**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 appropr

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

iate symbols

**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 relatarguments 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

ionships, then develop logical

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 tto 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

ime, e.g. inches

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, decnumbers

Understand and apply divisibility rules

Round decimals to the nearest thousandths

Understand the concepts of ratio, percent and percentage

imals, percents and mixed

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 perform

Use indirect measurement such as similar triangles to solve problems

**Data Analysis and Probability **

Calculate the probability of independent and dependent events

ing computations

Construct a multiple line graph

Make logical inferences from statistical data

Calculate the odds

Design an experiment to test a theoretical probability and exp

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

lain how the results may vary

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