4K

5K

Number Operations and Relationships
 Identify numerical value 110
 Identify and write numbers 110
 Understand onetoone correspondence
 Count by ones to 50
 Use manipulatives to show addition and subtraction to 5

Number Operations and Relationships
 Identify numerical value 110
 Identify and write numbers 130
 Understand number value: sets, one more than, one less than, and number that comes between two numbers
 Use manipulatives to count and compare numbers
 Count by ones, fives, and tens to 100
 Understand the process of addition and subtraction
 Use manipulatives to show addition and subtraction through 10
 Identify doubles to 10 (2+2=4)

Measurement
 Compare and/or sequence objects by size
 Know days of week

Measurement
 Estimate and compare amounts and sizes
 Use manipulatives to estimate
 Use manipulatives to measure
 Use nonstandard units to measure weight
 Know months of the year
 Tell time on the hour
 Understand value of a penny, nickel, and dime
 Locate and identify temperatures on a thermometer

Probability and Statistics
 Read graphs by telling mostleast

Probability and Statistics
 Read graphs to identify more, less, least (how many more, how many less)

Geometry
 Identify basic shapes (circle, square, rectangle, triangle)
 Match and use shapes to create new designs

Geometry
 Identify basic shapes to include oval
 Create and copy symmetrical pattern block designs
 Match and use shapes (including oval) to create new designs

Algebraic Relationships
 Identify and copy patterns (AB)
 Complete patterns (AB)
 Sort and classify objects with one attribute

Algebraic Relationships
 Identify and copy patterns (ABC)
 Complete and create patterns (ABC)
 Sort and classify objects with one or more common attributes
 Use math symbols to represent simple equations (+, , =)

1st

2nd

Number Operations and Relationships
 Identify place value of 10's & 1's with one and two digit numbers
 Write & order numbers to 100
 Count backward and forward from a given number
 Model and write fact families
 Understand the use of ordinal numbers 1st through 10th
 Identify numbers that come before, after, between given numbers
 Count by 1's, 2's, 5's, and 10's to 100
 Develop and use counting strategies
 Demonstrate concept of 1/2, 1/3, and 1/4 using manipulative
 Use basic fact strategies of addition and subtraction through 18
 Use manipulatives and sttrategies to add and subtract to 20
 Recognize the relationship between addition and subtraction
 Count objects & esimate the number when shown a group of objects
 Compare #'s and put #'s in order to 100
 Use daily applications to read 3 digit numbers (i.e. page #'s in books, school days, etc)
 Master addition and subtraction facts up to 12

Number Operations and Relationships
 Understand place value: ones, tens, hundreds
 Identify and order numbers to 1000
 Use a number line
 Understand odd and even numbers
 Compare numbers and sets of objects using greater than, less than, or equal to
 Use ordinal numbers to describe position
 Count by 2's, 3's, 5's and 25's to 100
 Understand decimal notation for money and parts of a dollar
 Understand fractions as equal parts of a whole
 Use strategies of addition and subtraction through 18
 Model two and threedigit algorithms using manipulatives
 Add and subtract one, two, and threedigit numbers without regrouping
 Add and subtract twodigit numbers with regrouping
 Know the inverse relationship between addition and subtraction
 Master addition and subtraction facts up to 18
 Estimate using a number line

Measurement
 Estimate and compare measures of cup and quart
 Estimate using nonstandard units
 Measure length using standard and nonstandard units of measure
 Measure weight using standard and nonstandard units of measure
 Write dates with day, month, year
 Use digital and analog clocks to read and write the time to the hour and 1/2 hour
 Represent money amounts using penny, nickel, dime, quarter, and dollar
 Make exchanges between coins
 Make change for a dollar bill

Measurement
 Compare and order objects by length, weight, or capacity
 Estimate and compare measures of pint, liter, quart, halfgallon, and gallon
 Estimate to nearest foot, inch, and yard
 Measure length to nearest whole standard unit (in, ft, yd)
 Use calendar to determine date
 Use digital and analog clocks to read and write time to the quarter hour and fiveminute intervals
 Represent money amounts using dollars and all coins
 Read and interpret a thermometer
 Determine elapsed time

Probability and Statistics
 Read concrete and pictorial bar graphs by telling which has more or less
 Sort and classify objects
 Collect & organize data
 Interpret events as likely or unlikely
 Create tally charts and pictographs

Probability and Statistics
 Read concrete and pictorial bar graphs comparing elements
 Make and use a Venn diagram
 Represent objects or data on a bar graph
 Organize given data
 Predict possible outcomes

Geometry
 Estimate and compare measures of cup and quart
 Estimate using nonstandard units
 Recognize and identify geometric shapes in the environment
 Recognize and name solid figure shapes including trapezoid, rhombus, and hexagon
 Identify shapes having lines of symmetry
 Identify lines of symmetry
 Recognize congruent figures
 Identify, describe, and compare 2D shapes such as circle, square, triangle, oval, rectangle, rhombus, trapezoid, hexagon, and parallelogram
 Identify, describe and compare 3D shapes such as cone, sphere, cylinder, cube, and rectangular

Geometry
 Identify hexagons, octagons, pentagons, and parallelograms
 Identify and sort: sphere, cone, cylinder, rectangular prism, cube, and pyramid
 Recognize similarities and differences between threedimensional shapes
 Draw a line of symmetry
 Draw congruent figures
 Identify acute, obtuse, and right angles

Algebraic Relationships
 Identify and describe patterns
 Read, create, and extend 3part patterns
 Identify and use numbers on a number grid
 Create patterns using manipulatives
 Sort, classify, and order objects
 Understand mathematical symbols to represent expressions and equations (+, , =, <, and >)
 Compare pairs of numbers less than 16
 Solve word problems using manipulatives
 Solve addition & subtraction number stories
 Solve algebraic equations using number sentences, missing addends, and minuends

Algebraic Relationships
 Identify and extend patterns
 Complete and create growing and repeating number patterns
 Sort, classify, and order numbers
 Determine what mathematical symbols are used to represent expressions and equations (+, , =, ? )
 Solve word problems using addition and subtraction number sentences
 Identify extra information in word problems
 Find missing numbers in + and  examples
 Solve word problems using the Guess and Check strategy

3rd

4th

Number Operations and Relationships
 Read, write, compare, and order #'s to 1,000,000
 Create and use a number line
 Compare whole numbers using the appropriate symbols (greater than, less than, or equal) to 5 digits
 Compute addition and subtraction with money (decimals to the hundredths place)
 Understand and compare fractional parts including equivalent fractions through models and manipulatives (1/2, 1/3, 1/4, 1/5 and 1/6)
 Identify equivalent fractions in picture form
 Compute up to 3digit addition and subtraction with regrouping
 Use strategies to solve multiplication and division facts to 12
 Demonstrate the relationship between multiplication and addition
 Estimate sums to tens and hundreds and differences to ten
 Round two and threedigit numbers to tens and hundreds
 Use mental math to find sums and differences of multiples of 10 and 100
 Addition and Subtraction facts to 12 will be mastered
 Multiplication and Division facts to 12 will be proficient
 Add, subtract, and multiply accurately single digit numbers and fact extensions (i.e. 70 + 80)
 Use different equations to represent an equivalent whole number
 Use tools to multiply 2digit and 3digit whole #'s
 Read and write problems using +, , x, / and use < and > to solve equations

Number Operations and Relationships
 Identify place value to hundred millions
 Identify decimals to tenths
 Read and represent whole numbers in expanded form
 Identify negative numbers
 Use arrays to solve problems
 Identify factors and multiples of numbers
 Understand multiples of 10, 100, 1000
 Use appropriate dollar and cent notation
 Compare whole numbers and fractions with like denominators using the appropriate symbols (<,>,=)
 Master addition, subtraction, multiplication and division facts
 Compute addition and subtraction problems using fractions with the same enominator
 Find patterns in multiplication and division tables
 Multiply 1,2,3 digit numbers by 1 and 2 digit numbers
 Understand inverse operations (addition/subtraction and multiplication/division
 Estimate sums, differences, products, and quotients
 Round to the nearest thousandth
 Use mental math to multiply by 10
 Divide with remainders
 Add and subtract multidigit numbers
 Understand the relations among fractions, decimals, percents mixed and whole numbers (whole, 1/4, 1/2, 3/4)
 Tell time to the nearest minute
 Understand properties of addition and multiplication
 Use different equations to represent equivalent whole numbers
 Solve addtion, subtraction, multiplication, and division word problems
 Identify the whole for fractions, parts of a collection of objects and regions

Measurement
 Estimate using appropriate units of measure
 Measure length to the nearest yard, quarterinch, meter, cm
 Find perimeter using measurement and addition
 Use digital and analog clocks to read, write, and translate time to one minute intervals and notations of AM and PM
 Count, compare, make change, and solve problems using a collection of coins (up to one dollar) and onedollar bills
 Make change up to $10
 Compare temperatures using C and F scales
 Describe relationships between units of measure (i.e. inches and feet)
 Find area of rectangles
 Find capacity and weight of objects

Measurement
 Estimate and compare mass and volume (metric and customary units) accurately
 Estimate and compare length (metric and customary units)
 Measure length accurately to the nearest quarter inch and mm
 Measure area by counting square representations
 Use conversion to solve simple problems within a system of measurement
 Solve simple problems using time
 Count, compare, and make change up to twenty dollars
 Calculate problems involving money
 Solve elapsed time word problems

Probability and Statistics
 Read circle, bar, and line graphs
 Create a simple graph to represent data
 Collect data using observations, surveys, and experiments
 Experiment to determine possible outcomes
 Determine fair and unfair games based on probability

Probability and Statistics
 Interpret circle, bar, and line graphs
 Create a table to represent data
 Predict and list possible outcomes
 Find mean, median, range, and mode
 Use simple models to conduct probability experiments

Geometry
 Identify, describe, and compare 2d shapes such as trapezoid, hexagon, square, triangle, rectangle, parallelogram, and other polygons
 Identify, describe, and compare faces, and edges of 3D shapes such as cone, sphere, cube, cylinder, rectangular prism
 Identify plane and space figures and their relationships to each other
 Create symmetrical figures
 Draw lines of symmetry in symmetrical figures
 Identify properties of symmetry: slide, flip, and turn
 Match simple shapes through use of slides
 Understand and create congruent figures
 Identify concept of angles (right, greater than, less than)
 Identify and draw points, intersecting and parallel lines, and rays

Geometry
 Describe and represent 2 and 3 dimensional figures (polygons and circles, cubes, prisms, cones, cylinders)
 Identify obtuse, acute, right, and straight angles
 Identify and draw: point, line segment, line, ray, perpendicular lines, and parallel lines
 Identify cubes and square pyramid shapes from their nets (flat patterns)
 Calculate perimeter and area of plane figures
 Calculate perimeter and area of polygons
 Identify lines of symmetry, reflection, & reflected figures

Algebraic Relationships
 Identify and create patterns
 Use patterns to solve problems
 Determine what mathematical symbols are used to represent expressions and equations (greater than, less than, =, x, division)
 Solve multistep word problems (+, )
 Locate and name coordinates of a point on a graph in the first quadrant
 Describe commutative and associative properties of addition and multiplication and apply them to mental math
 Solve simple open sentences involving addition, subtraction, multiplication, and division
 Find the missing value to make a number sentence true (ex. 5 +8 = __ +7)

Algebraic Relationships
 Apply number patterns to a variety of real world situations
 Use tables to solve problems
 Solve problems involving an unknown using manipulatives
 Substitute number values for letters to find a sum, difference, or product
 Complete function tables (input/output)

5th

6th

Number Operations and Relationships
 Identify decimals to hundred thousandths
 Identify practical uses of negative numbers
 Know exponential notation for powers of ten
 Compare and order whole numbers, decimals, and fractions
 Find multiples of numbers and the LCM of a number pair
 Find factors of numbers and the GCF of a number pair
 Know divisibility rules for 2, 3, 4, 5, 6, 9, and 10
 Rename improper fractions to mixed numerals
 Recognize equivalent fractions
 Simplify fractions
 Add & subtract fractions and mixed numbers with like and unlike denominators
 Add & subtract decimals
 Multiply 2 digit numbers by 2 and 3, 4, 5, and 6 digit numbers
 Divide by 1, 2, and 3 digit numbers
 Estimate sums, differences, products, and quotients
 Round decimals to the nearest tenths and hundredths
 Use mental math to multiply by powers of tens
 Understand equivalent forms of basic %, fractions, and decimals (e.g. 1/2 is equivalent to 50% is equivalent to .5) and when one form of a number might be more useful than another
 Convert among fractions, decimals, and %

Number Operations and Relationships
 Identify decimals to millionths
 Identify negative numbers on a number line
 Understand exponential notation and the functions involved
 Convert fractions to decimals and percentages and vice versa
 Identify and represent equivalent forms of fractions, decimals, and percents
 Use prime factorization to find GCF, LCM, and prime numbers
 Identify prime and composite numbers 1? (no set limit, numbers will be higher than 50)
 Use divisibility rules for 2, 3, 4, 5, 6, 9, 10
 Use cross products algebraically to determine equivalence
 Multiply fractions and decimals (including mixed numbers)
 Review of adding and subtracting fractions and decimals (including mixed numbers)
 Divide decimals by whole numbers and decimals (including mixed numbers)
 Divide fractions (including mixed numbers)
 Extend estimation skills
 Round decimals to the nearest hundredths when rounding to the nearest %
 Determine reasonableness of answers
 Extend mental math skills
 Apply order of operations to problems including whole numbers, fractions, and decimals
 Review of all computations (+, , x, /) of whole numbers, decimals, amd fractions
 Provide an introductory understanding of ratio, rates, and proportions
 Introduction of adding and subtracting all positive and negative integers
 Finding percentages of numbers

Measurement
 Measure length accurately to the nearest 8th inch
 Determine area using multiplication
 Measure mass and volume given the appropriate unit of measurement
 Convert units of time through decade and century
 Determine elapsed time and dates
 Find temperature changes with negative numbers

Measurement
 Measure length accurately to the nearest 1/16 th inch
 Choose the appropriate tools and units to estimate, compare, and measure
 Convert units of weight /mass and capacity (g, mg, kg, ton, lb, oz, ml, L, cup, pt, qt, gal)
 Add and subtract units of time and elapsed time

Probability and Statistics
 Compare & contrast information on graphs and tables
 Predict and list possible outcomes
 Find mean, median, range, and mode
 Use simple models to conduct probability experiments
 Plot points on a quadrant grid

Probability and Statistics
 Create surveys and interpret data using frequency tables and line plots
 Draw and read circle graphs to interpret information
 Formulate questions, design studies, and collect data
 Interpret experimental and theoretical probabilities
 Create and interpret stem and leaf plots
 Model situations by experimentation or simulation
 Use of computers for graphing
 Introduce probability of independent events

Geometry
 Identify, compare, and draw 2d figures (quadrilaterals, hexagon, pentagon, octagon)
 Identify and compare 3d figures
 Identify properties of geometric solids (edge, face, curved, surface, vertex, base, and height)
 Identify multiple lines of symmetry for a figure
 Define and identify congruent shapes
 Define and identify similar shapes
 Draw angles (right, acute, obtuse, straight)
 Estimate the measure of an angle, measure an angle within 2 degrees
 Represent a line, ray, segment
 Identify and draw points, intersecting and parallel lines, and rays
 Identify cubes, rectangular and triangular prisms, and rectangular and triangular pyramids from simple nets
 Apply formulas for perimeter and area of rectangles
 Use formulas to find the areas of polygons and circles, triangle

Geometry
 Represent 3d figures (prism, pyramid, cylinder, cone, sphere)
 Identify relationships between edges, faces, and vertices of solids
 Draw and design shapes with multiple lines of symmetry
 Construct and represent congruent shapes
 Construct and represent similar shapes
 Construct triangles (scalene, isosceles, equilateral)
 Describe and compare cubes, rectangular and triangular prisms, and rectangular and triangular pyramids from nets
 Use slides, flips, and turns on figures
 Apply formulas for perimeter and area of triangles and quadrilaterals
 Calculate area and circumference using pi

Algebraic Relationships
 Find and extend number patterns
 Use arrays to solve problems
 Write a number sentence to solve a word problem
 Evaluate simple expressions
 Find missing factors in equations
 Solve number sentences involving parentheses
 Solve problems with multiple operations using correct order of operations
 Find missing numbers in equivalent fractions and proportions

Algebraic Relationships
 Recognize arithmetic and geometric patterns
 Find missing components of mathematical statements (addend, factor, sum, product, quotient, divisor, etc.)
 Understand order of operations
 Identify x and y axis
 Identify rational numbers on a number line
 Substitute numbers for variables

7th

8th

Number Operations and Relationships
 Review the identification of decimals to millionths
 Read and represent decimals in expanded form
 Use exponential notation to solve problems
 Review the use of order relationships for whole numbers, fractions, decimals, and percents (rational number)
 Convert between fractions, decimals, and percents greater than 1 and < 0
 Review the divisibility rules to find GCF, LCM, and prime numbers in solving problems
 Identify prime and composite numbers to 100
 Add and subtract integers
 Multiply and divide integers
 Extend and apply estimation skliis to all operations involving whole numbers, fractions, and decimals (rational numbers)
 Extend and apply mental math skills to all operations involving whole numbers, fractions, and decimals (rational numbers)
 Understand and identify concept of irrational numbers
 Understand and identify reciprocal and exponents
 Understand concept of real number system
 Apply the concept of percent to discounts, simple interest, and sales tax
 Round appropriately using precision

Number Operations and Relationships
 Identify irrational numbers
 Identify reciprocals and exponents
 Convert fractions, decimals, and percents greater than 1 and less than 0
 Apply GCF, LCM, and prime numbers in solving problems
 Apply the concept of percent to discounts, simple interest, and sales tax
 Apply all operations to rational numbers
 Extend and apply estimation skills to rational numbers
 Round appropriately using precision
 Extend and apply mental math skills to rational numbers

Measurement
 Estimate an area given a reference
 Measure and draw angles up to 360 degrees
 Determine actual distance between two points using a scale
 Add, subtract, multiply and divide measurements where grouping or conversions of like measure may be required
 Compare temperature differences (C and F)

Measurement
 Measure and draw angles up to 360^{o }
 Add, subtract, and multiply measurements where grouping may be required

Probability and Statistics
 Review analyzing tables, graphs, and charts
 Review the creation of tables and graphs
 Construct circle graphs
 Determine the likelihood of occurrence of simple events using a variety of strategies (experimentation, simulation, and theoretical)
 Create and interpret box and whisker plots
 Apply and represent data to solve problems
 Collect, organize, and analyze data and draw conclusions using various methods
 Select, create, and use appropriate graphical representations
 Distinguish between dependent and independent events
 Create and interpret line of best fit and quartile data

Probability and Statistics
 Collect, organize, and analyze data and draw conclusions using various methods
 Select, create, and use appropriate graphical representations
 Distinguish between dependent and independent events
 Create and interpret line of best fit and quartile data

Geometry
 Classify figures as plane or solid
 Identify symmetry of geometric figures
 Apply proportions in relation to congruent figures
 Apply proportions in relation to similar figures
 Describe and represent adjacent, supplementary, complementary, vertical, and congruent angles
 Construct ** parallel and perpendicular lines, triangles, and transversals
 Identify transformations as reflections, translations, and rotations
 Name, define, and give examples of comlex figures (rhombus, polyhedron, cylinder) and their component parts (base, altitude, and slant height)
 Draw * 2dimensional sketches of 3dimensional objects
 Review application of formulas for area, surface area, and volume for 2 and 3 dimensional figures
 Describe relationships of special right triangles (3060, 4545, Pythagorean Theorem)

Geometry
 Name, define, and give examples of complex figures (rhombus, polyhedron, cylinder) and their component parts (base, altitude, and slant height)
 Draw* 2dimensional sketches of 3dimensional objects
 Construct** parallel and perpendicular lines, triangles, and transversals
 Apply formulas for area, surface area, and volume for 2 and 3dimensional figures

Algebraic Relationships
 Identify and use arithmetic and geometric patterns and Fibonacci sequence to solve problems
 Write multistep number sentences to solve word problems
 Apply concepts of variable expression and equation to solve multi step problems
 Understand concepts of ratios/percents/proportions & apply them to problem solving
 Solve multistep equations and inequalities (with variables on both sides)
 Apply properties (commutative, associative, distributive, etc.) to solve equations and inequalities
 Understand concepts of expression, equation, and variable
 Solve equations and inequalities using order of operations
 Plot ordered pairs in all four quadrants
 Graph equations and inequalities
 Use integer exponents and square roots
 Understand concepts of ratio and percent
 Convert large and small numbers using scientific notation
 Identify functions
 Use problem solving to develop numerical/algebraic relationships
 Add and subtract like expressions
 Create and evaluate expressions
 Interpret equations using graphs and tables

Algebraic Relationships
 Analyze pattern relationships
 Identify functions
 Use problem solving to develop numerical/algebraic relationships
 Add and subtract like expressions
 Apply concepts of variable expression and equation to solve simple problems
 Graph equations
 Apply four operations to rational numbers
 Use integer exponents and square roots
 Apply percents and ratios/proportions to solve problems
 Use generalized properties (commutative, associative, distributive, etc.)
 Convert small and large numbers into scientific notation
