle

* Use the Pythagorean Theorem to see if a triangle is a right

##### Apply the Pythagorean Theorem in real-world and mathematical problems

* Apply the Pythagorean Theorem to three dimensional figures

* Find the length of the hypotenuse of a right triangle using pythagorean theorem

* Solve for diagonals in rectangular prisms by applying the pythagorean theorem

* Solve for unknown side lengths using the Pythagorean Theorem

##### Apply the Pythagorean Theorem to find the distance between two points

* Find distance between two points on the coordinate plane using the Pythagorean theorem

* Find the length of a line segment on the coordinate plane using Pythagorean

* Find the distance between two points on the same axis on a coordinate grid

* Find the perimeter of a two dimensional figure on the coording plane

* Solve real-world, mathematical problems involving coordinate plane

##### Solve real world problem of cones, cylinders, and spheres

* Develop and apply the formula for volume

* Develop and apply the formula for volume of a sphere

* Develop and apply the formula for volume of a cylinder

* Solve real world problems by finding volume of cones

##### Construct and interpret scatter plots for bivariate measurement data

* Construct a scatter plot

* Describe patterns in scatter plots

* Interpret a scatter plot by identifying clusters and outlier

* Interpret and distinguish linear and non linear scatter plot

##### Fit a straight line, and informally assess the model fit by data points to the line.

* Construct a line of best fit

* Draw a line of best fit

* Determine the strength of an association by comparing scatter plots

* Use bivariate measurement data to make a prediction

##### Use the equation of a linear model to interpreting the slope and intercept

* Write an equation for line of best fit

* Interpret the y-intercept of a line of best

* Interpret association in lines of best fit

* Compare linear and non-linear functions

* Use the equation of a line of best fit to make predictions