Delaware Standards

Delaware Standards working document for Grades K-3 | 4-5 | 6-8 | 9-10 |

Correlation to Delaware Mathematics Content Standards

Directly Addresses Standard

Indirectly Addresses Standards

Delaware Mathematics Content Standards

Mathematical Processes	K-3	4-5	6-8	9-10
Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections.
Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats.
Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning.
Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways.
Mathematical Knowledge
Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results.
Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers.
Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities.
Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures.
Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability.
Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe real-world functional relationships

Delaware Standards for Grades K-3

Delaware Standards	Performance Indicators	K-3
Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections	1.01 persist and solve problems from start to finish
	1.02 investigate and build their understanding of mathematical content
	1.03 formulate problems from everyday and mathematical situations
	1.04 develop and apply strategies to solve problems
	1.05 interpret results with respect to the original problem
	1.06 generalize strategies and solutions to new problem situations
Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats.	2.01 model real-world situations using oral, written, concrete, pictorial, graphical and algebraic methods
	2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas
	2.03 use mathematical notation and language to describe and discuss real-world situations
	2.04 read mathematics with understanding
	2.05 develop common understandings of mathematical ideas and use generalizations discovered through investigations to formulate definitions
	2.06 ask questions to clarify the problem situation
Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning.	3.01 formulate and test conjectures
	3.02 draw and then justify conclusions
	3.03 construct and follow logical arguments
	3.04 use properties, models, known facts, and relationships to explain and defend their thinking
Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways.	4.01 make connections linking conceptual and procedural knowledge
	4.02 integrate mathematical problem-solving with other curricular areas
	4.03 use connections among mathematical topics
	4.04 use various representations of the same concept
	4.05 make connections from manipulative solutions to algorithmic solutions to technological solutions
	4.06 determine the reasonableness of a mathematical solution as it applies in a real-world situation
Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results.	5.10 estimate and then measure length, perimeter, time, temperature, and weight/mass to the nearest unit using standard and nonstandard units
	5.11 determine the value of a given set of coins
	5.12 measure and compute the perimeter of rectangles
	5.13 use multiple computational procedures with whole numbers
	5.14 add and subtract single-digit and multi-digit whole numbers
	5.15 multiply whole numbers using at least one single-digit factor
	5.16 divide whole numbers using single-digit divisors
	5.17 make estimates before measuring, counting and computing
	5.18 round whole numbers and values of money as an estimation strategy
	5.19 select appropriate measures to compare objects
	5.20 compare objects through measurable attributes
	5.21 read and write decimal notation when representing money
Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers.	6.10 connect physical, verbal and symbolic representations of whole numbers
	6.11 show whole/part relationships
	6.12 use fractions to represent part of a whole and part of a set
	6.13 decompose and recompose whole numbers using addition and subtraction
	6.14 build whole numbers using the concept of place value using base ten
	6.15 demonstrate an understanding of order relations for whole numbers
	6.16 examine the relative effect of operations on whole numbers
	6.17 recognize the arbitrary size of a unit
	6.18 connect repeated addition with multiplication and repeated subtraction with division
	6.19 recognize inverse operations: subtraction/addition and division/multiplication
	6.20 count sets of objects and units of measure
	6.21 count on, count back, and count by multiples
Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities.	7.10 represent operations with symbols
	7.11 use symbols as representations of variables such as missing addends or factors
	7.12 generate and write number sentences vertically and horizontally
	7.13 solve open sentences using informal methods
Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures.	8.10 sort solid and plane figures by common attributes
	8.11 recognize congruence of geometric figures in the real world
	8.12 identify and create symmetrical shapes (line symmetry)
	8.13 draw an example of a flip, slide, or turn given a model
	8.14 draw a square, rectangle, and triangle on grid paper
	8.15 describe the effect of combining two or more shapes
Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability.	9.10 collect data by observing, measuring, surveying and counting
	9.11 demonstrate a variety of techniques for representing and organizing data such as using physical objects, tallies, pictographs, and bar graphs
	9.12 interpret data by: looking for patterns and relationships, considering cause and effect, drawing conclusions, answering the stated question or related questions
	9.13 determine the likelihood of a simple chance event
Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe real-world functional relationships.	10.10 sort and classify objects by common attributes
	10.11 recognize, analyze, create and extend visual, symbolic, oral and physical patterns
	10.12 sort numbers into different classes such as evens, odds, multiples and factors

Delaware Standards for Grades 4-5

Delaware Standards	Performance Indicators	4-5
Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections.	1.01 persist and solve problems from start to finish
	1.02 investigate and build their understanding of mathematical content
	1.03 formulate problems from everyday and mathematical situations;
	1.04 develop and apply strategies to solve problems;
	1.05 interpret results with respect to the original problem;
	1.06 generalize strategies and solutions to new problem situations
Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats.	2.01 model real-world situations using oral, written, concrete, pictorial, graphical and algebraic methods
	2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas
	2.03 use mathematical notation and language to describe and discuss real-world situations
	2.04 read mathematics with understanding
	2.05 develop common understandings of mathematical ideas and use generalizations discovered through investigations to formulate definitions
	2.06 ask questions to clarify the problem situation
Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning.	3.01 formulate and test conjectures
	3.02 draw and then justify conclusions
	3.03 construct and follow logical arguments
	3.04 use properties, models, known facts, and relationships to explain and defend their thinking
Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways.	4.01 make connections linking conceptual and procedural knowledge
	4.02 integrate mathematical problem-solving with other curricular areas
	4.03 use connections among mathematical topics
	4.04 use various representations of the same concept
	4.05 make connections from manipulative solutions to algorithmic solutions to technological solutions
	4.06 determine the reasonableness of a mathematical solution as it applies in a real-world situation
Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results.	5.40 estimate and then measure length, perimeter, time, temperature, weight/mass, capacity and area to the degree of accuracy required using standard and nonstandard units
	5.41 describe the structure and the use of systems of measurement
	5.42 estimate, measure and compute the perimeter of polygons
	5.43 use algorithms for addition, subtraction, multiplication and division with understanding
	5.44 use multiple computational procedures to add and subtract fractions and decimals, to multiply fractions, and to divide whole numbers using multi-digit divisors
	5.45 estimate, measure and compute the area of rectangles
	5.46 make estimates before measuring and computing and determine if an estimate is reasonable
	5.47 round decimals as an estimation strategy
	5.48 determine if an estimate is more appropriate than an exact answer
	5.49 make change by counting on and counting back
Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers.	6.40 connect physical, verbal and symbolic representations of fractions, decimals, and whole numbers
	6.41 decompose and recompose whole numbers using all arithmetic operations
	6.42 build decimal representations using base ten
	6.43 demonstrate the need for and the connection between decimals and fractions
	6.44 demonstrate an understanding of order relations for fractions, decimals, and whole numbers using physical, verbal and symbolic representations
	6.45 examine the relative effect of operations on whole numbers, fractions, and decimals
	6.46 recognize the arbitrary size of a unit and its relationship to fractional and decimal parts
Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities.	7.40 solve equations using methods such as inverse operations, mental math, and guess and check
	7.41 find solutions to inequalities from a given replacement set
	7.42 use letters as variable representations
Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures.	8.40 visualize, represent, and draw geometric figures (triangle, quadrilaterals, and regular polygons)
	8.41 given a net, build three dimensional figures such as a cube, rectangular prism, cylinder and square pyramid
	8.42 manipulate and draw polygons using flips, slides and turns
	8.43 define polygons using their attributes such as number of sides, parallel or perpendicular sides, number of vertices, and classification of angles
	8.44 identify, describe, compare and classify two dimensional figures and investigate their relationships
Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability.	9.40 systematically collect, organize and describe data
	9.41 construct and describe displays of data
	9.42 calculate and use the mean to interpret data
	9.43 select and use data displays such as line plots, tables, histograms, and scale pictographs
	9.44 interpret data and make convincing arguments that are based on data analysis and previous experiences
	9.45 list all possible outcomes for an experiment using a tree diagram
	9.46 find the probability of a single event based on an experiment with equally likely outcomes
Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe real-world functional relationships	10.40 recognize, analyze, create, extend and describe a wide variety of patterns
	10.41 investigate and predict the results of combining, subdividing and changing shapes
	10.42 use tables, rules, variables, open sentences and graphs to describe patterns, functions, and other relationships
	10.43 identify patterns for explaining the concepts of computation

Delaware Standards for Grades 6-8

Delaware Standards	Performance Indicators	6-8
Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections.	1.01 persist and solve problems from start to finish
	1.02 investigate and build their understanding of mathematical content
	1.03 formulate problems from everyday and mathematical situations;
	1.04 develop and apply strategies to solve problems;
	1.05 interpret results with respect to the original problem;
	1.06 generalize strategies and solutions to new problem situations
Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats.	2.01 model real-world situations using oral, written, concrete, pictorial, graphical and algebraic methods
	2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas
	2.03 use mathematical notation and language to describe and discuss real-world situations
	2.04 read mathematics with understanding
	2.05 develop common understandings of mathematical ideas and use generalizations discovered through investigations to formulate definitions
	2.06 ask questions to clarify the problem situation
Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning.	3.01 formulate and test conjectures
	3.02 draw and then justify conclusions
	3.03 construct and follow logical arguments
	3.04 use properties, models, known facts, and relationships to explain and defend their thinking
Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways.	4.01 make connections linking conceptual and procedural knowledge
	4.02 integrate mathematical problem-solving with other curricular areas
	4.03 use connections among mathematical topics
	4.04 use various representations of the same concept
	4.05 make connections from manipulative solutions to algorithmic solutions to technological solutions
	4.06 determine the reasonableness of a mathematical solution as it applies in a real-world situation
Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results.	5.60 estimate and then measure angles, circumference, volume and surface area to the degree of accuracy required using standard and nonstandard units
	5.61 convert measurement units within the same system
	5.62 apply ratios, proportions and percents to real life situations
	5.63 compute circumference; areas of triangles, parallelograms, trapezoids, and circles; and surface area and volume of cylinders, triangular and rectangular prisms and pyramids
	5.64 apply order of operations
	5.65 choose and explain an appropriate method for calculating an answer in a given situation
	5.66 use multiple computational procedures with rational numbers
	5.67 determine if an estimate is an over-estimate or an under-estimate
Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers.	6.60 connect physical, verbal and symbolic representations of rational numbers
	6.61 apply multiple representations of numbers: integers, fractions, decimals, percents, exponents, and scientific notation
	6.62 model integer representations using manipulatives
	6.63 demonstrate an understanding of order relations for rational numbers
	6.64 examine the relative effect of operations on rational numbers
	6.65 use various forms of "one" to demonstrate the equivalence of fractions
Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities.	7.60 represent situations with tables, graphs, verbal rules, and equations; and describe the interrelationships of the representations
	7.61 model and solve real-world and mathematical problems using algebraic methods
	7.62 evaluate algebraic expressions and formulas for given values of the variable
	7.63 solve linear equations using concrete, informal, and formal methods
	7.64 solve proportions
	7.65 solve linear inequalities and non-linear equations using informal methods
Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures.	8.60 identify, describe, compare and classify two and three dimensional figures
	8.61 use a compass and straight edge as tools for basic geometric constructions
	8.62 investigate and discover geometric relationships through the use of manipulatives, constructions and computer graphic software
	8.63 create models of nets of three dimensional figures such as a cube, rectangular prism, cylinder and square pyramid
	8.64 visualize and draw orthographic projections
	8.65 discover and apply geometric properties and relationships such as congruence, similarity, parallelism, perpendicularity and symmetry
	8.66 apply geometric properties and relationships to make conjectures
Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability.	9.60 collect, organize, describe, and make predictions with data
	9.61 construct and describe displays of data such as stem-and-leaf plots, scatter plots, box plots, and circle graphs
	9.62 make and evaluate arguments that are based on data analysis
	9.63 calculate and use mean, median, mode and range to interpret data
	9.64 analyze a sample to make inferences about a population
	9.65 compare and make predictions based on theoretical and experimental probabilities
	9.66 construct a sample space to determine theoretical probabilities
Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe real-world functional relationships.	10.60 recognize, analyze, create, extend, describe and generalize a wide variety of patterns and relationships
	10.61 analyze functional relationships to explain how a change in one quantity results in a change in another
	10.62 identify geometric patterns and relationships
	10.63 detect patterns and functions from statistical data
	10.64 use a calculator and computer software to explore number patterns and mathematical relationships
	10.65 use patterns and functions to represent and solve problems

Delaware Standards for Grades 9-10

Delaware Standards	Performance Indicators	9-10
Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections.	1.01 persist and solve problems from start to finish
	1.02 investigate and build their understanding of mathematical content
	1.03 formulate problems from everyday and mathematical situations;
	1.04 develop and apply strategies to solve problems;
	1.05 interpret results with respect to the original problem;
	1.06 generalize strategies and solutions to new problem situations
Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats.	2.01 model real-world situations using oral, written, concrete, pictorial, graphical and algebraic methods
	2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas
	2.03 use mathematical notation and language to describe and discuss real-world situations
	2.04 read mathematics with understanding
	2.05 develop common understandings of mathematical ideas and use generalizations discovered through investigations to formulate definitions
	2.06 ask questions to clarify the problem situation
Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning.	3.01 formulate and test conjectures
	3.02 draw and then justify conclusions
	3.03 construct and follow logical arguments
	3.04 use properties, models, known facts, and relationships to explain and defend their thinking
Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways.	4.01 make connections linking conceptual and procedural knowledge
	4.02 integrate mathematical problem-solving with other curricular areas
	4.03 use connections among mathematical topics
	4.04 use various representations of the same concept
	4.05 make connections from manipulative solutions to algorithmic solutions to technological solutions
	4.06 determine the reasonableness of a mathematical solution as it applies in a real-world situation
Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results.	5.90 compute permutations and combinations
	5.91 compute areas and volumes by partitioning and indirect methods
	5.92 compute with real numbers
	5.93 compute with matrices
	5.94 extend computation procedures to algebraic procedures
	5.95 determine if errors are within tolerance limits
	5.96 estimate and calculate derived measures
	5.97 assess the error resulting from estimation and rounding
	5.98 estimate algebraic solutions on a graphics calculator
Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers.	6.90 connect physical, verbal and symbolic representations of real numbers
	6.91 demonstrate an understanding of order relations for real numbers
	6.92 examine the relative effects of operations on real numbers
	6.93 recognize inverse operations: powers and roots
Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities.	7.90 model relationships among quantities using symbols and expressions
	7.91 develop appropriate symbol sense to use algebraic technology
	7.92 use tables and graphs to interpret expressions, equations and inequalities
	7.93 describe relationships between variable quantities verbally, symbolically and graphically (including slope as a rate of change)
	7.94 translate and make connections from narrative to table, graph and function
	7.95 solve linear and quadratic algebraic problems using graphs, tables, equations, formulas and matrices
	7.96 solve systems of equations algebraically, graphically and with matrices
	7.97 solve inequalities graphically and symbolically
	7.98 explore algebraic relationships using technology
Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures.	8.90 explore, draw and construct three dimensional objects
	8.91 construct geometric figures on a coordinate plane
	8.92 identify congruent and similar figures using transformational, Euclidean, and coordinate geometries
	8.93 deduce properties of figures using coordinate and Euclidean geometries
	8.94 explore geometric patterns and generalize results using algebraic expressions
	8.95 apply similarity, congruence and proportionality
	8.96 use the properties and relationships in two and three dimensional figures including circles and spheres
	8.97 apply right triangle trigonometry and the Pythagorean Theorem to problem situations involving right triangles
Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability.	9.90 explore and analyze sampling methods to collect data
	9.91 collect, explore, compare and interpret one or two-variable real world data
	9.92 use curve-fitting to model and draw inferences from real life data
	9.93 summarize and interpret single-variable data by exploring and choosing measures of central tendency and dispersion
	9.94 analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by choices of scale, inappropriate choices of central tendency, incorrect curve fitting, or in appropriate use of control groups
	9.95 define a sample space using the fundamental counting principle
	9.96 compare and determine the reasonableness of outcomes
	9.97 model mathematical situations, using simulations or experiments, to determine probabilities of independent and dependent events
Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe real-world functional relationships.	10.90 model real-world phenomena with appropriate functions
	10.91 search for and describe algebraic, geometric and statistical patterns using mathematical models
	10.92 classify relationships between variable expressions as linear, quadratic, inverse, direct or exponential
	10.93 use technology to explore transformations of functions caused by parameter changes
	10.94 identify and interpret maximum and minimum values of functional relationships graphically