MATHEMATICS CURRICULUM (K-12)

As stated in the NH Framework:

Students must understand numbers if they are to make sense of the ways numbers are used in their everyday world. Numbers are used to describe and interpret real-world phenomena. Students need to use numbers to quantify, to identify location, to identify a specific object in a collection, to name, to measure, and to model real-world situations. Logical reasoning as well as estimating and mental computations must be used to determine the validity of a solution. Students need to understand relative magnitude in order to make sense of everyday situations. Students will use appropriate technology, write with precision, and interpret uses of mathematics in literature.

Kindergarten

• Explore and discuss a variety of real-life mathematics problems
• Explore quantities represented by numbers from 1-20
• Recognize and sequence numbers 1-10
• Practice forming numbers
• Make, count, and analyze sets
• Investigate counting patterns
• Compare amounts using mathematical language (for example: same, different, more, less, and equal)
• Develop meaning for operations of addition and subtraction by using concrete materials
• Develop recognition of symbols for addition, subtraction, and equality
• Explore a variety of problem-solving strategies
• Group objects into tens and ones, and record findings in concrete ways
• Estimate number in collections of objects, discuss estimating strategies, and check to confirm estimates
• Explore and use metric, standard, and non-standard units and tools of measurement
• Develop an understanding of the clock and the calendar as tools to measure time
• Recognize passage of time throughout the day
• Play constructively with coins
• Listen to and discuss stories related to mathematics
• Identify and make sense of real-life events using mathematical concepts

Grade 1

• Explore and discuss a variety of real-life mathematics problems
• Explore a variety of strategies to solve problems
• Choose appropriate strategies to solve a particular problem
• Explain and evaluate strategies used to solve problems
• Create story problems
• Identify and use simple number patterns when counting by one, two, five, and ten (for example: use number lines, hundred charts, and calendar)
• Identify odd and even numbers
• Recognize numbers and explore quantities 1-100 by connecting concrete materials and abstract representations
• Write numbers to 100
• Make, count, and analyze sets
• Develop an understanding of addition and subtraction using concrete materials
• Explore, develop, and set up addition and subtraction equations
• Construct and apply one's own algorithms
• Recognize and interpret language and symbols for addition, subtraction, and equal
• Develop an understanding of the relationship between addition and subtraction
• Develop strategies to check reasonableness of solutions to addition and subtraction problems
• Recognize and demonstrate knowledge of number families to 10
• Explore base ten system (for example: group objects into tens and ones, use hundreds chart, and place value grid)
• Record and explain findings from place value activities
• Develop mathematical language and concepts (for example: same, different, more, less, equal, greater than, less than)
• Understand one-to-one correspondence, count, and conserve values
• Explore fractions and equal shares
• Explore and use metric, standard, and non-standard units and tools of measurement
• Develop understanding of need for standard units of measurement
• Develop language of both non-standard and standard measurement systems
• Understand the clock and the calendar as tools to measure time
• Tell time to the half hour and hour
• Read calendar to determine date
• Understand seasons as passage of time
• Name, recognize, and explore the value of coins (for example: quarter, dime, nickel, penny)
• Explore use of a calculator
• Explore and explain mathematical understandings through pictures, diagrams, and writing
• Listen to, read, and explore books related to mathematics
• Discuss and use numeration skills throughout the day
• Identify and make sense of real-life events using mathematical concepts

Grade 2

• Explore and discuss a variety of real-life mathematics problems
• Explore a variety of strategies to solve problems
• Choose appropriate strategies to solve a particular problem
• Explain and evaluate strategies used to solve problems
• Identify and use number patterns when counting by 1's, 2's, 5's, and 10's (for example: number lines, hundred charts, calendar)
• Understand one-to-one correspondence, count and conserve values
• Understand and count by odd and even numbers
• Count, using ordinal and cardinal numbers
• Read, write, and understand numbers, and explore quantities 1-100 by connecting concrete materials and abstract representations (for example: name whole number immediately before and after any two-digit number or compare any two-digit numbers to determine which one is larger or smaller)
• Explore numbers to 1,000
• Make, count, and analyze sets
• Develop and use a variety of strategies to add and subtract numbers
• Explore and construct addition and subtraction algorithms
• Develop an understanding of the relationship between addition and subtraction
• Develop strategies to check reasonableness of solutions
• Explain how problems were solved
• Recognize and demonstrate knowledge of number families to eighteen
• Explore the relationship between addition and multiplication using concrete materials
• Explore and develop an understanding of the base ten number system
• Record and explain findings from place value activities
• Develop and use mathematics language and concepts (for example: same, different, greater than, less than, equal)
• Recognize and interpret symbols for addition, subtraction, equal to, greater than, and less than
• Recognize fractions as equal shares
• Explore and use non-standard measurement units and tools
• Develop understanding of need for standard units of measurement
• Explore and use metric and standard measurement units and tools
• Develop language for both non-standard and standard measurement systems
• Tell time to the quarter hour
• Read calendar to determine day, month, and year
• Understand passage of time
• Name, recognize, and explore the value of coins
• Explore the relationships among coins (for example: nickel, dime, quarter, half dollar)
• Explore use of a calculator
• Explore and explain mathematical understandings through pictures, diagrams, and writing
• Create, develop, and write word problems
• Listen to, read, and explore books related to mathematics
• Discuss and use numeration skills throughout the day
• Identify and make sense of real-life events using mathematical concepts

Grade 3

• Explore and discuss a variety of real-life mathematics problems
• Explore a variety of strategies to solve problems
• Choose appropriate strategies to solve a particular problem
• Explain and evaluate strategies used to solve problems
• Identify, develop, and use number patterns (for example: multiples, number lines)
• Understand and count by odd and even numbers
• Count using ordinal and cardinal numbers
• Explore numbers to 100,000
• Read, write, understand numbers, and explore quantities 1-1,000 by connecting concrete materials and abstract representations (for example: name whole number immediately before and after any three-digit number or compare any three-digit numbers to determine which one is larger or smaller)
• Estimate answers to problems
• Develop and use a variety of strategies to add and subtract numbers
• Explore and construct addition and subtraction algorithms (for example: two- and three-digit addition and subtraction with or without regrouping)
• Understand the relationship between addition and subtraction
• Develop strategies to check reasonableness of solutions
• Explain how problems were solved (for example: talking, writing, drawing)
• Recognize and demonstrate knowledge of number families to eighteen
• Develop concept of multiplication
• Understand the relationship between addition and multiplication
• Explore and develop an understanding of the base ten number system
• Record and explain findings from place value activities
• Use mathematics language and concepts (for example: same, different, greater than, less than, equal)
• Recognize and interpret symbols for addition, subtraction, multiplication, division, equal to, greater than, and less than
• Recognize fractions as equal shares
• Represent fractions using non-conventional and conventional forms
• Explore fractional relationships
• Explore and use non-standard measurement units and tools
• Explore and use metric and standard measurement units and tools
• Develop language for non-standard, metric, and standard measurement systems
• Develop concepts of perimeter and area
• Tell time to five-minute intervals
• Read calendar to determine day, month, and year
• Understand the passage of time
• Name, recognize, and explore the value of coins
• Explore the relationships among coins (for example: nickel, dime, quarter, half dollar)
• Explore the use of a calculator
• Explore and explain mathematical understandings through pictures, diagrams, and writing
• Create, develop, and write word problems
• Listen to, read, and explore books related to mathematics
• Discuss and use numeration skills throughout the day
• Identify and make sense of real-life events using mathematical concepts

Grade 4

• Explore and discuss a variety of real-life mathematics problems
• Explore a variety of strategies to solve problems
• Choose appropriate strategies to solve a particular problem
• Explain and evaluate strategies used to solve problems
• Identify, develop and use number patterns (for example: multiples, palindromes, number lines)
• Explore numbers to 1,000,000
• Estimate answers to problems
• Read, write, and understand numbers, and explore quantities 1-1,000,000 by connecting concrete materials and abstract representations (for example: name whole number immediately before and after any number, or compare any number to determine which one is larger or smaller)
• Understand concepts of multiplication and division
• Understand the relationships among operations
• Explore and construct algorithms for addition, subtraction, multiplication, and division (for example: multiply 364 by 9, divide 224 by 4)
• Develop strategies to check reasonableness of solutions (for example: writing, talking, diagramming, building)
• Understand and use regrouping when adding and subtracting
• Recognize and interpret symbols for multiplication, division, decimals, percent, equal, greater than, less than
• Develop and use mathematics language and concepts (for example: multiples, factors, equivalency, divided by)
• Recall multiplication and division facts of numbers to eighty-one
• Explore and develop an understanding of base ten system, including decimals
• Record and explain findings from place value activities
• Recognize fractions as equal shares of a whole or part of a group
• Represent fractions in a variety of ways
• Explore fractional relationships using concrete materials
• Add and subtract fractions using concrete materials
• Connect concrete models of fractions to abstract representations
• Explore the relationship among fractions, decimals, money, and percents
• Add and subtract decimals (for example: money)
• Use non-standard measurement units and tools
• Use metric and standard measurement units and tools
• Use language for non-standard, metric, and standard measurement systems
• Tell time accurately
• Use the calendar and understand passage of time
• Understand the relationship among coins (for example: nickel, dime, quarter, half dollar)
• Use mental mathematics to solve problems
• Use the calculator as a tool
• Create, develop, and write word problems
• Find mathematics in literature
• Discuss and use numeration skills throughout the day
• Identify and make sense of real-life events using mathematical concepts

Grade 5

• Given a physical representation, identify a whole number, fraction, or decimal
• Identify and write or create a model of a given number
• Read and write rational numbers from billions to thousandths
• Perform the four basic operations with whole numbers
• Recall multiplication and division facts to 81
• Use divisibility rules for 1,2,3,4,5,6,8,9,10
• Multiply whole numbers by two- and three-digit multipliers
• Divide whole numbers by one- and two-digit divisors
• Estimate answers for problems; check to determine if answers are reasonable
• Identify prime and composite numbers, factors, and multiples
• Use a factor tree to write the prime factors of composite numbers
• Demonstrate the relationships among fractions, decimals, and common percents
• Using physical models and illustrations, determine the sum or difference of fractions with like or unlike denominators (for example: halves, fourths, and eighths)
• Given a decimal representation in tenths, write an equivalent fraction
• Using physical models, illustrations, and calculators, determine the sum, difference, and product of decimals
• Use units of measurement accurately (for example: measure to closest inch or one centimeter)
• Convert commonly used measurements to equivalent ones within a measurement system (for example: inches, feet, yards)
• Solve problems using mental math
• Use calculators as tools for exploring various mathematical situations
• Devise and write word problems
• Use mathematics in all disciplines
• Use mathematics in real-life situations

Grade 6

• Divide whole numbers by two and three-digit divisors
• Divide three-digit whole numbers by two-digit whole numbers
• Use the order of operations to evaluate expressions (for example: multiply/divide and add/subtract)
• Identify and illustrate the commutative and associative laws of addition and the commutative law of multiplication with manipulatives
• Use the divisibility rules for 1,2,3,4,5,6,8,9,10
• Identify and use prime and composite numbers
• Identify multiples and factors
• Rename expression in exponential form to standard form
• Demonstrate the relationship between fractions and decimals
• Given a decimal representation in hundredths, write an equivalent fraction
• Using physical model and illustrations, determine the sum or difference of fractions with like or unlike denominators
• Develop and use algorithms to add, subtract, and multiply decimals
• Multiply and divide two- and three-digit decimals
• Read and write rational numbers to millionths
• Explore the meaning of percent
• Use appropriate units of measurement accurately
• Estimate and measure the area of a rectangular region using a standard unit
• Estimate the area of any region using a standard unit
• Estimate weight using pounds or kilograms
• Estimate capacity using quarts, gallons, or liters
• Use proper notation, names, and mathematics symbols

Grade 7

• Identify the relationship among the basic operations as applied to positive rational numbers
• Identify, develop, and use order relations for integers and positive rational numbers
• Use the associative, commutative, and distributive properties in a problem-solving situation
• Divide two- and three-digit decimals
• Use appropriate units of measurement accurately
• Generate properties and relationships related to prime numbers, composite numbers, rational numbers, multiples, and factors
• Apply number theory to the process of prime factorization and the use of multiples
• Use physical models of integers
• Explore types of common percent computations
• Convert equivalent common fractions to decimals to percent
• Use the correct order of operation with emphasis on MD and AS (multiply/divide and add/subtract)
• Simplify perfect squares
• Use exponents in appropriate problem-solving situations
• Add and subtract integers using a variety of representations and models

Grade 8

• Identify the relationships among the four basic operations on rational numbers
• Develop and use order relations for integers and positive and negative rational numbers
• Compare and order real numbers
• Perform the four basic operations with rational numbers
• Set up and compute the three types of percent problems
• Determine equivalent rationals (for example: fraction to decimal to percent)
• Use correct order of operation (for example: understanding the fraction bar as a grouping symbol)
• Identify, use, and apply the associative, commutative, and distributive properties in a problem-solving situation (including using variables)
• Use exponents with variables in performing operations with positive, negative, and zero exponents

Grade 9

Number patterns

• Recognize and use number patterns such as perfect squares

The real number system

• Use and simplify rational numbers
• Use and simplify square roots
• Use the properties of additive and multiplicative identities and inverses

Representation of numbers

• Use scientific notation to represent large and small numbers
• Use scientific notation to estimate and compare the magnitude of numbers
• Use the connections among operations to evaluate expressions

Number sense

• Use mental mathematics to estimate solutions
• Present solutions using a reasonable number of significant digits

Scale and measurement

• Use appropriate scales on graphs
• Use metric and standard units

Grade 10

Number patterns

• Recognize and use number patterns such as perfect squares, perfect cubes, and Pythagorean triples

The real number system

• Use and simplify rational numbers
• Use and simplify square roots
• Use the properties of additive and multiplicative identities and inverses
• Use irrational numbers

Number sense

• Use mental mathematics to estimate solutions
• Present solutions using a reasonable number of significant digits

Grade 11

Number patterns

• Recognize and use number patterns such as perfect squares, perfect cubes, and Pythagorean triples

The real number system

• Use and simplify rational numbers
• Use and simplify rational roots and rational powers
• Use the properties of additive and multiplicative identities and inverses
• Simplify expressions with complex numbers

Number sense

• Use mental mathematics to estimate solutions
• Present solutions using a reasonable number of significant digits

Grade 12

Number patterns

• Use summation symbols to generalize number patterns
• Recognize arithmetic and geometric sequences and series
• Recognize the sequence patterns involved in real-world applications

Number sense

• Recognize the reasonableness of the probability of a given event