Math


4K

5K

Number Operations and Relationships

  • Identify numerical value 1-10
  • Identify and write numbers 1-10
  • Understand one-to-one correspondence
  • Count by ones to 50
  • Use manipulatives to show addition and subtraction to 5 

Number Operations and Relationships

  • Identify numerical value 1-10
  • Identify and write numbers 1-30
  • 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 non-standard 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 most-least

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 three-digit algorithms using manipulatives    
  • Add and subtract one-, two-, and three-digit numbers without regrouping    
  • Add and subtract two-digit 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 non-standard units    
  • Measure length using standard and non-standard units of measure    
  • Measure weight using standard and non-standard 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, half-gallon, 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 five-minute 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 non-standard 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 three-dimensional 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 3-part 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 3-digit 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 three-digit 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 2-digit and 3-digit 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, quarter-inch, 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 one-dollar 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 2-d  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 multi-step 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 2-d figures (quadrilaterals, hexagon, pentagon, octagon)    
  • Identify and compare 3-d 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 3-d 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 360o
  • 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 * 2-dimensional sketches of 3-dimensional objects    
  • Review application of formulas for area, surface area, and volume for 2- and 3- dimensional figures    
  • Describe relationships of special right triangles (30-60, 45-45, Pythagorean Theorem)

Geometry

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

Algebraic Relationships

  • Identify and use arithmetic and geometric patterns and Fibonacci sequence to solve problems    
  • Write multi-step 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 multi-step 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