Fifth Grade Curriculum Outline (updated fall 2006)
National Council Teachers of Mathematics Standard 
Nebraksa Standards Competency or Indicator 
Teacher created concept, objective, outcome, competency 
Curriculum investigations, units, chapters, modules... 
Activities 
Evaluation Levels 
Numeration/Number Sense 
8.1 Numeration/Number Sense 

8.1.1 By the end of eighth grade students will recognize natural numbers whole numbers, integers, and rational numbers. 
Say, read, and write numbers to billions 

8.1.2 By the end of eighth grade, students will determine equivalencies among fractions, decimals, and percents. 
Recognize the tenths and hundredths place of decimals. Recognize, read and write place value of decimals numbers. Identify, read, and write decimal place values up to 10,000ths 
Generate random numbers, write them on the board and read them. With a partner, verbally identify the place & value of an underlined digit in a number. Fill in the missing numbers on a number grid starting with a number above 10,000. 

Find the equivalencies among fractions, decimals, and percents. Solve problems with appropriate equivalencies. 
When working with decimals, 3.123 the ones place is to the left of the decimal point. The number value of the positions become smaller as we read to the right of the decimal point. Identify inequalities <,> and = Rounding numerals to the tenŐs and hundredŐs place value Round numerals in all places of the thousandŐs value Round numbers to 10,000 Round numerals in all three places of the millionŐs Round whole numbers to the nearest named place, such as rounding 1,234 to the nearest hundred would be 1,200. 
Use a hundreds chart to explain a rule for rounding numbers to ten. Use hundreds charts to 500 to explain rounding numbers to one hundred. Create a hundreds chart from .01 to 1.00 and use it to explain a rule for rounding numbers to tenths. Use a state map, find the population of several towns near where you live or where you would like to visit. Round the selected distances to the nearest ten, hundred, thousands and million miles. Survey the newspaper for the largest number that can be found. Say, read, and write the number and the place value of each digit. Check the USA population figure. Compare it to the population of the hometown. What is the distance to the moon and back? 

8.1.3 By the end of eighth grade, students will write and use numbers in expanded exponential form and scientific notation. Write numbers in expanded form using exponential notation. Express small and large numbers using scientific notation. 
Building on Numbers You Know Assessment
Master 23
Reads, writes, and orders large numbers (Building on Numbers You Know) Rounds larger numbers to the nearest multiple of 100 or 1000 (Building on Numbers You Know) Develops, records, explains, and compares strategies for estimating subtraction, multiplication, and division problems in more than one way (Building on Numbers You Know) Uses a rectangulararray model to represent factor pairs of numbers 10,000 and greater (Building on Numbers You Know) Understands and explains the relationships among the four basic operations and uses those relationships to solve problems and model situations (Building on Numbers You Know) Skip counts by 2, 3, and 4digit numbers (including numbers that are not landmarks) (Building on Numbers You Know) Finds and uses patterns in sequences of multiples and uses those patterns to helps solve multiplication and division problems (Building on Numbers You Know) Uses numerical strategies for determining and comparing distances between numbers (Building on Numbers You Know) Breaks difficult computation problems into manageable parts (Building on Numbers You Know) Makes sense of remainders (Building on Numbers You Know) Interprets, records, and uses division and multiplication notation accurately (Building on Numbers You Know) Understands the magnitude of large quantities such as thousands, ten thousands, and hundred thousands and begins to develop a sense of the size of 1,000,000 (Building on Numbers You Know) Communicates mathematical thinking through written language and spoken language (Building on Numbers You Know) 
Create a place value chart with the value of each place written in numerals and words below each place. Time foot races using a digital sports clock to hundredths of seconds and order the times. Round grocery bills to the nearest tenths. Shuffle ten cards (with a 0  9), deal 7 cards face down, turn over one card at a time and place it into one of seven places, continue until all the places are filled. Say each place value and tell what number is in that place. Tenths place has a one, the hundredth's place has a 5. Could use the activity above and say or write the numbers in expanded form: 3000+400+50+9+.1+.05+.006 

Write numbers in expanded form Combine and decompose numbers to create equivalent forms. Say, read, and write numbers in expanded notation Combine expanded notation *** Mathematical Thinking Assessment Master 5 Can read, write, and order numbers to 10,000 (Mathematical Thinking) Uses mental and written strategies based on numerical reasoning to find sums and differences of 3 and 4digit numbers (Mathematical Thinking) Uses mental and written strategies based on numerical reasoning to find products of 2and 3digit numbers (Mathematical Thinking) Uses mental and written strategies based on numerical reasoning to find quotients for landmarks up to 10,000 (Mathematical Thinking) Can represent factor pairs as dimensions of a rectangular array (Mathematical Thinking) Understands the following number characteristics and their relationships: multiples, factors, primes, and squares (Mathematical Thinking) Uses the following strategies for exploring number compositions: repeated addition, skip counting, finding factors and factor pairs using a calculator to check divisibility (Mathematical Thinking) Uses factors of 100 and multiples of those factors to explore landmarks up to 1000 (Mathematical Thinking) Knows the factor pairs of 100 and can relate them to the factor pairs of 1000 and 10,000 (Mathematical Thinking) Skip counts by the factors of 100 and the factors of 10,000 (Mathematical Thinking) Solves problems that have one or more solutions (Mathematical Thinking) Demonstrates an understanding of the magnitude of 10,000 (Mathematical Thinking) 13. Communicates mathematical thinking through written language and spoken language (Mathematical Thinking) 

Create fractional parts of a whole Create fractional parts of a group Find equivalent fractions 
Match number cards with expanded notation cards (Concentration or Old Maid). Verbally identify the place & value of an underlined digit in numbers. Write a number less than 1 billion on the board, (582,107,473). Select 9 students and assign sequence. The first student says the ones place value (3); the second student says the number in the first two place values and their values 7 tens, 3 ones; or seventy plus three, or seventythree). Continue through the whole number to the 9^{th} student who identifies the expanded form for the whole number. Five hundred million plus eighty million plus two million, É or five hundred eightytwo million, one hundred seven thousand, four hundred seventythree. 

Reduce fractions to the lowest terms 

Add and subtract fractions with the same denominators. Add and subtract fractions that have one denominator as a multiple of the other. Add and subtract fractions that have denominators that are not multiples of each other. *** Name that Portion Assessment Master 14 Identifies everyday situations that involve fractions, decimals, and percents. 1, 2, 16 (Name that Portion) Use fractions to describe portions of groups. 3, 4 (Name that Portion) Use percents to describe portions of groups. 3 (Name that Portion) Understand percent as "out of 100" 5, 6, 28 (Name that Portion) Understands decimals as part of the base ten system. 19 (Name that Portion) Uses decimals to describe portions of groups. 19 Breaks fractions, decimals, and percents into familiar parts 11, 17 (Name that Portion) Approximates data as familiar fractions, as percents, and in circle graphs 7, 11, 12, 27, 30 (Name that Portion) Identifies and uses equivalent fractions, decimals, and percents. 3, 5, 14, 15, 16, 1`, 11, 17, 30 (Name that Portion) Compares and orders fractions. 1, 8, 14, 20, 24, 25 (Name that Portion) Chooses appropriate models and notations to compute with fractions, decimals, and percents. 18, 21, 22, 23 (Name that Portion) Identifies, orders, and labels fractions between 0 and 1 on a number line. 8, 10, 13, 15 (Name that Portion) Solves word problems involving fractions, decimals, and percents express answers appropriately. 9, 17, 23 (Name that Portion) Finds decimals that are smaller than, larger than, or in between other decimals. 20 (Name that Portion) Plans and conducts surveys and presents the resulting data using fractions, decimals, and percents. 26, 29, 30 (Name that Portion) Communications mathematical thinking through written language and spoken language. 10, 18, 24, 25, 28, 29, 30 (Name that Portion) 
Use cardboard fraction circles (wholes, halves, fourths, and eighths) to show how to solve addition and subtraction problems that have fractional values. Use a check register to record deposits and withdrawals. Read a sales page. Create a list of items he/she would like to purchase. Add the list to find the total amount. State the place value of each numeral, both whole and decimal numerals. Use a set of decimal name cards and put the name cards in order or match the place names to underlined places of a digit on a numeral card. Make a grocery list and use a number line to model the sum of the items. Record amounts of rainfall/snow for a month. Model the sum in decimals on a number line. Fraction cards: 2 equal but not necessarily congruent pieces for 1/2, 3 equal but not necessarily congruent pieces for 1/3, etc. Use the recipe for Indian Fry Bread and 3 different measuring cups: 1/8, 1/4 & 1/3 (or 1/2) cups and make a chart or write a paragraph to show how to use only one at a time to make the fry bread. 1 cup flour 1 tsp. Salt 1 tablespoon shortening 1 cup water Oil or shortening for frying. Add shortening to dry ingredients. Blend. Add water to make a soft dough. Set 30 to 60 minutes on a floured board or table top, roll the dough to 1/2 inch thick. Cut in shapes and fry in 375 degree oil 

Compare decimals to fractions 

Multiples and factors of numbers from 0100 Multiples of 2, 3, 4, 5, 6, 7, 8, 9, and 10 
Multiple hunt Select two different numbers from one to ten and generate the multiples for both. What multiples do both numbers have? What patterns can be found? On a hundred chart color multiples of 3 red, and multiples of 4 blue. Repeat with a new grid for 2 multiples, 5 and 6. Repeat with a 99 chart for multiples 

Factors Prime Numbers Composite numbers can be factored to prime numbers. 
Factor hunts Find and list prime numbers through 50. Identify the prime numbers to 100 on a 100Õs chart. Use factor trees as a model to identify primes Find the factors of numbers from 025, discuss patterns and methods for finding the factors. Have students use the different methods that they proceduralized to find factors of numbers 2650, discuss patterns, and methods for finding the factors. Repeat for numbers 5010 Find the greatest common factor 16, 32: Find factors 32, 16 (1,2,4 8,16,32) Write 1 & 32 spread out, then try 2 if works, write factor, next try 3 if doesnÕt work, try next (4) continue until meet coming down, then done. Repeat for next number. (1,2,4,8,16) The greatest in both is 16, GCF 

Recognize negative and positive signs for integers Identify examples in life where positive and negative numbers are used. Record steps toward solutions and solutions to problems with pictures, chart, graphs, models, in writing, orally, and with symbols. Compute scores in a card game where the winning and loosing hands are represented by positive and negative numbers. Create a check book register with debits and credit. Identify positive and negative numerals along the X and Y axis. Plot points on an X and Y axis using positive and negative integers. 
Check the internet weather records for a spot on that has winter subzero temperatures, record and chart temperatures over a period of time, list the degrees of change, and compare it with another location. Check Tiger WoodÕs and others golf scores for under and over par. Make a human number line by drawing a positive or negative number card and lineup in order according to the number on the card. Trade cards and repeat. 

Identify all coins and paper money up to $100 

Describe how to make change from any combination of money up to $100 

Relate decimals tenths and hundredths to money. Add and subtract decimals 

8.2 Computation/Estimation 

8.2.1 By the end of eighth grade, students will add, subtract, multiply, and divide decimals and proper, improper, and mixed fractions with uncommon and common denominators with and without the use of technology. 

Memorize division facts through 12. 

8.2.1 By the end of eighth grade, students will add, subtract, multiply, and divide decimals and proper, improper, and mixed fractions with uncommon and common denominators with and without the use of technology. 
Add and subtract 5 digit numerals with/without regrouping Apply regrouping in addition and subtraction problems up to 10,000 

Compute 2 digit multiplication problems with and without 0 as one of the factors. 
Multiplication cards to practice the facts. Put the children in groups of two and have them practice by listing ways to remember the fact, e.g. 4x6=24 is double 6 two times: 6, 12, 24. Teach students how to take blood pulse count. Tell the students to record the amount of heartbeats that they find in a minute. Then have them multiply to see how many times that it beats in an hour, a day, a week, a month, and a year. 

Use strings of problems and rectangle grids as a model to transition from mental multiplication to algorithms. 

Solve 2 digit division problems with remainders. Remainders can worked with in at least four different ways 
Put a pile of 42 counters on the table in the front of the class. Answer the following questions: How many counters can be put equally in 6 boxes? If you put 6 counters in each box, how many boxes do you need? Discuss the amount in each box and then change the number of counters and repeat the process. Pick a whole number, list other whole numbers that divide into the number along with any remainders. What pattern do you see? How many different ways can remainders be interpreted? Write a sample problem to illustrate each way. 

8.2.2 By the end of eighth grade, students will identify the appropriate operation and do the correct calculations when solving word problems 

Identifies everyday situation that involve fractions, decimals, and percents. *** Name that portion 

Multiply and divide whole numbers, tenths, and hundredths 
Use a piece of graph paper and make a rectangle. If a 10 X 10 square is one what is the length and width of the rectangle? What is the size of the rectangle using the 10 x 10 rectangle as one? Use a digital scale and mass one paper clip. How much would 10, 20, 25, 30, 40, 50, 75 weigh? Add one paper clip at a time and chart the masses and explain the relationship of both answers 

8.2.3 By the end of eighth grade, students will solve problems involving whole numbers, integers, and rational numbers (fractions, decimals, ratios, proportions, and percents) with and without the use of technology. 

Use proportions to solve scalemodel problems with fractions and decimals. Problems should be of increasing level of difficulty and involve reallife situations. 

Multiplication and division of fractions 
Draw a square on the board. Draw a line to divide the object in half and then divide the half into half. Write a problem and solution that can be explained with this drawing. Could do the same with thirds (1/3 of 1/3 = 1/9) and other fractions. Create a model to show how many sandwiches can be made from a loaf of bread? How much of a loaf of bread does it take to make a sandwich? Explain what 7/8 divided by 1/8 is with words, pictures, manipulatives, and actions. Explain how multiplication and division are related 

8.2.4 By the end of eighth grade, students will apply the order of operations to solve problems with and without the use of technology. Evaluate all types of numerical expressions, including grouping symbols and exponents. 

8.2.5 By the end of eighth grade, students will apply strategies of estimation when solving problems with and without the use of technology. Example indicators: á Properly round to an appropriate place value if context permits. á Perform estimation prior to calculation. á Without a calculator, estimate square roots of whole numbers up to one hundred to the nearest whole number. á Use compatible numbers to perform mental math. á Use estimation to check reasonableness of an answer. 

Measurement 
8.3 Measurement 

8.3.1 By the end of eighth grade, students will select measurement tools and measure quantities for temperature, time, money, distance, angles, area, perimeter, volume, capacity, and weight/mass in standard and metric units at the designated level of precision. 

8.3.2 By the end of eighth grade, students will convert units within measurement systems using standard and metric, given conversion factors. 
Estimate relative distance between two points by comparison to a known distance Cm and m. 
List five different starting and stopping points for five different distances outside the school, record an estimate for each distance, and a reason for how you determined it. 

Convert between various units of area and various units of volume (square foot to square yards and cubic decimeters to liters, etc.). Check solutions to problems using unit analysis (feet/second to miles/hour). 
Cm and m Compare meter/yard, km/mile, and cm/in 
Compare the distance between two objects in cm/in and m/yd. Go for a walk and compare the distance in ft./m/yd./km/mi. Take a roll of toilet paper and have the students measure things by counting the amount of squares they use. Then compare that to many others things that you can use. 

8.4 Geometry/Spatial Concepts 
Measure liquid amounts up to a gallon and liter 
You are asked to create a container that makes people think there is more in the container than there actually is. First collect a variety of containers that you think would cause this to happen and ones that would not (at least ten), put them in order according to their volume by sight, record the data, measure their volume, put them in order according to their actual volume, what shape of containers make people think there is more than there actually is? 

8.4.1 By the end of eighth grade, students will identify, describe, compare, and classify twoand threedimensional geometric figures such as plane figures like polygons and circles; solid figures like prisms, pyramids, cones, spheres, and cylinders; and lines, line segments, rays, angles, parallel and perpendicular lines. 
Measurement Benchmarks Assessment
Master 28
Identifies benchmarks for the measure of: length, weight, volume, and time (Measurement Benchmarks) Chooses and accurately uses appropriate tools for measuring: length, weight, volume, and time (Measurement Benchmarks) Determines when precise measurement is required and when estimates are good enough (Measurement Benchmarks) Recognizes and explains possible sources of measurement errors (Measurement Benchmarks) Identifies everyday benchmarks as comparable to standard units of measurement (Measurement Benchmarks) Recognizes which measurement units are U.S. standard and which are metric (Measurement Benchmarks) Compares lengths expressed in different ways, such as meters and centimeters, meters and decimal fractions of a meter, and meters and fractions of a meter (Measurement Benchmarks) Keeps track of and calculates total measurements (Measurement Benchmarks) Distinguishes between quantity and weight (Measurement Benchmarks) Orders items by measures of weight and by measures of liquid amount (Measurement Benchmarks) Reasons about factors that influence capacity (e.g., the height, width, and other features of the shape of a container) (Measurement Benchmarks) Has a sense of volume as the amount of space something takes up or the amount of pourable substance a container can hold (Measurement Benchmarks) Compares and explores conversion relationships between U.S. standard and metric measures of weight and liquid capacity (Measurement Benchmarks) Is beginning to develop meaning for the concept of density (Measurement Benchmarks) Compares distances expressed in hundreds or thousands of miles of kilometer (Measurement Benchmarks) Uses the scale on a map to calculate approximate distances (Measurement Benchmarks) Uses vocabulary for describing units of time (Measurement Benchmarks) 

8.4.2 By the end of eighth grade, students will use geometric properties, the Pythagorean theorem, and the relationships of congruence, similarity, and symmetry. 
Identify fractional parts of a ruler to the 1/8^{th} of an inch Identify fractional parts of a yard 
Make a ruler and marks it to show 1/2, 1/3rd, 1/4^{th}, and 1/8^{th} of an inch. Explain how the spaces and lines represent fractional parts. Make a chart that tells what part of a yard one inch, 2 inches, 3 inches,É 36 inches are. Measure the classroom and draw a scale map. Measure and map the school playground. 

8.4.3 By the end of eighth grade, students will use formulas to solve problems involving perimeter and area of a square, rectangle, parallelogram, trapezoid and triangle, as well as the area and circumference of circles. 
Convert ounces to pounds 
Using food package labels put them in order from lightest to heaviest. Measure sand or water in 4, 8, 12, and 16 ounces. Blind fold a partner and have them feel the containers (no shaking just lifting) and put them in order. How good are people at telling the difference in weight by feel? 

8.4.4 By the end of eighth grade, students will solve problems given formulas for volume and surface area of rectangular prisms, cylinders, and cones. 
Measure liquid amounts up to a gallon and liter Convert liquid amounts to gallons. 

8.4.5 By the end of eighth grade, students will apply transformations to twoand threedimensional geometric figures. á Draw geometric figures using translations or slides, rotations or turns, reflections or flips, and scale. 

8.4.6 By the end of eighth grade, students will use geometric terms and representations to describe the physical world. 

Tell the correct time to the minute 

Solve problems with time Identify time zones in the world and the international date line. Identify the time zones in the United States Calculate time in two different zones 
Create and solve time problems using a television guide. Use a globe and find the number of time zones in the world. Calculate the difference from the studentÕs time zone to other zones in the USA. Relate years to events: (year you were born, members of the family, dates of important cultural events, date of birth, milestones in student's lives, United States became a nation, election of a new president every four years 2000, 1867 Nebraska becomes a state. Why do people say nineteentwenty, or twothousandfour? 

Money Identify all coins and paper money up to $100.00. Describe how to make change from any combination of money up to $100.00 

Geometry 

Shapes Identify 3D geometric shapes (sphere, cone, cube) Describe and create 2 and 3 dimension shapes Picturing Polygons Assessment Master 9 Distinguishes between polygons and shapes that are not polygons and between regular and nonregular polygons (Picturing Polygons) Recognizes and names polygons by the number of sides (Picturing Polygons) Locates and plots points on a coordinate grid (Picturing Polygons) Generates geometric figures with certain properties (on and off the computer) (Picturing Polygons) Sorts and classifies triangles and quadrilaterals and uses mathematical vocabulary to describe them (Picturing Polygons) Has an understanding of parallel lines (Picturing Polygons) Distinguishes and sees relationships between turns and angles (Picturing Polygons) Uses known angles to find the measures of other angles (Picturing Polygons) Estimates and measures the sizes of angles and turns (Picturing Polygons) Finds the sizes of turns and angles and the sums of turns and angles in regular and nonregular polygons; explores the relationship of turns and angles to the total number of sides (Picturing Polygons) Writes computer procedures that draw regular polygons and figures that are similar to a given figure (Picturing Polygons) Creates geometric patterns that grow in regular ways (Picturing Polygons) Finds and understands connections between geometric and numerical patterns (Picturing Polygons) Finds and understands relationships among angles, line lengths, and areas of similar polygons (Picturing Polygons 
Use 3D shapes to make nets for each shape. Compare the properties of each net to 2D shapes. Record the different shapes on a chart for all 3D shapes and compare the shapes to the shapes names and type of 3D shapes and see what patterns can be found. Color patterns. Identify polygon shapes in the school and community (checkerboards, baseball diamond,É) Make cards with the name of a shape and its properties on one side and pictures on the other side. Looking at one side tell what is on the other side. Use 4 bands to make an open figure on the geoboard. Change 1 band to make polygons of 3, 4, 5, 6, and 8 sides. 

Construct geometric shapes (circle, square, triangle and rectangle) with varying dimensions. *** Containers and Cubes Assessment Master 35 Understands 3D rectangular arrays of cubes as congruent layers (Containers and Cubes) Determines the number of cubes that fit in a rectangular box (Containers and Cubes) Uses multiplication to determine the total number of cubes in a box (Containers and Cubes) Understands and uses the relationship between the number of cubes that fill a rectangular box and the dimensions of the box (Containers and Cubes) Can figure out how to organize rectangular packages so that they fill rectangular boxes (Containers and Cubes) Has at least one strategy for counting the number of rectangular packages that fill a given box (Containers and Cubes) Designs boxes to hold packages of different sizes (Containers and Cubes) Understands the relationship between the dimensions of a box and how many rectangular packages fill the box (Containers and Cubes) Understands the notion of volume and units of volume (Containers and Cubes) Sees and uses cubic centimeters as a unit for measuring volume (including that of nonrectangular solids) (Containers and Cubes) Decides on, constructs, and visualizes appropriate units of volume for measuring a largescale space, such as a classroom (Containers and Cubes) Understands characteristics of units of volume, such as shape and size (Containers and Cubes) Develops, uses, describes, and justifies methods of determining volume (Containers and Cubes) Compares the volume of one large space to another (Containers and Cubes) Explores volume relationships between differently shaped containers and between solids, particularly those having the same base and height (Containers and Cubes) Uses geometric solids to design models and determines their volume (Containers and Cubes) 
Study quilt patterns, particularly the Winnebago Star quilt. Use a ruler, compass, & protractor to draw quilt patterns of squares, rectangles, and triangles on graph paper. 

Identify and draw points, lines, line segments, rays, and angles. Identify angles (obtuse, right, acute). Identify parallel and perpendicular lines 
Define a point, line, ray, line segment, and angle and give examples. List examples for each geometric term. Construct 10 angles and classify them into at least three groups. 

Identify geometric instruments such as the ruler, protractor, and the compass. Bisect angles with a compass Measure angles with a protractor Construct right, obtuse, and acute angles of various degrees with a protractor. Identify Acute, Obtuse and Right angles 
Illustrate a procedure to bisect angles with a compass, and straight edge. Draw several shapes with different kinds of angles. Trace one angle on each shape with a different color that was used to make the shape, measure each traced angel with a protractor, label the degrees of the angle, glue it onto a chart under the appropriate category of acute, obtuse or right. List as many times for each kind of angle in 6 minutes (use approximately 2 minutes per angle). "What times do the hands form right angles?" "What times do the hands form acute angles?" "What times do the hands form obtuse angles?" Construct the biggest polygon that will fit on a sheet of paper, construct several more with different numbers of sides, measure the angles, add them and record their results on a class chart. Compare the number of sides to the size of the angles and their sums. 

Identify lines of symmetry Analyze, compare, and solve problems with congruence, symmetry, similarity and simple transformations. 
Classify the letters of the alphabet at to the number of symmetry lines each has. (mirrors, tracing, folding, or cutting may be utilized. Construct different shapes and classify the shapes as congruent, similar or both. 

Calculate perimeter of shapes. Calculate perimeter of a shape in inches and centimeters 
Compute the perimeter of the playground if it is enclosed with a fence, or where a fence could be placed. The third grade teacher wants to put a number line all the way around the room. How long will the paper have to be? 

Find the area of different shapes. Identify different shapes where the same procedure can be used to find the area. Use tiles to model surface area. Calculate area of a shape in square feet and square yards 
Compare area to perimeter on graph paper Ñ draw squares and rectangles, find the area and perimeter, chart the data, and see if there is a relationship or pattern. Compute the area of the classroom. Find the cost to purchase carpeting for it You want to help a friend that is going to wall paper a room. The room is 12 foot x 10 foot and the walls are about seven and onehalf feet tall. There is a door and one window. However, they can be discounted because when the pattern is matched the dropoff probably won't be of much use since they will be too small for the height of the room after the pattern is matched. Your friend also wants to put a border around the ceiling. How much will s/he need. The border comes in inches or centimeters. 

Identify and locate radius, diameter and arc of a circle. Identify and construct parallel lines. Recognize the difference between horizontal and vertical lines. 
Explain the difference between: radius, diameter, arc, rays, segments in words and diagrams. How does the word parallel help you remember its definition? Measure the distance between the walls in a hallway in several places. "How do construction workers use the technique of parallel lines? Shingles on the roof? Sidewalk forms?" How does the word horizontal give a clue that helps a person remember what it means? Measure studentsÕ "vertical" jump. Measure the studentsÕ broad jump. Chart and compare the vertical jump to the long jump. Is there a pattern among different students? 

Data Analysis 
8.5 Data Analysis, Probability, and Statistical Concepts 

8.5.1 By the end of eighth grade, students will collect, construct, and interpret data displays and compute mean, median, and mode.


8.5.2 By the end of eighth grade, students will read and interpret tables, charts, and graphs to make comparisons and predictions. 
Compute arithmetic mean, median, and mode in practical applications: grade, precipitation, weight, length *** Data: Kids, Cats, and Ads Assessment Master 39 Finds medians and other fractional parts of data sets (Data: Kids, Cats, and Ads) Theorizes and makes statements, conclusions, and recommendations based on organized data (Data: Kids, Cats, and Ads) Uses data characteristics to identify data sets, to describe numerical and categorical variables, and to compare a sample to a larger population (Data: Kids, Cats, and Ads) Collects and organizes data and makes line plots and tables to examine and compare data sets (Data: Kids, Cats, and Ads) Frames questions about associations between variables in a data set and constructs representations and descriptions that help answer those questions (Data: Kids, Cats, and Ads) Uses a computer and database to enter, analyze, and examine data in a computer database (Data: Kids, Cats, and Ads) Compares and adds fractions using numerical reasoning, using visual representations, and by converting unfamiliar fractions to more familiar fractions (Data: Kids, Cats, and Ads) Finds equivalents among fractions, decimals, and percents and uses them to compare data from a sample to a target fraction (Data: Kids, Cats, and Ads) Knows what a sample is, what some of the factors (including size) that make a sample reasonable are, and why a larger sample tends to reflect a population better than a smaller one (Data: Kids, Cats, and Ads) Develops strategies for finding a representative sample (Data: Kids, Cats, and Ads) Formulates, tests, defines, and refines survey questions and uses background information in designing a survey (Data: Kids, Cats, and Ads) 
Keep the temperature and amount of precipitation for a week or go to an internet site and print out a sequence of meteorological data. Chart the data for a week or more; compute the mean, median, and mode; and illustrate each on the chart. Chart the number of right answers in a subject for five or more events; compute the mean, median, and mode; and illustrate each on the chart. 

Develop a Survey Create charts, graphs and tables using the data from the survey Interpret information displayed on graphs, charts, and tables. 
Select a topic and create 5 questions that you would like to know how people would answer. Ask ten or more people your questions, record the data; display it on charts and/or graphs; and write statements about what was learned and compare the information. 

8.5.3 By the end of eighth grade, students will conduct experiments or simulations to demonstrate theoretical probability and relative frequency. Compare the results of a simulation (relative frequency) to the theoretical probability (a threecolor spinner or a coin). 
Between Never and Always Assessment Master 18 Distinguishes events that are certain from those that are not and distinguishes among events with different probabilities (Between Never and Always) Understands probability as how likely something is to occur (Between Never and Always) Understands that the probability of an event ranges from never to always (Between Never and Always) Can accurately describe the probability of an event using numbers or words (Between Never and Always) Recognizes that probability can be described using fractions, decimals, or percents (Between Never and Always) Can numerically identify the probability of a simple event (Between Never and Always) Recognizes that repeating a probability experiment several times can yield a variety of results (Between Never and Always) Uses the probability of an event to predict about how often some event will happen in a given number of trials and to select events that are most likely to occur (Between Never and Always) Plots the results of probability experiments on line plots and interprets the data represented. (Between Never and Always) Compares expected outcomes with actual outcomes (Between Never and Always) Can estimate probabilities based on results of actual trials (Between Never and Always) Predicts and analyzes features of outcome data, including range, mode, outliers, and clusters (Between Never and Always) Interprets the ŇfairnessÓ of a game as equal probably of winning (Between Never and Always) Can break Composite events into elementary events (Between Never and Always) Uses systematic ways to generate a list of all possibilities (Between Never and Always) Applies knowledge of probability to design a fair game (Between Never and Always) Distinguishes games of chance from games of skill (Between Never and Always) Appreciates that, even in fair games, variability in the results can make a game appear to be unfair (Between Never and Always) 

8.5.4 By the end of eighth grade, students will identify statistical methods and probability for making decisions. Example indicators: Identify the use of appropriate sampling techniques. Identify the use of appropriate charts and graphs. Identify the use of measures of central tendency (mean, median, and mode) appropriately. 

Algebra 
8.6 Algebraic Concepts 

8.6.1 By the end of eighth grade, students will demonstrate knowledge and use of the one and twodimensional coordinate systems. 

Order numbers on a number line. Graph ordered pairs on a coordinate plane. Generate a table of ordered pairs to graph an equation in two variables. 
Algebraic Unknowns Calculate the numerical value for an unknown/variable. 
Explain how the following story problem and equation are related. "You have 3 pickles on your sandwich and there are 6 more in the jar." "How many did you begin with?" N Ñ 3 = 6 Create another one of your own 

8.6.2 By the end of eighth grade, students will apply algebraic concepts and operations to solve linear equations and word problems. 
Identify and create patterns (arithmetic progressions {created by adding a constant to each proceeding term: 1, 3, 5, 7, 9É; or 0, 5, 10, 15É,} or geometric progressions {created by multiplying each proceeding term by a constant:1, 2, 4, 8, 16,É; or 1, 3, 9, 27,É}) and describe them mathematically. 

Solve multistep equations with one variable. Use order of operations to evaluate algebraic expressions for given replacement values of the variables Recognize and apply commutative, associative, distributive, inverse, and identity properties, and the properties of zero. 
Patterns of Change Assessment Master 31 Builds tile designs that grow according to regular number patterns, continues them, and predicts later steps of number patterns, tile designs, and graphs (Patterns of Change) Compares sequences of numbers and shapes of graphs that show the number of tiles added in each step and the total at each step (Patterns of Change) Compares graph shapes to describe the rates of growth (Patterns of Change) Demonstrates an understanding of and represents relationships among distance, time, and speed (Patterns of Change) Make, interprets, and compares tables, graphs, and stories that show accumulated distance and speed (Patterns of Change) Collects and records data in regular time intervals to analyze patterns of change (Patterns of Change) Explores relationships between discrete and continuous descriptions of motion (Patterns of Change) Compares relative motion (Patterns of Change) Relates number patterns to graphical shapes (Patterns of Change) Illustrates relative change or motion in an animation (Excursive) (Patterns of Change) 

8.6.3 By the end of eighth grade, students will describe and represent relations, using tables, graphs, and rules. 

Use variables to recognize and describe patterns. 
Dr. Robert Sweetland's Notes ©