MATHEMATICS K-8

KINDERGARTEN MATH

NUMERATION

Read, Write, and Compare Numbers

Count by Memory

• Stage 1 (0-9)
• Stage 2 (10-100)
• Stage 3 (0-100)

Count Movable Objects (cubes, paper clips, counters, pencils, etc.)

• Count up to 20 from memory
• One to one correspondence - touch and count each item in the right order

Count to 10 by 2’s, 5’s and 10’s

Count backwards from 10

Match Sets with Numbers to Ten

• Recognize numbers 1 to 10
• Count ordered objects up to 10
• Count unordered objects up to 10

Recognize Numbers 0-20 in Random Order

• Recognize numbers 0-20
• Recognize number patterns
• Point to numbers that are named
• Name numbers in random order

Writing Numbers

• Write numbers 0-9 using correct number formation
• Write numbers 0-20 using correct number formation

MEASUREMENT

Describe Objects

• Sort and describe objects by color, weight, shape, and any other kinds of size
• Use the words for size (more/less, large/small, heavy/light, short/long, some/none, least/most, few/many, little/big, thin/fat, and thick/thing)
• Use the words for position and direction (up/down, out/in, top/middle/bottom, over/under, closed/open, go/stop, high/low, inside/outside, beginning/end, off/on, far/near, below/above, beside/in front of/behind, first/second/third/etc.)

Time

• Demonstrate understanding of the concepts of time (morning, afternoon, evening, day, week, month, year, yesterday, tomorrow)
• Tools used to measure time (clock, calendar)
• Tell time to the hour

Money

• Identify a penny, nickel, dime and state its value

ESTIMATION AND COMPUTATION

Understand and describe simple addition and subtraction operations

• Recognize +, – , and = signs
• Understand one-to-one correspondence
• Use up to 10 objects to join, separate, sort, and classify sets

Simple Addition and Subtraction Using Objects

• Join sets
• Separate sets
• Explain how they are joining and separating sets

FUNCTIONS AND RELATIONSHIPS

Recognize, describe, extend, and create simple patterns

• Identify, sort, and classify objects by attribute
• Identify objects that do not belong to a particular group
• Identify, describe, and extend simple patterns according to shape, size, color or object
• Predict what comes next, add to a given pattern, copy a pattern from a model, make their own pattern
• Identify basic patterns in number (counting by1’s, 5’s and 10’s)

GEOMETRY

Identify geometric shapes and their features

• Identify and describe circles, triangles, rectangles, squares, oval, and diamond
• Compare objects by position, shape, size, number of corners, etc.

STATISTICS/PROBABILITY

Collect, Display, and Interpret Information about Objects and Events in the Environment

• Make and use pictographs, bar graphs, and real object graphs
• Use graphs to compare and make simple predictions

PROBLEM SOLVING, COMMUNICATION, REASONING

• Develop strategies to solve problems
• Talk about strategies

FIRST GRADE MATH

NUMERATION:

Read, Write, and Compare Numbers to 100

• Count aloud to 100
• Counting on (0-100)
• Counting backwards
• Write numbers to 100 in order
• Identify and write numbers to 100 out of order
• Put two-digit numbers in order
• Tell if numbers are greater than, less than, or equal using words and symbols (<, >, =)

Count to 100 in Many Ways

• See the pattern in numbers from 0-100
• Count and write by 2’s (both even and odd numbers), 5’s and 10’s to 100

Place Value of Ones and Tens

• Group objects by ones and tens
• Identify the ones place and tens place in two-digit numbers
• Count and group objects into tens and ones, and use words, models, and symbols to represent the numbers

Identify Simple Fractions

• Identify part of a whole and part of a group ( ½ , 1/3, ¼ )

MEASUREMENT

Choose a Unit of Measure

• Measure using nonstandard units (paper clips, cubes, pencils, shoes, etc.)
• Estimate and measure length in inches, a foot, centimeters(longer/shorter), yard, and meter
• Compare the weight of an object to a pound, kilogram
• Compare cups, pints, quarts, and liter
• Relate temperature on a thermometer to pictures
• Calendar (months, days of the week)

Time

• Tell and write time to hour and half hour using analog and digital clocks (before/after and shorter/longer)

Money

• Identify the value of a nickel as 5 cents (counting groups of pennies and nickels)
• Identify the value of a dime as 10 cents (counting groups of dimes and pennies)
• Identify the value of a quarter as 25 cents (explore groups of coins whose value is 25 cents)
• Count groups of coins using one quarter, dimes, nickels, and pennies with values less than a dollar

ESTIMATION AND COMPUTATION

Addition and Subtraction Process

• Know the meaning of symbols (+, -, =)
• Use manipulatives to add and subtract
• Add or subtract using numbers vertically and horizontally
• Identify one more than, one less than
• Missing addends
• Estimate computation
• Learn and memorize basic addition and subtraction facts (sums through 20)
• Know fact families and “double” facts

Add and Subtract Two-Digit Numbers Without Regrouping

• Solve two-digit addition and subtraction problems using manipulatives
• Identify ten more than, ten less than
• Estimate and check quantities 10-100
• Start addition or subtraction process in the ones columns
• Correctly line up addition and subtraction problems with two-digit numbers

FUNCTIONS AND RELATIONSHIPS

• Create and Solve Problems
• Recognize and use the symbols +, - and =
• Explore inverse operations with addition and subtraction
• Sort objects and recognize , describe, extend , and create patterns involving numbers, shape, size, rhythm, or color
• Create addition and subtraction sentences which demonstrate understanding of commutative identity properties using manipulatives and pictures

GEOMETRY

Identify, Describe, Classify Geometric Shapes and Describe their Position/Location in Space

• Identify and describe circles, triangles, rectangles, and squares
• Solid shapes: identify real life objects with solid shapes (cube, cylinder, sphere, cone)
• Flat shapes: learn names, number of sides, number of corners
• Draw and build familiar shapes
• Open and closed figures
• Use terms such as left, right, middle, near, far, below, above, up, etc. to give and respond to directions about location (inside/outside) and to describe
• Identify objects that are symmetrical
• Congruency

STATISTICS/PROBABILITY

• Collect, Organize, Display, and Interpret Data on Simple Graphs and Charts
• Make and use pictographs, bar graphs, and real object graphs
• Use graphs to interpret and compare data and make predictions
• Use tally marks to tabulate data
• Determine if the outcomes or possible or impossible
• Sort using 2 circle Venn diagrams

PROBLEM SOLVING, COMMUNICATION, REASONING

• Solve and create simple word problems
• Calculate simple problems mentally
• Develop and apply strategies to solve problems
• Explain thinking about problem strategies and solutions
• Children act out a story problem

SECOND GRADE MATH

NUMERATION

Understand Place Value of Three-Digit Numbers in the Base Ten Number System

• Recognize, read, order, and count from 0-1,000
• Use, model, and identify place value positions of 1’s, 10’s, 100’s, and 1,000’s
• Recognize and use less than (<), greater than (>), and equal to
• Identify odd and even numbers
• Know that a group of ten can be broken into ten ones and that ten ones equals a group of ten
• Know that a group of 100 can be broken into 10 tens and that 10 tens equal a group of 100
• Know the sequence of numbers up to 1,000

Count to 1,000 in Many Ways

• See the pattern in numbers 0-1,000
• Skip count by 2’s, 5’s and 10’s forwards and backwards
• Count backwards from 20
• Skip count starting at any point
• Count by 10’s starting with a number such as 43

Understand and Use Fractions as Parts of a Set and Parts of a Whole

• Identify part of a whole up to 1/12
• Recognize that when all parts are included the result is one
• Divide a circle, square, rectangle into ½, 1/3, 2/3, ¼, and ¾

MEASUREMENT

Select and Use Appropriate Tools of Measurement

• Read a calendar (length of the day, week, month, and year)
• Tell time on an analog and digital clock to the nearest quarter hour and five minute intervals

Compare Length, Width, Capacity and Time Using Standard and Nonstandard Units of Measure

• Use standard linear measures (inch, foot, yard, centimeter and meter)
• Use liquid measures (cup, pint, quart, gallon, and liter)
• Measure down to one-half inch and one centimeter

Money

• Identify and recognize the value of dollar bills ($1, $5, $10, $20, $50) and coins, (penny, nickel, dime, quarter, half-dollar) and the value of given sets of coins
• Exchange money for equal values and make change

ESTIMATION AND COMPUTATION

Perform Basic Arithmetic Functions Using Mental Math and Pencil and Paper

• Know fact families and “double” facts
• Know basic addition and subtraction facts from 1-20 (memorization)
• Identify 10 more than and ten less than
• Solve 2- and 3-digit addition and subtraction problems using a variety of models and algorithms
• Understand the meaning of addition and subtraction
• Demonstrate the commutative and identity properties of addition
• Model multiplication as repeated addition and division as “sharing equally” and grouping objects
• Determine whether a solution to a problem is reasonable (estimate sums and differences in a 2-digit problem)
• Work number sentence vertically and horizontally
• 2-digit addition, subtraction, and 3 single digit column addition
• 2-digit addition, subtraction regrouping

FUNCTIONS AND RELATIONSHIPS

Recognize, Identify, and Complete Patterns

• Make their own patterns and describe them
• Complete a pattern
• Skip count by 2’s, 5’s and 10’s
• Use a calculator to find and extend patterns in the number system
• Complete a problem with a missing operation (missing addend, subtrahend)

GEOMETRY

Construct, Compare, Classify, and Analyze the Relationship between Geometric Figures

• Identify and classify 3-dimensional shapes
• Demonstrate an understanding of symmetry and congruency
• Understand and measure the area and perimeter of rectangles
• Solid shapes: cubes, spheres, cylinders, cones, pyramids, and rectangular prisms

STATISICS/PROBABILITY

Predict and Record Outcomes of Events

• Explain differences between chance and certainty, giving examples
• Collect, Record, and Interpret Data Using Graphs
• Represent the data in a variety of ways (tally marks, bar graphs, pictographs, and a two circle Venn diagram)
• Interpret data by reading graphs, use graphs to compare and problem solve
• Use the terms maximum and minimum when working with a data set

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Solve and create word problems
• Calculate simple problems mentally
• Choose appropriate operations to solve problems
• Build links between abstract and concrete
• Discuss problem strategies and solutions
• Draw logical conclusions (justify solutions, thinking processes, and conjectures in a variety of ways)
• Defend estimations, solutions and/or predictions
• Apply mathematical skills and process to literature
• Apply mathematical skills and processes to situations with self and family
  

THIRD GRADE MATH

Benchmark Level 1
Given During the Spring

NUMERATION

Understand Place Value of Four-Digit Numbers in Base Ten Number System

• Recognize, read, order and count from 0-10,000
• Use less than (<), greater than (>), and equal to in order to compare and order numbers
• Compare odd and even numbers
• Round to the nearest 10’s and 100’s
• Use, model, and identify place value positions of 1’s, 10’s, 100’s and 1,000’s
• Understand and Use Fractions as Parts of a Set and Parts of a Whole
• Develop a numbers sense for fractions
• Demonstrate equivalent fractions
• Know the meaning of denominator as the whole and numerator as parts of the whole and be able to tell which simple fraction is larger
• Compare, read, write, add, and subtract decimals with tenths and hundredths

MEASUREMENT

• Choose and Use Appropriate Tools of Measurement
• Tell time on an analog and digital clock to the nearest minute and elapsed time
• Compare, estimate, and measure length, volume, weight in metric and traditional units
• Compare and order objects by various measurable attributes including calendar and temperature
• Applies problem solving strategies to determine a specific date on a calendar
• Money
• Recognize, read, write, and use money through $100
• Exchange money for equal values and make change through $100

ESTIMATION AND COMPUTATION

Perform Basic Arithmetic Functions Using Mental Math and Pencil and Paper

• Readily recall addition and subtraction facts through 20 and multiplication and division 0-5 (orally and with pencil and paper without a calculator)
• Use strategies to memorize facts
• Check addition using subtraction and subtraction using addition
• Add and subtract 4-digit numbers with or without regrouping
• Model multiplication as “repeated addition” and division as “equally sharing”
• Use arrays area as a model of multiplication and division
• Add and subtract whole numbers to 10,000 using a variety of models and algorithms
• Line up four-digit numbers to add and subtract
• Discriminates between useful and non-useful information in problems
• Solves multi-step problems

FUNCTIONS AND RELATIONSHIPS

Recognize, identify, and complete patterns

• Recognize, describe, extend, and create a wide variety of patterns with a variety of materials, including symbols, objects and manipulatives
• Identify the input or output number in a function table, given a rule
• Use a calculator to find and extend patterns in a number sequence
• Complete a problem with a missing operation (missing addend, subtrahend, factor)
• Complete open space sentences with missing numbers and appropriate vocabulary
• Solve simple functions by identifying and applying addition and subtraction patterns
• Applies strategies to a given story problem to extend a pattern
• Solve addition, subtraction, and multiplication problems (e.g. 9’s finger strategy, doubles strategy, 0 on 10’s strategy, neighbors, etc.)

GEOMETRY

Construct, Compare, Classify, and Analyze the Relationship among Geometric Figures

• Identifies simple transformations spatially (slides, flips, and turns)
• Identify, sort, describe, model, and compare 2- and 3- dimensional shapes
• Demonstrate an understanding of symmetry (draw a line of symmetry) and congruency
• Determine area and perimeter of polygons
• Recognize geometric shapes in the environment
• Use comparative directional and positional words (horizontal, vertical)
• Combines shapes to make a new shape
• Identify, sort, describe, model, and compare solid figures including cube, spheres, cylinders, cones, pyramids, and rectangular prisms

STATISITICS/PROBABILITY

Predict and Record Outcomes of Events

• List possible outcomes of events
• Explore concepts of chance
• Draws conclusions about mathematical problems
• Collect, Record, and Interpret Data Using Graphs
• Collect data, construct, and interpret graphs and tables
• Find and record the possibilities of simple probability experiments
• Conduct a survey and tally the results
• Finds examples that support or refute mathematical statements
• Uses everyday language to explain graphical data

PROBLEM SOLVING, COMMUNICATION, REASONING

• Solve word problems using addition, subtraction, multiplication, and division
• Calculate problems mentally
• Justify answers and solution processes (verbally and through writing)
• Apply concepts and practices to situations outside math class
• Uses everyday language to explain own thinking about solutions
  

FOURTH GRADE MATH

NUMERATION

• Read, Write, and Compare Whole Numbers
• Read, write, model and order positive and negative whole numbers to 1,000,000 including thermometers and number lines
• Use manipulatives to show understanding of number value, computation, properties, operations and place value
• Know each place value to million
• Recognize 100 and 1,000 more or less than a given number
• Describe a number using expanded notation
• Read, write, round and order decimals to tenths and hundredths
• Demonstrate the commutative and identity properties of multiplication
• Understand the meaning of division
• Read and write Roman numerals to 100

MEASUREMENT

• Convert standard units of money, distance, and time
• Measure line segments to the nearest centimeter
• Convert between millimeters, centimeters and meters
• Convert between inches, feet, and yards
• Solve problems regarding the measurement of the perimeter and area of real and represented objects
• Draw, measure, and classify basic geometric shapes
• Find perimeter of regular and irregular shapes
• Write and solve word problems involving map scales, elapsed time and temperature
• Read and create schedules, timetables, and timelines to solve time/distance/rate problems

ESTIMATION AND COMPUTATION

Perform Basic Arithmetic Functions Using Mental Math and Paper and Pencil

• Know multiplication facts through 10's
• Recognize fact families of multiples through 12's
• Know division facts through 10's
• Solve one- and two-digit multiplication problems
• Divide multi-digit numbers by one-digit divisors
• Add and subtract decimals to tenths and hundredths, including money amounts, using model and algorithm
• Add and Subtract Whole Numbers and Fractions with Common Denominators to 12 using Models and Algorithms
• Give equivalent names for whole number, fractions and decimals
• Understand and Use Fractions
• Add and subtract fractions with like denominators
• Demonstrate one whole has many fractional representations
• Create Estimates Based on Rounding Off and Use of Compatible Numbers
• Multiplying by the powers of 10
• Decide to what place it is reasonable to round given data
• Round numbers to estimate the answer to a word problem
• Make Reasonable Estimates and Determine if They Are Appropriate and Valid
• Use Mental Math when Appropriate
• Develop and Interpret Scales and Scale Models

FUNCTIONS AND RELATIONSHIPS

• Identify, predict, and complete patterns in increasingly complex form
• Skip count by odd, even, and intervals
• Recognize and solve problems based on existing patterns
• Describe patterns within a number chart
• Identify and complete input/output rules (find the rule, the input, or the output to input/output scenarios to a sum or product of 100)
• Write number sentences using letters or shapes to represent missing numerals
• Write and solve word problems that use equations containing a variable (at least one unknown)
• Decide which operation is necessary to make an equation true
• Use parentheses in numerical equations
• Use a calculator to find a missing item in a number sequence

GEOMETRY

Construct, Compare, Classify, and Analyze the Relationship among Geometric Figures

• Draw, measure, and classify basic geometric shapes and describe their attributes (plane and solid figures)
• Draw and label parallel and perpendicular lines
• Classify angles as right, obtuse, acute or straight
• Identify and describe properties of polygons
• Recognize congruent shapes after they have been rotated, reflected, enlarged, or reduced
• Use standard terms to describe a location of objects in space
• Compare and contrast plane and solid figures using relevant attributes, including the number of vertices, edges and the number and shape of faces
• Locate points specified by ordered pairs, on a rectangular coordinate grid
• Identify, classify, and compare various triangles and quadrilaterals according to their sides and/or angles

STATISTICS AND PROBABILITY

• Find the mean, median, mode and range within a given set of data
• Collect and organize pertinent data; use it to construct chart, table, or graph
• Prepare and conduct a survey and tally or otherwise organize the results
• Describe and explain data from tables, charts, and graphs
• Use data to make predictions
• Present probability data using fractions
• Conduct simple probability experiments using concrete materials and represent results using fractions and probability
• Create and solve probability problems about chance occurrences that are expressed as simple fractions

PROBLEM SOLVING, COMMUNICATION, REASONING

• Use a variety of techniques to investigate and solve problems
• Verbal, written, tabled, and tallied explanation of techniques used to analyze problems
• Create relevant and accurate graphs and tables
• Demonstration with manipulatives
• Organization and presentation of information by a group
• Pattern discovery and use of predictions based on patterns
• Estimation, mental math, and trial and error
• Working backwards
• Use mathematical vocabulary appropriate to the problem
• Determine if sufficient data exists to solve the problem and develop an organized approach to solve it
• Verify results to determine validity of answers
• Justify answers, solutions, process, and mathematical strategies

FIFTH GRADE MATH

(Revised May 2005)

Statistics (Statistics and Probability Standard)

I. Students will read and interpret graphs.

a. Pictographs
b. Bar graphs
c. Line graphs
d. Line plot
e. Stem and leaf plot
f. Students will compare information from different graphs.

II. Students will use, organize and display data using graphs and charts

a. Construct bar graphs with appropriate scale
b. Construct line graphs
c. Construct stem and leaf plots
d. Construct tables
e. Construct tally charts
f. Students will explain the reasons why they chose to create a particular graph, chart or table.

III. Students will calculate and analyze data

a. Determine range
b. Determine median
c. Determine mean
d. Determine mode
e. Students will use patterns in a table to determine missing values.

IV. Students will collect data

a. Students will collect and organize information to be used in graphs, tables or charts.

i. Experiments
ii. From real-world materials (magazines, newspapers, graphs)

Number Theory (numeration and function/relationships standards)

I. Students will explain, model, and identify patterns in numbers

a. Identify and explain prime and composite numbers using pictures, models, symbols and words
b. Discover, describe and follow numerical rules using words, lists or tables
c. Identify and complete patterns in increasingly complex form

i. Extend patterns represented by tables or models

d. use addition, subtraction, multiplication or division to solve an unknown in a number sentence
e. find and describe patterns within a number chart.

Understanding Large Numbers (Numeration Standard)

II. Students will understand and work with large numbers from thousandths to billions

a. Students will write numbers in word form
b. Students will write numbers in standard form
c. Students will write numbers in expanded form
d. Students will use exponents
e. Students will round numbers
f. Students will compare numbers
g. Students will order numbers
h. Students will understand place value patterns in base 10 (example: multiply by 10 to move to the next place value)

III. Students will use large numbers in math problems

1. Know basic multiplication and division facts through 12's
2. Estimate answers using front-end estimation, rounding, or multiplying by a power of 10.
3. Use manipulatives to model and explain multiplication and division.
4. Students will add large numbers
5. Students will subtract large numbers
6. Students will multiply large numbers
7. Students will divide large dividends by 2-digit divisors

a. Students will write remainders as decimals, remainders or round off as necessary.

Understanding Decimals ( Numeration Standard)

I. Students will understand decimals to the thousandths place.

a. Read, identify and name decimal numbers (ie "eight-tenths" instead of "zero point eight")
b. Write decimal numbers
c. Round decimal numbers
d. Compare decimal numbers
e. Order decimal numbers
f. Model decimal numbers
g. Describe decimal numbers
h. Illustrate decimal numbers

II. Students will use decimals in math problems

a. Estimate the answer to addition, subtraction and multiplication problems with decimals.
b. Addition with decimals
c. Subtraction with decimals
d. Multiplication with decimals
e. Division with decimals in the dividend. This includes money problems.

Geometry of two-dimensional figures (Geometry standard)

I. Students will be able to identify, classify, compare and sketch geometric figures.

a. 2-dimensional shapes
b. Similar, congruent and symmetrical figures
c. Line segments, midpoints, intersections, parallels and perpendicular lines

II. Students will be able to measure geometric figures

a. Use a protractor to draw and measure angles.

III. Students will draw, describe, and analyze the results of transformations of polygons

a. Flips
b. Slides
c. rotations

Fractions (Numeration Standard)

I. Students will understand fractions

a. Students will compare and order fractions using models, pictures, symbols and descriptions
b. Find equivalent fractions
c. Convert between simple fractions, decimals and percents
d. Convert between mixed numbers and improper fractions
e. Reduce fractions to the lowest terms
i. Find the greatest common factor of a set of numbers

ii. Find the least common multiple of a set of numbers

f. Find fractional parts of a whole number using mental math.

II. Students will solve math problems involving fractions

a. Estimate the answers to addition, subtraction and multiplication problems involving fractions.
b. Model and explain adding and subtracting proper fractions and mixed numbers.
c. Add fractions and mixed numbers with like and unlike denominators
d. Subtract fractions and mixed numbers with like and unlike denominators
e. Multiply fractions

Measurement (Measurement Standard)

I. Students will understand and use customary units of measurement

a. Students will be familiar with the following units:

i. Length (inch, feet, yard, mile)
ii. Capacity (fl. Oz, cup, pint, qt, gal)
iii. Weight (oz, lb, ton)

b. Estimate using customary units
c. Measure to the nearest 1/8 inch
d. Choose the best customary unit of measure for a given situation
e. Possess a "mental picture" of each of the units of customary measure (ie, an inch is about as long as…)
f. Convert and use units within the customary system.
g. Use appropriate tools to measure length, capacity and weight

II. Students will understand and use metric units of measurement

a. Students will be familiar with the following metric units

i. Length (mm, cm, m, km)
ii. Volume (mL, L)
iii. Mass (g, kg)

b. Estimate using metric units
c. Measure to the nearest mm using a ruler
d. Choose the best metric unit of measure for a given situation
e. Possess a "mental picture" of each of the units of metric measure (ie. A centimeter is about as long as…)
f. Know metric prefixes (kilo, centi, milli) and values
g. Convert and use units within the metric system.
h. Use appropriate tools to measure length, volume and mass.

Area and Perimeter of Polygons (Measurement and Geometry Standards)

I. Students will find perimeter of polygons

a. Possess a conceptual understanding of perimeter
b. Understand how to determine the perimeter of a polygon
c. Understand and use a formula to find perimeter of rectangles.
d. Convert metric or customary units to find perimeter of a polygon.

II. Students will find the area of polygons, including squares, rectangles, parallelograms and triangles.

a. Build a conceptual understanding of what area is
b. Use various methods to determine area of polygons

i. Use grid paper
ii. Draw a grid

c. Use formulas to determine the area of polygons
d. Compare and contrast the usefulness of various methods for finding area

Circles (measurement and geometry standards)

I. Students will estimate and determine the circumference of a circle using manipulatives.
II. Students will explore the relationship between the diameter and the circumference of a circle (pi).
III. Students will identify, compare or describe attributes and properties of circles (radius, diameter, circumference).
IV. Students will use a formula to find the circumference of a circle.

Solids and Measurement (Geometry and measurement standards)

I. Students will classify, compare, and sketch solids

a. Pyramids
b. Prisms
c. Nets

II. Students will find surface areas of rectangular prisms and cubes

a. Modeling with manipulatives
b. Using formulas

III. Students will find the volumes of rectangular prisms and cubes

a. Modeling with manipulatives
b. Using formulas

Money, Time and Temperature (statistics and probability standard, measurement standard)

I. Students will use time in mathematical problems

a. Tell time using an analog clock to the nearest minute, using AM or PM

II. Students will use money in math problems

a. Demonstrate an understanding of basic economics, comparison shopping, money sense, making change, and counting money.
b. Convert standard units of money
c. Solve problems with money combinations

III. Students will measure and use temperature in math settings

a. Use appropriate tools to measure temperature
b. Accurately measure temperature using Fahrenheit and Celsius

Ratios, Percents and Proportions (Numeration, Estimation and Computation standards)

I. Students will have a conceptual understanding of a ratio

a. Equal ratios
b. Proportions

II. Students will use percents

a. Estimate percent of a number
b. Find percent of a number
c. Convert between fractions, ratios and percents.

III. Students will understand, calculate, describe and analyze probability

a. Fairness
b. Using probability to predict an outcome in situations and experiments
c. Writing probability as simple fractions.

Embedded Problem Solving (Problem Solving Standard)

I. Students will read, analyze, summarize and understand familiar and unfamiliar multi-step problems
II. Students will select, modify, and apply appropriate strategies to solve multi-step problems.
III. Students will verify, evaluate, communicate and interpret solutions

Embedded Communication (Communication Standard)

I. Students will communicate mathematical thinking by:

a. Using appropriate mathematical language and vocabulary
b. Using pictures to support explanations
c. Using concrete materials to support explanations
d. Using correct symbols to support explanations

II. Students will justify answers, solutions, process, and mathematical strategies using examples

Embedded Reasoning (Reasoning standard)

I. Students will use informal deductive reasoning in concrete contexts.

a. Make appropriate generalizations and apply them to new situations.

Embedded Connections (Connections standard)
Emphasized throughout all areas of instruction

I. Students will apply mathematical skills and processes to other disciplines and areas of life.
II. Listen and observe mathematical information from the real world.

SIXTH GRADE MATH

(Revised May 2005)

Statistics (Statistics and Probability Standard)

I. Students will read and interpret graphs.

a. Bar graphs
b. Pictographs
c. Line graphs
d. Scatterplots (identify trends)
e. misleading graphs

II. Students will use, organize and display data using graphs and charts.

a. Bar graphs (identify appropriate scale, broken scale)
b. Stem and leaf diagrams
c. Tally charts
d. Frequency charts
e. Line plots

III. Students will calculate and analyze statistical data.

a. Mean
b. Mode
c. Median
d. Range
e. Outlier (determine and analyze its effect on a set of data)

IV. Students will collect data.

a. Students will design investigations and collect and display data from investigations throughout the content areas.

Understanding Large Numbers and Operations (Numeration Standard)

I. Students will understand and work with large numbers from thousandths to millions.

a. Word form
b. Number-word form
c. Exponents
d. Rounding
e. Compare numbers
f. Order numbers

II. Students will display number and operation sense.

a. Recall basic addition, subtraction, multiplication, and division facts efficiently upon entering sixth grade
b. Mental math (when appropriate)
c. Showing work clearly (when appropriate)
d. Use a calculator (when appropriate)
e. Use estimation for many mathematical purposes
f. Model distributive property in Base 10
g. Order of operations

Variables, Expressions and Equations (Functions and Relationships Standard)

I. Students will understand and use variables.
II. Students will understand, evaluate and create their own mathematical expressions.
III. Extend patterns up to ten terms found in tables, sequences or problem situations.
IV. Use rules to give a verbal/written generalization of a pattern using words, lists, tables with or without variables.
V. Identify or apply multiplication or division to find missing values in a function.
VI. Students will solve and write equations with whole numbers.

a. Understand what an equation is
b. Determine if an equation is true or false
c. Find the value of the variable that makes the equation true
d. Write equations from given information

Decimals (Numeration Standard)

I. Students will understand decimals.

a. Read, identify and name decimal numbers to the thousandths place (ie, "eight tenths" instead of "zero point eight")
b. Write decimal numbers
c. Round decimal numbers
d. Compare decimal numbers
e. Order decimal numbers
f. Count using decimal numbers
g. Model decimal numbers
h. Describe decimal numbers
i. Illustrate decimal numbers

II. Students will understand and use scientific notation.
III. Students will use decimals in math problems.

a. Addition with decimals
b. Subtraction with decimals
c. Multiplication with decimals
d. Division with decimals in the dividend and the divisor

Measurement (Measurement Standard)

I. Students will understand and use metric units of measure.

a. Students will be familiar with the following metric units

i. Length (mm, cm, m, km)
ii. Volume (ml, l)
iii. Mass (g, kg)

b. Estimate using metric units
c. Measure to the nearest millimeter using a ruler on a map or drawing
d. Choose the best metric unit of measure for a given situation
e. Possess a "mental picture" of each of the units of metric measure (i.e., a centimeter is about as long as…)
f. Convert and use units within the metric system

II. Students will understand and use customary units of measure.

a. Students will be familiar with the following customary units

i. Length (in, ft, yd, miles)
ii. Capacity (fl. oz, cup, pint, qt, gal)
iii. Weight (oz, lb, ton)

b. Estimate using customary units
c. Measure to the nearest 1/8 inch using a ruler on a map or drawing
d. Choose the best customary unit of measure for a given situation
e. Possess a "mental picture" of each of the units of customary measure (ie, an inch is about as long as…)
f. Convert and use units within the customary system

III. Solve real world problems involving elapsed time between US time zones.

Perimeter and Area of Polygons (Measurement and Geometry Standards)

I. Students will find perimeter of polygons.

a. Possess a conceptual understanding of perimeter
b. Understand how to determine the perimeter of a polygon
c. Understand and use a formula to find perimeter of rectangles
d. Convert metric or customary units to find perimeter of a polygon

II. Students will find the area of polygons, including squares, rectangles, parallelograms, and triangles.

a. Build a conceptual understanding of what area is
b. Use various methods to determine area of polygons

i. Use grid paper
ii. Draw a grid
iii. Etc.

c. Use formulas to determine the area of polygons
d. Compare and contrast the usefulness of various methods for finding area

Circles (Measurement Standard)

I. Students will estimate and determine the circumference of a circle using manipulatives.
II. Students will explore the relationship between the diameter and the circumference of a circle (pi).
III. Students will identify, compare or describe attributes and properties of circles (radius, diameter, circumference)
IV. Estimate the area of a circle using a grid or manipulatives.

Number Theory (Numeration Standard)

I. Students will explain, define, and use concepts of number theory

a. Divisibility rules
b. Prime and composite numbers
c. Prime factorization using factor trees
d. Least common multiples
e. Greatest common factor

Connecting Fractions to Decimals (Numeration and Estimation and Computation Standards)

I. Students will understand ideas about fractions and mixed numbers

a. Find equivalent fractions
b. Compare and order fractions
c. Convert mixed numbers to improper fractions
d. Convert improper fractions to mixed numbers
e. Express answers in simplest form

II. Students will understand the relationship between fractions and decimals.

a. Convert fractions to decimals
b. Convert decimals to fractions

Adding and Subtracting Fractions (Numeration and Estimation and Computation Standards)

I. Students will understand, compute and solve problems using addition and subtraction with fractions.

a. Estimate to predict results and check accuracy
b. Add and subtract fractions with like and unlike denominators
c. Add and subtract mixed numbers, including borrowing
d. Express answers in simplest form

Multiplying and Dividing Fractions (Numeration and Estimation and Computation Standards)

I. Students will understand, compute and solve problems using multiplication and division with fractions and mixed numbers.

a. Estimate to predict results and check accuracy
b. Express answers in simplest form

Geometry of Polygons (Geometry Standard)

I. Students will review lines.

a. Lines
b. Segments
c. Rays
d. Endpoints
e. Intersecting lines
f. Parallel lines
g. Perpendicular lines

II. Students will review angles.

a. Angles
b. Sides
c. Vertex
d. Acute angles
e. Right angles
f. Obtuse angles
g. Straight angles

III. Students will measure and draw angles.

a. Estimate angle measurements
b. Use a protractor to measure acute, right, straight, and obtuse angles
c. Use protractor to accurately draw angles of a given measure

IV. Polygons

a. Students will identify, compare, draw, visualize, and classify polygons by their sides and angles.

i. Triangles

1. Acute
2. Right
3. Obtuse
4. Find the measurement of a missing angle
5. Equilateral
6. Isosceles
7. Scalene

ii. Regular and Irregular Quadrilaterals
iii. Regular and Irregular Pentagons
iv. Regular and Irregular Hexagons
v. Regular and Irregular Octagons

V. Students will draw, describe, and analyze the results of transformations of polygons.

a. Flips

i. Line Symmetry

b. Turns

i. Rotational Symmetry

c. Slides

i. Tessellations

Integers and the Coordinate Plane (Numeration, Functions and Relationships, and Geometry Standards)

I. Students will read, write, compare, order, understand, compute, and solve problems with integers.

a. Addition
b. Subtraction

II. Students will graph, label, and identify whole number ordered pairs on the coordinate plane.

a. Locate points

i. Vocabulary

1. coordinate plane
2. coordinate
3. x-axis
4. y-axis
5. origin
6. quadrants
7. ordered pair

b. Identify midpoint (ie: using a map to trace a route and calculate distance)

Ratio, Proportion, and Percent, Similar Figures (Numeration and Estimation and Computation Standards)

I. Students will compare quantities using ratios and rates.

a. Equal ratios
b. Unit rates

II. Students will express equal ratios as proportions and solve proportions.
III. Students will learn about similar figures.
VI. Use proportions to find lengths in similar figures
VII. Students will identify, create, and draw geometric figures that are congruent, similar, or symmetrical.
IV. Students will express ratios as percents and convert to fractions and decimals.

a. Estimate percents
b. Find percent of a number

Solids and Measurement (Geometry and Measurement Standards)

I. Students will identify, compare, and describe three-dimensional shapes and polyhedrons.

a. Vocabulary

i. Solid
ii. Polyhedron
iii. Face
iv. Edge
v. Vertex/Vertices
vi. Base
vii. Prism
viii. Pyramid
ix. Cylinder
x. Cone
xi. Sphere
xii. Net
xiii. Cube

II. Students will identify a three dimensional shape from a two dimensional drawing of the shape.
III. Students will explore surface area

a. Use manipulatives and formulas to find surface area

i. Rectangular prisms

b. Explore surface area with manipulatives

i. Pyramids
ii. Cylinders

IV. Students will explore drawing, describing, and analyzing three dimensional figures.

a. Include front, side, and top views
b. State how many cubes in a solid
c. Describe a growth pattern in a set of solids

V. Students will understand and calculate the volume of a cube and a rectangular prism.

Probability (Statistics and Probability Standards)

I. Students will understand, calculate, describe and analyze probability.

a. Experiments
b. Outcomes
c. Events
d. Probability of events
e. Sample data
f. Geometric models
g. Tree diagrams
h. Compound events

II. Student will represent probability as a ration, decimal, fraction, and percent.

III. Students will understand, determine, describe, and analyze fairness of a game by explaining all possible outcomes.

Embedded Problem Solving (Problem Solving Standard)

Emphasized throughout all areas of mathematics instruction.

I. Students will read, analyze, summarize, and understand familiar and unfamiliar multi-step problems.
II. Students will select, modify, and apply appropriate strategies to solve multi-step problems.
III. Students will verify, evaluate, communicate, and interpret solutions.

Embedded Communication (Communication Standard)

Emphasized throughout all areas of mathematics instruction.

I. Students will communicate mathematical thinking by:

a. Using appropriate mathematical language and vocabulary
b. Using pictures to support explanations
c. Using concrete materials to support explanations
d. Using correct symbols to support explanations

II. Students will justify answers, solutions, process, and mathematical strategies using examples.

Embedded Reasoning (Reasoning Standard)

Emphasized throughout all areas of instruction.

I. Students will use informal deductive reasoning in concrete contexts.

Embedded Connections (Connections Standard)

Emphasized throughout all areas of instruction.

I. Students will apply mathematical skills and processes to other disciplines and areas of life.

SEVENTH GRADE MATH

NUMERATION

• Explain, define, and use concepts of number theory
• Order of operations and grouping symbols
• Square number and square roots
• Number properties with integers
• Scientific notation
• Exponential notation
• Identify, compare, and order rational numbers
• Use exponents to write the prim factorization of a number
• Convert fractions, decimals, and percents, and select the most appropriate form
• Use rules of divisibility to determine if one number is a factor or a multiple of another
• Use prime factors to find GCF’s and LCM’s
• Compare and order whole numbers, fractions, decimals and integers using >, <, or =
• Use models or diagrams to explain place value relations of decimals

MEASUREMENT

• Use a variety of methods and tools to measure and make geometric models
• Use a protractor and compass to construct
• Use a metric and standard scale for mass
• Use a variety of volumetric measures (i.e., graduated cylinders, measuring cups)
• Select the appropriate unit for measuring
• Measure length, weight/mass, area, and volume using the appropriate tool in metric and standard units
• Use, compare, and convert between units in the standard system for length, time, weight, area, volume, and money
• Explain the range of error that can be expected when measuring
• Find perimeter, circumference, and area of circles and polygons, and verify the solution using a different method
• Use ratios to solve problems about perimeters and areas of similar figures
• Write and solve rate problems and use appropriate units for the solutions
• Explain how to find the circumference and area of a circle (pi)

ESTIMATION and COMPUATION

• Understand, compute, and solve problems with rational numbers (select and use an appropriate method for computing: e.g., mental math, paper and pencil, calculator, computer)
• Add, subtract, multiply, and divide whole numbers, decimals, factions, and integers (with and without a calculator)
• Decimals-terminating and repeating
• Fractions-review computation with fractions(e.g., adding/subtracting mixed numbers, multiplying fractions/mixed numbers, dividing fractions/mixed numbers), convert fractions to decimals and percents
• Use ration, proportion, and percent to solve problems-unit price, interest, discount, sale price, percent of increase, percent of decrease
• Integers-find opposites and absolute value, multiply and divide integers
• Convert numbers between standard form and scientific notation using positive exponents
• Apply the rules of operations to rational numbers
• Use mental math to solve problems involving basic operations, powers of 10, and simple percents
• Use estimation in:
  • Computation
  • Problem solving
  • Predicting results
  • Solutions to problems to check reasonableness of answers
  • Decide when an estimate is appropriate and when an exact answer is needed
  • Apply, explain, and assess the appropriateness of a variety of estimation strategies

FUNCTIONS and RELATIONSHIPS

• Find patterns to continue arithmetic sequences
• Find the next term and the nth term
• Write a rule describing the pattern
• Use variables in expressions and equations
• Evaluate an expression for different values of the variable
• State properties using variables
• Use algebraic operations symbols (i.e., fraction bar for division) to solve one-step equations, including formulas, using inverse operations, inequalities
• Combine like terms to simplify expressions
• Problem solving with two-step equations
• Check solution
• Substitute values for a variable and evaluate the expression, equation, or inequality
• Use the order of operations
• Fraction or division bar and brackets as grouping symbols
• Evaluate variable expressions
• Understand and use a calculator to solve problems
• Ratio and proportion problems
• Percent
• Integers
• Memory key
• Describe linear data with tables, graphs (relate graphs to stories), and lines
• Substitute values into a linear equation to make a table of ordered pairs; graph the points on a coordinate plane

GEOMETRY

• Sketch, compare, visualize, describe, classify, and analyze relationships among geometric figures
• Classify by similar, congruent, and concentric (having a common center)
• Circles, irregular polygons, spheres, cylinders, cubes, pyramids, and prisms
• Vocabulary-circumference, diameter, center radius, pi, skew, plane, supplementary, complementary, regular polygons, and irregular polygons
• Use geometric knowledge to solve problems involving perimeters, angles, mass, shapes, areas, circumference, surface areas, volumes
• Polyhedron vocabulary-tetrahedron, octahedron, dodecahedron
• Find the sum of the angles in any polygon
• Find areas of parallelograms and trapezoids
• Find surface areas and volumes of cylinders
• Draw shapes using coordinate ordered pairs
• Draw 3-D figures
• Estimate and measure distances, areas, volumes
• Use the scale on maps and models to estimate distances
• Convert to other units in the same system
• Name and classify angles formed by parallel, perpendicular and intersecting lines
• Classify, construct and identify properties of angles
• Describe the relationship of angles in different types of triangles and areas of triangles
• Graph a figure and its image formed by translation, reflections, and dilations of plane figures
• Use characteristics of polygons to explain tessellations
• Use manipulatives to create a figure that tessellates and explain why it tessellates

STATISITICS/PROBABILITY

• Collect, organize, display data, and make an argument for which graph best represents the data
• Scatter plot, stem and leaf plots, line plot, bar graph
• In histograms
• From surveys and census
• Using computer spreadsheet software
• From a variety of sources including the Internet
• Interpret and compare data, look for patterns, and make inferences and predictions from graphic displays
• Circle graphs
• Box and whisker plots
• Locate median and mode
• Look for coorelations and dispersed points
• Use interpolations and extrapolations
• Compute and understand the concept of average with respect to mean, median, mode and range for a given set of data and justify one as the best representation of the data
• Analyze real world graphs for accuracy and misleading information
• Understand labeling and sources
• Identify and communicate trends based on statistics from data
• Express the probability of a single event as a fraction, decimal, or percent
• Determine probability and make predictions from real world data
• Independent and dependent events
• Predict the outcome of an independent event, design an experiment to test the probability, compute the actual outcome and compare the results to the prediction
• Use sample spaces
• Explain how determine probability if the odds are known and fairness
• Predict the probability of a future even, using a table of evidence from the past, and defend your conclusion

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Analyze problems, then select, modify, and apply appropriate strategies to solve increasingly complex problems
• Represent situations verbally, geometrically, graphically, and numerically
• In consumer, content area, and practical problems
• Translate real world problems into mathematical expressions and equations using variables
• Apply mathematical skills and processes to other disciplines
• Demonstrate, explain methods and results of various solutions to problems orally and in writing
• Recognize other strategies to solve the same problem
• Justify solutions or use counter examples to disprove statements
• Use inductive and deductive reasoning to verify conclusions, solve problems, recognize patterns, and propose solutions
• Deductive-conclusions are drawn from given information by using rules of logic
• Inductive-making a conjecture by looking at examples and recognizing a pattern
• Use spreadsheets as a tool to problem solving

EIGHTH GRADE MATH

BENCHMARK LEVEL 3
Given During the Spring

NUMERATION

• Use number properties to solve equations
• Understand place value in a different base system (model counting)
• Simplify variable expressions
• Recognize and combine like terms
• Apply properties, especially distributive
• Use and explain the order of operations
• Exponents and square roots
• Use manipulatives or diagrams to explain how to approximate a square root
• Explain absolute value
• Use inverse operations and the properties of zero and 1 to solve problems with variables and rational numbers
• Use and explain prime factorization

MEASUREMENT

• Use a variety of methods, tools, and technology to measure and make geometric models
• Use draw software
• Select the appropriate tools for measuring
• Show an understanding of significant digit concept
• Construct a scale model (apply the concepts of ration, proportion and scale)
• Use, compare, and convert between units in the metric system for length, mass, area , and volume
• Use compare, and convert between units in the standard system for length, time, weight, area, and volume
• Use indirect measurement to solve problems
• Explain what happens to ratios when changes are made to one or more dimensions of a figure
• Use manipulatives or diagrams to explain the Pythagorean Theorem
• Solve practical problems involving proportions, the Pythagorean Theorem
• Apply information about time zones and elapsed time to solve problems

ESTIMATION and COMPUTATION

• Use estimation in
  • Computation
  • Problem solving
  • Predicting results
  • Checking reasonableness of answers
• Use paper and pencil, mental math, or a calculator to efficiently and accurately solve problems with real numbers (calculators are not permitted on Benchmark Exams)
• Add, subtract, multiply and divide fractions, decimals, and integers with and without a calculator
• Understand, compute, and solve problems with real numbers
• Decimals-non-repeating decimals, irrational numbers, decimals and scientific notation, use decimals in equations
• Fractions – use fractions in equations
• Integers- graph coordinates in all four quadrants, use integers in equations
• Approximations or exact irrational numbers, including pi and square roots
• Ratio, proportion, and percent-
• Use an equation to find a percent or to find a percent of a number
• Use a ration and proportion to solve percent problems and to make scale drawings
• Convert numbers between standard form and scientific notation using both positive and negative exponents
• Organize data in matrices (rectangular array of numerical or algebraic quantities treated as an algebraic entity

FUNCTIONS and RELATIONSHIPS

• Understand and use a calculator to solve problems: square roots, powers (calculators can not be used on the Benchmark Exam)
• Recognize, describe, and predict patterns from various data sources
• Using geometric or arithmetic sequences, write expression for the nth term
• Using formulas
• Using graphs
• Using tables or charts to represent a linear function
• Solve equations, including formulas and inequalities
• Rational, including integers
• Graph two-step equations and inequalities
• Use commutative, associative, and distributive properties of 0 and 1 to solve two-step equations and check the solution
• Manipulate linear equations as tools to represent and analyze patterns
• Graph on coordinate plane using a table of ordered pairs
• Translate from ordered pairs to graphs
• Solve by creating a table of ordered pairs
• Graph solutions from a table
• Predict the graph of each function

GEOMETRY

• Construct, draw, measure, compare, transform, label, visualize, analyze, and classify relationships among geometric figures
• Label figures using symbols
• Derive angle sums in plane figures
• Define: concave, convex
• Construct or draw geometric figures in three dimensions including tetrahedrons, dodecahedrons, triangular prisms, and rectangular prisms
• Use geometric knowledge (words and symbols) to solve problems involving perimeters, shapes, areas, surface areas, angle relationships, similarity, congruency, transformations, scale, Pythagorean theorem, and volumes
• Define: hypotenuse, leg, radicals, square root, rotation, reflections, translations, dilation, symmetry, tessellation (Escher drawing), polyhedron, interior and exterior angles
• In formulas, the relations and an effect of one variable on the other values
• Model and apply pi and Pythagorean theorem
• Draw polygons using coordinate pairs, given lists or a pattern
• Draw a polygon that will not tessellate and explain why
• Estimate and measure areas and volumes using manipulatives and formulas
• Irregular shapes (polygons)
• Convert to other units in the same system
• Identify corresponding parts in similar and congruent geometric figures using a scale factor

STATISITICS/PROBABILITY

• Collect, organize, and display data using
• Scatter plot, stem and leaf, circle graph, line graph, histogram, box and whiskers, and bar graph; make an argument for which best represents the data
• Interpret and compare data, look for patterns, and make inferences and predictions from graphic displays
• Use tree diagrams and samples spaces to make predictions about independent events
• From equations, formulas, and graphs
• From graphs of inequalities
• Using line of best fit or trend line to predict future outcomes
• Use patterns or trends and make decisions or defend a conclusion
• Analyze real world statistics for accuracy and misleading information (newspapers, magazines, and graphical displays)
• Check for reasonability
• Understand compilation and sampling methods
• Understand factors influencing real world data
• Understand decision-making processes using statistics and probability
• Determine probability and make predictions from real world data
• Multiple (compound) events
• Use permutations, combinations, counting principle, and factorials
• Translate real world problems into mathematical expressions, equations, and inequalities with variables
• Compute and understand the concept of average with respect to mean, median, mode, and range for a given set of data and justify one as the best representation of the data

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Analyze problems, then choose and apply appropriate strategies to solve increasingly complex problems
• Represent situations verbally, geometrically, graphically, symbolically, numerically and translate between these alternative representations
• Apply in consumer, content area, and practical problems
• Generalize solutions from familiar patterns
• Evaluate, interpret, and justify solutions to problems
• Defend solutions to mathematical problems, orally, in writing and by using a variety of strategies to solve the same problem
• Use math vocabulary, symbols, and notation to explain, justify, and defend mathematical ideas from one area of mathematics to another area (e.g., algebra to geometry)
• Recognize and use inductive and deductive reasoning in both concrete and abstract contexts
• Use examples and counterexamples (to disprove statements)

PRE-ALGEBRA

• Grade Level: 8th/9th
• Length of Course: 1 Year
• Credit: 1 credit for 9th grade
• Textbook: Pre-Algebra, An Integrated Transition to Algebra & Geometry
• ISBN#: 0-07-822873-5
• Publisher: Glencoe

COURSE DESCRIPTION
This course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what students should be able to do after successfully completing the course. Pre-Algebra is intended to prepare students for success in algebra and then geometry. Number and operation sense, estimation skills and the ability to judge reasonableness of results will be strengthened in the context of practical applications and problem solving. Students engage in activities, which require them to perform operations (with integers, rational numbers, ratios, proportions, percents, square roots, radicals, equations, and inequalities) and apply properties. This course revolves around a broadened approach to core topics integrating algebra and geometry. Students will use the skills of reading, writing, listening, and modeling to investigate, interpret, and evaluate mathematical ideas.

NUMERATION, NUMBER SENSE, NUMERICAL OPERATIONS

• Read, write, model, and order real numbers, explaining scientific notation, exponents, and percents
• Convert between fractions, decimals, and percents
• Write and solve proportions
• Know and use scientific notation (converting)
• Write the prime factorization of a number using exponents
• Know and use multiples, primes, and factors
• Rename and compute with simple powers
• Know and use the order of operations
• Compare and order real numbers using >, “greater than or equal to”, <, “less than or equal to”, =, and “not equal to”
• Simplify expressions using rules of divisibility
• Find greatest common factors (GCF) and least common multiples (LCM) using prime factorization
• Solve problems using ratio, proportion, percent, and unit pricing
• Solve problems using equivalent fractions, decimals, or percents
• Perform simple operations in other number systems and bases
• Explain absolute value
• Use inverse operations and the properties of zero and 1 to solve problems with variables and rational numbers

MEASUREMENT

• Use, compare, and convert between units in metric system for length, mass, area, and volume
• Use, compare, and convert between units in the standard system for length, time, weight, area, and volume
• Compare units of measurement in the metric system to similar units of measurement in the standard system
• Apply multiple strategies, including formulas and manipulatives, to find area, perimeter, surface area, and volume, and include labels in appropriate units.
• Solve practical problems involving proportion and scale
• Solve practical problems involving conversion between degrees Celsius and degrees Fahrenheit
• Solve practical problems involving rate, time, and distance

ESTIMATION and COMPUTATION

• Use formula to solve problems
• Recognize and combine like terms
• Use estimation to check the reasonableness of answers involving real numbers
• Explain when an estimate is appropriate and when an exact answer is needed
• Use estimation to check calculator or computer accuracy
• Estimate the square root of a number
• Select appropriate scales or graphing windows for graphing data
• Add, subtract, multiply, and divide fractions, decimals and integers with and without a calculator
• Write and solve problems involving order of operations
• Use identity and inverse properties of addition and multiplication to solve problems
• Use commutative and associative properties of addition and multiplication to solve problems
• Use the distributive property of multiplication over addition to solve problems
• Solve problems using percent of increase and decrease
• Perform basic operations on expressions involving exponents and square roots
• Simplify expressions involving absolute value of real numbers
• Convert between standard and scientific notation using both negative and positive exponents
• Solve problems with real numbers using paper and pencil, mental math, and a calculator (calculators are not permitted on Benchmark or Exit exams)

FUNCTIONS and REALTIONSHIPS

• Identify and expand classic patterns such as primes, square and triangular numbers, and Pascal’s Triangle
• Express an arithmetic pattern as a rule and determine the nth term
• Apply patterns as a strategy for solving problems
• Apply properties of real numbers especially the distributive property
• Use proper algebraic terminology in both written and oral communication
• Present work in an organized and orderly fashion
• Simplify expressions using the properties of real numbers
• Solve and graph one- and two-step inequalities
• Graph linear equations and inequality solutions on a number line
• Graph ordered pairs in coordinate plane
• Provide a verbal and written explanation for solutions
• Translate word problems into numerical expressions, inequalities, or equations
• Create word problems from symbolic statements
• Create a table of values from a linear function
• Graph the equation of a line in slope and y-intercept form
• Compute the slope of a line given two points
• Use and evaluate formulas including Pythagorean theorem and geometric formulas
• Solve problems involving algebraic expressions using order of operations, grouping symbols and exponents

GEOMETRY

• Identify, classify and compare triangles and quadrilaterals
• Identify, classify and compare regular and irregular polygons
• Identify, classify and compare simple polyhedra
• Construct or draw geometric figures in two-dimensions and three-dimensions
• Create three-dimensional models from two-dimensional views
• Know the properties of perpendicular and parallel lines
• Construct parallel and perpendicular line segments
• Construct bisections of lines and angles
• Solve problems using the relationships of angles formed by parallel, perpendicular and intersecting lines
• Describe the relationship of angles in different types of polygons
• Identify corresponding parts in similar and congruent geometric figures
• Find missing angles or sides of figures using similarity and congruence
• Describe the symmetry found in various figures
• Identify and graph reflections, rotations and translations on the Cartesian plane and describe these transformations in words and symbols
• Find the perimeter and area of various polygons
• Find the circumference and area of any circle
• Find the surface area and volume of various polyhedra
• Apply the Pythagorean Theorem to real-world situations
• Design a shape that will tessellate and use it to cover a surface

STATISTICS/PROBABILITY

• Create circle graphs using percents
• Present experimental or collected data using both paper and pencil, and technology, in various forms including a table, scatter plot, circle graph, line graph, stem-and-leaf, box-and-whiskers, and histogram
• Calculate mean, median, mode and range for a given set of data in a table or a graph
• Chooses between mean, median, and mode as the best representation of data and explain the choices
• Approximate a line of best fit or trend line for a given set of data
• Analyze data using patterns or trend lines and use this information to predict future outcomes, influence decisions, and defend conclusions
• Analyze, interprets, and constructs graphs and diagrams to display data
• Analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by a wide variety of factors including choices of measure of center, incorrect curve fitting, and inappropriate use of controls or sample groups
• Calculate the probability of a simple event
• Express the probability of an event using decimals, ratios, or percents
• Calculate the probabilities of independent events
• Conduct an experiment and use the data to find the probability of a simple event
• Know and use counting principles to determine number of possible outcomes and probability

PROBLEM SOLVING, COMMUNICATION, REASONING, CONNECTIONS

• Utilize estimation, proportional reasoning, and computation to evaluate the reasonableness of a given problem and solution, without completely solving the problem, emphasizing on being familiar with number forms, patterns, and operations, and using this familiarity to quickly evaluate reasonableness
• Analyze and summarize a problem using the relationships between the know and the unknown information
• Uses appropriate vocabulary and symbols to explain, justify, and defend solutions to mathematical problems
• Develop strategies for understanding the nature and elements of a problem, and outline steps to study, and solve the problem
• Use different strategies to solve problems such as guess and check, patterns, diagrams, pictures, tables, charts, graphs, inverse operations, and breaking it up into an easier problem
• Use a variety of solution strategies to solve problems including: patterns, tables, working backwards, lists, pictures, guess and check, and breaking up.
• Solve story problems which include irrelevant information
• Solves multi-step problems
• Explains answers in written form showing all steps of solving the problem