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MATH
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KEY LEARNINGS: MATH
 
Standards of problem solving, reasoning, communications and representation are embedded in teaching the standards listed below.     

 

KINDERGARTEN 

Number and Operations 
• Count and understand numbers to 20 
• Write numbers 0 to 10 
• Use one-to-one correspondence with numbers and objects 
• Understand and represent adding two numbers with sums to ten 
• Add and subtract two numbers using objects to ten 
Algebra
• Recognize and explain how objects can be classified 
• Sort, classify and order objects by time, size, number and other properties 
• Compare and contrast objects 
• Identify, create, copy, describe and extend sequences e.g. sounds, shapes, motions, numbers 
• Model a mathematical problem situation using manipulatives 
Geometry 
• Compare, sort and arrange similar and different objects by size, color and shape 
• Identify triangles, squares and circles 
• Describe relative position of objects in space 
• Identify and fit pieces of puzzles or shapes that go together 
• Construct 3-dimensional objects 
Measurement 
• Compare the weight of two objects and the capacity of two containers 
• Compare and describe length, size, distance, temperature e.g. long, longer, longest, same length 
• Measure length by counting non-standard units 
• Recognize how a thermometer denotes hot, cold and medium temperatures 
• Measure area using concrete objects 
• Order events by time e.g. before, after 
• Identify that clocks, watches and calendars are used to measure time 
• Tell time to the hour 
• Know and name the seven days of the week in order (relate to Sabbath) 
Data Analysis and Probability 
• Discuss events as likely or unlikely 
• Pose questions and gather data about themselves and their surroundings 
 

FIRST GRADE                                                                                                                          

Number and Operations 
• Count, write and understand numbers 0 to 100 
• Count by twos, fives, tens and twenty-fives to 100 
• Skip count by tens e.g. 17, 27, 37 … 
• Connect numbers to the qualities they represent using various models and representations 
• Understand place value of tens and ones 
• Explore the concept of zero 
• Compare numbers using symbols >, < and = 
• Understand the meaning of addition and subtraction and relate to appropriate symbols 
• Understand basic addition and subtraction fact families 
• Develop a counting strategy for addition and subtraction facts to 20 
• Memorize addition with sums to 12 and related subtraction facts 
• Add and subtract 1- and 2-digit numbers, with no renaming 
• Understand basic fractions, e.g. halves, thirds and fourths 
• Read number words to ten 
• Understand and use a number line 
 
Algebra                                                                                                                                     
• Recognize and express expanding and repeating math patterns - orally and with manipulatives 
• Identify properties of patterns; create and describe using letters and symbols 
• Use variables and open sentences to express relationships e.g. missing numbers in number 
sentences using symbols to represent missing numbers 
• Use the commutative property and solve number sentences with numbers and symbols 

Geometry  
• Describe attributes and parts of 2- and 3-dimensional objects 
• Describe shapes from different perspectives, e.g. front, back, top, bottom and side 
• Apply ideas about direction and space 
• Recognize and apply slides, flips and turns 
• Recognize rectangles and spheres 
• Recognize sides and corners of shapes 
• Recognize geometric shapes and structures in the environment 
• Recognize and draw a line of symmetry in objects 
• Copy figures and draw simple 2-dimensional shapes from memory 

Measurement 
• Identify and recognize various measurable attributes of an object 
• Estimate and measure length, weight, volume and mass using nonstandard and standard units 
• Compare objects in terms of length, area, capacity and weight 
• Recognize and explain the need for measuring tools and fixed units 
• Order sequence of events with respect to time, e.g. seasons; morning, afternoon, night; o’clock 
• Know the number of minutes in an hour 
• Tell time to the hour and half hour using both digital and analog clocks 
• Identify pennies, nickels, dimes, quarters, half-dollars and dollars 
• Determine the value of a set of coins to $1.00 
• Determine the equivalent value of coins to $1.00 e.g. 10 dimes, 4 quarters, etc. 
• Know and name the twelve months of the year 
Data Analysis and Probability 
• Use whole number units to construct graphic representations 
• Understand information represented in simple bar graphs, line graphs and pictographs 
• Collect first-hand information by conducting surveys, measuring and performing simple 
experiments 
• Collect and organize data into charts using tally marks 

 

SECOND GRADE                                                                                                                     

Number and Operations 
• Count and understand numbers with 3-digits 
• Skip count by two, e.g. 23, 25, 27… 
• Understand and use ordinals 1-20 
• Understand even and odd numbers 
• Understand the place value of hundreds, tens, ones 
• Given a math fact, construct the other three in the fact family 
• Know addition and subtraction facts through 20 by recall 
• Add and subtract 2-digit numbers with renaming 
• Add and subtract 3-digit numbers with no renaming 
• Add a series of three numbers 
• Using a number line, explain rounding to the nearest ten 
• Write, add and subtract money using appropriate symbols 
• Understand situations that entail multiplication and division, i.e. equal groupings of objects and 
sharing equally 
 
Algebra                                                                                                            
• Use patterns to make generalizations and predictions 
• Analyze patterns in tables and graphs 
• Describe qualitative and quantitative changes involving addition and subtraction 
• Understand equivalence concepts using symbols 

Geometry 
• Investigate and predict results of assembling and disassembling 2- and 3- dimensional shapes 
• Find locations using simple coordinates 
• Recognize prisms, pyramids, cylinders and cones 
• Relate ideas in geometry to number and measurement 

Measurement 
• Select and use appropriate measuring tools 
• Select and use appropriate units of measurement 
• Use different units to measure the same thing 
• Use nonstandard units to compare weight of real objects and capacity of real containers 
• Estimate the weight of an object 
• Apply and use measurements in problems and “real life” situations 
• Tell time to the nearest minute (digital) and the nearest 5 minutes (analog) 
• Use and compare A.M. and P.M. time designations 
• Count coins and dollars to $5.00 
• Determine correct change to $1.00 by counting 
• Estimate to the nearest dollar 
• Use correct symbols in writing money amounts 
• Understand one hour of elapsed time 
• Identify days and dates on a calendar and one week before and after a certain date on a calendar 

Data Analysis and Probability 
• Construct and interpret data using a simple bar graph 
• Interpret data as represented in a simple table or chart 
• Make predictions, test validity and do a probability study with a 50/50 chance 

 

THIRD GRADE                                                                                                                        

Number and Operations 
• Understand and describe place value to the ten-thousands place 
• Design and label number lines appropriate to the situation 
• Compare and order numbers through 10,000 
• Skip count by threes, e.g. 1, 18, 21, 24… 
• Understand the commutative property of addition and multiplication 
• Understand the zero property of multiplication 
• Understand the meaning of the decimal point 
• Understand the concept of tenths written as a decimal 
• Understand the meaning of multiplication and division 
• Know the multiplication and division fact families 
• Know multiplication and corresponding division facts 
• Add and subtract numbers up to four digits with and without renaming 
• Multiply mentally by 10 and 100 
• Multiply and divide 2-digit number by a 1-digit number 
• Divide a 2-digit number by a 1-digit number with remainder 
• Understand the meaning and structure of fractions between zero and one 
• Understand and write simple mixed numbers 
• Compare fractions with like denominators      
• Add and subtract fractions with like denominators 
• Add and subtract money 
• Use strategies to estimate the results of whole number computations
 
Algebra                                                                                                
• Analyze mathematical sequences with and without a calculator 
• Use patterns to make predictions, solve problems and identify relationships 
• Understand and explain mathematical relationships in equations and inequalities 
• Solve equations and inequalities 
• Identify such properties as commutative, and associative - use to compute with whole numbers 
• Understand and use grouping symbols e.g. 8 + 6 = 8 + (2 + 4) 

Geometry 
• Explore congruence and similarity 
• Add to find perimeter 
• Count squares to find area 
• Count cubes to determine volume 
• Create models of 2-dimensional objects 
• Investigate simple nets 
• Analyze/describe 2- and 3-dimensional objects using terms: vertex, edge, angle, side, face 
• Find and name locations on a labeled grid or coordinate system 
• Identify shapes that can be put together to make a given shape, e.g. tangrams 

Measurement 
• Use correct measurement vocabulary 
• Explain and measure temperature using Celsius and Fahrenheit scales 
• Read and understand a simple time line 
• Measure length, weight, volume using metric and US customary units to nearest ½ unit as 
appropriate 
• Using appropriate tools, draw a line or shape with specified measurements 
• Count money up to $10.00 
• Understand attributes of second, minute, hour 
• Tell time to the minute, before or after the hour, using analog and digital clocks 
• Measure elapsed time using a calendar or clock 
• Read and understand a calendar using day, week, month and year 
• Count weeks before and after certain dates on the calendar 

Data Analysis and Probability                                                                                                      
• Organize and interpret data using line graphs 
• Construct graphs using data from a table 
• Discover patterns in tables and graphs by creating, organizing, recording and analyzing data 
• Formulate questions and categories for data collection and actively collect first-hand information 
• Describe the shape and important features of a set of data and compare related data sets, with 
an emphasis on how the data are distributed 

 

FOURTH GRADE                                                                                                                     

Number and Operations 
• Understand place value through millions 
• Understand concept and representation of numbers between zero - one, i.e. fractions - decimals 
• Recognize representations for equivalent numbers 
• Read, write and compare decimals to the hundredths 
• Know equivalents in counting money, e.g. 5 nickels equal 1 quarter 
• Know how to count up to make change 
• Understand how multiplication and division relate to each other to solve problems 
• Interpret the meaning of a remainder in a division problem 
• Memorize multiplication and division facts through 12 
• Multiply a 3- and 4-digit number by a 1-digit number 
• Divide using 1-digit divisor and 1- 2- or 3-digit dividend 
• Multiply two 2-digit numbers 
• Understand simple equivalent fractions 
• Convert improper fractions to mixed numbers and vice versa 
• Add and subtract fractions and mixed numbers with common denominators 
• Estimate solutions involving whole number, fraction and decimal computations 
• Understand basic concepts of least common multiple (LCM) and greatest common factor (GCF) 
• Reduce simple fractions to lowest terms 
• Explore numbers less than zero by extending the number line and through familiar applications 

Algebra 
• Construct a table of values to solve problems in a mathematical relationship 
• Understand how a change in one variable affects the value of another variable 
• Use distributive properties to simplify and perform computations 
• Make and justify predictions using numerical and non-numerical patterns 

Geometry 
• Describe points, lines and planes 
• Use columns and rows to determine position on a grid 
• Use coordinate systems to specify locations 
• Identify line symmetry in 3-dimensional shapes 
• Create models of 3-dimensional objects 
• Multiply to find area of rectangles 
• Make and test conjectures about geometric properties and relationships, then develop logical 
arguments to justify conclusions 
• Compare similarities and differences of quadrilaterals 

Measurement 
• Measure length to the nearest ¼ inch 
• Use measures less than one unit 
• Solve multi-step problems involving measurement 
• Estimate and measure the perimeter of irregular shapes 
• Compare the number of units to the size of units, e.g. number of feet compared to number of 
yards in a given length, estimating/determining cups in a 2-liter container 
• Draw a simple time line 
• Determine elapsed time by the hour and half-hour 
• Understand time zones and read timetables 
• Read a Celsius thermometer knowing the significance of 0 and 100 degrees; and read a 
Fahrenheit thermometer knowing the significance of 32 and 212 degrees 
• Know equivalent measures for simple metric and customary units of length, capacity, 
weight/mass and time e.g. inches to feet, meters to kilometers 
• Convert simple metric and customary units of length, capacity, weight/mass, and time, e.g. inches 
to feet, kilograms to grams, quarts to gallons 

Data Analysis and Probability 
• Collect and organize data into tables and graphs using different scales 
• Read and interpret data presented in circle graphs 
• Conduct simple probability experiments 
• Interpret and construct Venn diagrams 
• Evaluate the process of data collection 

 

FIFTH GRADE                                                                                                                         

Number and Operations 
• Understand place value through billions       
• Be proficient in counting money and making change 
• Develop and use number sense for whole numbers, fractions and decimals 
• Develop and apply number theory concepts, e.g. multiples, primes and factors in real world and 
mathematical situations 
• Determine pairs of numbers given a relation or rule, and determine the relation or rule of given 
pairs of numbers
• Understand how basic mathematical operations are related 
• Develop, analyze and explain procedures for computation and techniques for estimation 
• Select appropriate methods and tools for computing with whole numbers, fractions and decimals 
from among mental computation, estimation, calculator and paper/pencil 
• Round whole numbers to the designated place value 
• Identify and generate equivalent forms of fractions, decimals and percents 
• Recognize, model and describe multiples, factors, composites and primes 
• Determine the greatest common factor (GCF) and least common multiple (LCM) of two numbers 
• Convert fractions to the least common denominator (LCD) 
• Reduce fractions to simplest form (lowest terms) 
• Add and subtract time using renaming    

Algebra 
• Graph linear equations with one variable 
• Use calculators, computers, tables and graphs to develop and interpret patterns 
• Understand and use formulas 
• Develop skill in solving and writing linear equations using informal and formal methods 
• Investigate inequalities and nonlinear equations 
• Apply order of operation rules 

Geometry 
• Learn the relationship between radius and diameter 
• Classify angles according to the measure 
• Identify and select appropriate units to measure angles (degrees) 
• Understand and use linear, square and cubic units 
• Count faces, vertices and edges 
• Create perspective drawings 
• Describe ray, segment, interior and exterior of an angle 
• Recognize and create patterns with tessellations 

Measurement 
• Identify the paths between points on a grid or coordinate plane and compare the lengths of the 
paths, e.g. shortest path, paths of equal lengths 
• Demonstrate and describe the difference between covering the faces (surface area), and filling 
the interior (volume), of 3-dimensional objects 
• Use standard angles (45º,90º,120º) to estimate the measure of angles and use a protractor to 
measure and draw angles 
• Convert one metric unit to one customary unit and one customary unit to one metric unit 
• Understand that measurement is not exact, e.g. when measured multiple times, measurements 
may give slightly different numbers 
• Understand and explain how differences in units affect precision 
• Measure length to the nearest cm and ⅛ of an inch  
Data Analysis and Probability 
• Collect and organize data, then determine appropriate method and scale to display data 
• Find the mean, median, mode and range of a given set of data and use these measures to 
describe the set of data 
• Use calculators  to simplify computations and use computers to assist in generating and 
analyzing information 
• Sample and analyze data, making predictions and conjectures based on samples 
• Distinguish between a population and a sample 
• Discuss the reasonableness of the data and the results 
• List all possible outcomes of an event 
• Read, construct and interpret frequency tables 
• Make predictions based on experimental and theoretical probabilities 

 

SIXTH GRADE                                                                                                                         

Number and Operations 
• Understand the meaning and use of exponents 
• Understand the associative property of addition and multiplication 
• Extend understanding of whole number operations to fractions, decimals, percents and mixed 
numbers 
• Understand and apply divisibility rules 
• Round decimals to the nearest thousandths 
• Understand the concepts of ratio, percent and percentage 
• Compare and order improper fractions, mixed numbers and decimal fractions to thousandths 
• Develop meaning for integers and use integers to represent and compare quantities 
• Add, subtract, multiply and divide integers 
• Give the prime factorization of a number 
• Use factor trees to give the prime factorization of a number 
• Convert fractions to decimals to percents and vice versa 
• Convert fractions to terminating, repeating or rounded decimals 
• Solve proportions with an unknown 
• Understand and use mathematical vocabulary appropriately 
• Write a remainder as a fraction or decimal 
• Find the percent of a number 
• Find the percent one number is of another and find the original number when the percent is given 
• Use percents to determine sales tax, commission, discount and simple interest 

Algebra 
• Write, solve and graph linear equations 
• Use two-step operations to solve linear equations 
• Write and solve inequalities 
• Infer and use a rule to determine a missing number 
• Use appropriate mathematical vocabulary and properties 
• Compare integers on a number line 

Geometry 
• Define and use appropriate geometrical vocabulary 
• Use strategies to develop formulas for determining perimeter and area of triangles, rectangles 
and parallelograms and volume of rectangular prisms 
• Find the area of parallelograms and triangles 
• Find the circumference and area of circles 
• Find the volume and surface area of prisms 
• Classify triangles according to the angles and sides 
• Understand parallel, intersecting, and perpendicular lines 
• Measure an angle using a protractor 
• Draw similar figures that model proportional relations 
• Explore fractal patterns 
• Do geometric construction, e.g. bisect a segment 

Measurement 
• Describe how perimeter, area and volume are affected when dimensions of a figure are changed 
• Use strategies to develop formulas for finding circumference and area of circles, and area of 
sectors (½ circle, ⅔ circle, ⅓ circle, ¼ circle) 
• Express solutions to the nearest unit 
• Estimate length, area, volume, perimeter, circumference, area of a circle, various shapes and 
surfaces using everyday objects, e.g. string, arms, etc. 
• Make conversions within the same measurement system while performing computations 
• Use indirect measurement such as similar triangles to solve problems 
Data Analysis and Probability 
• Calculate the probability of independent and dependent events 
• Construct a multiple line graph 
• Make logical inferences from statistical data 
• Calculate the odds 
• Design an experiment to test a theoretical probability and explain how the results may vary 
• Construct a scatter plot 
• Make organized lists and tree diagrams 

 

SEVENTH GRADE                                                                                                                   

Number and Operations 
• Understand and use scientific notation 
• Evaluate powers that have negative and zero exponents 
• Use integers to express quantities that occur naturally in problem situations, e.g. representing 
direction, loss, gain, etc. 
• Develop and use number sense for integers, rational and irrational numbers 
• Understand and use the additive inverse property 
• Understand the principles of the distributive property 
• Apply properties of operations with whole numbers, fractions and decimals 
• Use proportions to solve problems 
• Compute with rational numbers using a calculator to perform difficult computations 
• Understand squares and square roots 
• Estimate the square root of a number less than 100 
• Find the percent of increase and/or decrease 

Algebra 
• Use and apply ratios, proportions, averages and percentage 
• Graph inequalities 
• Choose a formula to use in problem solving 
• Demonstrate proficiency in using the laws of exponents 
• Use the Pythagorean Theorem 
• Manipulate simple polynomials 

Geometry 
• Find the area of a trapezoid 
• Find the surface area of a cylinder 
• Find the volume of various geometric solids, e.g. pyramids and cones 
• Use transformations to explore congruence and create designs 
• Explore the angle measures in a triangle 
• Understand complementary, supplementary and vertical angles 
• Draw and interpret scale diagrams 

Measurement 
• Use graphs, charts and formulas to convert between a variety of standard/metric measures 
• Apply ratios to solve measurement problems 
• Use scale models to represent measures of real-life objects 
• Relate ancient monetary values to current values, e.g. shekel, denari, mite 
• Develop a proportionately correct time line using complex concepts 
• Use strategies to develop formulas for finding volume and surface areas of solids 
• Explain how time zones are determined 

Data Analysis and Probability 
• Understand the number of possible permutations 
• Predict the number of times an event will occur 
• Construct a multiple bar graph 
• Construct a circle graph 
• Make a histogram 
• Make a stem and leaf plot

 

EIGHTH GRADE                                                                                                                     

Number and Operations 
• Use appropriate significant digits in calculations 
• Extend understanding of number operations to irrational numbers 
• Know the definition of real numbers, set notation and set operations 

Algebra 
• Add and subtract matrices 
• Recognize slope and intercept relationships 
• Use information to determine whether situations are functions 
• Recognize minimum and maximum values 
• Understand the properties of arithmetic and geometric sequences 
• Develop an initial conceptual understanding of different uses of variables 
• Identify functions as linear or nonlinear and contrast their properties from tables, graphs or 
equations 

Geometry 
• Find the surface area of various geometric shapes, e.g. pyramids and cones 
• Find the volume of spheres using formula 
• Define objects by geometric properties 
• Recognize sine, cosine and tangent relationships with respect to the right triangle 

Measurement 
• Draw picture to assist in solving measurement problems 
• Find the size of interior and exterior angles of convex polygons using formula and protractor 
• Use appropriate significant digits in calculations 
• Convert temperature between Fahrenheit and Celsius 
Data Analysis and Probability 
• Determine the number of combinations from a given set 
• Make a box and whisker plot