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 tenÕs and hundredÕs place value

Round numerals in all places of the thousandÕs value

Round numbers to 10,000

Round numerals in all three places of the millionÕs

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, sixty-four, three hundred sixty-four, 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.

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.

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 seventy-three). 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 eighty-two million, one hundred seven thousand, four hundred seventy-three.

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

Compare decimals to fractions

Multiples and factors of numbers from 0-100

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 0-25, discuss patterns and methods for finding the factors. Have students use the different methods that they proceduralized to find factors of numbers 26-50, discuss patterns, and methods for finding the factors. Repeat for numbers 50-10

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

8.2.1 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.

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Name that portion
Investigation one session 1-7
SS 1, 2, 16

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 scale-model problems with fractions and decimals.

Problems should be of increasing level of difficulty and involve real-life 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.

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.

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

8.4 Geometry/Spatial Concepts

Measure liquid amounts up to a gallon and liter

8.4.1 By the end of eighth grade, students will identify, describe, compare, and classify two-and three-dimensional 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

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 two-and three-dimensional 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 nineteen-twenty, or two-thousand-four?

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 3-D shapes to make nets for each shape. Compare the properties of each net to 2-D shapes. Record the different shapes on a chart for all 3-D shapes and compare the shapes to the shapes names and type of 3-D 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 geo-board. 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.

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 one-half feet tall. There is a door and one window. However, they can be discounted because when the pattern is matched the drop-off 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?

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

• Select appropriate representations of data when constructing data displays (graphs, tables, or charts

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.

Develop a Survey

Create charts, graphs and tables using the data from the survey

Interpret information displayed on graphs, charts, and tables.

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 three-color spinner or a coin).

Conduct experiments to demonstrate an understanding of probability.

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.