Sixth 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? Write a number in the billions. The first student says the ones place value. The second student says the total value of the digits in the tens & ones places. E.g. 2,364, four, sixtyfour, three hundred sixtyfour, etc. This process continues until the billions place value is reached. 


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. 
Place Value Identify, read and write numerals to billions.  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 Transpose a five and six digit number into expanded notation. 
Write
random numerals to make a number between 100,000 and 999,999. Write
the number in expanded notation. e.g. 86,972 = 80,000 + 6,000 + 900
+ 70 + 2 

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. 


Identify
exponential form. Transpose the expanded notation of five and six
digit numerals into exponential form. 
Identify
the standard number for expanded notation or identifying the expanded
notation for the standard number. 

Identify,
read and write Roman numerals 
Select
a random number. Write its Roman numeral equivalent, the Roman numeral
for one less, and one more than the given number. Use 10 toothpicks
to make Roman numerals or equations. E.g. XXXVII (10 picks) V + I
+ VI (10 picks) and X + I + XI (10 picks). Record each and see how
many can be made in 10 minutes. 

Round
numbers to billions 
Select
a random number less than ten billion. Round the number to tens,
hundreds, thousands, ten thousands… for each place to billions. 

Round
decimals to the tenth, hundredth, and thousandth place. 
Randomly
select a number and round it to tenths, hundredths, or thousandths. 

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. 
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 


Addition
and subtraction Add and subtract numbers with regrouping to one hundred
thousands. 
Randomly
select three to six digit numbers so that regrouping is necessary.
Find the sum and difference. 

Multiplication
and division Memorize multiplication and division facts through 12
Recognize the terms divisor and dividend. Solve division problems
with and without remainders. 
Write
a division problem (e.g. 15/3 =5, or 15 divided by 3 =, Chris had
12 cookies and shared them with three friends. All four ate equal
amounts of cookies. How many cookies did each person eat? …)
identify the divisor and the dividend. Solve division problems. 

Fractions Add and subtract mixed and improper fractions. 
Add
and subtract 2/4 and 1/4 and illustrate each answer with the use
of a model. Add and subtract 2 1/2 and 1 1/2. and illustrate each
answer with the use of a model. Note: fractions presented by circles
(pizza or pie) are more difficult than squares or rectangles. If
a person takes a piece of paper and repeatedly cuts one and a half
inches from it, how many pieces can be cut off and how big will the
last piece be? Show your solution with a model and equation. 

Multiply
and divide mixed and improper fractions. 
Select
a recipe that has three or more fractional measurements. Find how
much of each ingredient would be needed to double, triple, and quadruple
the recipe. What if the same recipe were cut in half or a third? 

Decimals Multiply and divide decimal numbers. 
Create
and solve problems using information in a newspaper e.g. winning
percentages for teams listed in the newspaper, prices of sale items
reduced by percentages or fractional parts, buying multiple items, … 

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. 


Geometry  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. 


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. 

Shapes Identify geometric 2D shapes (circle, polygon, quadrilaterals, triangle, square, rhombus, trapezoid, rectangle, hexagon, pentagon, & octagon)Identify geometric 3D shapes (sphere, cylinder, cone, cube, triangular prism, & rectangular prism)  Identify and sort polygons by their mathematical properties. Draw an example for each 3D geometric shape and identify an object that has the same shape. Identify a face that has each of the following 2D shapes: circle, square, triangle, and rectangle) Identify listed 2D shapes when 3D objects are intersected by a plane.  
Use geometry and patterns for reallife situations.  Design a floor tile pattern using no more than five different combinations of color and shape. Research the size and color of tiles to make the design as realistic as possible. Draw the floor plan on graph paper to illustrate the pattern and what a room with the pattern would look like.  
Measures geometric angles and sort by right angle, obtuse, and acute.  Measure and describe the kinds of angles in a geometric pattern (e.g. The floor tile design).  
Find the area for nonuniform shapes.  
Measure the diameter, radius, and circumference of a circle.  In a large area of the room, or outside, draw a large circle with chalk. Measure the diameter, radius, and circumference. Describe how the measurements are related.  
Find area of circles.  
Construct figures using lines, rays and segments  Create a drawing with at least 5 lines, 5 rays and 5 line segments. Make every line red, every ray green, and every line segment purple.  
Calculate volume of given objects.  Measure the volume of water in milliliters and cubic centimeters and see if their is a relationship (volume containers can be purchased with right angles that usually hold 1 liter, .5 l, and .125 l). Measure the volume of various household objects e.g. milk container, pop can, water bottle, soup can in milliliters with water. Measure the containers in centimeters and explain how the measurements could be used to calculate the volume.  
Estimation Estimate the depth of relative places and objects  Go to the playground and estimate various distances, e.g. from one place to another, from the top of the slide to the bottom, then measure the distance and draw it on a map. Use the map to estimate other distances, then measure them to see how accurate the map is.  
Identify freezing point and boiling point in Celsius and Fahrenheit  Take the temperature (in Celsius and Fahrenheit)
of water as it is heated to boiling. Fill a container to about 1/3
with tap water. Take its temperature in (Celsius and Fahrenheit). Add
ice one cube at a time, stir, and take the temperature again. Continue
until the temperature stabilizes. Put the container on a heat source, record the starting temperature in C & F and the temperature each minute until two minutes after it boils. Graph the results. 

Thermometer Distinguish between Celsius and Fahrenheit on a thermometer.  Fill four containers with different temperatures of water. Measure the temperature of each container in both Celsius and Fahrenheit. Make a chart and explain how the temperatures are related.  
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 


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. 
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 
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. 


Fractions Reduces fractions to lowest terms.  Label a bag with 1/2, 1/3, 1/4, 1/5, and 1/6. Use blank cards and write an equivalent fraction on each card (e.g. 5/10) and place it in the appropriate bag. See how many can be made in five minutes. Or sort premade equivalent cards into the appropriate bag.  
Change fractions to and from decimals and percents.  Make a chart with three columns one labeled fractions, one decimals and one percent. Make ten rows and put a different fraction, decimal, or percent in one cell for each row. Fill in the appropriate equivalent for the rest of the cells in each row  
Identify multiples of numbers.  Select a random number from 110. Count from 1 to 40 and each time a multiple of the number is reached identify it by marking it on a hundred chart or number line, saying "_ is a multiple of _", or other way.  
Recognize factors for a given number.  Select a random number from 150. Start with the number 1 and identify all of the number's factors.  
Identify, read and write decimal values greater than or in millionths.  Create a chart with the place values from millions to millionths. Randomly put a numeral in each place. (E.g. put a 3 in the ones place, 7 in the thousandths place.) Read the number.Randomly select a numeral and a place value. Put the numeral in the appropriate place. Continue till all the places are filled and read the number.  
Identify the fractional or decimal equivalent of a percent.  
Prime Numbers Define prime numbers and list examples through 50.  Write numbers from 1 to 50 and circle the prime numbers.  
Factor whole numbers into their prime factor equivalents.  Randomly select a composite number from 12 to 100 and find the prime factor equivalent. e.g. 12 2 * 6 2 * 3  
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). 
Conduct experiments to demonstrate an understanding of probability. 
Open a bag of M&M's and write
how many M & Ms there are for each color. Open a second bag and
repeat the process. How would you use the information to predict the number of each color in a bag of M&M's? What if any further information would you like to have? 

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. 
Create and interpret tables, charts, and graphs using mean, median, and mode and other mathematical relationships.  Make a questionnaire and poll their family members about selected activities and how often each has done them in the last year. e.g. quilt, dance, tell stories, …. Use the data to compute averages for the skills and find out which skill has the highest average. Create a class graph of foot sizes. Use the graph to answer questions e.g. How many people have the largest foot size? What size is the most common?  
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. 


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. 

Integers Add and subtract positive and negative integers.  Use red and black checkers. Let the red checkers stand
for positive numbers and the black checkers stand for negative numbers.
Randomly create problems as +3  +4 and solve them using the checkers.
Create a number line from –20 to 20. Create problems with positive and negative integers. Show how the solutions can be found by using the number line. 
Dr. Robert Sweetland's Notes ©