subjectmathematics

organizerK­8

Note: If a benchmark is not applicable to a particular grade level, that number is omitted in the performance indicators.

Standard 1

Use a variety of strategies in the problem-solving process

K-2 Benchmarks

1. Represent problems using physical objects.

2. Solve everyday problems using addition and subtraction of whole numbers.

3. Make rough estimates of answers.

4. Explain to others how he/she went about solving a numerical problem.

5. Classify sets of objects into two or more groups using their attributes.

6. Distinguish between important and unimportant mathematical information.

7. Create and use an organized list to determine possible outcomes or solve problems.

K-2 Performance Indicators

Kindergarten

1. Use manipulatives such as dinosaur counters to add and subtract numbers one

through five.

Grade 1

1. Use manipulatives such as unifix cubes to demonstrate whether to add or subtract to solve a problem using the numbers from one through nine.

2., 4. Draw and explain pictures to illustrate understanding of a problem such as: 5 bugs are on a leaf and 2 fly away. How many are left?

5. Sort sets of tiles by color, size, and shape.

Grade 2

1. Make up or act out stories to go with number sentences - i.e., 5 + 9.

2. Draw and write to illustrate understanding of a problem such as: Find the number of students having lunch if 5 have sandwiches, 6 have pizza, and 3 have hot dogs.

3. Estimate the number of links in a paper chain and be able to explain in oral, or written form, how they arrived at an answer.

4. Teach or explain to partners or group members how to solve a numerical problem.

5. Classify plane figures by type of side (straight, curved).

6. Solve a simple problem by finding and using relevant information.

7. Determine the possible arrangement for a triple ice cream cone given three flavors.

3-5 Benchmarks

1. State problem in his/her own words.

2. Clarify problems using discussions with peers.

3. Clarify and explain problems and solutions through writing.

4. Estimate and check reasonableness of solutions.

5. Use a variety of strategies to solve problems (Venn diagrams, organized lists).

6. Check the reasonableness of results through estimation.

7. Model problems using graphic representations.

8. Solve real world problems using addition, subtraction, multiplication, and division of whole numbers.

9. Solve real world problems using decimals.

10. Make a solution into a general rule that applies to other situations.

11. Construct physical representations for complex problems.

12. Articulate similarities and differences between problem-solving strategies.

3-5 Performance Indicators

Grade 3

1-6. Show how 3 pizzas can be shared by 4 people and explain the process.

7. Create pictographs and bar graphs to represent class birthdays.

8-10. Calculate the cost of 3 grocery store items and determine the change from $10.

11. Construct tangram pictures based on

MSAD #16 Framework for Academic Standards Fall 1997

Grandfather Tangs' Storybook.

Grade 4

1-6. Use base ten blocks to solve 43 X 68 and explain the process.

7. Compare rainfall of our area with that of another area using bar, picto, or line graph.

8-10. Propose a budget to buy one item for everyone in the class using classified ads.

11. Create a pattern to completely cover a given area using two different pattern blocks.

Grade 5

1-6. Show different coin combinations that make seventy-five cents and explain the process.

7. Gather data and create a bar, picto, or line graph using self-selected topic.

8-10. Write checks and maintain a register given a set budget.

11. Show how many hundreds are in a million using base ten blocks.

12. Explain and defend choice of strategy given a problem-solving situation (3-5).

6-8 Benchmarks

1. Follow a model for solving real world problems that includes making assumptions, constructing a representation, choosing the appropriate operations or formula, making computations, verifying answers, and checking accuracy.

2. Identify a similar problem type.

3. Solve a problem by working backwards.

4. Use substitution in formulas and expressions.

5. Verify solutions.

6. Identify similarities and differences between problem types and problem- solving strategies.

7. Break larger problem into smaller one(s).

8. Understand there is often more than one right way to solve a mathematical problem.

6-8 Performance Indicators

Grade 6

1. Decide which operations to use, compute and estimate their answer to check for accuracy given a real life money problem.

2. Choose proper operation to determine an answer.

3. Recognize the various steps in problem- solving (identify question, technique, operation, computation, estimation, and check).

4. Evaluate an expression given numbers for variables.

5. Support answers using addition to check subtraction problems.

6. Identify key words to complete a problem.

7. Use compatible numbers to break problems down into smaller parts.

8a. Examine completed problems and investigate other ways to solve and verify.

8b. Show that three-fourths of an apple pie is equivalent to 6 out of 8 pieces of

pizza.

8c. Solve problems involving unit pricing.

8d.Decide which of the four basic operations to use to solve problems.

Grade 7

1. Determine which problem-solving technique to use (picture, list, guess, and check) and incorporate it into computation.

2. Prioritize which plan to use with various types of problems.

3. Discriminate between necessary and unnecessary information in a problem.

4. Solve an equation with a variable and have a basic concept of variable.

5. Assess an answer to a computation for reasonableness and determine which operations to use.

6. Determine and predict which plan will be most effective for various problems.

7. Distinguish which parts of the problem can be solved first and incorporate various other parts of the problem to obtain a solution.

8a. Strategize how to solve a problem and formulate several plans to help solve it.

8b. Solve a problem in mileage computation or cooking computation using operations with fractions or decimals, converting from one to the other or to percent (6-7).

8c. Determine the ratio of two numbers and use proportion in comparing two ratios.

8d. Discover the relationship between

MSAD #16 Framework for Academic Standards Fall 1997

Math

distance, rate, and time in a problem.

8e. Choose from a variety of techniques used to solve problems and incorporate several techniques into one problem.

8f.. Calculate the number of fence posts necessary to enclose a 14 x 8 foot area with a post at each corner and a spacing of two feet apart (6-8).

8g. Calculate the area of a square given one side.

Grade 8

1. Demonstrate appropriate use of problem- solving strategies and produce a graphic illustration to depict relationships given a real life problem.

2. Combine and compile various types of problem-solving techniques to solve similar problems.

3. Use alternate strategy if appropriate.

4. Apply single variable expressions and evaluate them.

5. Use substitution to check the answer given (3/4)x+10 =19 and a solution, x=12.

6. Identify the problem-solving strategy that is appropriate.

7. Dissect a problem into smaller parts to simplify it.

8. Understand the need for alternate problem-solving skills.

Standard 2

Understand and apply basic and advanced properties of the concept of numbers

K-2 Benchmarks

1. Understand that a number is a symbol for how much of something there is.

2. Order relatively small sets of numbers.

3. Understand that in sharing or measuring things, there is sometimes a need to use numbers between whole numbers.

4. Understand the role of place value ones,

tens, and one-hundreds with whole numbers.

5. Understand the difference between odd and even numbers.

6. Understand that zero can mean none of something or it can represent a point on a number line.

7. Understand the concept of less than, more than, and equal to.

K-2 Performance Indicators

Kindergarten

1. Write numbers one to ten to indicate amount of objects.

2. Write numbers from one to ten in order.

6. Show an empty hand when asked to show zero or none of something.

7.Show that six is larger than three using beans in a cup.

Grade 1

1. Write numbers from one to ninety-nine.

2. Arrange three numbers in order from least to greatest.

4. Trade ten pennies for a dime. Group place value blocks (tens and ones) to make a two digit number - e.g., seventeen.

5. Select odd and even numbers on a calendar. Count by twos up to fifty and count by fives and tens up to one hundred.

6. Use zero to represent no objects.

Grade 2

1. Write numbers from one to nine hundred ninety-nine .

2. Explain how an object's order corresponds with an ordinal number.

3. Measure small classroom objects to the half inch and record answer.

4. Group place value blocks (one hundreds, tens, ones) to make a three digit number - e.g., two hundred sixty-three.

5. Determine odd and even numbers on a ninety-nine chart or number line; count by twos from one to ninty-nine.

6. Locate zero on a number line or ruler.

7. Use less than, greater than, and equal to when comparing two numbers or groups.

3-5 Benchmarks

1. Understand the role of place value with whole numbers and decimals.

2. Rename numbers.

3. Understand the relationship of decimals to whole numbers.

4. Understand the characteristics of mixed numbers.

5. Use number lines to model a variety of numbers.

6. Understand that if zero and one are located on any line, any other number can

MSAD #16 Framework for Academic Standards Fall 1997

be depicted as a position on that line.

3-5 Performance Indicators

Grade 3

1. Represent a three or four digit number using place value blocks.

2. Read and record numbers in standard, expanded, and word forms (3-5).

5. Arrange a given set of numbers on a number line (3-5).

6. Plot a given number on a number line (3- 5).

Grade 4

1. Accurately record a time from a stop watch in minutes, seconds, and milliseconds.

2. Read and record numbers in standard, expanded, and word forms (3-5).

3. Show the meaning of a fraction using pattern blocks.

4. Decide how to share equally 4 pizzas among 3 people.

5. Arrange a given set of numbers on a number line (3-5).

6. Plot a given number on a number line (3-

5).

Grade 5

1. Construct a place value strip to accurately represent whole numbers and decimals.

2. Read and record numbers in standard, expanded, and word forms (3-5).

3. Decide how many items you can buy given $50 and a flyer.

4. Determine which two mixed numbers give a difference closest to 2 using estimation (3 1/3, 4 1/4, 5 3/8).

5. Arrange a given set of numbers on a number line (3-5).

6. Plot a given number on a number line (3- 5).

6-8 Benchmarks

1. Understand the characteristics of rational and irrational numbers, proportions, and percents.

2. Understand the role of integers in the number system.

3. Understand the relationship of prime numbers to other numbers.

4.Express numbers using powers and/or scientific notation.

5. Model numbers using two-dimensional regions.

6. Understand the Arabic system is not the only system for representing numbers; the Roman system is used for dates and ordering; and the Babylonian system for time and angular measurement.

7. Understand that negative numbers result from some subtractions on a number line; understand that number lines are used when ordering or measuring something on either side of a reference point (temperature, altitude).

8. Understand inverse relationships between addition and subtraction and multiplication and division.

6-8 Performance Indicators

Grade 6

1a. Recognize and differentiate between fractions and decimals.

1b. Understand .5=1/2 and vice versa.

3. Factor the number 28 recognizing which factors are prime (6-7).

4. Introduce the effect of increasing power on the size of the number.

6. Convert Roman to Arabic numerals and reverse.

Grade 7

1. Convert 3/4 to a decimal or a percent.

3. Factor the number 28 recognizing which factors are prime (6-7).

4a. Write 3,271,000 in scientific notation.

4b. Illustrate the number 1,000,000 using powers of 10.

5. Determine area and perimeter of figures from diagrams.

7a. Understand subtraction of a larger number from a smaller one.

7b. Graph inequalities using integers.

Grade 8

1a. Differentiate between the values of 3/7 and square root 3.

1b. Simplify $48/8 hours to $/hour.

1c. Represent 5/7 in other equivalent forms.

2. Combine -8 and +7 using a number line.

3. Differentiate between prime and composite numbers explaining why five is prime and twelve is composite.

4. Use scientific notation to represent the distance from earth to Neptune.

MSAD #16 Framework for Academic Standards Fall 1997

Math

5. Determine the number of rectangles that are possible with an area of 48 sq. cm.

7a. Convert -32° F to degrees Celsius.

7b. Graph inequalities using rational numbers.

8. Solve equations using properties of equality and inverse operations.

Standard 3

Use basic and advanced procedures while performing the process of computation

K-2 Benchmarks

1. Add and subtract whole numbers with accuracy.

2. Use common, everyday fractions to count, order, and measure things encountered in everyday experiences.

3. Understand that it is useful to estimate quantities without knowing them exactly.

4. Understand use of calculator; perform basic addition and subtraction problems.

K-2 Performance Indicators

Kindergarten

1. Use cubes to model addition and subtraction to ten.

2. Show how an apple can be shared equally by two people.

3. Estimate the number of objects in a container; explain the method used; compare with the actual count; evaluate the estimation process (K-2).

Grade 1

1. Add and subtract numbers to nineteen

and memorize facts up to 6+6; make the correct addition and subtraction sentences and write related facts.

2. Divide a group of objects into two equal groups.

3. Estimate the number of objects in a container; explain the method used; compare with the actual count; evaluate the estimation process (K-2).

4. Solve basic addition and subtraction problems with the calculator (1-2).

Grade 2

1. Add and subtract two digit numbers with regrouping and memorize facts up to 9+9.

2. Divide a group of objects into two, three, and four equal groups; write a fraction for a part of a region; color part of a figure represented by a given fraction.

3. Estimate the number of objects in a container; explain the method used; compare with the actual count; evaluate the estimation process (K-2).

4. Solve basic addition and subtraction problems with the calculator (1-2).

3-5 Benchmarks

1. Round whole numbers and decimals.

2. Add, subtract, multiply, and divide whole numbers and dollars and cents with accuracy using mental math, paper and pencil, or calculator.

3. Add and subtract decimals accurately.

4. Determine the effects of addition, subtraction, multiplication, and division on size and order of numbers.

5. State the purpose for each step in basic calculations.

6. Understand that choices must be made when determining which operation to use.

7. Understand the nature of and similarities to and differences between multiples and factors.

8. Understand that addition and subtraction are inverses of each other as are

multiplication and division.

3-5 Performance Indicators

Grade 3

1. Round whole numbers to the nearest indicated place.

2. Solve three and four digit addition and subtraction problems and one digit multiplication problems; memorize addition and subtraction facts up to 10+10.

3. Add and subtract money ( $3.49+$7.63).

4. Compare resulting quantities given a set of operations and numbers (10+2, 10-2, 10x2, 10/2) (3-5).

5. Solve an addition or subtraction computation and explain the purpose of the steps.

6. Choose the necessary operation(s) to solve the problem given a set of numbers in a problem-solving situation (one, two, three, four to equal ten) (3-5).

8. Given a number, name its fact family (3-5).

MSAD #16 Framework for Academic Standards Fall 1997

Grade 4

1. Round a decimal to the nearest indicated place (4-5).

2. Solve addition, subtraction, and multiplication problems with three and four digit numbers and one digit division problems.

3. Add and subtract fractions with like denominatorsestimating answers.

4. Compare resulting quantities given a set of operations and numbers (10+2, 10-2, 10x2, 10/2) (3-5).

5. Solve an addition, subtraction, or multiplication computation and explain the purpose of the steps.

6. Choose the necessary operation(s) to solve the problem given a set of numbers in a problem-solving situation (one, two, three, four to equal ten) (3-5).

7. Identify the multiples of a given number using a hundreds chart.

8. Given a number, name its fact family (3-5).

Grade 5

1. Round a decimal to the nearest indicated place (4-5).

2. Solve addition, subtraction, multiplication, and division problems with multiple digits.

3. Add and subtract decimals through thousandths.

4a. Compare resulting quantities given a set of operations and numbers (10+2, 10-2, 10x2, 10/2) (3-5).

4b. Memorize multiplication and division facts up to 12 X 12.

5. Solve a basic computation using any of the four operations and explain the purpose of the steps.

6. Choose the necessary operation(s) to solve the problem given a set of numbers in a problem-solving situation (one, two, three, four to equal ten) (3-5).

7. Name all of a number's factors.

8. Given a number, name its fact family (3-5).

6-8 Benchmarks

1. Perform operations on rational numbers appropriately.

2. Round decimals and fractions.

3. Mentally multiply and divide basic combinations of whole numbers with reasonable accuracy.

4. Use basic estimation techniques effectively.

5. Use order of operations effectively.

6. Calculate what percentage one number is of another.

7. Use a calculator to compare amounts proportionally.

8. Understand the three basic meanings of the expression a/b (a is the number of units each of which has size 1/b; a divided by b; and a compared to or in relationship to b).

9. Convert fractions and mixed numbers to decimals and percentages, percentages to fractions and decimals, and decimals to percentages and fractions.

10. Translate between decimals and commonly encountered fractions.

6-8 Performance Indicators

Grade 6

1. Add, subtract, multiply, and divide simple fractions and decimals.

2. Round a decimal.

3-5. Mentally multiply 53x8; explain skills used (6-8).

9. Convert .26 to a fraction or 1 3/8 to a decimal.

Grade 7

1. Add, subtract, multiply, and divide mixed and improper fractions and decimals.

2. Round .86 to .9.

3-5. Mentally multiply 53x8; explain skills used (6-8).

6. Evaluate 24% of $75.00.

7. Use a calculator to show 5/10 and 3/6 are equal ratios by cross multiplication (6-7).

8. Determine unit rate using division given a $12 cost for 3 tickets.

9. Interchange decimals, percents, and fractions such as .375, 37.5%, and 3/8.

10. Identify that .75 = 75/100=3/4 (7-8).

Grade 8

1. Evaluate expressions using fractions and multiple operations.

2. Round 13.86 to the nearest tenth; write 1.66 as a fraction.

3-5. Mentally multiply 53x8; explain skills

MSAD #16 Framework for Academic Standards Fall 1997

Math

used (6-8).

6. Find 3% of what number is 15.

7. Determine the largest fraction by cross multiplication.

8. Show that x/6=(1/6)x and is equivalent to x:6.

9. Change a repeating decimal to a fraction.

10. Identify that .75 = 75/100=3/4 (7-8).

Standard 4

Understand and apply basic and advanced properties of the concept of measurement

K-2 Benchmarks

1. Understand the basic characteristics of weight and how it is measured.

2. Have a basic understanding of the concept of time and how it is measured.

3. Have a basic understanding of the concept of temperature and how it is measured.

4. Make quantitative estimates of familiar lengths, widths, and time interval, and check them against measurements.

5. Have a basic understanding of the calendar and its uses.

6. Have a basic understanding of money and how it is identified and valued.

K-2 Performance Indicators

Kindergarten

1. Arrange 3 animals (cat, mouse, elephant) by rank order of weight, least to greatest.

5. Name the current season.

6. Recognize a group of coins as money.

Grade 1

1. Arrange 3 objects (books, rocks, pumpkins) by rank order of weight, least to greatest.

2. Tell, read, write, and show time to hour and half-hour on a standard clock.

4. Use non-standard units of measurement to determine length.

5. Name the current month and the days of the week in order.

6. Identify and give value of penny, nickel, dime, and dollar.

Grade 2

1. Estimate whether the weight of an object is more than, less than, or equal to a pound.

2. Tell, read, write, and show time to 5 and 15 minute intervals.

3. Read temperature and tell whether it is hot or cold.

4. Distinguish whether a door is 6 feet or 6 inches; measure the length of objects choosing the appropriate tool for measurement.

5. Identify days and dates on a calendar; name the current date.

6. Show different coin combinations that make $.75; identify all coins and values.

3-5 Benchmarks

1. Understand length, width, and height.

2. Understand the basic characteristics of area, perimeter, volume, weight, time, and temperature and how it is measured.

3. Make effective use of tools for making measurements.

4. Determine whether measurements of length, area, volume, weight, or time are reasonable by referring to standard and metric measurement.

5. Understand that area and volume are determined from linear dimensions.

6. Understand that measurements can be converted from one system to another.

7. Approximate the area of irregular shapes using squares.

8. Understand that scale drawings can be used to represent shapes and compare locations of things very different in size.

9. Understand the basic characteristics of circumference and how it is measured.

3-5 Performance Indicators

Grade 3

1. Given a plane figure, measure length, width, and height (3-5).

2. Given a calendar or clock, determine past, future, and elapsed time.

3. Measure the length of various objects choosing an appropriate unit for measurement (3-5).

4. Estimate measurements of length or time and check accuracy using standard and metric measurement .

5. Show and construct area in terms of unit squares given a rectangle (3-4).

7. Determine the area using a standard square unit given an irregular shape(3-5).

8. Discriminate between real objects and

MSAD #16 Framework for Academic Standards Fall 1997

scaled objects (Maine map).

Grade 4

1. Given a plane figure, measure length, width, and height (3-5).

2-6. Given a perimeter, design shapes with different areas using different systems.

3. Measure the length of various objects choosing an appropriate unit for measurement (3-5).

4. Estimate measurements of length, time, area, volume, weight, and temperature and check accuracy using standard measurement (4-5).

5. Given a rectangle, show and construct area in terms of unit squares (3-4).

7. Given an irregular shape, determine the area using a standard square unit (3-5).

8. Calculate mileage using a distance scale.

9. Measure the circumference of round objects.

Grade 5

1. Given a plane figure, measure length, width, and height (3-5).

2a. Given a shape, determine its area, perimeter, volume, and weight.

2b. Given a train schedule, determine arrival and departure times.

3a. Measure the length of various objects choosing an appropriate unit for measurement (3-5).

3b. Convert from one unit to another (cm to m).

4. Estimate measurements of length, time,

area, volume, weight, and temperature and check accuracy using standard measurement (4-5).

5. Given a shape, determine area using formula l x w=A.

6. Given a season, determine a range of temperatures using degrees Fahrenheit and Centigrade.

7. Given an irregular shape, determine the area using a standard square unit (3-5).

8. Design a map of Mexico to scale.

9. Compare the circumference of a student's head, arm, and leg to those of the Statue of Liberty.

6-8 Benchmarks

1. Have a basic understanding of the concept of rate, time, and distance, and how each is measured.

2. Make effective use of a tool for measuring weight, length, or volume.

3. Determine appropriate forms of measurement in a variety of situations and

convert from one measurement system to another.

4. Determine level of accuracy for significant digits in measurement.

5. Calculate the volumes of rectangular solids.

6. Calculate perimeter and area of rectangles, triangles, and circles.

6-8 Performance Indicators

Grade 6

1. Use a scale on a map, copy it, and apply it

to the map to find the number of units in length of the road (6-7).

2a. Use a meter stick and make metric conversions (6-7).

2b-3a. Distinguish between units of measurement of length.

3b. Determine use of standard or metric tools when measuring a house for flooring.

4. Determine the accuracy necessary when measuring mileage.

Grade 7

1a. Formulate rate and incorporate it into problem-solving situations.

1b. Use a scale on a map, find the number of units in length of the road (6-7).

2a. Use a meter stick and make metric conversions (6-7).

2b. Compare various measurements to observe a pattern or difference.

3a. Devise a plan to use appropriate form of measurement to measure the volume of a bucket of water.

3b. Use correct abbreviations for measurements (hrs., lbs., g, kg, etc.).

3c. Use a metric scale and convert from mm to cm or g to kg.

5. Use appropriate formulas and tools to measure and find perimeter and area of a rectangular solid.

6. Use appropriate tools and formulas to find perimeter and area of a given triangle.

MSAD #16 Framework for Academic Standards Fall 1997

Math

Grade 8

1a. Determine the rate of speed when given the distance and time.

1b. Convert scale measurements from a map to actual distances.

2a. Measure the perimeter of a rectangular object with a meter stick.

2b. Measure the weight, length, width, or volume of an object in metric units.

3a. Convert inches to meters when measuring distances.

3b. Decide on appropriate unit of measurement (cm or dm).

4. Identify the number of significant digits necessary in the area based on the measurement taken.

5. Design a pool and give its dimensions and volume in metric measure.

6. Use appropriate tools and formulas to find circumferance and area of a given triangle.

Standard 5

Understand and apply basic and advanced properties of the concept of geometry

K-2 Benchmarks

1. Understand the basic properties of and similarities and differences between circles, squares, rectangles, and triangles, plane and solid figures.

2. Understand the meaning of the concepts inside, outside, between, over, under, beside, before, often, to the left, etc.

3. Understand that shapes/solids such as circles, squares, rectangles, and triangles

can be found in nature and things people make and can be used to describe many things.

4. Understand that patterns can be made by putting different shapes together or taking them apart.

K-2 Performance Indicators

Kindergarten

1. Identify a circle, square, and triangle from drawings or shapes.

3. Relate square, triangle, and circle shapes to objects in the classroom or environment.

4. Replicate/continue simple patterns using cubes.

Grade 1

1. Identify an oval and a rectangle from drawings or shapes.

3. Relate oval and rectangle to objects in the environment.

4. Replicate or continue simple pattern using pattern blocks.

Grade 2

1. Identify a cylinder, cone, and cube from drawings or shapes.

2. State which numbers are between two given numbers on a number line.

3. Relate solids to objects in the environment.

4. Construct and name a new shape using pattern blocks.

3-5 Benchmarks

1. Understand and analyze the basic characteristics of one, two, and three dimensional figures.

2. Understand the basic characteristics of angles.

3. Analyze the effects of combining, sub-dividing, and changing basic shapes.

4. Understand the basic concepts of parallel, perpendicular, congruent, and symmetric.

5. Compare shapes in terms of such concepts as parallel, perpendicular, congruent, and symmetrical.

6. Understand that symmetry can be analyzed by performing reflections, turns, and slides.

7. Understand graphing of number pairs on a coordinate plane.

3-5 Performance Indicators

Grade 3

1. Describe a one, two, or three dimensional shape according to its characteristics (polygons, polyhedrons, circles, spheres, circumference, area, volume, angle, vertex, edge, face) (3-5).

2. Identify the angles of a tangram piece.

3. Create a figure using tangram pieces and explain the steps in its construction (3-5).

4-5. Compare a set of figures in terms of parallel, perpendicular, congruency, and symmetry (3-5).

6. Create symmetrical figures using pattern blocks (3-5).

MSAD #16 Framework for Academic Standards Fall 1997

7. Play Battleship (3-5).

Grade 4

1. Describe a one, two, or three dimensional shape according to its characteristics (polygons, polyhedrons, circles, spheres, circumference, area, volume, angle, vertex, edge, face) (3-5).

2. Measure the angles of a tangram piece with a protractor (4-5).

3. Create a figure using a tangram piece and explain the steps in its construction (3-5).

4-5. Compare a set of figures in terms of parallel, perpendicular, congruency, and symmetry (3-5).

6. Create symmetrical figures using pattern blocks (3-5).

7. Play Battleship (3-5).

Grade 5

1. Describe a one, two, or three dimensional shape according to its characteristics (polygons, polyhedrons, circles, spheres, circumference, area, volume, angle, vertex, edge, face) (3-5).

2. Measure the angles of a tangram piece with a protractor (4-5).

3. Create a figure using a tangram piece and explain the steps in its construction (3-5).

4-5. Compare a set of figures in terms of parallel, perpendicular, congruency, and symmetry (3-5).

6. Create symmetrical figures using pattern blocks (3-5).

7. Play Battleship (3-5).

6-8 Benchmarks

1. Understand the basic characteristics of the concept of symmetry.

2. Understand the basic characteristics of and the relationship between distance and midpoint.

3. Understand the basic characteristic of slope.

4. Understand the basic characteristics of and the similarities and differences between pyramids and prisms.

5. Visualize and perform algebraic translations, rotations, and reflections of geometric shapes.

6. Analyze the effects of flips, turns, and slides on geometric shapes.

7. Analyze the intersection of two- dimensional figures.

8. Understand that triangular shapes tend to make structures rigid.

9. Understand that shapes can match exactly or have the same shape in different sizes.

10. Understand that it takes two numbers to locate a point on a map; the numbers may be two perpendicular distances from a point.

11. Understand that the scale chosen for a graph or drawing makes a big difference in how useful it is.

12. Use appropriate tools to draw, measure, and construct geometric figures.

6-8 Performance Indicators

Grade 6

1. Detect symmetry in shapes and designs (6-7).

5-6. Use tessellation techniques to display slides of geometric shapes (6-8).

9. Depict different shapes in various sizes (6- 7).

Grade 7

1. Detect symmetry in shapes and designs (6-7).

4. Display, verbally and kinesthetically, the differences in pyramids and prisms.

5-6. Use tessellation techniques to display slides of geometric shapes (6-8).

7. Compute complementary and supplementary angles based on right and straight angles.

9. Depict different shapes in various sizes (6- 7).

Grade 8

1. Evaluate symmetry from given shapes.

2. Determine the midpoint and length given a line segment.

3. Determine the slope of a line given two points.

4. Find the volume and surface area of a square pyramid or a rectangular prism.

5-6. Use tessellation techniques to display slides of geometric shapes (6-8).

7. Graph two lines and find their point of intersection.

9. Determine if two objects are congruent or

MSAD #16 Framework for Academic Standards Fall 1997

Math

similar.

10. Plot a point on the coordinate plane given an ordered pair of numbers.

11. Determine an appropriate scale while constructing a graph.

12. Construct a 3 cm x 5 cm rectangle.

Standard 6

Understand and apply basic and advanced concepts of data analysis and distributions

K-2 Benchmarks

1. Understand that simple graphs can help one to understand observations.

K-2 Performance Indicators

Kindergarten

1. Know which bars on a graph represent the greatest and least; interpret bar graph - e.g., favorite choice.

Grade 1

1. Use information from tally chart to complete bar graph and ask a question using the graph.

Grade 2

1. Tally marks and interpret pictographs and ask a question using the graph.

3-5 Benchmarks

1. Have an understanding of the basic concept of data as specific pieces of information about something that is being studied.

2. Collect and organize simple data sets to

answer questions.

3. Understand that the basic function of tables and graphs is to make explicit how the values of one quantity are related to the values of another and that tables and graphs can make it easier to identify patterns.

4. Construct simple bar graphs, pie charts, pictographs, and line graphs.

5. Understand that spreading data on a number line helps to see what the extremes are, where they pile up, and where the gaps are.

6. Understand that a summary of data should include mean, median, mode, and range.

3-5 Performance Indicators

Grade 3

1-4. Conduct a survey, analyze data, construct a graph, and write a concluding statement to demonstrate knowledge (3-5).

Grade 4

1-4. Conduct a survey, analyze data, construct a graph, and write a concluding statement to demonstrate knowledge (3-5).

5-6. Explain the distribution of data using the results of the survey (1-4) (4-5).

Grade 5

1-4. Conduct a survey, analyze data,

construct a graph, and write a concluding statement to demonstrate knowledge (3-5).

5-6. Explain the distribution of data using the results of the survey (1-4) (4-5).

6-8 Benchmarks

1. Understand that a distribution portrays the manner in which data is organized when it is considered as a whole.

2. Understand basic characteristics of and calculate measures of central tendency (mean, median, mode).

3. Understand similarities and differences between tables, bar graphs, and circle graphs.

4. Understand that comparison of data from two groups involves comparing their middles and the spreads around them.

6-8 Performance Indicators

Grade 6

2. Compute the mean, median, and mode given a list of numbers (6-7).

3. Choose the appropriate type of display to use based on data given using the rules for bar, line, and circle graphs (6-7).

Grade 7

1. Transform given or derived data and organize it on a graph, chart, or data matrix.

MSAD #16 Framework for Academic Standards Fall 1997

2. Compute the mean, median, and mode given a list of numbers (6-7).

3. Choose the appropriate type of display to use based on data given using the rules for bar, line, and circle graphs (6-7).

4. Compare production output

of two machines from a multiple line graph.

Grade 8

1. Evaluate organized data in a distribution of a flight/distance experiment.

2. Determine the mean, median, and mode height of the eighth graders.

3. Create an appropriate graph from data given.

4. Compare measures of central tendency and distribution of data given flight data.

Standard 7

Understand and apply basic and advanced concepts of probability and statistics

K-2 Benchmarks

1. Understand that some events are more likely to happen than others.

K-2 Performance Indicators

Kindergarten

Not applicable.

Grade 1

1. Predict which color cube is more likely to

be chosen given a bag of cubes (5 red and

3-5 Benchmarks

1. Understand that the word "chance" refers to how likely an event is.

2. Understand that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event.

3. Understand that events can be described in terms of being more or less likely and how often events will occur rather than exactly when they will occur.

4. Understand that summary predictions about large collections of events are usually more accurate than summary predictions of just a few events.

3-5 Performance Indicators

Grade 3

1. Determine chances of winning in a game situation (3-5).

2. Make a prediction based on what you know about past events and check it (weather, science experiment) (3-5).

3. Predict which result is more likely to happen given a game of chance (3-5).

Grade 4

1. Determine chances of winning in a game

situation (3-5).

2. Make a prediction based on what you know about past events and check it (weather, science experiment) (3-5).

3. Predict which result is more likely to happen given a game of chance (3-5).

4. Predict (using an almanac) the average monthly rainfall for a given month based on the previous ten years.

Grade 5

1. Determine chances of winning in a game situation (3-5).

2. Make a prediction based on what you know about past events and check it (weather, science experiment) (3-5).

3. Predict which result is more likely to happen given a game of chance (3-5).

4. Predict (using an almanac) the average seasonal precipitation for a geographic area of student's personal choice based on the previous ten years.

6-8 Benchmarks

1. Understand the basic features of a sample and sampling error.

2. Estimate probability using simulation.

3. Understand that probabilities are ratios that can be expressed as fractions, percentages, or odds.

4. Understand that statistical predictions are better for describing what proportion of a group will experience something rather than which individuals within the group will experience something, and how often

Grade 2

1. Predict which color cube is more likely to be chosen given a bag of cubes (5 red and 3 blue).

MSAD #16 Framework for Academic Standards Fall 1997

Math

events will occur rather than exactly when they will occur.

5. Estimate probabilities of events in familiar situations using what has happened in the past or by making rough calculations.

6. Understand that the larger a well-chosen sample is, the more likely it is to represent the whole and that there are many ways of choosing a sample that can make it unrepresentative of the whole.

7. Find all possible combinations and permutations of a set.

6-8 Performance Indicators

Grade 6

2. Use a coin toss to show probability of one- half.

3. Find the probability of rolling a 6 on a die.

5. Find the probability of picking a red ball in a bag of 4 blue and 1 red.

7. Find the number of ways to choose 3 numbers in the lottery.

Grade 7

1. Record each airplane's distance and note variables that affect performance.

2. Predict the probability of getting eliminated when playing a game of chance.

3. Transform 3 wins and 4 losses to a ratio, percentage, or odds.

4. Take the statistics of a sample and compute what will happen to the rest of the population.

5. Compare twp numbers to form ratios representing events and determine if they are equivalent.

Grade 8

1. Record each airplane's distance and note variables that affect performance.

2. Predict the probability of getting eliminated when playing a game of chance.

3. Express the probability of rolling a 2 with a pair of dice as a fraction, percentage, or odds.

4. Differentiate the group size of non- winners and winners given the probability of winning the megabucks.

5. Predict, from past experience, when a 1 is going to appear in the game of Skunk.

6. Create a sample of flight distances that best represents weight distribution and make observations that affect performance.

7. Find the number of possible three digit locker combinations.

Standard 8

Understand and apply basic and advanced properties of functions and algebra

K-2 Benchmarks

1. Recognize basic number patterns.

2. Understand the concept of missing addends.

3. Understand the concept of missing subtrahends.

4. Use language and symbols to express numerical relationships.

K-2 Performance Indicators

Kindergarten

4. Write symbolically 2 buttons added to 3 buttons.

Grade 1

1. Find a basic number pattern on the calendar (#s and 5s).

4. Write the sum of 6 and 5 is 11 in symbols.

Grade 2

1. Find, make, and describe patterns using a hundred chart.

2. Supply the missing addend in the equation up to 19.

3. Supply the missing subtrahend in the equation up to 19.

4. Write 15 minus 8 is 7 symbolically.

3-5 Benchmarks

1. Understand the basic characteristics of a variable (x+y has infinite answers if y=x+3 limits answers).

2. Extend simple patterns of numbers.

3. Identify simple patterns of numbers.

4. Understand that mathematics is the study of many kinds of patterns including numbers and shapes and operations.

3-5 Performance Indicators

Grade 3

1. Solve a problem with a missing number

MSAD #16 Framework for Academic Standards Fall 1997

variable (3-4).

2. Extend the pattern given the beginning of a pattern (3-5).

3. Describe the characteristics of a given pattern (3-5).

4. Observe, describe, and/or produce patterns that they see (3-5).

Grade 4

1. Solve a problem with a missing number (variable) (3-4).

2. Extend the pattern given the beginning of a pattern (3-5).

3. Describe the characteristics of a given pattern (3-5).

4. Observe, describe, and/or produce patterns that they see (3-5).

Grade 5

1. Solve a problem containing a variable with a stated value.

2. Extend the pattern given the beginning of a pattern (3-5).

3. Describe the characteristics of a given pattern (3-5).

4. Observe, describe and/or produce patterns that they see (3-5).

6-8 Benchmarks

1. Understand the basic features of a mathematical expression.

2. Understand the characteristics and uses of the concept of rectangular coordinates.

3. Have a basic understanding of the concept of equation.

4. Understand that an equation containing a variable may be true for just one value of the variable.

5. Understand that mathematical statements can be used to describe how one quantity changes when another changes.

6-8 Performance Indicators

Grade 6

1. Evaluate a mathematical expression involving several operations and exponents.

Grade 7

1. Represent an unknown quantity with a variable in an expression.

3. Find the solution of x - 3 = 9.

4. Explain why x + 2 = 6 has only one solution.

5. Show how the area of a circle changes as its radius is increased.

Grade 8

1. Write an expression for your sibling's age if she is three years younger than you.

2a. Plot (-7,7).

2b. Identify the quadrants and the x and y axes.

3. Write an equation for the best fit line.

4. Find the solution for the variable if 2x + 7 = 11 and check the answer.

5. Rewrite an equation for the balanced scale if a weight of five pounds is removed from

each side.

Standard 9

Understand the general nature and uses of mathematics

K-2 Benchmarks

1. Understand the uses of numbers.

K-2 Performance Indicators

1. Explain how numbers are used in calendars, recipes, money, or measurement .

3-5 Benchmarks

1. Use mathematical ideas and concepts to predict and explain the world.

2. Understand that math is used in calendars, recipes, games, money, measurement, art, nature, etc.

3. Understand that the concept of number is represented differently in different cultures.

3-5 Performance Indicators

1 ,2. Survey students to determine favorite pizzas, create a graph, and present the data, graph, and written explanation to the cafeteria staff to help in planning (3- 5).

3. Compare our number system to those of other countries (Japanese, Aztec, Spanish, French, Roman) and translate numbers from one to the other (3-5).

MSAD #16 Framework for Academic Standards Fall 1997

Math

6-8 Benchmarks

1. Understand that mathematics has been helpful in practical ways for many centuries.

2. Understand that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent.

6-8 Performance Indicators

Grade 6

1. Understand the use of Roman numerals in dates and outlines.

2. Show how abstract math concepts are used in fields such as carpentry or science.

Grade 7

1. Explain contributions of great mathematicians to the field.

2. Show how abstract math concepts are used in carpentry or science.

Grade 8

1. Understand that the Pythagorean theorem can be used to solve many practical problems.

2 Pace out the dimensions of a playing field and translate to a metric measurement.

SUBJECTMATHEMATICS

ORGANIZERPRE-ALGEBRA (9-12)

Standard 1

Use a variety of strategies in the problem-

solving

9-12 Benchmarks

1. Classify problem-solving strategies or problem types by underlying general characteristics.

2. Solve real world problems using fractions, decimals, and percent.

3. Solve real world problems using ratio and proportion.

4. Use equations with variables to solve real world problems.

5. Solve problems using tables and graphs.

9-12 Performance Indicators

1. Recognize that many problems have similar characteristics and that once they are recognized lend themselves to the same strategy for finding the solution.

2. Determine the sale price of an item sold at a certain percent of discount and find total cost with a percent sales tax.

3. Use a given ratio to mix oil with gasoline to determine the correct proportions for different size containers.

4. Recognize that many conversions such as feet to inches or liters to quarts are often easier to solve using given formulas.

5. Given a round-robin tournament, determine the number of games participants will play.

Standard 2

Understand and apply basic and advanced properties of the concepts of numbers

9-12 Benchmarks

1. Understand the basic characteristics of roots.

2. Understand the basic characteristics of exponents.

3. Express and compare very small and very large numbers using powers of ten notation.

4. Understand the concept of inequalities.

5. Understand how to read, write, and interpret ratios and proportions.

6. Understand that the Arabic system is not the only system for representing numbers (Roman and bases other than ten).

7. Understand the use of the number line in addition and subtraction and in real world applications.

8. Understand the relationship between fractions, decimals, and percents.

9. Understand the relationship between natural numbers, whole numbers, integers, rational, and irrational numbers.

9-12 Performance Indicators

1, 2. Differentiate and compare the characteristics of roots and exponents.

2. Realize the concept of exponents by finding the volume of a cube.

3. Express distances in the solar system or magnifications in science in scientific

MSAD #16 Framework for Academic Standards Fall 1997

notation.

4. Realize that most measurements are not whole numbers and fall between a minimum and a maximum.

5. Alter the amount of ingredients in a recipe serving six people so that it will serve fourteen people.

6. Recognize and use other numbering systems in outlines, time, angle measurement, and computer technology.

7. Visualize a number through problems relating to positive and negative numbers in sequence such as a checking account with deposits and withdrawals or rise and fall in temperature.

8. Convert between fractions, decimals, and percents and be able to choose the best form for a particular situation.

9. Chart or diagram the real number system.

Standard 3

Use basic and advanced procedures while performing the process of computation

9-12 Benchmarks

1. Add, subtract, multiply, and divide rational numbers.

2. Use estimation techniques.

3. Understand that the reasonableness of the result of a computation can be estimated from the inputs and operations.

4. Understand the order of operations.

5. Use mental math accurately when appropriate.

6. Use a scientific calculator to perform basic

operations.

9-12 Performance Indicators

1. Add, subtract, multiply, and divide numbers such as one-third, three-fourths, and one-half.

2. Estimate the grade necessary on the next test to get a certain letter grade given previous test scores.

3. Determine the reasonableness of a result knowing that multiplication will yield a higher answer than addition and subtraction and that division will yield a lower result.

4. Perform work involving grouping symbols, exponents, multiplication, division, addition, and subtraction in the appropriate order .

5. Choose mental math over a calculator, when appropriate, such as adding like fractions, multiplying by powers of ten, or when using basic multiplication tables.

6. Use a calculator correctly for more complicated calculations.

Standard 4

Understand and apply basic and advanced properties of the concept of measurement

9-12 Benchmarks

1. Understand the basic characteristics of the concept of capacity and how it is measured.

2. Understand and use formulas that exist for calculating the perimeter,

circumference, surface areas, and volumes of regular shapes and recognizes those formulas.

3. Convert from one measurement system to another.

4. Perform basic metric conversions involving weight, distance, and volume.

9-12 Performance Indicators

1, 2. Measure the length, width, and height of a box and choose an appropriate formula to determine its surface area and volume understanding the relationship between volume and capacity.

3, 4. Convert a metric volume to United States measurement or a United States distance to a metric distance.

Standard 5

Understand and apply basic and advanced properties of the concepts of geometry

9-12 Benchmarks

1. Identify basic geometric shapes.

2. Understand and calculate perimeters, areas, and volumes.

9-12 Performance Indicators

1. Identify each given illustrations or manipulatives of different geometric figures.

2a. Find the perimeter and area of a given square, rectangle, parallelogram, and triangle.

2b. Calculate the volume of a rectangular

MSAD #16 Framework for Academic Standards Fall 1997

Math

solid.

Standard 6

Understand and apply basic and advanced concepts of data analysis and distributions

9-12 Benchmarks

1. Understand and calculate measures of location for a set of data.

9-12 Performance Indicators

1. Find the mean, median, and mode of the test scores on the last test.

Standard 7

Understand and apply basic and advanced properties of functions and algebra

9-12 Benchmarks

1. Understand the basic concept of equation.

2. Understand the characteristics and uses of rectangular coordinates.

3. Understand the features of mathematical expressions.

4. Understand the relationship that exists between two variables and the way these relationships look on a graph.

9-12 Performance Indicators

1. Convert word sentences into mathematical statements using operational and equal signs.

2, 4. Graph simple equations with two variables and show their relationship on the rectangular plane.

3. Simplify an expression that includes

variables, numbers, and operations.

Standard 8

Understand the general nature and uses of mathematics

9-12 Benchmarks

1. Understand that mathematics is necessary and helpful in many practical ways.

2. Understand that mathematicians often represent real things using abstract symbols.

9-12 Performance Indicators

1. Explain how mathematics is used in real world situations such as consumer problems and measurements.

2. Convert words such as is, of, less than, at most, the sum of, or unequal into mathematical symbols for operations or equality.

subjectmathematics

organizeralgebra 1a (9-12)

Standard 1

Use a variety of strategies in the problem- solving process

9-12 Benchmarks

1. Use diagrams, possibilities, patterns, and working backwards to solve problems.

2. Solve problems using tables and graphs.

9-12 Performance Indicators

1a. Use a diagram to set up ladder or single and double elimination tournament.

1b. Determine the initial weight of ice knowing its present weight and its melting rate.

2. Solve for the missing variable among time, rate, and distance using diagrams and charts.

Standard 2

Understand and apply basic and advanced properties of the concepts of numbers

9-12 Benchmarks

1. Understand the basic characteristics of the real number system and its subsystems.

2. Understand the basic concept of inequalities.

3. Understand how to read, write, and interpret ratios and proportions.

4. Understand the difference between direct and inverse variation.

9-12 Performance Indicators

1. Construct a tree diagram of the number system and, given a number, determine its location on the tree and its relationship

to other numbers.

MSAD #16 Framework for Academic Standards Fall 1997

2. Graph an inequality on the number line.

3. Alter the amount of ingredients in a recipe serving six people so that it will serve fourteen people.

4. Set up a proportion to find a missing

quantity if the given values vary inversely.

Standard 3

Use basic and advanced procedures while performing the process of computation

9-12 Benchmarks

1. Perform basic operations with polynomials.

2. Determine the reasonableness of the result of a computation.

3. Evaluate algebraic expressions.

4. Perform basic operations with rational numbers.

5. Understand the concept of the absolute value of a number.

6. Perform operations on a scientific calculator.

9-12 Performance Indicators

1. Add, subtract, multiply, and divide algebraic expressions.

2. Estimate a solution based on inputs and operations and compare it with the actual solution.

3. Substitute values for variables and find a numerical solution.

4. Add, subtract, multiply, and divide

rational numbers.

5. Describe the relationship between the absolute value of a number and its distance from zero on the number line.

6. Add, subtract, multiply, and divide very large or very small numbers with a calculator.

Standard 4

Understand and apply basic and advanced properties of the concept of measurement

9-12 Benchmarks

1. Understand basic concept of velocity and how it is measured.

9-12 Performance Indicators

1. Solve problems involving distance, time, and velocity.

Standard 5

Understand and apply basic and advanced properties of the concepts of geometry

9-12 Benchmarks

1. Use algebraic techniques to solve for variables in geometric formulas.

2. Understand the basic characteristics of the concept of capacity and how it is measured.

3. Understand that formulas exist for calculating the surface areas and volumes of regular shapes and recognize those formulas.

9-12 Performance Indicators

1. Given the height and one base of a trapezoid, find the other base.

2. Find the volume of a geometric shape after measuring the appropriate dimensions.

3. Utilize formulas to find areas and volumes of geometric shapes.

Standard 6

Understand and apply basic and advanced concepts of data analysis and distributions

9-12 Benchmarks

1. Calculate the mean for a set of data.

9-12 Performance Indicators

1. Find the mean number of points scored by the basketball team last season.

Standard 7

Understand and apply basic and advanced properties of functions and algebra

9-12 Benchmarks

1. Understand algebraic terminology and axioms.

2. Understand the basic concept of polynomial expressions and how to perform operations on them.

3. Understand how to solve first degree equations and inequalities.

MSAD #16 Framework for Academic Standards Fall 1997

Math

9-12 Performance Indicators

1. Identify, in an algebraic statement, the use of the associative, commutative, and distributive properties.

2. Add, subtract, and multiply two polynomials.

3. Solve for the variable using order of operations and properties of equality given a linear equation.

Standard 8

Understand the general nature and uses of mathematics

9-12 Benchmarks

1. Understand that mathematics is the study of patterns and relationships.

2. Understand that in mathematics, simplicity is one of the highest values.

3. Understand that new mathematics continues to be invented today.

9-12 Performance Indicators

1a. Discover the pattern and write an equation that describes the relationship given a set of ordered pairs.

1b. Analyze to find the next two terms in the

sequence given a sequence of numbers.

2. Choose the most economical method of solving a problem when given the choice of several methods.

3. Research and report new mathematical concepts or on the use of mathematics in a particular career.

subjectmathematics

organizeralgebra 1B (9-12)

Standard 1

Use a variety of strategies in the problem- solving process

9-12 Benchmarks

1. Classify problem-solving strategies or problem types by underlying general characteristics.

2. Make up and write simple algorithms for solving problems.

3. Represent real world problems using algebraic functions and graphs of those functions.

4. Solve real world problems involving constant rates.

5. Understand that there is no one right way to solve mathematical problems.

6. Solve problems represented by inequalities.

9-12 Performance Indicators

1. Recognize that many problems have similar characteristics and that once they are recognized lend themselves to the

same strategy for finding the solution.

2. Use equations with variables to solve word problems.

3. Use the distance formula to compute speed, time, or distance on a trip.

4. Estimate the time needed to type a given length paper knowing how many words per minute you can type.

5. Solve the same word problem using several methods.

6. Determine the grade necessary on the next test to attain at least a 90 average.

Standard 2

Understand and apply basic and advanced properties of the concepts of numbers

9-12 Benchmarks

1. Operate with numbers in scientific notation.

2. Understand the basic characteristics of roots.

3. Understand the basic characteristics of exponents.

9-12 Performance Indicators

1. Find the population density of a country using scientific notation, given the area and population of the country.

2, 3. Differentiate and compare the characteristics of roots and exponents.

Standard 3

Use basic and advanced procedures while performing the process of computation

MSAD #16 Framework for Academic Standards Fall 1997

9-12 Benchmarks

1. Find the exact root or power of a number.

2. Perform basic operations on a scientific calculator.

3. Use a scientific calculator for computation of operations with real numbers, powers, roots, and scientific notation.

9-12 Performance Indicators

1. Evaluate the cubed root of 125 or 45 (four to the fifth power).

2. Evaluate appropriately an expression with multiple operations using a scientific calculator.

3. Evaluate appropriately a calculation with multiple operations using a scientific calculator.

Standard 4

Understand and apply basic and advanced properties of the concept of measurement

9-12 Benchmarks

1. Understand basic generalizations about the nature of the Cartesian coordinate system.

2. Understand and apply formulas for finding the midpoint and length of a line

segment.

9-12 Performance Indicators

1a. Graph a point or a linear equation on the coordinate plane.

1b. Solve a system of equations by finding the point of intersection of the two graphs.

2. Given two points, find the length and the midpoint of the segment connecting them.

9-12 Benchmarks

1. Use algebraic techniques to solve for variables in geometric formulas.

9-12 Performance Indicators

1. Given the two bases in a trapezoid, find the height.

Standard 6

Understand and apply basic and advanced properties of functions and algebra

9-12 Benchmarks

1. Understand the basic concept of function, domain, and range.

2. Understand the basic concept of linear and quadratic polynomial equations.

3. Understand that symbolic statements can be combined to look for values that will satisfy all of them at the same time.

4. Understand that in an algebraic equation, values can be substituted for all but one of the symbols giving 0, 1, or more solutions.

5. Understand the solution of pairs of

simultaneous equation.

6. Construct linear mathematical models for real world phenomena.

7. Understand polynomial operations.

8. Understand the relationship between an equation or inequality and its graphical representation.

9. Understand rational expressions.

9-12 Performance Indicators

1. Discern whether a set of ordered pairs constitutes a function or a relation and find the domain and range given a mapping diagram, a table, an equation, or a graph.

2. Determine the number of solutions of an equation based on its degree.

3. Solve a system of two linear equations in two variables to find a common solution.

4. Determine in a system of linear equations, the number of solutions that exist.

5. Solve a system of two linear equations by substitution, elimination, or graphing.

6. Compute weekly salaries using a linear equation and graph a person's possible salary for a variety of hours worked given a time sheet and pay scale.

7. Add, subtract, multiply, and divide two polynomials.

8. Graph a linear equation or inequality from standard form using the x and y- intercepts, from slope-intercept form, or from a table of values.

9. Relate operations with arithmetic fractions to operations with rational expressions.

Standard 5

Understand and apply basic and advanced properties of the concepts of geometry

MSAD #16 Framework for Academic Standards Fall 1997

Math

Standard 7

Understand the general nature and uses of mathematics

9-12 Benchmarks

1. Understand that mathematics is the study of patterns and relationships.

2. Understand that in mathematics, simplicity is one of the highest values.

3. Understand that new mathematics continues to be invented today.

9-12 Performance Indicators

1a. Discover the pattern and write an equation that describes the relationship given a set of ordered pairs.

1b. Analyze to find the next two terms in the sequence given a sequence of numbers.

2. Choose the most economical method of solving a problem when given the choice of several methods.

3. Research and report new mathematical concepts or on the use of mathematics in a particular career.

subjectmathematics

organizeralgebra I (9-12)

Standard 1

Use a variety of strategies in the problem- solving process

9-12 Benchmarks

1. Classify problem-solving strategies or

problem types by underlying general characteristics.

2. Makeup and write simple algorithms for solving problems.

3. Represent real world problems using algebraic functions and graphs of those functions.

4. Solve real world problems involving constant rates.

5. Understand that there is no one right way to solve mathematical problems.

6. Use diagram, listing possibilities, patterns, and working backwards to solve problems.

7. Solve problems represented by inequalities.

9-12 Performance Indicators

1. Recognize that many problems have similar characteristics and that once they are recognized lend themselves to the same strategy for finding the solution.

2. Use equations with variables to solve word problems.

3. Use the distance formula to compute speed, time, or distance on a trip.

4. Estimate the time needed to type a given length paper knowing how many words per minute you can type.

5. Solve the same word problem using several methods.

6a. Use a diagram to set up ladder or single and double elimination tournament.

6b. Determine the initial weight of ice, knowing its present weight, and its rate of melting.

7. Determine the grade necessary on the next test to attain at least a 90 average.

Standard 2

Understand and apply basic and advanced properties of the concepts of numbers

9-12 Benchmarks

1. Understand the basic characteristics of the real number system and its subsystems.

2. Understand the basic characteristics of exponents.

3. Understand the basic characteristics of roots.

4. Operate with numbers in scientific notation.

5. Understand the basic concept of inequalities.

6. Understand how to read, write, and interpret ratios and proportions.

7. Understand the difference between direct and inverse variation.

9-12 Performance Indicators

1. Chart the real number system using a tree diagram or a Venn diagram.

2. Explain the relationship between multiple factors and exponents.

3. Differentiate and compare the characteristics of roots and exponents.

4. Find the population density of a country

MSAD #16 Framework for Academic Standards Fall 1997

using scientific notation, given the area and population of the country.

5. Graph an inequality on the number line.

6. Alter the amount of ingredients in a recipe serving six people so that it will serve fourteen people.

7. Set up a proportion to find a missing quantity if the given values vary inversely.

Standard 3

Use basic and advanced procedures while performing the process of computation

9-12 Benchmarks

1. Perform operations on algebraic expressions.

2. Determine the reasonableness of the result of a computation.

3. Evaluate algebraic expressions.

4. Perform basic operations with rational numbers and expressions.

5. Understand the concept of absolute value.

6. Use a scientific calculator for computation of operations with real numbers, powers, roots, and scientific notation.

7. Use a graphing calculator to graph linear equations.

8. Find the exact root or power of a number.

9-12 Performance Indicators

1. Add, subtract, multiply, and divide algebraic expressions.

2. Estimate the answer to an arithmetic computation, find its actual solution, and compare the results.

3. Substitute values for variables and find a numerical solution.

4. Add, subtract, multiply, and divide rational numbers.

5a. Describe the relationship between the absolute value of a number and its distance from zero on the number line.

5b. Evaluate expressions which include absolute value.

6. Evaluate appropriately a calculation with multiple operations using a scientific calculator.

7. Use a TI-82 or TI-83 to graph equations in the form y=mx+b.

8. Evaluate the cubed root of 125 or 45.

Standard 4

Understand and apply basic and advanced properties of the concept of measurement

9-12 Benchmarks

1. Understand the basic concept of velocity and how it is measured.

2. Understand basic generalizations about the nature of the Cartesian coordinate system.

3. Understand and apply the formulas for finding midpoints and lengths of line segments.

9-12 Performance Indicators

1. Solve problem involving distance, rate, and time using two measurements to find the third.

2. Graph a point or a linear equation on the

coordinate plane.

3a. Solve a system of equations by finding the point of intersection of their graphs.

3b. Given two ordered pairs or points on a graph, find the length and midpoint of the segment.

Standard 5

Understand and apply basic and advanced properties of the concepts of geometry

9-12 Benchmarks

1. Use algebraic techniques to solve for variables in geometric formulas.

2. Understand the basic characteristics of the concept of capacity and how it is measured.

3. Understand that formulas exist for calculating the surface areas and volumes of regular shapes and recognize those formulas.

9-12 Performance Indicators

1. Find the height of a trapezoid given the two bases.

2, 3. Find the surface area and volume of a basic geometric solid utilizing formulas after measuring the appropriate dimensions.

Standard 6

Understand and apply basic and advanced

MSAD #16 Framework for Academic Standards Fall 1997

Math

concepts of data analysis and distributions

9-12 Benchmarks

1. Calculate the mean for a set of data.

9-12 Performance Indicators

1. Find the mean height of the students in the class or the mean number of points scored per game by the basketball team last season.

Standard 7

Understand and apply basic and advanced properties of functions and algebra

9-12 Benchmarks

1. Understand algebraic terms and axioms.

2. Understand the basic concept of polynomials and how to perform operations on them.

3. Understand the basic concept of the solution of linear and quadratic polynomial equations.

4. Understand that in an algebraic equation, values can be substituted for all but one of the symbols giving 0, 1, or more solutions.

5. Understand the basic concept of function, domain, and range.

6. Understand the basic concept of the solution of pairs of simultaneous equations.

7. Understand the relationship between an equation or inequality and its graphical representation.

8. Understand the basic concept of rational

expressions.

9. Construct linear mathematical models for real world phenomena.

9-12 Performance Indicators

1. Identify in an algebraic statement the use of the associative, commutative, and distributive properties.

2. Add, subtract, multiply, and divide two polynomials.

3. Determine the number of solutions of an equation based on its degree.

4. Determine the number of solutions that exist in a system of linear equations.

5. Discern whether a set of ordered pairs constitutes a function or a relation and find the domain and range given a mapping diagram, a table, an equation, or a graph.

6. Solve a system of linear equations in two variables to find a common solution by substitution, elimination, or graphing.

7. Graph a linear equation or inequality from standard form using the x and y- intercepts, from slope-intercept form, or from a table of values.

8. Relate operations with arithmetic fractions to operations with rational expressions.

9. Given a pay scale, compute and graph weekly salaries using a linear equation.

Standard 8

Understand the general nature and uses of mathematics

9-12 Benchmarks

1. Understand that mathematics is the study of patterns and relationships.

2. Understand that in mathematics, simplicity is one of the highest values.

3. Understand that new mathematics continues to be invented today.

9-12 Performance Indicators

1a. Discover the pattern and write an equation that describes the relationship given a set of ordered pairs.

1b. Analyze to find the next two terms in the sequence given a sequence of numbers.

2. Choose the most economical method of solving a problem when given the choice of several methods.

3. Research and report new mathematical concepts or on the use of mathematics in a particular career.

subjectmathematics

organizeralgebra I honors

(9-12)

Standard 1

Use a variety of strategies in the problem- solving process

9-12 Benchmarks

1. Classify problem-solving strategies or problem types by underlying general characteristics.

MSAD #16 Framework for Academic Standards Fall 1997

2. Makeup and write simple algorithms for solving problems.

3. Represent real world problems using algebraic functions and graphs of those functions.

4. Solve real world problems involving constant rates.

5. Understand that there is no one right way to solve mathematical problems.

6. Use diagrams listing possibilities, patterns, and working backwards to solve problems.

7. Solve problems represented by inequalities.

9-12 Performance Indicators

1. Recognize that many problems have similar characteristics and that once they are recognized lend themselves to the same strategy for finding the solution.

2. Use equations with variables to solve word problems.

3. Determine the break-even point for a business given the profit expectation and expenses.

4. Find