We believe that all students can achieve success in Mathematics
which is an integral part of all curriculum areas. Mathematical
instruction is a part of everyday routines and should involve real-life
situations, current technology, and hands-on experiences. We believe
that Mathematical instruction should cultivate creative problem solving
and critical thinking skills and should be differentiated to
accommodate individual learning styles. Standard 1. Uses a variety of strategies in the problem-solving process Benchmark 1. Uses a variety of strategies to understand problem situations (e.g., discussing with peers, stating problems in own words, modeling problem with diagrams or physical objects, identifying a pattern) Knowledge/skill statements 1. States problem in own words 2. Makes diagrams of a problem 3. Uses physical objects to model a problem 4. Discusses with peers to understand a problem situation 5. Uses patterns to solve problems Benchmark 2. Represents problems situations in a variety of forms (e.g., translates from a diagram to a number or symbolic expression) Knowledge/skill statements 1. Translates from a diagram to a numeric expression 2. Translates from a diagram to a symbolic expression 3. Uses pictures to represent problem situations 4. Uses manipulatives to model problem situations Benchmark 3. Understands that some ways of representing a problem are more helpful than others Knowledge/skill statements 1. Selects best representation of a problem Benchmark 4. Uses trial and error and the process of elimination to solve problems Knowledge/skill statements 1. Uses trial and error to solve problems 2. Uses process of elimination to solve problems Benchmark 5. Knows the difference between pertinent and irrelevant information when solving problems Knowledge/skill statements 1. Identifies pertinent and irrelevant information in a problem Benchmark 6. Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not") Knowledge/skill statements 1. Understands logic operator “and” 2. Understands logic operator “or” 3 Understands logic operator “not” Benchmark 7. Uses explanations of the methods and reasoning behind the problem solution to determine reasonableness of and to verify results with respect to the original problem Knowledge/skill statements 1. Determines reasonableness of a problem solution 2. Verifies results of problem solution Benchmark 8. Understands basic valid and invalid arguments (e.g., counter examples, irrelevant approaches) Knowledge/skill statements 1. Understands valid counter examples 2. Recognizes invalid approaches based on irrelevant information Standard 2. Understands and applies basic and advanced properties of the concepts of numbers Benchmark 1. Understands basic number theory concepts (e.g., prime and composite numbers, factors, multiples, odd and even numbers, divisibility) Knowledge/skill statements 1. Knows that numbers are odd or even 2. Knows what makes a number prime 3. Knows what makes a composite number 4. Understands the basic concept of a factor 5. Understands the concept of divisibility 6. Understands the concept of multiples Benchmark 2. Understands equivalent forms of basic percents, fractions, and decimals (e.g., 1/2 is equivalent to 50% is equivalent to .5) and when one form of a number might be more useful than another Knowledge/skill statements 1. Converts fractions to percents 2. Converts percents to decimals 3. Converts fractions to decimals 4. Knows the equivalence of common fractions and percents 5. Knows the equivalence of common fractions and decimals 6. Knows the equivalence of common percents and decimals Benchmark 3. Understands the basic difference between odd and even numbers Knowledge/skill statements 1. Recognizes numbers as odd or even Benchmark 4. Understands the basic meaning of place value Knowledge/skill statements 1. Understands the concept of place value Benchmark 5. Understands the relative magnitude and relationships among whole numbers, fractions, decimals, and mixed numbers Knowledge/skill statements 1. Understands the concept of whole numbers 2. Understands the concept of fractions 3. Understands the concept of decimals 4. Understands the concept of mixed numbers 5. Understands the relative magnitude among whole numbers, fractions, decimals, and mixed numbers 6. Understands the relationships among whole numbers, fractions, decimals, and mixed numbers Benchmark 6. Uses models (e.g., number lines, two-dimensional and three-dimensional regions) to identify, order, and compare numbers Knowledge/skill statements 1. Understands the concept of ordered triplets 2. Understands the concept of ordered pairs 3. Uses two-dimensional space to represent ordered pairs 4. Uses number line to represent numbers 5. Uses three-dimensional space to represent ordered triplets 6. Uses models to identify numbers 7. Uses models to order numbers 8. Uses models to compare numbers Standard 3. Uses basic and advanced procedures while performing the processes of computation Benchmark 1. Multiplies and divides whole numbers Knowledge/skill statements 1. Understands the concept of multiplication 2. Multiplies whole numbers 3. Understands the concept of division 4. Divides whole numbers Benchmark 2. Adds, subtracts, multiplies, and divides decimals Knowledge/skill statements 1. Understands the concept of decimal addition 2. Adds decimals 3. Understands the concept of decimal subtraction 4. Subtracts decimals 5. Understands the concept of decimal multiplication 6. Multiplies decimals 7. Understands the concept of decimal division 8. Divides decimals Benchmark 3. Adds and subtracts simple fractions Knowledge/skill statements 1. Understands the concept of addition of fractions 2. Adds simple fractions 3. Understands the concept of subtraction of fractions 4. Subtracts simple fractions Benchmark 4. Uses specific strategies (e.g., front-end estimation, rounding) to estimate computations and to check the reasonableness of computational results Knowledge/skill statements 1. Understands the concept of estimation for computations 2. Uses front-end estimation to estimate computations 3. Uses front-end estimation to check reasonableness of computation results 4. Uses rounding to estimate computations 5. Uses rounding to check the reasonableness of computation results Benchmark 5. Performs basic mental computations (e.g., addition and subtraction of whole numbers) Knowledge/skill statements 1. Mentally adds whole numbers 2. Mentally subtracts whole numbers 3. Mentally multiplies whole numbers 4. Mentally divides whole numbers Benchmark 6. Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers Knowledge/skill statements 1. Determines the effects of addition on the size and order of numbers 2. Determines the effects of division on the size and order of numbers 3. Determines the effects of subtraction on the size and order of numbers 4. Determines the effects of multiplication on the size and order of numbers Benchmark 7. Understands the properties of and the relationships among addition, subtraction, multiplication, and division (e.g., reversing the order of two addends does not change the sum; division is the inverse of multiplication) Knowledge/skill statements 1. Understands that multiplication and division are inverse operations 2. Understands multiplication as repeated addition 3. Understands division as repeated subtraction 4. Understands effects of reversing order of things added 5. Understands effects of reversing order of things subtracted 6. Understands effects of reversing order of things multiplied 7. Understands effects of reversing order of things divided Benchmark 8. Solves real-world problems involving number operations (e.g., computations with dollars and cents) Knowledge/skill statements 1. Solves money-based problems using multiplication 2. Solves money-based problems using division 3. Solves money-based problems using addition 4. Solves money-based problems using subtraction 5. Determines whether a real-world problem can be solved with computation Benchmark 9. Knows the language of basic operations (e.g., "products," "multiplication") Knowledge/skill statements 1. Understands the term "addend" 2. Understands the term "sum" 3. Understands the term "minuend" 4. Understands the term "subtrahend" 5. Understands the term "difference" 6. Understands the term "product" 7. Understands the term "divisor" 8. Understands the term "dividend" 9. Understands the term "quotient" Standard 4. Understands and applies basic and advanced properties of the concepts of measurement Benchmark 1. Understands the basic measures perimeter, area, volume, capacity, mass, angle, and circumference Knowledge/skill statements 1. Understands the concept of circumference 2. Understands the concept of perimeter 3. Understands the concept of mass 4. Understands the concept of angle 5. Understands the concept of volume 6. Understands the concept of area 7. Understands the concept of capacity Benchmark 2. Selects and uses appropriate tools for given measurement situations (e.g., rulers for length, measuring cups for capacity, protractors for angle) Knowledge/skill statements 1. Selects appropriate tools for given measurement situations 2. Uses appropriate tools for given measurement situations 3. Selects appropriate tool to measure temperature 4. Uses a thermometer to measure temperature 5. Selects appropriate tools to measure length 6. Uses a ruler to measure length 7. Selects appropriate tools to measure width 8. Uses a ruler to measure width 9. Selects appropriate tools to measure height 10. Uses a ruler to measure height 11. Selects appropriate tools to measure mass 12. Uses a scale to measure mass 13. Selects appropriate tools to measure capacity 14. Uses measuring cups to measure capacity 15. Selects appropriate tool to measure angles 16. Uses a protractor to measure angles Benchmark 3. Knows approximate size of basic standard units (e.g., centimeters, feet, grams) and relationships between them (e.g., between inches and feet) Knowledge/skill statements 1. Knows the approximate size of a centimeter 2. Knows the approximate size of a meter 3. Knows the approximate size of an inch 4. Knows the approximate size of a foot 5. Knows the approximate weight of an ounce 6. Knows the approximate weight of a pound 7. Knows the approximate weight of a gram 8. Knows the approximate weight of a kilogram 9. Knows the relationship between an inch and a foot 10. Knows the relationship between a centimeter and a meter 11. Knows the relationship between an ounce and a pound 12. Knows the relationship between a gram and a kilogram Benchmark 4. Understands relationships between measures (e.g., between length, perimeter, and area) Knowledge/skill statements 1. Understands the relationship between length and perimeter 2. Understands the relationship between length and area 3. Understands the relationship between perimeter and area Benchmark 5. Understands that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times) Knowledge/skill statements 1. Understands that repeated measures may yield different numbers 2. Understands that measurement is not exact Benchmark 6. Uses specific strategies to estimate quantities and measurements (e.g., estimating the whole by estimating the parts) Knowledge/skill statements 1. Estimates measurement of whole by estimating parts 2. Uses specific strategies to estimate quantities 3. Uses specific strategies to estimate measurements Benchmark 7. Selects and uses appropriate units of measurement, according to type and size of unit Knowledge/skill statements 1. Selects measurement units based on the size of measure needed 2. Knows that certain measurement tools are used for certain sizes of measurement 3. Selects measurement units based on the type of measure needed Standard 5. Understands and applies basic and advanced properties of the concepts of geometry Benchmark 1. Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere) Knowledge/skill statements 1. Understands the concept of a trapezoid 2. Understands the concept of a parallelogram 3. Understands the concept of a sphere 4. Understands the concept of a cube Benchmark 2. Understands basic properties of figures (e.g., two- or three-dimensionality, symmetry, number of faces, type of angle) Knowledge/skill statements 1. Understands the concept of two-dimensionality 2. Understands the concept of three-dimensionality 3. Understands the concept of symmetry 4. Understand the defining number of faces for a three-dimensional object 5. Understands that objects have a defining number and types of angles Benchmark 3. Predicts and verifies the effects of combining, subdividing, and changing basic shapes Knowledge/skill statements 1. Predicts the effects of subdividing shapes 2. Predicts the effects of changing shapes 3. Predicts the effects of combining shapes 4. Verifies the effects of subdividing shapes 5. Verifies the effects of changing shapes 6. Verifies the effects of combining shapes Benchmark 4. Understands that shapes can be congruent or similar Knowledge/skill statements 1. Understands the concept of similar shapes 2. Understands the concept of congruent shapes Benchmark 5. Uses motion geometry (e.g., turns, flips, slides) to understand geometric relationships Knowledge/skill statements 1. Understands the concept of motion geometry 2. Understands the concept of slides 3. Understands the concept of turns 4. Understands the concept of flips Benchmark 6. Understands characteristics of lines (e.g., parallel, perpendicular, intersecting) and angles (e.g., right, acute) Knowledge/skill statements 1. Understands the concept of intersecting lines 2. Understands the concept of perpendicular lines 3. Understands the concept of parallel lines 4. Understands the concept of an obtuse angle 5. Understands the concept of an acute angle 6. Understands the concept of a right angle Benchmark 7. Understands how scale in maps and drawings shows relative size and distance Knowledge/skill statements 1. Understands how scale in maps and drawings depicts relative distance 2. Understands how scale in maps and drawings depicts relative size Standard 6. Understands and applies basic and advanced concepts of statistics and data analysis Benchmark 1. Understands that data represent specific pieces of information about real-world objects or activities Knowledge/skill statements 1. Understands that data represents specific pieces of information about the real world Benchmark 2. Understands that spreading data out on a number line helps to see what the extremes are, where the data points pile up, and where the gaps are Knowledge/skill statements 1. Understands the concept of gaps in data 2. Understands the concept of extremes in data 3. Understands the concept of clusters in data 4. Uses a number line to see gaps in data 5. Uses a number line to see extremes in data 6. Uses a number line to see clusters in data Benchmark 3. Understands that a summary of data should include where the middle is and how much spread there is around it Knowledge/skill statements 1. Understands the concept of the middle of the data distribution 2. Understands the concept of the spread of data 3. Understands the concept of summarizing data Benchmark 4. Organizes and displays data in simple bar graphs, pie charts, and line graphs Knowledge/skill statements 1. Constructs circle (pie) graphs using data 2. Constructs bar graphs using data 3. Constructs line graphs using data Benchmark 5. Reads and interprets simple bar graphs, pie charts, and line graphs Knowledge/skill statements 1. Interprets bar graphs 2. Interprets circle (pie) graphs 3. Interprets line graphs 4. Reads bar graphs 5. Reads circle (pie) graphs 6. Reads line graphs Benchmark 6. Understands that data come in many different forms and that collecting, organizing, and displaying data can be done in many ways Knowledge/skill statements 1. Understands that data can be organized in many ways 2. Understands that data can be collected in many ways 3. Understands that data can be displayed in many ways 4. Understands that data comes in different forms Benchmark 7. Understands the basic concept of a sample (e.g., a large sample leads to more reliable information; a small part of something may have unique characteristics but not be an accurate representation of the whole) Knowledge/skill statements 1. Understands that a small sample of something may be unique and not representative of the whole 2. Understands the basic concept of a sample 3. Understands that large sample sizes lead to more reliable information Standard 7. Understands and applies basic and advanced concepts of probability Benchmark 1. Understands that the word "chance" refers to the likelihood of an event Knowledge/skill statements 1. Understands the concept of "chance" Benchmark 2. Recognizes events that are sure to happen, events that are sure not to happen, and events that may or may not happen (e.g., in terms of "certain," "uncertain," "likely," "unlikely") Knowledge/skill statements 1. Identifies events that are sure to happen 2. Identifies events that may or may not happen 3. Identifies events that are sure not to happen 4. Understands the term "certain" 5. Understands the term "uncertain" 6. Understands the term "likely" 7. Understands the term "unlikely" Benchmark 3. Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event Knowledge/skill statements 1. Understands that predictions assume that things will stay the same 2. Understands that predictions apply to the frequency of occurrence better than to specific events Benchmark 4. Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents) rather than which individuals within the group will experience something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur Knowledge/skill statements 1. Understands that predictions apply to proportions of groups better than individuals 2. Understands that predictions apply to how often events will occur better than when events will occur Benchmark 5. Uses basic sample spaces (i.e., the set of all possible outcomes) to describe and predict events Knowledge/skill statements 1. Understands the concept of sample space 2. Uses basic sample spaces (set of all outcomes) to describe events 3. Uses basic sample spaces (set of all outcomes) to predict events Standard 8. Understands and applies basic and advanced properties of functions and algebra Benchmark 1. Recognizes a wide variety of patterns (e.g., basic linear patterns such as [2, 4, 6, 8 . . .] ; simple repeating and growing patterns) and the rules that explain them Knowledge/skill statements 1. Understands the concept of a growing pattern 2. Understands the concept of a simple repeating pattern 3. Recognizes linear patterns 4. Recognizes increasing patterns 5. Recognizes decreasing patterns 6. Recognizes the rules that explain simple patterns Benchmark 2. Understands that the same pattern can be represented in different ways (e.g., geometrically or numerically; the pattern of numbers [7, 14, 21, 28 . . .] is equivalent to the mathematical relationship 7 × n) Knowledge/skill statements 1. Understands that patterns can be represented numerically 2. Understands that patterns can be represented geometrically 3. Represents simple patterns geometrically 4. Represents simple patterns numerically Benchmark 3. Knows that a variable is a letter or symbol that stands for one or more numbers 1. Understands that a letter or symbol can stand for one or more numbers Benchmark 4. Understands the basic concept of an equality relationship (i.e., an equation is a number sentence that shows two quantities that are equal) Knowledge/skill statements 1. Understands the concept of an equation Benchmark 5. Solves simple open sentences involving operations on whole numbers (e.g., ? + 17 = 23) Knowledge/skill statements 1. Understands the concept of an open sentence Benchmark 6. Knows basic characteristics and features of the rectangular coordinate system (e.g., the horizontal axis is the X axis and the vertical axis is the Y axis) Knowledge/skill statements 1. Understands the horizontal axis is the X axis 2. Understands the vertical axis is the Y axis 3. Knows that the X axis and the Y axis are perpendicular 4. Knows the rectangular coordinate system is divided into four quadrants Standard 9. Understands the general nature and uses of mathematics Benchmark 1. Understands that numbers and the operations performed on them can be used to describe things in the real world and predict what might occur Knowledge/skill statements 1. Understands that operations on numbers apply to real world situations 2. Understands that numbers apply to real world situations 3. Understands that numbers can be used to predict what might occur in the real world 4. Understands that operations on numbers can be used to predict what might occur in the real world Benchmark 2. Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically Knowledge/skill statements 1. Understands that mathematical ideas can be represented concretely 2. Understands that mathematical concepts can be represented graphically 3. Understands that mathematical concepts can be represented symbolically |
3-5 Mathematics |