Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MATHEMATICS MISSION STATEMENT The Battle Creek mathematics program will promote an understanding and application of mathematics through communication, reasoning, real world connections and problem solving. The framework for this program will be based on the following concepts: number sense, geometric/measurement, algebraic, and data analysis/probability. Communicating mathematics through reading and writing and the use of technology will be an integral part of the mathematical program. Target Area Outcomes Target Outcome 1: Number Sense Target Outcome 2: Geometric/measurement Target Outcome 3: Algebraic Target Outcome 4: Data analysis/probability Target Outcome 1: Number Sense The learner will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. This will include the following: number system, operations, computation, and estimation. Updated September 25, 2013 Target Outcome 2: Geometric/Measurement The learner will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. This will include the following: characteristics, coordinate geometry, transformations, spatial modeling, and measurement. Target Outcome 3: Algebraic The learner will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. This will include the following: relationships, modeling in context, and procedures. Target Outcome 4: Data Analysis/Probability The learner will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. This will include the following: display and analysis, predictions and inferences, and probability . GRADE KINDERGARTEN FOCUS AREA: Numbers PURPOSE STATEMENT: TLW identify numbers in relationship with real world objects. Outcome 1: TLW communicate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics. 1.1 1.2 Count, read, and write numbers 0-20 (MA0.1.1.a) Sequence objects using ordinal numbers 01st – 5th (MA0.1.1.b, MA0.1.1.c) Updated September 25, 2013 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Orally count by ones and tens to 100 Identify more and less than with numbers (MA0.1.1.f)) Match numerals to the quantities they represent 0-20, using a variety of models and representations (MA0.1.1.d) Match one to one correspondence up to the number 20 Demonstrate relative position of whole numbers 0-10 (e.g., 5 is between 2 and 10; 7 is greater than 3) (MA0.1.1.f) Use concrete objects and words to solve addition problems (MA0.1.2.a, MA0.1.2.b) Use concrete objects or words to solve subtraction problems (MA0.1.2c, MA0.1.2.d) Outcome 2: TLW communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Name days of week, months, and seasons. Identify and describe the use of a clock, ruler, scale and thermometer Use measurement vocabulary to describe and compare measurements used in everyday life Identify the name and amount of a penny, nickel, dime, and quarter (MA0.2.5.a) Identify time to the hour (MA0.2.5.b) Measure using nonstandard units (MA0.2.5.c) Compare objects according to length (MA0.2.5.d) Demonstrate positional words (e.g., above/below, near/far, over/under, in/out, around/through) (MA0.2.4.a) Sort and name common geometric shapes (i.e.: triangle, rectangle, square, and circle) (MA0.2.1.a) Identify and describe common geometric shapes in their environment Draw common geometric shapes Outcome 3: TLW communicate algebraic concepts using multiple representations to reason, solve problems and apply real world connections within mathematics. 3.1 Sort and classify objects by color, shape, and size and create a rule (MA0.3.1.a, MA0.3.1.b and MA0.4.1.a) 3.2 Identify, describe, and extend patterns 3.3 Model situations that involve the addition and subtraction of whole numbers 0-10 using objects (MA0.3.2.a) Updated September 25, 2013 3.4. Use objects to solve addition and subtractions of whole numbers 0-10 (MA0.1.3.3.a) Outcome 4: TLW communicate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics. 5.1 5.2 Create a pictograph or bar graph using manipulative and or graph paper Use non-standard and standard objects to classify different groups as being more or less 5.2.1 Identify the attributes of sorted data (MA0.4.1.b) 5.4 Compare the attributes of the data (e.g., most, least, same) (MA0.4.1.c) GRADE FIRST FOCUS AREA: Signal Digit Computation PURPOSE STATEMENT: TLW identify and apply the concepts of addition and subtraction for single digit numbers. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 Count, read, and form numbers correctly and neatly to 100 (MA 1.1.1.a) Count and recognize numbers by 5’s to 100 (MA 1.1.1.c) Count by multiples of 2 up to 50 (MA 1.1.1.b) Count by multiples of 10 up to 100 (MA 1.1.1.d) Understand and apply place value for ones and tens for numbers 1 – 100 (MA 1.1.1.h) Count backwards from 10 to 0 by 1’s (MA 1.1.1.f) Understand and apply fractions to the whole, half, and fourth Connect number words to the quantities they represent 0-20 (MA 1.1.1.g) Use and recognize ordinal numbers and words (first through tenth) (MA 1.1.1.e) Compare and order whole numbers 1-100 (MA 1.1.1.i) Demonstrate relative position of whole numbers 1-100 (e.g., 52 is between 50 and 60) (MA 1.1.1.j) Recognize and demonstrate the use of pennies, nickels, dimes, and quarters to 100 cents or less Recognize and use symbols +,-, and = Solve basic story problems up to 10 using addition and subtraction Updated September 25, 2013 1.15 1.16 1.17 1.18 1.19 1.20 Communicate basic facts of addition and subtraction and show value using concrete objects, drawings, words, and symbols (MA 1.1.2.a, MA 1.1.2.b, MA 1.1.2.c, MA 1.1.2.d) Use objects, drawings, words, and symbols to explain subtraction as a comparison (e.g., Nancy has 8 hair ribbons. Jane has 5 hair ribbons. How many more hair ribbons does Nancy have than Jane?) (MA 1.1.2.e) Estimate numbers under 80 and compare to actual size Fluently add and subtract whole numbers up to 10 (MA 1.1.3.a, MA 1.1.3.b) Add and subtract two-digit numbers without regrouping (MA 1.1.3.c) Use a variety of methods and tools to compute sums and differences (e.g., models, mental computation, paper-pencil) (MA 1.1.3.d) Outcome 2: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Measure with nonstandard units of measurement for comparing two or more items finding length, height, and weight (i.e.: paperclips, chalk, foot, etc.) (MA 1.2.5.f) Tell time to the half hour and hour and know the terms hour and minutes (digital and analog) (MA 1.2.5.b) Identify units of measurement using meters, liters, gallons, pounds, miles, minutes, hours, temperature, balance, scale, cents, dollars, calendars, clocks, and rulers (MA 1.2.5.d) Demonstrate understanding of orientation in time for past, present, future, earlier, and later (Time line sequencing [Social Studies and L.A. links]) (MA 1.2.5.c) Count like coins to $1.00 (MA 1.2.5.a) Measure length using inches (MA 1.2.5.e) Compare two-dimensional shapes, and describe the attributes (e.g., square, circle, rectangle, and triangle) (MA 1.2.1.a, MA 1.2.1.b) Identify the position of a whole number on a horizontal number line (MA 1.2.2.a) Identify one line of symmetry in two-dimensional shapes (e.g., circle, square, rectangle, triangle) (MA 1.2.3.a) Understand and demonstrate the relative position and sequential nature using up, down, left, right, near, far, over, under, above, and below (MA 1.2.4.a) Construct congruent shapes and designs using manipulative to create squares, circles, rectangles, and triangles (MA 1.2.4.b) Outcome 3: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. Updated September 25, 2013 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Complete and create patterns using objects, colors, shapes, movements, and sounds (MA 1.3.1.c) Sort or order objects by their attributes (e.g., color, shape, size, number) then identify the classifying attribute (MA 1.3.1.a) Create multiple rules for sorting beyond color, shape, and size (MA 1.3.1.b) Use <, =, > to compare quantities (MA 1.3.1.d) Model situations that involve the addition and subtraction of whole numbers 0-20, using objects and pictures (MA 1.3.2.a) Describe and model qualitative changes (e.g., a student growing taller) (MA 1.3.2.b) Write number sentences to represent fact families (MA 1.3.3.a) Use concrete, pictorial, and verbal representations of the commutative property of addition (MA 1.3.3.b) Outcome 4: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 4.1 4.2 4.3 4.4 4.5 Count and collect data using charts, tally marks, and tables (MA 1.4.1.c) Count and collect data using line, bar, and picture graphs Make comparisons from displayed data such as more, less, and fewer than (MA 1.4.1.d) Sort and classify objects by more than one attribute (MA 1.4.1.a) Organize data by using concrete objects (MA 1.4.1.b) GRADE SECOND FOCUS AREA: Double Digit Computation PURPOSE STATEMENT: TLW identify and apply the concepts of addition and subtraction of double digit numbers. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 1.1 1.2 1.3 Read and write numbers to 1-1,000 (MA 2.1.1.a) Recognize and write numbers with place value to 1,000 (MA 2.1.1.e) Comparing numbers using <, >, and = signs to 1000’s (MA 2.11.f and MA 2.1.1.g) Updated September 25, 2013 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Round numbers up to the nearest 10’s place. Understand and solve addition and subtraction fact families using objects, drawing, words, and symbols 1-20 (MA 2.1.2.a, 2.1.3.a, 2.1.3.b) Count by 2’s (using even and odd numbers) to 100 (MA 2.1.1.b) Choose addition or subtraction operations in story problems Solve 3 digit addition and subtraction problems with and without regrouping (MA 2.2.5.a) Count backwards from 20-0 (MA 2.1.1.c) Connect number words to the quantities they represent 0-100 (MA 2.1.1.d) Use visual models to represent fractions of one-half as a part of a whole (MA 2.1.1.h) Outcome 2: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 Measure with rulers in centimeters and meters Measure with a ruler, compare, and order yards, feet, inches, and half inches (MA 2.2.5.d and 2.2.5.e) Read and interpret Fahrenheit. Tell time to the half, quarter, and five minute intervals (MA 2.2.5.b) Measure distance around objects in inches and non standard units. Identify, describe, and create 2 and 3 dimensional geometric shapes (MA 2.2.1.a, MA 2.2.1.c, and MA 2.2.1.d) Compute money amounts and count cents using pennies, nickels, dimes, and quarters, half dollar and $1.00 (MA 2.2.5.a) Use objects, drawings, words, and symbols to explain the use of subtraction to find a missions addend (e.g., if 3 + ___ = 7, then 7 – 3 = ____) (MA 2.2.2.b) Use a variety of methods and tools to compute sums and differences (e.g., models, mental, computation, paper-pencil) (MA 2.1.3.d) Estimate the results of two-digits whole number sums and differences and check the reasonableness of such results (MA 2.1.4.a) Estimate the number of objects in a group (MA 2.1.4.b) Determine if two shapes are congruent (MA 2.2.1.b) Identify and compare whole numbers using locations on a vertical and horizontal number line (MA 2.2.2.a and MA 2.2.2.b) Identify the direction moved by adding and subtracting using a number line (MA 2.2.2.c) Identify and draw lines of symmetry in two-dimensional shapes Sketch two-dimensional shapes (MA 2.2.4.a) Identify and use appropriate tools for the attribute being measured (e.g., clock, calendar, thermometer, scale, ruler) (MA 2.2.5.c) Updated September 25, 2013 Outcome 3: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 3.1 3.2 3.3 3.4 3.5 Create and describe patterns using concrete and pictorial representations (MA 2.3.1.a) Model situations that involve the addition and subtractions of whole numbers 0100, using objects and number lines (MA 2.3.2.a) Describe and model quantitative change involving addition (e.g., a student grew 2 inches) (MA 2.3.2.b) Use symbolic representations of the commutative property of addition (e.g., 2 + 3 = ∆ + 2) (MA 2.3.3.a) Illustrate mathematical problems using manipulatives, drawing pictures, and diagrams Outcome 4: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 4.1 4.2 Represent data using pictographs (MA 2.4.1.a) Interpret data using pictographs (e.g., 7 more; 2 less; 12 all together) (MA 2.4.1.b) GRADE THIRD FOCUS AREA: Multiplication PURPOSE STATEMENT: TLW memorize and apply the basic concepts of multiplication facts. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Read and write place values to the 100,000’s (MA 3.1.1a) Compare and order to the ten thousands using <, >, = (MA 3.1.1g) Round whole numbers to the nearest 1, 10, 100, 1000 (MA 3.1.1i) Write in expanded form, word form, and short word form from the 10,000 place to the tenths place. (MA 3.1.1e, MA 3.1.1f) Find parts of whole and parts of a set for ½. 1/3, or ¼ (MA 3.1.1h) Understand that subtraction is the opposite of addition and multiplication as repeated addition (MA 3.1.2a) Understand and utilize multiplication fact families to 10 (MA 3.1.3a) Updated September 25, 2013 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 Illustrate mathematical concepts of addition and multiplication by using objects to draw pictures, diagrams, and arrays (MA 3.1.2a, MA 3.1.2b, MA 3.1.2c, MA 3.1.2d) Demonstrate number system of base 10 using one dime to 10 pennies and 10 dimes to one dollar (MA 3.1.1e) Count out money and make change to $10.00 (MA 3.2.5b) Count by multiples of 5 to 200, 10 to 400, 100 to 1000 (MA 3.1.1b, MA 3.1.1c, MA 3.1.1d) Estimate and accurately calculate sums and differences up to 4 digits and products up to 2 digits (MA 3.1.3b, MA 3.1.4a) Multiply 2 and 3 digit numbers by 1 digit numbers without regrouping Add and subtract 4 digit numbers with regrouping (MA 3.1.3b) Apply the appropriate methods of computation when problem solving with 4 digit whole numbers through the thousands (MA 3.1.3c) Outcome 2: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Measure and compare to the nearest centimeter, meter, foot, inch and ½ inch (MA 3.2.5g, MA 3.2.5a, MA 3.2.5f) Calculate perimeter and area (MA 3.2.5g, MA 3.2.5a, MA 3.2.5f) Read time to the half, quarter, and minutes for a.m. and p.m. (MA 3.2.5c, MA 3.2.5d) Identify the appropriate customary unit for measuring length, weight, and capacity/volume (MA 3.2.5e) Describe attributes and construct three-dimensional structures (MA 3.2.4b, MA 3.2.1d) Identify and utilize congruency, symmetry, similarity, and transformations (MA 3.2.3a, MA 3.2.1b) Use shapes and numbers to create patterns (MA 3.3.1a, MA 3.3.1b) Identify characteristics and draw (sides, angles, vertices, lines, line segments, rays, and angles) and describe properties of 2 dimensional shapes (MA 3.2.1a, MA 3.2.1b, MA 3.2.1c, MA 3.2.4a) Construct number lines and identify distances between plotted points (MA 3.2.2.a, MA 3.2.2b) Outcome 3: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 3.1 Write number sentences, story problems, and use symbols appropriately (+, -, x, /) (MA 3.3.3a, MA 3.3.3b, MA 3.3.3c) 3.2 Multiplying 3 facts (associative properties) Updated September 25, 2013 3.3 Describe and model mathematical situations that involve addition and subtractions of whole numbers (MA 3.3.2a, MA 3.3.2b) Outcome 4: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 4.1 4.2 Read and interpret bar graphs and draw conclusions (MA 3.4.1a, MA 3.4.1b, MA 3.4.1c) Perform simple experiments (e.g., flip a coin, toss a number cube, spin a spinner) and describe outcomes as possible, impossible, or certain (MA 3.4.3a) GRADE FOUR FOCUS AREA: Division PURPOSE STATEMENT: long division TLW understand and utilize the process of Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Round whole numbers to the millions (MA4.1.1.i) Read and write numbers in word form, expanded form, and short word form to the millions(MA4.1.1.a) Read, write, represent, add, and subtract decimals to the hundredths (MA4.1.1.b, MA4.1.1.c, MA4.1.3.b) Demonstrate equivalent representations for decimals through the hundredths. (MA4.1.1.b) Choose an operation to solve problems (MA4.1.3.f) Compute and order common fractions and decimals through the hundredths using symbols <, >, =, (MA4.3.1.c) Understand fact families in division to twelve Identify positive and negative numbers and fractions on a number line (MA4.1.1.h) Read, write, count, and make change to the amount of $20.00 Classify a number as even or odd (MA4.1.1.d) Represent a fraction as parts of a whole and/or parts of a set and use visual models to find equivalent fractions (MA4.1.1.e, MA4.1.1.f) Updated September 25, 2013 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 Determine the size of a fraction relative to one half using equivalent forms (MA4.1.1.g) Calculate quotients with a three-digit and a one-digit with or without a remainder (MA4.1.3.d) Demonstrate fluency, written and mentally, basic division and multiplication facts form 1-10 and the powers of 10 (MA4.1.3.a, MA4.1.3.e) Estimate whole 3-digit products and 2-digit quotients by checking for reasonability (MA4.1.4.a) Multiply two digit numbers (MA4.1.3.c) Add and subtract 4-5 digit numbers. Estimate and round decimals up to the nearest hundredths. Add and subtract fractions in like denominators (one-half, one-fourth, oneeighth) Use drawings, words, and symbols to explain the meaning of division {e.g. as repeated subtraction: Sarah has 24 candies. She put them into bags of 6 candies each…..} (MA4.1.2.a) Outcome 2: TLW communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics. 2.1 Compute and estimate simple unit conversions for length, capacity, and mass (to the nearest ml/g, and nearest ½ in/cm.) (MA4.2.5.g, MA4.2.5.e) I 2.2 Identify the appropriate metric units for length, area, mass and weight, and capacity (in., ft., one-fourth in., oz., fluid oz.) (MA4.2.5.d) 2.3 Measure amounts of time to the minute on an analog clock. (MA4.2.5.b) 2.4 Solve problems involving elapsed time. (MA4.2.5.c)) 2.5 Select and use appropriate tools to find perimeter and area of polygons (MA4.2.5.a) 2.6 Measure weight and temperature using customary units (MA4.2.5.f) 2.7 Identify and describe 2 and 3 dimensional shapes according to their sides and angle properties and relate them to real world items (MA4.2.4a) 2.8 Creating and describing 2- and 3- dimensional shapes () 2.9 Identify, draw and classify lines that are parallel, perpendicular and intersecting lines, line segments and points, angles, and rays in real world items (MA4.2.1.c, MA4.2.4.a) 2.10 Identify and name shapes that are similar and congruent, identify lines of symmetry, and identify the transformation (MA4.2.3.a, MA4.2.1.d) 2.11 Classify an angle as acute, obtuse, and right (MA4.2.1b) 2.12 Make predictions based on data to answer questions from tables and bar graphs (MA4.2.2.a) Updated September 25, 2013 Outcome 3: TLW communicate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections to mathematics. 3.1 3.2 3.3 3.4 3.5 Write number sentences using appropriate symbols +, -, X, , ( )( ), *,, n, and for unknown, ( ) for grouping and translate words to algebraic expressions and vice versa (MA43.3.a, MA4.3.3b, MA4.3.3.c, MA4.3.1.d) Identify, describe, extend, and apply rules about numeric patterns (MA4.3.1a) Solve and explain simple one-step whole number equations (e.g., x+2=3; 3*y=6 (MA4.3.3.d) Represent and analyze a variety of patterns using words, tables, and graphs (MA4.3.1b) Model situations that involve the multiplication of whole numbers using number lines and symbols (MA4.3.2.a) 3.6 Describe and model quantitative change involving multiplication (e.g. money doubling) (MA4.3.2.b) Outcome 4: TLW communicate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real life connections within mathematics. 4.1 Make predictions based on data using tables and bar graphs, pie graphs, pictographs, and line graphs (MA4.4.21.a, MA4.4.1.b) 4.2 Express simple experimental probabilities (MA4.4.3.a) 4.3 Represent and interpret data using dot/line plots (MA4.4.1.a) 4.4 Find the mode, range, and whole number mean for a set of whole numbers (MA4.4.1.c, MA4.4.1.d) 4.5 Make predictions based on data using tables and bar graphs, pie graphs, pictographs, and line graphs (MA4.4.2a), MA4.4.1.b) 4.6 Express simple experimental probabilities (MA4.4.3.a) 4.7 Represent and interpret data using dot/line plots (MA4.4.1.a) 4.8 Find the mode, range, and whole number mean for a set of whole numbers (MA4.4.1.c, MA4.4.1.d) GRADE FIVE FOCUS AREA: Adding and subtracting fractions and decimals Updated September 25, 2013 PURPOSE STATEMENT: TLW identify fractions and decimals to compute their sums and differences. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Identify a number as prime or composite (MA 5.1.1.e) Demonstrate expanded form, compare and order whole numbers and decimals through the thousandths place (MA 5.1.1.a, MA 5.1.1.b) Identify, name, and order fractions in their simplest form and find common denominators for fractions (MA 5.1.1.c) Identify factors and multiples of any whole number (MA 5.1.1.f) Use words and symbols to explain the meaning of the following properties for addition and multiplication: identity, commutative, and associative; and the distributive property of multiplication over addition (MA 5.1.2.a, MA 5.1.2.b) Convert between percents and decimals (common fractions such as 1/2, 1/5, 1/10, 1/20, 1/100) Add and subtract fractions and decimals with regrouping through the thousandths place (MA 5.1.3.a) Select, apply and explain the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology) (MA 5.1.3.b) Add, subtract, multiply, and divide decimals (MA 5.1.3.c and MA 5.1.3d) Read, write, and find percentages and create equivalent ratios Estimate sums and differences of positive rational numbers and decimals. (MA 5.1.4.a) Round whole numbers and decimals to appropriate place value (MA 5.1.1.g) Outcome 2: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 Will use standard units of measure for the customary units to the ¼ inch (temperature, length, capacity/volume, and weight) (MA 5.2.5.c, MA 5.2.5.d) Will use standard units of measure for the metric system (temperature, length, capacity, and weight/mass) (MA 5.2.5.e) Identify correct unit (customary or metric) to the measurement situation (MA 5.2.5.b) Work with money and time. Measure and identify perimeter and angles within three degrees (MA 5.2.5.a) Identify parts and degrees on a circle (MA 5.2.1d) Updated September 25, 2013 2.7 2.8 2.9 2.10 2.11 2.12 Identify, name, and justify the classification and congruence of polygons (two dimensional shapes) (MA 5.2.1.b, MA 5.2.1.c) Identify the terms: point, line, line segment, parallel and perpendicular, ray, plane; number of edges, faces, and vertices of triangular and rectangular prisms (MA 5.2.1a) Recognize and build a geometric model to solve a problem, and sketch congruent shapes, and build rectangular prisms using cubes. (MA 5.2.4.a, MA 5.2.4.b, MA 5.2.4.c) Plot the location of an ordered pair in the first quadrant (MA 5.2.2.a) Perform one-step transformations on two dimensional shapes (e.g., translation, rotation, reflection, of 90, 180, and 270) (MA 5.2.3.a) Determine the area of rectangles and squares (MA 5.2.5.f) Outcome 3: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 Describe, extend, apply rules, and make generalizations about numeric, and geometric patterns (MA 5.3.1.a) Create and analyze numeric patterns using words, tables, and graphs (MA 5.3.1.b) Identify, compare, and order integers on a number line Communicate relationships using expressions and equations (MA 5.3.1.c) Model situations that involve the addition, subtraction, and multiplication of positive rational numbers using words, graphs and tables (5.3.2.a) Represent a variety of quantitative relationships using tables and graphs (MA 5.3.2.b) Compare different models to represent mathematical situations (MA 5.3.2.c) Explain the addition property of equality (MA 5.3.3.a) Use symbolic representations of the associative property (MA 5.3.3.b) Evaluate numerical expressions by using parentheses with respect to order of operations (MA 5.3.3.c) Evaluate simple algebraic expressions involving addition and subtraction (MA 5.3.3.d) Solve one-step addition and subtraction equations involving common positive rational numbers (MA 5.3.3.e) Identify and explain the properties of equality used in solving one-step equations involving common positive rational numbers (MA 5.3.3.f) Outcome 4: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply to real world connections within mathematics and across disciplines. Updated September 25, 2013 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Represent the same set of data in different formats (e.g., table, pictographs, bar graphs, line graphs) and draw conclusions based on a set of data (MA 5.4.1.a, MA 5.4.1.b, and MA 5.4.1.c) Find the mean, median, mode, and range for a set of whole numbers (MA 5.4.1.d) Generate questions and answers from data sets and their graphical representations (MA 5.4.1.e) Make predictions based on data to answer questions from tables, bar graphs, and line graphs (MA 5.4.2.a) Perform and record results of probability experiments (MA 5.4.3.a) Generate a list of possible outcomes for a simple event (MA 5.4.3.b) Explain that the likelihood of an event that can be represented by a number from 0 (impossible) to 1 (certain) (MA 5.4.3.c) GRADE SIX FOCUS AREA: Multiplication of fractions and decimals PURPOSE STATEMENT: TLW identify fractions and decimals to compute their properties. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Write and solve story problems using decimals and fractions (MA 6.1.3.b) Demonstrate expanded and exponent numerals through millions as well as compare and order them (MA 6.1.1.d) Convert standard and word form Identify, compare, and order positive and negative integers on a number line (MA 6.1.1.b and MA 6.1.1.c) Identify prime and composite properties (MA 6.1.1.e) Classify natural, whole and integer numbers (MA 6.1.1.f) Use drawings, words, and symbols to explain the meaning of addition and subtraction of fractions and decimals (MA 6.1.2.a and MA 6.1.2.b) Convert fractions to mixed numbers and decimals Write ratios and percentages in three different ways (decimals, fractions, and percentages) (MA 6.1.1.a) Estimate and solve products and quotients to the nearest whole number. (MA 6.1.3.a and MA 6.1.4.a) Updated September 25, 2013 Outcome 2: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Estimate and measure length, perimeter, and area using customary and metric units to the nearest 1/16 in and mm (MA 6.2.5.a, MA 6.2.5.d, and MA 6.2.5.e) Determine the volume of rectangular prisms (MA 6.2.5.f) Convert length, weight (mass) and capacity measurements within each system (MA 6.2.5.c) Measure volume/capacity using the metric system (MA 6.2.5.b) Identify the ordered pair of a plotted point in the coordinate plane (MA6.2.2.a) Find the missing angle in a triangle (with two angles given) Find the circumference of circles Translations, rotations, reflections in dilations and scale in geometry (MA 6.2.3.a) Classify three-dimensional objects and identify two-dimensional drawings of three-dimensional objects (MA 6.2.1.a and MA 6.2.4.a) Outcome 3: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Describe and create simple algebraic expressions from story problems (MA6.3.1.a and MA 6.3.1.b) Model contextualized problems using a graph or table, identify relationships as increasing, decreasing, or constant (MA 6.3.2.a) Explain the multiplication property of equation (e.g., if a = b, then ac = bc) (MA 6.3.3.a) Evaluate numerical expressions containing multiple operations with respect to order of operations (e.g., 2 + 4 x 5) (MA 6.3.3.b) Evaluate simple algebraic expressions involving multiplication and division (MA 6.3.3.c) Solve one-step equations involving positive rational numbers (MA 6.3.3.d) Identify and explain the properties of equality used in solving one-step equations (e.g., addition, subtraction, division) (MA 6.3.3.e) Outcome 4: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 4.1 4.2 Collect and record data to make frequency tables, stem and leaf plots, and histograms. (MA 6.4.1.a) Construct circle, bar, line, and pictographs Updated September 25, 2013 4.3 4.4 4.5 4.6 4.7 4.8 Read a chart or table to make comparisons, predictions, and inferences (MA 6.4.1.b, 6.4.2.a) Find the mean, median, mode, and range for a set of data (MA 6.4.1.c) Compare the mean, median, mode, and range from two sets of data (MA 6.4.1.d) Describe the theoretical probability of an event using a fraction, percentage, decimal, or ratio (MA 6.4.3.a) Compute theoretical probabilities for independent events (MA 6.4.3.b) Find experimental probability for independent events (MA 6.4.3.c) GRADE SEVEN FOCUS AREA: Dividing fractions and decimals PURPOSE STATEMENT: TLW demonstrate the division process of using fractions and decimals Outcome 1: TLW will demonstrate number sense concepts using multiple representations to reason, solve problems, and apply realworld, connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 Recognize and utilize rational numbers and integers. (MA 7.1.1.b, MA 7.1.2.c, MA 7.1.3.b) Compute addition and subtraction problems involving integers. (MA 7.1.2.c, MA 7.1.3.a) Write decimals, percents, and fraction equivalents interchangeably (MA 7.1.1a) Learn to write large numbers using scientific notation in standard form and vice versa. (MA 7.1.1.c) Learn divisibility rules Identify sub-sets and properties of the real number system. (MA 7.1.1.d, MA 7.3.3.a, MA 7.3.3.b) Find the least common multiple and greatest common divisor given two numbers. (MA 7.1.1.e) Add, subtract, multiply and divide fractions and mixed numbers. (MA 7.1.2.a) Convert between decimals, fractions and percents in simplest form. (MA 7.1.1a) Multiply and divide decimals by decimals. (MA 7.1.2.b) Solve problems involving percent of numbers. (MA 7.1.3.c) Estimate using sub-sets of the real number system.(MA 7.1.4.a) Perform mental math using compatible numbers. (MA 7.1.4.a) Updated September 25, 2013 Outcome 2: TLW will demonstrate geometric concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Read and interpret scale drawings to actual measurements and vice versa. (MA 7.2.1.a) Identify and draw lines, line segments, rays, and angles. (MA 7.2.1.b) Name or locate an ordered pair in a coordinate plane. (MA 7.2.2.a, MA 7.2.2.b) Find the length of horizontal and vertical line segments on a coordinate plane. (MA 7.2.2.c) Identify lines of symmetry for a reflection. (MA 7.2.3.a) Perform a single transformation and locate the coordinates of the new shape. (MA 7.2.3.b) Identify two-dimensional shapes that create nets of a three-dimensional object. (MA 7.2.4.a, MA 7.2.4.b) Draw and measure angles to the nearest degree. (MA 7.2.4 c, MA 7.2.5.a) Learn formulas for area of two-dimensional figures. (MA 7.2.5.b) Find the perimeter and area of quadrilaterals, triangles, and circles utilizing different units. ( MA 7.2.5.b, MA 7.2.5.c) Outcome 3: TLW will demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 3.1 3.2 3.3 3.4 3.5 Describe relations using tables, graphs, and rules. (MA 7.3.1.a) Solve and explain the properties of 1-step and 2-step equations involving rational numbers. ( MA 7.3.2.b, MA 7.3.3.d, , MA 7.3.3.f) Solve and explain the properties of 1-step inequalities involving rational numbers. (MA 7.3.1.b, MA 7.3.3.e) Translate verbal expressions into algebraic expressions and vice versa. (MA 7.3.1.c, MA 7.3.2.a) Evaluate algebraic expressions using substitution and order of operations. (MA 7.3.3.c) Outcome 4: TLW will demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 4.1 4.2 4.3 4.4 4.5 Calculate the mean, median, mode, and range from a set of data (MA 7.4.1.b) Create graphical representations of data (MA 7.4.1.a) Analyze tables, charts, and graphs (MA 7.4.1.a) Explain the difference between population and sample, and determine whether a sample is biased or unbiased. (MA 7.4.1.c, MA 7.4.1.d) Create and use survey questions within a population. (MA 7.4.1.e) Updated September 25, 2013 4.6 4.7 4.8 Find the probability of dependent events and independent compound events (MA 7.4.3.a) Use statistical methods and probability as a means of making decisions (MA 7.4.2.a) Compare and contrast theoretical and experimental probabilities. (MA 7.4.3.b) GRADE EIGHT FOCUS AREA: Number Theory PURPOSE STATEMENT: TLW apply and solve problems using number theory Outcome 1: TLW will demonstrate number sense concepts using multiple representations to reason, solve problems, and apply realworld, connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Recognize and compare real numbers with and without a number line (MA 8.1.1.a, MA 8.1.1.b) Compute addition, subtraction, multiplication, and division problems involving integers. (MA 8.1.2.a) Compute and explain addition, subtraction, multiplication, and division word problems involving all real numbers (MA 8.1.3.a, MA 8.1.3.d) Use properties and order of operations for replacement of multi-step equations (MA 8.1.3.a) Evaluate expressions involving absolute value of integers. (MA 8.1.3.b) Learn square roots of perfect squares (MA 8.1.3.c) Learn to write small numbers using scientific notation in standard form and vice versa. (MA 8.1.1.c) Write and solve ratios and proportions in problem-solving (MA 8.1.3.e) Classify subsets of real numbers (MA 8.1.1.d) Explain why division by zero is undefined. (MA 8.1.2.c) Outcome 2: TLW will demonstrate geometric concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 2.1 2.2 2.3 Solve problems involving corresponding parts of similar and congruent objects in two and three dimensions. (MA 8.2.1.a, MA 8.2.1.b) Find the length of the side of a right triangle using the Pythagorean theorem (MA 8.2.5.c) Identify angle relationships of two parallel lines cut by a transversal. (MA 8.2.1.c) Updated September 25, 2013 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Identify pairs of angles (e.g., adjacent, complementary, supplementary, vertical). (MA 8.2.1.d) Identify and explain the relationship of angles in a triangle. (MA 8.2.1.e) Use the length of horizontal and vertical line segments on a coordinate plane to represent and examine the properties of quadrilaterals. (MA 8.2.2.a) Convert units within measurement systems using standard and metric, given conversion factors. (MA 8.2.5.e) Calculate volume and surface area of prisms, cylinders, pyramids, cones, and spheres (MA 8.2.5.b) Find the perimeter and area of complex shapes. (MA 8.2.5.a) Perform and explain dilations and use scale factors to locate the coordinates of a new shape. (MA 8.2.3.a, MA 8.2.3.b, MA 8.2.5.d) Draw geometric objects with specified properties. (MA 8.2.4.a) Outcome 3: TLW will demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Create multiple representations of data (MA 8.3.1.a) Analyze tables, charts, and graphs (MA 8.3.1.a) Identify constant slope from multiple representations of data. (MA 8.3.1.c) Evaluate numerical expressions containing whole number exponents. (MA 8.3.3.b) Translate verbal expressions and equations to algebraic expressions and equations and vice versa (MA 8.3.2.a, MA 8.3.2.b) Solve and 1-step and multi-step equations and inequalities involving rational and irrational numbers (MA 8.3.1.b, MA 8.3.3.c, MA 8.3.3.d, MA 8.3.3.e) Recognize and apply commutative, associative, distributive, inverse, and identity properties, and the properties of zero. (MA 8.1.2.b, MA 8.3.3.a) Outcome 4: TLW will demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real-world, connections within mathematics and across disciplines. 4.9 4.10 4.11 4.12 4.13 4.14 Calculate and compare the mean, median, mode, range, and quartiles from a set of data (MA 8.4.1.c) Compare characteristics of sets of data and select the most appropriate unit of central tendency. (MA 8.4.1.b, MA 8.4.1.d, MA 8.4.2.b) Represent and interpret data using circle graphs and box plots with and without the use of technology. (MA 8.4.1.a, MA 8.4.1.e) Evaluate predictions to formulate new questions and plan new studies. (MA 8.4.2.a) Identify complementary events and calculate their probabilities. (MA 8.4.3.a) Conduct experiments that use probability and frequency (MA 8.4.3.b) Updated September 25, 2013 4.15 4.16 4.17 Compute the possible outcomes using counting principles, permutations, and combinations Use statistical methods and probability as a means of making decisions (Standard 8.5.4) Compute the probability of dependent events and independent compound events. (MA 8.4.3.b) ALGEBRA FOCUS AREA: Algebraic Concepts PURPOSE STATEMENT: TLW identify and apply the basic rules of algebra. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Identify different numbers in the real number system (MA 12.1.1b) Identify and simplify scientific and decimal notation (MA 12.1.3c) Identify and simplify equivalent forms of fractions, decimals, and percents (MA 12.1.1a, 12.1.3a) Identify and simplify forms of absolute value (MA 12.1.2b) Simplify radical expressions (MA 12.1.2a, MA 12.1.3b) Find the Greatest Common Factor using exponents (including variables) Recognize and utilize properties of real numbers (MA 12.1.1b, MA 12.1.3a) Apply the order of operations to solve problems involving the real numbers (MA12.1.3d) Solve problems involving radicals, exponents, scientific notation, and absolute value (MA 12.1.3c, MA 12.3.2d) Perform estimations and computations mentally, with paper and pencil, and with technology (MA 12.1.3d) Outcome 2: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 2.1 Illustrate, verbalize and symbolize solutions to algebraic equations and inequalities (MA 12.3.2a, MA 12.3.1a, MA12.3.2b) 2.2 Translate verbal sentences and numerical relations into mathematical expressions and equations (MA 12.3.2a) 2.3 Identify slope and x- and y-intercepts of a linear equation (MA 12.3.1c, MA 12.3.1d) Updated September 25, 2013 2.4 Use slope, point-slope, slope-intercept and standard formulas of lines to write and graph linear equations (MA 12.3.1e, MA 12.3.1f) 2.5 Solve and graph equations and inequalities containing absolute value, fractions, decimals, and/or grouping symbols (MA12.3.3g, MA 12.3.1g, MA 12.3.3o) 2.6 Apply properties to solve formulas for a specified variable (MA 12.3.3h) 2.7 Compute percent increase and decrease utilizing proportions and equations 2.8 Illustrate and solve problems involving mixtures and uniform motion 2.9 Solve systems of equations using graphing, substitution, and elimination (MA 12.3.3p) 2.10 Solve systems of linear inequalities by graphing (MA12.3.1g) 2.11 Identify and solve direct and indirect variation equations 2.12 Define function, domain and range, and demonstrate how to use functional notation to calculate function values (MA 12.3.1b, MA 12.3.1i) 2.13 Explain/apply the reflexive, symmetric, and transitive properties of equality (MA 12.3.3a) 2.14 Simplify algebraic expressions involving exponents (MA 12.3.3b) 2.15 Add and subtract polynomials (MA 12.3.3c) 2.16 Multiply and divide polynomials (MA 12.3.3d) 2.17 Solve quadratic equations (MA 12.3.3e, MA 12.3.3i) 2.18 Add, subtract, multiply, divide, and simplify rational expressions (MA 12.3.3j, MA 12.3.3k) Outcome 3: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 3.1 3.2 3.3 3.4 Calculate the probability and use to solve problems and make decisions (MA12.4.3c) Identify and illustrate the normal distribution curve and make conclusions based on interpretation of data from a normal distribution curve (MA12.4.1b, MA 12.4.1d) Calculate probabilities using counting principle, permutations, and combinations (M12.4.3c) Apply and analyze concepts of probability (e.g. sample space, probability distribution and outcome, dependent and independent events) (MA 12.4.3a, 12.4.3a b, 12.4.3a d, 12.4.3a e) ALGEBRA II FOCUS AREA: Algebraic Concepts PURPOSE STATEMENT: TLW identify and apply the basic rules of algebra. Updated September 25, 2013 Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. Identify different numbers in the real number system (MA 12.1.1b) Identify and simplify forms of absolute value (MA 12.1.2b) Simplify radical expressions (MA 12.1.2a, MA 12.1.3b) Find the Greatest Common Factor using exponents (including variables) 1.5 Recognize and utilize properties of real numbers (MA 12.1.1b, MA 12.1.3a) 1.6 Apply the order of operations to solve problems involving the real numbers (MA12.1.3d) 1.7 Solve problems involving radicals, exponents, scientific notation, and absolute value (MA 12.1.3c, MA 12.3.2d) 1.8 Justify the reasonableness of solutions (MA 12.1.4a, MA 12.1.4b) 1.9 Represent, interpret, and analyze functions and their inverses (MA 12.3.1h) Outcome 2: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 2.1 Illustrate, verbalize and symbolize solutions to algebraic equations and inequalities (MA 12.3.2a, MA 12.3.1a, MA12.3.2b) 2.2 Translate verbal sentences and numerical relations into mathematical expressions and equations (MA 12.3.2a) 2.3 Identify slope and x- and y-intercepts of a linear equation (MA 12.3.1c, MA 12.3.1d) 2.4 Use slope, point-slope, slope-intercept and standard formulas of lines to write and graph linear equations (MA 12.3.1e, MA 12.3.1f) 2.5 Solve and graph equations and inequalities containing absolute value, fractions, decimals, and/or grouping symbols (MA12.3.3g, MA 12.3.1g, MA 12.3.3o) 2.6 Apply properties to solve formulas for a specified variable (MA 12.3.3h) 2.7 Solve systems of equations using graphing, substitution, and elimination (MA 12.3.3p) 2.8 Solve systems of linear inequalities by graphing (MA12.3.1g) 2.9 Apply and solve problems involving matrices 2.10 Identify and solve direct and indirect variation equations 2.11 Define function, domain and range, and demonstrate how to use functional notation to calculate function values (MA 12.3.1b, MA 12.3.1i) 2.12 Explain/apply the reflexive, symmetric, and transitive properties of equality (MA 12.3.3a) 2.13 Simplify algebraic expressions involving exponents (MA 12.3.3b) 2.14 Add and subtract polynomials (MA 12.3.3c) 2.15 Multiply and divide polynomials (MA 12.3.3d) Updated September 25, 2013 2.16 Solve quadratic equations (MA 12.3.3e, MA 12.3.3i) 2.17 Add, subtract, multiply, divide, and simplify rational expressions (MA 12.3.3j, MA 12.3.3k) 2.18 Identify and generate equivalent forms of linear equations (MA 12.3.3f) 2.19 Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables (MA 12.3.3l) 2.20 Derive and use the formulas for the general term and summation of finite arithmetic and geometric series (MA 12.3.3m) 2.21 Combine functions by composition, as well as by addition, subtraction, multiplication, and division (MA 12.3.3 n) Outcome 3: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 3.1 Gather data, organize, display, and interpret data using multiple graphs or diagrams (MA 12.4.1f) 3.2 Compute, display, and analyze the mean, median, mode, range, and five number summary of a set of data (MA 12.4.1b, MA 12.4.1a, MA 12.4.1c) 3.3 Write an equation to fit a set of data and make inferences and predictions about a set of data using the line of regression (MA 12.4.2c) 3.4 Calculate the probability and use to solve problems and make decisions (MA12.4.3c) 3.5 Analyze the effects of data transformation on measures of central tendency (MA 12.4.1e, MA 12.4.1g, MA 12.4.2a) 3.6 Identify and illustrate the normal distribution curve and make conclusions based on interpretation of data from a normal distribution curve (MA12.4.1b, MA 12.4.1d) 3.7 Calculate probabilities using counting principle, permutations, and combinations (M12.4.3c) 3.8 Explain the differences between randomized experiment and observational studies (MA 12.4.1h) 3.9 Support inferences with valid arguments (MA 12.4.2b) 3.10 Recognize when arguments based on data confuse correlation with causation (MA 12.4.2d) 3.11 Apply and analyze concepts of probability (e.g. sample space, probability distribution and outcome, dependent and independent events) (MA 12.4.3a, 12.4.3a b, 12.4.3a d, 12.4.3a e) Extended Algebra A FOCUS AREA: Algebraic Concepts PURPOSE STATEMENT: TLW identify and apply the basic rules of algebra. Updated September 25, 2013 Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. Identify different numbers in the real number system (MA 12.1.1b) Identify and simplify equivalent forms of fractions, decimals, and percents (MA 12.1.1a, 12.1.3a) Identify and simplify forms of absolute value (MA 12.1.2b) 1.4 Recognize and utilize properties of real numbers (MA 12.1.1b, MA 12.1.3a) 1.5 Apply the order of operations to solve problems involving the real numbers (MA12.1.3d) 1.6 Perform estimations and computations mentally, with paper and pencil, and with technology (MA 12.1.3d ) Outcome 2: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 2.1 Illustrate, verbalize and symbolize solutions to algebraic equations and inequalities (MA 12.3.2a, MA 12.3.1a, MA12.3.2b) 2.2 Translate verbal sentences and numerical relations into mathematical expressions and equations (MA 12.3.2a ) 2.3 Identify slope and x- and y-intercepts of a linear equation (MA 12.3.1c, MA 12.3.1d) 2.4 Use slope, point-slope, slope-intercept and standard formulas of lines to write and graph linear equations (MA 12.3.1e, MA 12.3.1f) 2.5 Solve and graph equations and inequalities containing absolute value, fractions, decimals, and/or grouping symbols (MA12.3.3g, MA 12.3.1g, MA 12.3.3o) 2.6 Apply properties to solve formulas for a specified variable (MA 12.3.3h) 2.7 Compute percent increase and decrease utilizing proportions and equations 2.8 Solve systems of equations using graphing, substitution, and elimination (MA 12.3.3p) 2.9 Solve systems of linear inequalities by graphing (MA12.3.1g) 2.10 Define function, domain and range, and demonstrate how to use functional notation to calculate function values (MA 12.3.1b, MA 12.3.1i) 2.11 Explain/apply the reflexive, symmetric, and transitive properties of equality (MA 12.3.3a) 2.12 Add and subtract polynomials (MA 12.3.3c) 2.13 Multiply and divide polynomials (MA 12.3.3d) Updated September 25, 2013 Extended Algebra B FOCUS AREA: Algebraic Concepts PURPOSE STATEMENT: TLW identify and apply the basic rules of algebra. Outcome 1: TLW demonstrate number sense concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. 1.1 Identify and simplify scientific and decimal notation (MA 12.1.3c) 1.2 Simplify radical expressions (MA 12.1.2a, MA 12.1.3b) 1.3 Find the Greatest Common Factor using exponents (including variables) 1.4 Solve problems involving radicals, exponents, scientific notation, and absolute value (MA 12.1.3c, MA 12.3.2d) 1.5 Justify the reasonableness of solutions (MA 12.1.4a, MA 12.1.4b) 1.6 Represent, interpret, and analyze functions and their inverses (MA 12.3.1h) Outcome 2: TLW demonstrate algebraic concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 Illustrate and solve problems involving mixtures and uniform motion Apply and solve problems involving matrices Identify and solve direct and indirect variation equations Simplify algebraic expressions involving exponents (MA 12.3.3b) Solve quadratic equations (MA 12.3.3e, MA 12.3.3i) Add, subtract, multiply, divide, and simplify rational expressions (MA 12.3.3j, MA 12.3.3k) Identify and generate equivalent forms of linear equations (MA 12.3.3f) Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables (MA 12.3.3l) Derive and use the formulas for the general term and summation of finite arithmetic and geometric series (MA 12.3.3m) Combine functions by composition, as well as by addition, subtraction, multiplication, and division (MA 12.3.3 n) Outcome 3: TLW demonstrate data analysis/probability concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines Updated September 25, 2013 3.1 Gather data, organize, display, and interpret data using multiple graphs or diagrams (MA 12.4.1f) 3.2 Compute, display, and analyze the mean, median, mode, range, and five number summary of a set of data (MA 12.4.1b, MA 12.4.1a, MA 12.4.1c) 3.3 Write an equation to fit a set of data and make inferences and predictions about a set of data using the line of regression (MA 12.4.2c) 3.4 Calculate the probability and use to solve problems and make decisions (MA12.4.3c) 3.5 Analyze the effects of data transformation on measures of central tendency (MA 12.4.1e, MA 12.4.1g, MA 12.4.2a) 3.6 Identify and illustrate the normal distribution curve and make conclusions based on interpretation of data from a normal distribution curve (MA12.4.1b, MA 12.4.1d) 3.7 Calculate probabilities using counting principle, permutations, and combinations (M12.4.3c) 3.8 Explain the differences between randomized experiment and observational studies (MA 12.4.1h) 3.9 Support inferences with valid arguments (MA 12.4.2b) 3.10 Recognize when arguments based on data confuse correlation with causation (MA 12.4.2d) 3.11 Apply and analyze concepts of probability (e.g. sample space, probability distribution and outcome, dependent and independent events) (MA 12.4.3a, 12.4.3a b, 12.4.3a d, 12.4.3a e) GEOMETRY & APPLIED GEOMETRY FOCUS AREA: Geometry PURPOSE STATEMENT: TLW demonstrate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and apply real world connections within mathematics and across disciplines. Outcome 1: TLW analyze characteristics, properties, theorems, and relationships among geometric shapes and objects 1.1 1.2 1.3 Identify formulas and calculate surface area and volume of three dimensional figures (MA 12..2.5a, MA 12.2.5f) Recognize identify and define geometric terms, symbols, and theorems (MA 12.2.1a) Classify triangles by angles, sides, and their relationships (MA 12.2.1e, MA 2.2.2d ) Updated September 25, 2013 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Utilize triangle congruency conjectures (MA 12.2.1c ) Recognize and utilize ratios and proportions of similar figures (MA 12.2.1c, MA 12.2.1d ) Identify and utilize Pythagorean Theorem and converse of the Pythagorean Theorem (MA 12.2.1e) Identify and utilize Right Triangle Trigonometry (MA 12.2.1e) Relate Pythagorean Theorem to distance and midpoint formula (MA 12.2.2b, MA 12.2.2c) Integrate properties of parallel lines and write equations of lines (MA 12.2.2a) Discover and utilize properties of parallel and perpendicular lines (MA 12.2.2a, MA 12.2.1d) Discover and implement properties of circles (MA 12.2.1g) 1.12 1.13 Identify properties of chord, tangent, arc relationships (MA 12.2.5e) Identify and utilize properties of algebra and postulates and premises of Geometry 1.14 Use deductive reasoning to create flow-charts and two column proofs (MA 12.2.1c) 1.15 Recognize and implement inductive and deductive reasoning (MA 12.2.1b, MA 12.2.1c) 1.16 Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true (MA 12.2.1f) Outcome 2 : TLW apply and analyze transformations. 2.1 2.2 Use transformations to deduce geometric properties and shapes (MA 12.2.3a) Perform and describe multiple transformations (MA 12.2.3b) Outcome 3: TLW use visualization, spatial reasoning, and geometric modeling to solve problems. 3.1 3.2 3.3 3.4 3.5 3.6 Create sketch to model real world situations Construct, duplicate, and dissect angles and segments (MA 12.2.4a) Measure segments and angles to the nearest unit Construct parallel and perpendicular lines (MA 12.2.4a) Construct points of concurrency (MA 12.2.4a) Recognize and create number and picture patterns Outcome 4: TLW apply the units, systems, and formulas to solve problems. Updated September 25, 2013 4.1 4.2 4.3 4.4 4.5 4.6 Select the correct length, time, and volume or weight unit of measurement for a given situation (MA 12.2.4b ) Calculate and convert the areas of rectangles, parallelograms, triangles, trapezoids, regular polygons and circles (MA 12.2.5c) Identify similarity in areas and volumes of figures Recognize and utilize the circumference –diameter ratio Convert within and between the English and Metric systems (MA 12.2.5d) Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k2, and k3, respectively (MA 12.2.5g) TECHNICAL MATH FOCUS AREA: Mathematical Computation PURPOSE STATEMENT: TLW use correct numeration and computation to solve real world problems. Outcome 1: TLW identify and apply formulas for two and three dimensional shapes. 1.1 Calculate the areas of rectangles, parallelograms, triangles, trapezoids, regular polygons and circles (Standard 12.4.1) 1.2 Identify similarity in areas and volumes of figures (Standard 12.4.3) 1.3 Recognize and utilize the circumference –diameter ratio (Standard 12.4.3) Outcome 2: TLW utilize geometry vocabulary and analyze relationships among geometric forms. 2.1 Recognize identify and define geometric terms and symbols (Standard 12.4.2) 2.2 Create sketch to model real world situations (Standard 12.4.2) 2.3 Recognize and utilize ratios and proportions of similar figures (Standard 12.4.3) Outcome 3: TLW read and write real numbers. 3.1 Read and write numbers for whole numbers up to billions (Standard 12.1.1) 3.2 Identify different number systems: natural, whole, Integer, and rational (Standard 12.1.1) Updated September 25, 2013 3.3 3.4 3.5 3.6 Understand decimals to three places (Standard 12.1.2) Learn greatest common factor (Standard 12.1.2) Learn least common multiple (Standard 12.1.2) Learn the absolute value of a number (Standard 12.1.2) Outcome 4: TLW estimate and compute with real numbers. 4.1 Write ratios and proportional (Standard 12.2.1) 4.2 Determine equal fractions and mixed numbers (Standard 12.2.1) 4.3. Determine equal percents and decimals (Standard 12.2.1) 4.4 Round whole numbers (Standard 12.2.2) 4.5 Estimate sums, differences, products, and quotients of whole numbers (Standard 12.2.2) 4.6 Add, subtract, multiply, and divide whole numbers (Standard 12.2.3) 4.7 Add, subtract, multiply, and divide fractions (Standard 12.2.3) 4.8 Add, subtract, multiply, and divide with decimals (Standard 12.2.3) 4.9 Find the percent of a number (Standard 12.2.3) 4.10 Find what percent of one number is of another (Standard 12.2.3) Outcome 5: TLW select and utilize the appropriate measurements in daily life. 5.1 Learn to use U.S.A. time zones (Standard 12.3.1) 5.2 Identify units of measurement (Standard 12.3.2) Outcome 6: TLW make inferences and predictions using probability and statistics with real world data 6.1 Find the mean, median, mode, and range of a set of data (Standard 12.5.2) 6.2 Find the probability and use it to solve problems and make decisions (Standard 12.5.3) 6.3 Make conclusions based on interpretation of data from a normal distribution curve (Standard 12.5.5) Outcome 7: TLW interpret and solve algebraic equations and inequalities Updated September 25, 2013 7.1 7.2 7.3 7.4 7.5 Translate verbal expressions to mathematical expressions (Standard 12.6.1) Translate verbal sentences to mathematical equations (Standard 12.6.1_ Solve proportions (Standard 12.6.2) Add and subtract polynomials (Standard 12.6.2) Simplify, multiply, and divide monomials (Standard 12.6.2) CALCULUS Outcome 1: TLW define and determine limits and continuity of functions. 1.1 Given a graph or a table of a function, TLW determine if a limit exists and what it is exists. 1.2 TLW define the limit of a function using L, c, & notation, visually and verbally. 1.3 TLW identify limit theorems and apply them to functions to calculate limits algebraically. 1.4 TLW define continuity and classify discontinuities of functions. 1.5 TLW calculate limits of functions where either x goes to infinity, the limit is infinite, or both. 1.6 TLW apply the Intermediate Value Theorem and explain the consequences involved when utilizing the theorem. Outcome 2: TLW utilize derivatives to find optimal solutions to real world problems involving maximizing and minimizing. 2.1 TLW define the derivative of a function visually, verbally, numerically and using limit notation. 2.2 TLW calculate the derivative of functions using various methods including: the power function rule, the product rule, the chain rule, and implicit differentiation. 2.3 TLW apply derivatives to real world applications. 2.4 TLW define and determine extremes to functions. 2.5 TLW apply first and second derivative tests to real world problems. 2.6 TLW apply extremes to calculate optimization in real world problems. Outcome 3: TLW utilize definite integrals to compute area of regions under a curve. 3.1 TLW define and evaluate infinite and definite integrals. Updated September 25, 2013 3.2 3.3 3.4 3.5 3.6 TLW utilize method of substitution when evaluating integrals. TLW find Riemann sum of a function. TLW apply and prove the mean value theorem and Rolle’s theorem. TLW apply trapezoidal rule and Simpson’s rule to find area under a curve. TLW state and apply the Fundamental Theorem of Calculus to calculate the area under a curve. Outcome 4: TLW identify and calculate the derivative and the integral of the reciprocal function by using the exponential and logarithmic functions. 4.1 4.2 4.3 TLW find the derivatives and the antiderivatives of the following functions: 1/x, log x, ln x, and ex. TLW prove that the natural logarithm has the properties of logarithms. TLW find the limit of an expression in indeterminate form using l’Hospital’s Rule. Outcome 5: TLW utilize definite integrals to compute area between curves, volumes of solids. 5.1 TLW identify and classify critical points visually and algebraically. 5.2 TLW calculate the area between curves. 5.3 TLW find the volume of a solid of revolution. 5.4 TLW find the volume of a solid using a cross section of the figure or by slicing the figure into cylindrical shells. 5.5 TLW find the arc length of a function using a given interval. 5.6 TLW calculate the area of a surface of revolution by slicing the surface into frustrums of cones. 5.7 TLW find the area of a region bounded by the graph and a length of the graph using an equation of a polar function. Outcome 6: TLW find the derivatives and integrals of transcendental functions and apply them to real world situations. 6.1 6.2 6.3 6.4 6.5 TLW define and find the inverse of a function. TLW determine the derivatives and integral of natural logarithmic functions. TLW determine the derivative and integral of logarithmic functions. TLW calculate growth and decay of real world problems. TLW calculate the value of inverse trig functions and find derivative and integrals of the trigonometric functions. 6.6 TLW define hyperbolic functions and find the derivative and integrals of hyperbolic functions. 6.7 TLW define indeterminate forms and apply l’ Hopital’s rule. Updated September 25, 2013 Outcome 7: TLW apply calculus theory numerically, graphically and algebraically to real world problems involving motion. 7.1 TLW calculate the distance traveled and the displacement and object is from a starting point for a specified amount of time given the equation for velocity or acceleration. 7.2 TLW calculate the average value for a function given its equation. 7.3 TLW predict the rate of a quantity that is changing when given the other related rates. 7.4 TLW write the equation for the function to find a maximum or minimum value and identify the path the minimizes a total time or cost . TRIGONOMETRY / PRE CALCULUS Outcome 1: TLW graph relations and functions, analyze families of graphs, and identify: symmetry, continuity, transformations, asymptotes, intercepts and critical points of functions. 1.1 TLW identify symmetrical graphs, use symmetry to complete a graph, and identify odd and even functions. 1.2 TLW identify and graph the functions x2, x3, x4, x5, x, |x|, [x], 1/x using reflections, translations, and dilations. 1.3 TLW determine the inverse of a relation or function and graph a function and its inverse. 1.4 TLW graph rational functions and determine the horizontal, vertical, and slant asymptotes. 1.5 TLW graph polynomial, absolute value, and radical inequalities. 1.6 TLW find the critical points of the graph of a polynomial function and determine if each is a minimum, maximum, or point of inflection. 1.7 TLW determine continuity or discontinuity of functions and identify the end behavior of graphs. Outcome 2: TLW solve polynomial equations, inequalities, rational equations, and radical equations. 2.1 TLW determine roots of polynomial equations and apply the fundamental theorem of algebra. 2.2 TLW solve quadratic equations, use the discriminant to describe the roots of Updated September 25, 2013 2.3 2.4 2.5 2.6 2.7 quadratic equations and inequalities. TLW find the factors of polynomials using the remainder and factor theorems. TLW identify all possible rational roots of a polynomial equation by using the rational root theorem and identify the number of positive and negative real zeros a polynomial function has. TLW approximate the real zeros of a polynomial function and graph polynomial functions. TLW solve rational equations and inequalities and decompose a fraction into partial fractions. TLW solve radical equations and inequalities. Outcome 3: TLW convert angle measures between radians and degrees and utilize the unit circle and six trigonometric functions to solve for angles. 3.1 TLW convert angle measures from radians to degrees and vice versa. 3.2 TLW identify angles that are coterminal with a given angle and find the reference angle for a given angle. 3.3 TLW find the length of an arc given the measure of the central angle, find linear and angular velocities, and find the area of a sector. 3.4 TLW find the values of the six trigonometric functions of an angle in standard position given a point on its terminal side. 3.5 TLW find exact values and decimal approximations for the values of the six trigonometric functions for any angle. Outcome 4: TLW solve for parts of triangles and find area of triangles. 4.1 4.2 4.3 4.4 4.5 TLW solve right triangles using the six trigonometric functions. TLW determine whether a triangle has zero, one or two solutions. TLW solve triangles by using the law of sines. TLW solve triangles by using the law of cosines. TLW find the area of triangles. Outcome 5: TLW identify, graph and utilize transformations of trigonometric functions and the inverses of the trigonometric functions to solve real world problems. 5.1 TLW identify and utilize the graphs of trigonometric functions. Updated September 25, 2013 5.2 TLW identify the amplitude, period, and phase shift for a trigonometric function and write equations of trigonometric functions given the amplitude, period, and phase shift. 5.3 TLW graph various trigonometric functions. 5.4 TLW evaluate and find principle values of inverse trigonometric functions. 5.5 TLW graph and write equations for inverses of trigonometric functions. 5.6 TLW solve problems involving simple harmonic motion. Outcome 6: TLW verify and utilize trigonometric identities to solve trigonometric equations and write the normal form of a linear equation. 6.1 TLW identify and use reciprocal identities, quotient identities, Pythagorean identities, and symmetry identities. 6.2 TLW utilize the basic trigonometric identities to verify other identities and find numerical values of trigonometric functions. 6.3 TLW utilize the sum and difference identities and the double- and half-angle identities for the sine, cosine, and tangent functions to solve trigonometric equations. 6.4 TLW write a linear equation in normal form. Outcome 7: TLW manipulate vectors and parametric equations to solve problems related to the motion of a projectile. 7.1 TLW find equal, opposite, and parallel and add and subtract vectors geometrically. 7.2 TLW find ordered pairs that represent vectors and add, subtract, multiply, and find the magnitude of vectors algebraically. 7.3 TLW add, subtract, and find the magnitude of vectors in three dimensional space. 7.4 TLW find the inner and cross products of two vectors and determine whether two vectors are perpendicular. 7.5 TLW solve problems using vectors and right triangle trigonometry. 7.6 TLW write vector and parametric equations of lines and graph parametric equations. 7.7 TLW model the motion of a projectile using parametric equations and solve problems related to the motion of a projectile, its trajectory, and range. Outcome 8: TLW graph polar equations and manipulate complex numbers in both rectangular and polar form. 8.1 TLW graph polar equations, manipulate complex numbers in both rectangular and polar form, and convert between the two systems. 8.2 TLW graph polar coordinates and polar equations. Updated September 25, 2013 8.3 8.4 8.5 8.6 8.7 TLW write and graph the polar form of linear equations. TLW add, subtract, multiply, and divide complex numbers in rectangular form. TLW change complex numbers from rectangular to polar form and vice versa. TLW find the product and quotient of complex numbers in polar form. TLW find the products and roots of complex numbers in polar form using DeMoivre’s threorem. Outcome 9: TLW graph conic sections in the coordinate plane and write equations for parabolas, circles, ellipses, and hyperbolas. 9.1 TLW find the distance between two points and the midpoint of a line segment in the coordinate plane algebraically and geometrically. 9.2 TLW graph and write equations for parabolas. 9.3 TLW graph and write equations for circles. 9.4 TLW graph and write equations for ellipses. 9.5 TLW graph and write equations for hyperbolas. 9.6 TLW solve systems of equations involving quadratics graphically and algebraically. Updated September 25, 2013