Math Curriculum Kearney Public Mission Statement Create an environment that fosters mutual respect Inspire the love of learning Expect Excellence

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1 Math Curriculum Kearney Public Mission Statement Create an environment that fosters mutual respect Inspire the love of learning Expect Excellence from all Kearney Public Schools Math Purpose Statement Students completing the Kearney Public Schools mathematics curriculum will learn and communicate the value of mathematics and the quantitative nature of our world. Students will become mathematical problem solvers by understanding and connecting fundamental mathematical concepts, including the ability to perform routine computations and symbolic manipulations. Board of Education Approved-October 3, 2011 Page 1

2 Kindergarten Math Kindergarten Math Course Purpose Students in kindergarten will solve problems by thinking logically, communicating athematically and working both individually and cooperatively. Students will be mathematically competent in the following Students will demonstrate ways of representing whole numbers through identification and correct formation Distinguish relationships among whole numbers within the base-ten number system 0-20 Sort, classify and order objects by relationships M.K.01 Students will write numbers 0-20 with correct formation. Students will demonstrate knowledge of numerical order for numbers State Standards (0.1.1) Make lines from top to bottom Make lines from left to right Form numbers with Zaner Bloser guide path Construct groups of objects for numbers 0-20 Rote count to 20 Order numbers 0-20 from random order into numerical order M.K.02 Students will match sets of 0-10 objects with numerals. (These sets will be groups of mixed items or similar items.) Students will demonstrate concrete knowledge of number sets. State Standards (0.1.1) Build sets of numbers 0-10 with all like items o i.e. 10 bears Build sets of numbers 0-10 with unlike items o i.e. 6 bears and 4 frogs, 6 and 4 in a set equals 10 in the set 2 M.K.03 Students will sort, classify and create patterns with objects by relationships. State Standards (0.3.1) Sort objects by color Sort objects by shape Sort objects by size Sort objects by unique sorting attributes Explain and verify with language sorting rules used Extend created two part patterns o i.e. what comes next Use sets of sorted objects to build two part patterns Use sets of objects to create unique patterns that repeat Identify and explain patterns and relationships that are created Classify patterns o i.e. AB Board of Education Approved-October 3, 2011 Page 2

3 M.K.04 Students will identify two-dimensional geometric shapes and demonstrate knowledge of positional words. State Standards (0.2.1, 0.2.4) Sort and name 2 dimensional shapes o Square, triangle, circle, rectangle Demonstrate positional words o Above, below, near, far, over, under, in, out, down, up, around, and through M.K.05 Students will demonstrate the meaning of addition and subtraction with whole numbers. State Standards (0.1.2, 0.3.2, 0.3.3) Use objects and words to explain addition as a joining action Use objects and words to explain the meaning of addition as parts of a whole Use objects and words to explain the meaning of subtraction as a separation action Use objects and words to explain the meaning of subtraction as finding part of a whole Use concrete and verbal representations to solve number stories M.K.06 Students will identify and sort the penny, nickel, dime, and quarter. State Standards (0.2.5) Describe the attributes of a penny o i.e. color, size, edge texture, heads and tails Describe the attributes of a nickel Describe the attributes of a dime Describe the attributes of a quarter Identify the four coins Sort the four coins into like groups M.K.07 Students will sort, classify, and group concrete manipulative data into graphs and make comparisons using that information. State Standards (0.4.1) Examine graphs cooperatively Identify parts of graph Create graphs with manipulatives Classify information on the graph Make comparisons using a graph M.K.08 Students will measure using nonstandard units of measure. State Standards (0.2.5) Express knowledge of long and short with examples Order shortest to longest and longest to shortest Board of Education Approved-October 3, 2011 Page 3

4 Begin measuring objects by length at the edge of the manipulative Express the length of objects using nonstandard units of measure o i.e. variety of manipulative M.K.09 Students will communicate knowledge of their personal numbers and apply to daily tasks. State Standards Recite phone number Recite birth date Recite address Recite library and lunch number and apply this knowledge to check out books and utilize the cafeteria M.K.10 Students will express knowledge of time and discriminate a sequence of events. State Standards (0.2.5) Identify clock as a means to tell time Identify hour hand and minute hand Utilize terms first, next and last to Discriminate a sequence of events M.K.11 Students will use a calendar to express knowledge of time verbally. State Standards Identify seasons through picture discrimination Identify days of the week on a calendar Identify months of the year on a calendar Identify yesterday, today, and tomorrow verbally Use the calendar to identify and express the date verbally Board of Education Approved-October 3, 2011 Page 4

5 First Grade Math First Grade Math Course Purpose Students in first grade will solve problems by thinking logically, communicating mathematically and working both individually and cooperatively. Students will be mathematically competent in the following K- 12 mathematics outcomes. Students will: Demonstrate the meaning of addition and subtraction with whole numbers 0-20 Count, read and write numbers to 100 Demonstrate number understanding by identifying numbers that come before, after or between ADDITION AND SUBTRACTION M Students will demonstrate the meaning of addition and subtraction with whole numbers State Standards (1.1.2, 1.1.3, 1.3.2, 1.3.3) Use objects, drawings, words and symbols to explain addition as a joining action, parts of a whole and the commutative property Use objects, drawings, words and symbols to explain subtraction as a separation action, finding part of a whole and comparison Apply knowledge of basic addition and subtraction to compute two digit equations Fluently add and subtract whole numbers to 10 Write number sentences to represent fact families Use a variety of methods and tools to compute sums and differences NUMBER SENSE M Students will demonstrate whole numbers, ways of representing whole numbers and relationships among whole numbers within the base-ten number system. State Standards (1.1.1, 1.2.2, 1.3.1) Count, read and write numbers by 1 s, 5 s and 10 s Count, read and write numbers 0-50 by 2 s Connect number words to the quantities they represent 0-20 Demonstrate and identify multiple equivalent representations for numbers Use place value to compare and order whole numbers Demonstrate relative position of whole numbers Identify the position of a whole number on a horizontal number line Count backwards from 10-0 Sequence objects using ordinal numbers (first-tenth) Use <, =, > to compare quantities GEOMETRY Board of Education Approved-October 3, 2011 Page 5

6 M Students will identify characteristics of two-dimensional geometric shapes. State Standards (1.2.1, 1.2.3) Compare two-dimensional shapes o Square, circle, rectangle, and triangle Describe attributes of two-dimensional shapes Sketch two-dimensional shapes (square, circle, rectangle and triangle) Identify one line of symmetry in two-dimensional shapes MEASUREMENT M Students will measure using standard units. State Standards (1.2.5) Measure length using inches Compare and order objects according to length Select appropriate tool to measure o Clock, calendar, thermometer, scale and ruler M Students will tell time using analog and digital clocks. State Standards (1.2.5) MONEY Identify time to the half hour and hour Identify past, present and future as orientation in time Use calendar to identify days, months, and dates M Students will recognize and count coins. State Standards (1.2.5) Identify name and value of penny, nickel, dime and quarter Count like coins to $1.00 RELATIONSHIPS M Students will identify and describe relationships. State Standards (1.1.2, 1.3.1) Sort or order objects by their attributes o Color, shape, size, number Identify the classifying attribute Create multiple rules for sorting beyond color, shape and size Identify, describe and extend patterns Describe and model quantitative change (eg. growing taller) Board of Education Approved-October 3, 2011 Page 6

7 DATA ANALYSIS M Students will sort, classify, organize, describe and compare data. State Standards (1.3.1, 1.4.1) Sort and classify objects by more than one attribute Organize data by using concrete objects Represent data by using tally marks Compare and interpret information from displayed data o More, less, and fewer Create and read bar graphs and pictographs Board of Education Approved-October 3, 2011 Page 7

8 Second Grade Math Second Grade Math Course Purpose Students in second grade will solve problems by thinking logically, communicating mathematically, and working both individually and cooperatively. Students will be mathematically competent in the following outcomes. Students will compute fluently addition and subtraction with whole numbers 0-18 PLACE VALUE M Students will demonstrate ways of representing whole numbers, and relationships among whole numbers within the base-ten number system. State Standards (2.1.1) Identify values of numbers zero to one-thousand Model numbers zero to one-thousand using base-ten blocks Identify odd & even numbers zero through one-thousand Identify and list numbers zero to one-thousand Demonstrate multiple equivalent representations for numbers one to one-thousand o e.g. 423=4hundreds+2tens+3ones OR 3hundreds+12tens+3ones Compare and order whole numbers Round two-digit numbers to the nearest ten Demonstrate relative position of whole numbers zero to one-thousand greater than, less than, or equal to o e.g. 624 is between 600 and 700 ADDITION & SUBTRACTION M Students will demonstrate the meaning of addition and subtraction with whole numbers. They will compute fluently using appropriate strategies and tools. They will estimate and check reasonable sums and differences. State Standards (2.1.2, 2.1.3, 2.1.4) Use objects, drawings, words, and symbols to explain the relationship between addition and subtraction Identify the direction moved for adding and subtracting using a horizontal number line Compare whole numbers using location on a horizontal number line Compute fluently add / subtract whole numbers 0-18 Add three one-digit numbers Use a variety of methods and tools to compute sums and differences o e.g. models, mental, computation, and paper pencil Solve addition and subtraction problems using two-digit whole numbers with regrouping Estimate the sums and differences of two-digit whole numbers Use objects, drawings, words, and symbols to explain the use of subtraction to find a missing addend Use objects, drawings, words, and symbols to explain the use of addition to find a missing subtrahend Board of Education Approved-October 3, 2011 Page 8

9 Identify fractional parts of a whole o 1/2, 1/3, 1/4 GEOMETRY M Students will describe characteristics of two-dimensional shapes and identify threedimensional objects. State Standards (2.2.1, 2.2.2, 2.2.3, 2.2.4) Draw and describe attributes of two-dimensional shapes Identify triangular and rectangular prisms Identify cones, cylinders, pyramids, and spheres Identify numbers using location on a vertical number line Identify and draw a line of symmetry in two-dimensional shapes Compare two-dimensional shapes o Trapezoid and parallelogram MEASUREMENT M Students will examine a variety of measurement tools using standard units, time and money. State Standards (2.2.5) ALGEBRA Count mixed coins to $1.00 Identify time to the 5 minute intervals Identify and use appropriate tools for the attribute being measured o e.g. clock, calendar, thermometer, scale, or ruler Measure length using feet and yards Compare and order objects using inches, feet and yards M Students will create, describe, and extend relationships. They will use objects, pictures, and symbols as models to represent mathematical situations. State Standards (2.3.1, 2.3.2, 2.3.3) Create and describe patterns using concrete and pictorial representations Solve symbolic representations of the commutative property of addition o e.g. 2+3=_+2 Model situations that involve the addition and subtraction of whole number zero to one hundred, using objects and number lines Describe and model quantitative change involving addition o e.g. a student grew 2 inches DATA ANALYSIS M.02.6 Students will organize, display, compare, and interpret data. Board of Education Approved-October 3, 2011 Page 9

10 Organize and build data using pictographs Compare and interpret data using pictographs o e.g. 7 more, 2 less, 12 all together State Standards (2.4.1) Board of Education Approved-October 3, 2011 Page 10

11 Third Grade Math Third Grade Math Course Purpose The students will demonstrate application of basic addition, subtraction, and multiplication facts as well as solve multi-step problems. Students will distinguish the place and value of a digit based on its position within a given number through the thousands. Students will classify characteristics and properties of twodimensional shapes and three-dimensional objects. NUMBER SENSE ADDITION AND SUBTRACTION M Students will compute fluently to add and subtract to solve problems through four digit numbers with regrouping. Students will memorize the addition facts with sums from zero to twenty. Students will memorize the subtraction facts with differences from zero to twenty. Students will relate addition and subtraction through the development of fact family tables using three related numerals. Students will define and depict the associative property of addition, which states that the way in which the addends are grouped does not change the sum. Students will define and depict the commutative property of addition, which states that the order of the addends does not change the sum. Students will solve four digit addition problems with regrouping. Students will solve four digit subtraction problems with regrouping. Students will select and apply the appropriate methods when problem solving with four-digit whole numbers through the thousands. Students will model situations that involve addition and subtraction of whole numbers using objects, number lines, and symbols. Use symbolic representation of the identity property of addition o E.g. 3=0+3 PLACE VALUE M Students will use place value to construct numbers and classify numbers through the hundred thousands place by ordering, comparing, rounding, and writing the number in three forms. State Standards (3.1.1, 3.1.4) Students will identify a digit s place value within a number through the hundred thousands place. Students will examine a number to the hundreds place to determine how to round it. Students will give examples of a given number in three forms: word form, expanded form, and numeral form. Students will organize numbers according to their value (least to greatest, greatest to least) Students will use place value skills to compare two numbers. Students will use place value strategies to communicate and demonstrate problem solving. Board of Education Approved-October 3, 2011 Page 11

12 Students will estimate and check reasonableness of answers using appropriate strategies and tools in addition, subtraction, and multiplication. MULTIPLICATION SKILLS M Students will relate multiplication to the process of division. Students will compute their multiplication facts and utilize them to produce three digit products. State Standards (3.1.2, 3.1.3) Students will construct sets for multiples of two, five, and ten to the thousands place. Students will memorize the multiplication facts zero through ten fluently. Students will explain the multiplication concept as an equal number of members in a given number of sets using objects, drawings, words, and symbols to arrive at the product. Students will relate multiplication and division through the development of fact family tables using three related numerals. Students will use multiplication strategies to communicate and demonstrate problem solving. Students will compute products resulting from multiplying two digits by one digit factors. Students will compute using multiplication and estimation to produce a three-digit product. Students will use objects, drawings, words, and symbols to explain the relationship between multiplication and division. Students will develop arrays to explain the meaning of multiplication. FRACTIONS M Students will use visual models to construct fractional parts of a whole and set. State Standards (3.1.1) Students will construct visual models of fractional parts of a whole from halves to the twelfths. Students will use strategies involving fractions to communicate and demonstrate problem solving. Students will construct models of fractional parts of a set from halves to twelfths. Students will identify multiple equivalent representations through the tenths place (3 and 6 tenths = 3.6, 7.4 is 7 +.4) GEOMETRY AND MEASUREMENT GEOMETRY M Students will analyze and differentiate between various geometric figures ranging from lines to three-dimensional shapes. State Standards (3.2.1, 3.2.3, 3.2.4, 3.2.5) Students will make sketches of and label: lines, line segments, and rays. Students will differentiate between parallel and non-parallel lines. Students will make sketches of and label: right, acute, and obtuse angles. Students will construct visual models of right, scalene, isosceles, and equilateral triangles. Board of Education Approved-October 3, 2011 Page 12

13 Students will define similar and congruent two-dimensional shapes. Students will construct visual examples of each. Students will label all the lines of symmetry in a given two-dimensional figure. Students will calculate and record the perimeter of a plane figure using appropriate tools. Students will identify and create two-dimensional shapes incorporating sides, angles, and vertices. Students will use geometric concepts to communicate and demonstrate problem solving. Students will identify and create three-dimensional objects incorporating face, angles, vertices, and edges (triangular prism, rectangular prism, cones, cylinders, pyramids, spheres). MEASUREMENT M Students will demonstrate usage of measurement in time, length, capacity, temperature, weight and money. State Standards (3.2.2, 3.2.5) ALGEBRA Students will identify distance and plot points on a number line. Students will name the days of the week and months of the year in sequential order. Students will state the number of days in a week, months in a year, and days in a year. Students will identify time of day. o e.g. am, pm, noon, midnight Students will state multiple ways for the same time using fifteen-minute intervals o e.g. 2:15, quarter past two, 2:45, or a quarter until 3 Students will locate the correct placement of a decimal point in a given dollar amount. Students will compute the total of a given number of coins and bills to $ Students will compute dollar amounts using addition to $ with or without regrouping. Students will compute the difference of given dollar amounts from $ with or without regrouping. Students will compare and order objects according to length using centimeters and meters. Students will use measurement strategies to communicate and demonstrate problem solving. Students will identify and demonstrate using the appropriate unit for measuring length to the nearest inch or centimeter. Students will identify the appropriate unit for measuring customary capacity. Students will identify the appropriate unit for measuring customary weight. Students will identify the appropriate unit for measuring customary temperature. M Students will deduce the relationships between given symbols to identify patterns. State Standards (3.3.1, 3.3.3) Students will select the correct number(s) to balance an expression to 100. Students will use algebraic concepts to communicate and demonstrate problem solving. Students will identify, describe, and extend numeric and non-numeric patterns. Students will solve simple one-step whole number equations involving addition and subtraction o e.g. Δ +2=3 Board of Education Approved-October 3, 2011 Page 13

14 PROBABILITY AND STATISTICS M Students will organize data by creating and interpreting bar graphs, line graphs, pictographs and plotting ordered pairs. State Standards (3.3.1, 3.4.1, 3.4.2, 3.4.3) Students will predict the outcomes of simple experiments as possible, impossible, likely, unlikely, or certain. Students will use probability and statistics to communicate and demonstrate problem solving. Students will produce charts by collecting and organizing data. Students will create a pictograph using data they have collected. Students will create a bar graph using data they have collected. Students will create a line graph using data they have collected. Students will plot ordered pair coordinates based on data, on an x-y axis. Students will interpret data collected to draw conclusions. Board of Education Approved-October 3, 2011 Page 14

15 Fourth Grade Math Fourth Grade Math Course Purpose Students will communicate place value from hundredths to hundred millions. Students will demonstrate and apply the meaning of multiplication and division with whole numbers. Students will classify, transform, plot, identify, and construct geometric shapes. Students will organize, display, compare, and interpret data using dot/line plots. M Students will produce numbers in word, standard, and expanded form. Students will communicate the value of a given digit in a number and apply those skills to estimate numbers to the nearest 1,000. They will develop efficient procedures on the basis of place value through creating and solving problems. State Standards (4.1.1, 4.1.3) Define periods, place value, standard form, word form, expanded form, rounding, and estimating Reproduce numbers in word, standard, and expanded form Identify digits in a given period of a value Round numbers to the given place value Apply rounding to estimation of sums and differences Represent the idea of a variable as an unknown quantity using a letter or symbol Compare and order whole numbers 1 3 M Students will model multiplication and properties of operations as they develop methods to multiply multi-digit whole numbers. They will demonstrate fluency for multiplying whole numbers and apply the procedures to solve problems. State Standards (4.1.3, 4.1.4, 4.3.1, 4.3.2, 4.3.3) Define factors, product, multiples, and basic facts Memorize basic multiplication fact 0-10 Demonstrate the multiplication properties: zero, identity property, associative, and commutative Compute two-digit by one-digit factors Compute up to three-digit by two-digit factors Estimate the product and check for accuracy Demonstrate fluency for multiplying whole numbers and apply the procedures to solve problems Identify and calculate simple one-step whole number equations Mentally compute multiplication involving powers of 10 M Students will model division as they develop methods to divide whole numbers. They will demonstrate fluency for dividing whole numbers and apply the procedures to solve problems. State Standards (4.1.2, 4.1.3, 4.1.4, 4.3.3) Define divisor, dividend, quotient, remainder Memorize basic division facts 0-10 Give examples of horizontal, bracket, and vertical forms of division Compute two-digit by one-digit problems without and with remainders Board of Education Approved-October 3, 2011 Page 15

16 Compute three-digit by one-digit problems without and with remainders. Justify the quotient by checking with multiplication Estimate the quotient and check for accuracy Demonstrate fluency for dividing whole numbers and apply the procedures to solve problems Mentally compute and use drawings, words, and symbols to explain the meaning of division Mentally compute division involving powers of 10 M Students will choose the appropriate metric or customary unit to measure length, weight, capacity, and temperature. They will demonstrate proper procedures and use tools to determine measurement using customary and metric units. State Standards (4.2.5) Define meter, liter, gram, inch, pounds, liquid capacity, Celsius, and Fahrenheit Estimate and measure to the nearest cm and mm, 1 to the nearest ml, and g to kg Convert meter, liter, and gram measures Differentiate between yards, pounds, and liquid capacity Estimate and measure to the nearest ½ inch, pound, and liquid ounce Measure and convert length, capacity, and weight measurement in customary units Demonstrate proper procedures and use tools to determine measurement using customary and metric units Identify time to the minute on an analog clock Solve problems involving elapsed time Determine the appropriate time to use the various customary or metric units of measure (length, weight, capacity) M Students will classify two-dimensional and three-dimensional objects according to their sides and angle properties. They will identify lines, angles, properties of congruency, and simple transformations. They will differentiate between and construct geometric shapes according to their properties. State Standards (4.2.2, 4.2.3, 4.2.4, 4.2.5) Define polygons, three-dimensional, lines, angles, congruency, and transformations Identify parallel, perpendicular, and intersecting lines Classify an angle as acute, obtuse, and right Identify the properties of congruent and similar shapes Distinguish polygons according to sides and angles and calculate perimeter using appropriate tools Identify simple transformations translations, reflection, and rotation Identify names of three-dimensional objects Differentiate between and construct geometric shapes according to their properties Identify the ordered pair of a plotted point in the first quadrant Identify spatial models and use to solve problems M Students will organize, display, compare, and interpret data using dot/line plots. They will make predictions based on data. They will differentiate between mean, median, Board of Education Approved-October 3, 2011 Page 16

17 mode, and range. They will utilize data analysis/probability concepts to reason and solve problems. State Standards (4.4.1, 4.4.2, 4.4.3) Define dot/line plot, prediction, mean, median, mode, and range Calculate and interpret the mean, median, mode, and range Construct dot/line plots from given data Describe the probability of an event using the terms more, less, and equally likely Utilize data analysis/probability concepts to reason and solve problems Make predictions based on data to answer questions from the tables and graphs M Students will model, order and represent fractions and decimals. Students will compute with addition and subtraction numbers to the hundredths place. State Standards (4.1.1) Represent benchmark fractions as parts of a whole or parts of a set (1/2, 1/3, 2/3, 1/4, 3/4) with pictures Represent with pictures (graph paper) decimal values to the hundredths place and express in standard, expanded and word form Compare and order fractions, mixed numbers, and decimals on a number line Reduce fractions to simplest form Add and subtract decimals to the hundredths place (money) Understand the relationship between fractions and division Board of Education Approved-October 3, 2011 Page 17

18 Fifth Grade Math Fifth Grade Math Course Purpose Fifth grade math students will apply mathematical concepts and computational skills in reasoning, communicating, and problem solving. Students will: Demonstrate the appropriate use of number concepts, relationships, and operations by adding, subtracting, multiplying and dividing decimals; adding, subtracting, and multiplying fractions Utilize the properties and relationships of geometric shapes and values to interpret their relative positions by determining congruency, area, perimeter, edges, faces, and vertexes Demonstrate the ability to identify and compare unit values in building and interpreting data by building bar, line, and pictographs M Students will communicate the value of a given digit in a number and apply those skills to round and estimate numbers ranging from billions to thousandths. Students will demonstrate efficient computation procedures on the basis of place value and examination of properties to solve problems. State Standards (5.1.1g, 5.1.2b, 5.1.2c, 5.1.4, 5.3.3b) Define place value, standard form, word form, rounding, estimating, and periods Identify the value of a digit from billions to thousandths place Round numbers and decimals to the given place value Apply rounding to estimate and check reasonableness of answers Compute fluently and accurately Use words and symbols to explain the meaning of the identity commutative, associative, and distributive properties of addition Use words and symbols to explain the meaning of the commutative, associative, and distributive properties of multiplication Demonstrate efficient computation to solve problems with the use of properties, place value, regrouping, rounding, and estimating Demonstrate multiple equivalent representations for whole numbers and decimals through the thousandths place o e.g is ) M Students will demonstrate knowledge of decimals, factors, fractions, and mixed numbers through computation. State Standards (5.1.1a, 5.1.1b, 5.1.1c, 5.1.1d, 5.1.1e, 5.1.1f, 5.1.3a, 5.1.3d, 5.1.3b) Compare and order decimals through thousandths Accurately add, subtract, multiply, and divide decimals through thousandths Demonstrate knowledge of prime numbers, greatest common factors, and lowest common multiples Simplify, order, and compare fractions Compute fluently and accurately addition, subtraction, and multiplication of fractions with like and unlike denominators Board of Education Approved-October 3, 2011 Page 18

19 Compute fluently and accurately addition and subtraction mixed numbers with like and unlike denominators Recognize and generate equivalent forms of commonly used fractions, decimals, and percents o i.e..10,.25,.50,.75,.100 Demonstrate efficient computation to solve problems using decimals, factors, fractions, and mixed numbers Select, apply, and explain the appropriate method of computation when problem solving o e.g. models, mental computation, paper/pencil, and technology M Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. State Standards (5.2.1a, 5.2.1b, 5.2.1c, 5.2.1d, 5.2.2a, 5.2.3a, 5.2.5a, 5.2.5f) Identify geometric shapes of rectangle, square, rhombus, parallelogram, triangle, and circle Perform one-step translations, reflections, and rotations of 90, 180, and 270 on two dimensional shapes Justify congruence of two-dimensional shapes Identify the number of edges, faces, and vertices of triangular and rectangular prisms Accurately measure and label angels of 40, 45, 90, and 120 Identify 45, 90, 180, 270, and 360 on a circle Apply formulas to determine the perimeter and area of rectangles and squares Plot the location of an ordered pair in the first quadrant Demonstrate knowledge of geometric concepts and measurement through reasoning, solving problems, and making connections within mathematics and across disciplines. Justify the classification of two dimensional shapes o i.e. triangles, by-angles, and sides M Students will apply appropriate procedures and tools to determine measurements using customary and metric units. State Standards (5.2.5b, 5.2.5c, 5.2.5d, 5.2.5e) Estimate and measure length with customary units to the nearest % inch Measure capacity and volume with customary units Measure weight (mass) and temperature using metric units Select appropriate measurement tool and correctly identify unit (customary or metric), to the measurement situation. Solve problems involving elapsed time Demonstrate appropriate procedures and tools to determine measurements (customary and metric units) M Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. State Standards (5.3.2abc, 5.3.1abc, 5.4.1abcde, 5.4.2a, 5.4.3abc) Perform and record results of probability experiments Create a list of possible outcomes for a simple event Board of Education Approved-October 3, 2011 Page 19

20 Explain that the likelihood of an event can be represented by a number from 0 (impossible) to 1 (certain) Demonstrate the comparison of two numbers using ratio Organize and represent data using a line graph, pictograph, bar graph, and circle graph Predict and make conclusions based on a set of data Find the mean, median, mode and range of a set of numbers Demonstrate appropriate concepts using multiple representations of data analysis/probability Generate questions and answers from data sets and their graphical representations Model situations that involve the addition, subtraction, and multiplication of positive, rational numbers using words, graphs, and tables Compare different models to represent mathematical situations M Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. State Standards (5.3.3a, 5.3.3c, 5.3.3d, 5.3.3e, 5.3.3f) Communicate relationships using expressions and equations Evaluate numerical expressions by using parentheses with respect to order of operations Explain the addition property of equality o If A=B, then A+C=B+C Use symbolic representations of the associative property o ((2+3)+4=2+(3+n), (2x3)x4=2x(3xn)) Create and analyze numeric and non-numeric patterns using words, tables, and graphs Demonstrate appropriate algebraic concepts to solve problems and make connections within mathematics and across disciplines Identify and explain the properties of equality used in solving one step equations involving common positive, rational numbers Evaluate simple algebraic expressions involving addition and subtraction M Students will create and use geometric models to solve problems State Standards (5.2.4a, 5.2.4b, 5.2.4c) Build or sketch geometric model to solve a problem Sketch congruent shapes Build rectangular prisms using cubes M Students will represent, analyze, and generalize relationships State Standards (5.3.1a, 5.3.1b, 5.3.1c) Describe, extend, and apply rules and make generalizations about numeric and geometric patterns Create and analyze numeric patterns using words, tables, and graphs Communicate relationships using expressions and equations Board of Education Approved-October 3, 2011 Page 20

21 Sixth Grade Math Sixth Grade Math Course Purpose Sixth grade math students will compute, compare, estimate, and problem solve using decimals, fractions, and mixed numbers. Students will apply, convert, and estimate units of customary and metric measurement. FRACTIONS M Students will communicate the concept of a fraction. They will fluently compute fractions using all four mathematical operations. They will apply their knowledge of fractions to real world situations through problem solving activities. State Standards (6.1.2, 6.1.3, 6.1.4) DECIMALS Demonstrate relative size of a fraction by estimating to 0, '/2, 1 Apply factors, multiples, common factors, simplest terms, greatest common factors, and least common multiples to fractions when computing Find equivalent fractions Give fractions in lowest terms Compare and order fractions by size Change a mixed number into an improper fraction and an improper fraction into a mixed number Add and subtract fractions with like and unlike denominators Add and subtract mixed numbers with regrouping and borrowing Multiply and divide fractions and mixed numbers Rename a fraction as a decimal Use estimation to justify reasonableness of solutions Integrate fraction concepts into real world problem solving situations M Students will communicate the concept of decimals. They will fluently compute decimals using all four mathematical operations. They will apply their knowledge of decimals to real world situations through problem solving activities. State Standards (6.1.2, 6.1.3, 6.1.4) Demonstrate the relative size of decimals by estimating to 0, %2, 1 Compare and order decimals by size Add and subtract numbers containing decimals by correctly aligning the decimal points Multiply numbers containing decimals with the appropriate placement of the decimal point in the product Divide numbers containing decimals and divide by numbers containing decimals placing a decimal point correctly in the quotient Use estimation to justify reasonableness of solutions Rename a decimal as a fraction Integrate decimal concepts into real world problem solving situations Board of Education Approved-October 3, 2011 Page 21

22 GEOMETRY M Students will evaluate two dimensional and three dimensional figures. They will apply their knowledge of geometric concepts by utilizing real world applications. State Standards (6.2.1, 6.2.3, 6.2.4, 6.2.5) Draw, name, compare, and contrast two-dimensional and three-dimensional figures Calculate perimeter of polygons Calculate areas of squares, rectangles, and triangles Calculate volume of rectangular prisms Identify and draw the transformations: reflections, translations, and rotations Integrate geometric concepts into real world problem solving situations MEASUREMENT M Students will utilize systems of measurement to estimate and measure length, weight (mass), and volume. They will apply their knowledge of measurement to real world situations through problem solving processes. State Standards (6.2.5) Estimate and measure customary units of length (to the nearest sixteenth of an inch), weight (mass), and volume Estimate and measure metric units of length, weight (mass), and volume Add and subtract units of measure and time Convert units within the customary system of measure Convert units within the metric system of measure Apply measurement concepts to solve problems in real world situations DATA ANALYSIS AND PROBABILITY M Students will collect, analyze, and present data using central tendencies. They will interpret and make predictions using real world data from tables and graphs. State Standards (6.3.2, 6.4.1, 6.4.2, 6.4.3) Find mean, median, mode, and range from a set of data Compare the central tendencies of multiple sets of data Apply central tendencies to real world situations Analyze tables and graphs to draw conclusions and make predictions Interpret and construct stem and leaf plots, histograms, and frequency charts using real world information Make predictions using probability ALGEBRAIC CONCEPTS M Student will integrate basic algebraic strategies to solve problems. State Standards (6.1.1, 6.2.2, 6.3.1, 6.3.3) Board of Education Approved-October 3, 2011 Page 22

23 Apply order of operations to basic expressions Find relationships in a set of numbers to establish and extend patterns Solve whole number equations using a variable for all four operations Utilize a number line to verify the value of positive and negative integers Identify and plot points on a coordinate plane Apply algebraic concepts to solve problems in real world situations Board of Education Approved-October 3, 2011 Page 23

24 Seventh Grade Math Seventh Grade Math Course Purpose Seventh grade math students will make connections between fractions, decimals, and percents while fluently computing and converting these rational numbers. Students will develop algebraic skills using integers, expressions, and equations. Students will apply geometric concepts of perimeter and area to circles and complex polygons. FRACTIONS M Students will compute fluently with fractions using all four operations. They will estimate and check reasonableness of answers. Students will apply fraction operations to solve real world problems. State Standards (7.1.2, 7.1.3, 7.1.4) DECIMALS Add and subtract fractions, estimating, and checking for reasonable answers Explain the meaning of multiplication and division of fractions using words and pictures Multiply and divide fractions, estimating, and checking for reasonable answers Define, represent, and utilize ratios with data Select and apply the appropriate operation and method of computation when problem solving o Models, mental computation, paper-pencil, technology M Students will compute fluently with decimals using all four operations. Students will estimate and check reasonableness of answers. Students will apply decimal operations to solve real world problems. State Standards (7.1.2, 7.1.3, 7.1.4) Add and subtract decimals, estimating, and checking for reasonable answers Explain the meaning of multiplication and division of decimals using words and pictures Multiply and divide decimals, estimating and checking for reasonable answers Select and apply the appropriate operation and method of computation when problem solving o Models, mental computation, paper-pencil, technology CONNECTING FRACTIONS, DECIMALS AND PERCENTS M Students will demonstrate equivalencies between fractions, decimals and percents. They will compute common percentages mentally, solving complex percentages by estimating and utilizing technology. Students will solve real world percentage problems. State Standards (7.1.1, 7.1.2, 7.1.3, 7.1.4) Define and model percents Connect and convert percents to fractions and decimals Compare and order fractions, decimals, and percents Board of Education Approved-October 3, 2011 Page 24

25 INTEGERS Mentally compute common percents Calculate complex percents Estimate percentages and check for reasonable answers Apply percents using word problems M Students will relate integers to the real world. Students will demonstrate the meaning of operations with integers using models to help make connections to computation rules and to solve word problems. State Standards (7.1.2, 7.1.3, 7.2.2, 7.3.3) Relate integers with real world situations Represent integers using models Plot the location of an ordered pair on the coordinate plane Identify the location of a point on a coordinate plane Compare and order integers Model addition of integers Add integers checking for reasonable answers Model subtraction of integers Subtract integers checking for reasonable answers Model multiplication of integers Multiply integers checking for reasonable answers Model division of integers Divide integers checking for reasonable answers Solve word problems using integers ALGEBRA CONCEPTS M Students will write, simplify, and evaluate expressions. They will represent and analyze equations using algebraic models. Students will solve one and two-step equations. Students will use expressions and equations to make connections to the real world. State Standards (7.3.1, 7.3.2, 7.3.3) Evaluate numerical expressions containing multiple operations with respect to the order of operations Combine like terms to simplify algebraic expressions Write algebraic expressions as verbal phrases and verbal phrases as algebraic expressions Evaluate variable expressions given the value of the variables Represent and analyze equations using algebraic models Solve one-step equations with integers Solve two-step equations with whole numbers Utilize expressions and equations to make connections with the real world AREA AND PERIMETER Board of Education Approved-October 3, 2011 Page 25

26 M Students will investigate and apply the perimeter and area of triangles, parallelograms, trapezoids, irregular shapes and circles. Students will apply perimeter and area concepts to solve real world problems. State Standards (7.2.1, 7.2.4, 7.2.5) Define and identify characteristics of polygons Define and identify characteristics of circles Model and discover the meaning of pi Determine the circumference of a circle and the perimeter of polygons Discover the connections between the area of triangles, parallelograms, trapezoids, and circles using models Determine the area of polygons and circles Compare and contrast area and perimeter Apply perimeter, area, and measurement to solve real world problems GEOMETRY M Students will investigate and apply transformations and symmetry to analyze geometric shapes. Students will estimate, measure, and draw angles. Students will describe, compare, and contrast characteristics and relationships of lines and geometric shapes. State Standards (7.2.1, 7.2.3, 7.2.4, 7.2.5) GRAPHING Identify lines of symmetry for reflection on a coordinate plane Perform and describe positions and orientation of shapes under a single transformation (translation, rotations or reflection) on a coordinate plane Measure and draw angles to the nearest degree Identify and describe similarity of two-dimensional shapes using side and angle measurements Describe, compare, and contrast characteristics and relationships of lines and geometric shapes M Students will formulate questions that can be addressed with data. Students will organize, display, and analyze relevant data. State Standards (7.4.1, 7.4.2, 7.4.3) Formulate questions that can be addressed with data Calculate and interpret mean, median, mode, and range for data sets Organize, display, and analyze relevant data Determine if data collected from a sample can be used to make predictions about a population Find the probability of independent events Board of Education Approved-October 3, 2011 Page 26

27 Pre-Algebra (8 th Grade) Math Pre-Algebra (8 th Grade) Math Course Purpose Pre-Algebra students will fluently compute using real numbers to solve real world problems. Students will evaluate expressions and solve linear equations and inequalities with variables and construct graphic representations of these equations and inequalities. Students will use properties of angles and pairs of lines to distinguish characteristics and properties of two-dimensional shapes. Students will integrate skills and formulas to calculate surface area and. volume. M Students will compute fluently with integers using all four operations. Students will apply the appropriate operations to numeric expressions and solve and create real life applications with integers. State Standards (8.1.1, 8.1.2, 8.1.3) Represent integers on a number line and relate integers to real-life applications Define and demonstrate absolute value Demonstrate addition of integers with models Establish and apply rules for addition of integers Demonstrate subtraction of integers with models Establish and apply rules of subtraction of integers Develop equivalent expressions of addition and subtraction with integers o (-3+6=6-3) Apply rules of addition and subtraction of integers to real-life situations Create representations of real-life situations using addition and subtraction of integers Represent multiplication and division of integers with numeric patterns and real-life situations Establish and apply rules of multiplication and division with integers to expressions and real-life situations Create representations of real-life situations using multiplication and division of integers M Students will represent numbers in standard, exponential, and scientific notation forms. They will classify numbers within the real number system. Students will fluently simplify numeric expressions using the order of operations. State Standards (8.1.1, 8.1.3) Define and represent numbers in exponential form Define and compute square roots with and without calculator Approximate square roots Simplify numeric expressions containing exponents and square roots Simplify numeric expressions using the order of operations Represent large and small numbers using scientific notation Compare and order numbers written in scientific notation Classify real numbers as whole numbers, integers, rational numbers, and irrational numbers Board of Education Approved-October 3, 2011 Page 27

28 M Students will translate verbal phrases into variable expressions and evaluate fluently. State Standards (8.3.1) Define variable expression and its components o Variable, coefficient, term, and constant Select verbs that represent sum, difference, product, and quotient Translate verbal phrases into variable expressions Combine like terms to simplify variable expressions Apply the distributive property to simplify variable expressions Evaluate variable expressions using the order of operations M Students will solve linear equations requiring one, two, and multiple steps. They will translate verbal sentences into linear equations to solve real-life problems. Students will determine the appropriateness and accuracy of the solutions. State Standards (8.3.1, 8.3.2, 8.3.3) Define equation and identify words indicating an equation is required Define and identify inverse operations Distinguish between the meanings of simplifying expressions and solving equations Apply properties of equality to solve one step equations Identify the steps involved in solving one and two step equations Apply properties of equality to solve two step equations Establish rules to choose the correct order of inverse operations Apply the distributive property to transform linear equations Combine like terms of an equation when terms are on one side of the equal sign Apply correct order of inverse operations to solve multiple step equations Combine like terms of an equation when terms are on different sides of the equal sign Translate verbal sentences from real-life problems to linear equations and solve Verify solutions for accuracy Determine the appropriateness of a solution and choose the correct presentation M Students will solve one and two step linear inequalities. They will translate verbal sentences into linear inequalities to solve real-life problems. Students will represent solutions with the use of number lines. State Standards (8.1.1, 8.1.4, 8.3.1, 8.3.3) Define inequality symbols Define verbal phrases to indicate inequalities Illustrate inequalities on a number line Differentiate between the meanings and visual representations of "is less than" and "is less than or equal to", and between "is greater than" and "is greater than or equal to". Solve one step inequalities using inverse operations of addition and subtraction Solve one step inequalities with positive and negative coefficients using inverse operations of multiplication and division Solve two step inequalities using the correct order of inverse operations Translate verbal phrases into linear inequalities Board of Education Approved-October 3, 2011 Page 28