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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