Guidelines

NUMBER CONCEPTS

SCOPE AND SEQUENCE	SKILL	OBJECTIVE	VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION	RESOURCES
I – D	INTEGERS	M.8.1 The students will understand the concept of integers. M.8.2 The students will compare and order integers.	INTEGER positive negative whole number	+ 13 - 7 + 16 > - 32 - 23 < + 4	Give the integer that represents the following: 22 degrees below zero a deposit of $5.00 At the end of a card game, Tom’s score was +8; Ellen’s score was –23. Who had the higher score?	Real life: Temperatures, game scores, feet above or below sea level, gains and losses in the stock market, etc.
M	NUMBER SENSE PLACE VALUE	M.8.3 The student will maintain understanding of place value millionths through trillions.	decimal millionths hundred-thousandths ten-thousandths thousandths hundredths tenths units tens hundreds thousands ten-thousands hundred-thousands millions ten-millions hundred-millions billions trillions	Use place value chart	Draw a place value chart for thirty eight and four hundred twelve millionths. In a reference book (e.g. an almanac) search for things that are described in terms of very large and very small numbers.	Study Skills—use of reference materials. Language Arts—Writing large numbers within a paragraph/sentence. Social Studies, Science—larger and smaller numbers used in data. Physical Education—number used to record speed and distances. Technology—limitations of calculator display.
M	READING AND WRITING NUMBERS (NUMERALS)	M.8.4 The students will continue to develop skills in reading and writing numbers.	number numeral	Reading: Stress: decimal point is read as “and”. Stress: Correct reading of repeating decimals (e.g.) 0.63 is read as “63 hundredths, bar 3” Writing: Stress: correct formation of numerals and mathematical symbols; correct size of fractions and exponents.	Write in words: 4,003,016,024 (four billion, three million, sixteen thousand, twenty-four.) Write the inequality for the statement: Eight million is greater than eight millionths. (8,000,000 > 0.000008)	Language Arts—Handwriting; Reading; Vocabulary enrichment (number-related root words) Spelling Correct writing of numbers in sentences, outlines, tables, etc. Social Studies—reading and writing numerical data. Technology—interpreting spreadsheet data

NUMBER CONCEPTS

SCOPE AND SEQUENCE		SKILL	OBJECTIVE	VOCABULARY	EXAMPLE		PROBLEM SOLVING EXAMPLE		CONNECTIONS, INTEGRATION		RESOURCES
M I - D M M M	NUMBER PATTERNS Divisibility Perfect, Abundant, Deficient numbers Prime and Composite Numbers		M.8.5 The students will determine if a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. M.8.6 The students will determine if numbers are perfect, abundant or deficient. M.8.7 The students will determine if numbers are prime of composite. M.8.8 Using the Sieve of Erastothenes, the students will determine the prime numbers between 1 and 100. M.8.9 The students will find the prime factorization of composite numbers.	divisibility divisible factor perfect numbers abundant numbers deficient numbers prime number composite number Sieve of Erastothenes factor tree prime factorization Fundamental Theorem of Arithmetic relatively prime twin primes		48 is divisible by 2, 3, 4, 6, 8, 12, 16, 24 and 48 Perfect --a number is perfect if the sum of the factors less than the number is equal to the number ( The factors of 28 are 1, 2, 4, 7, and 14. The sum of these factors is 28). Abundant – a number is abundant if the sum of the factors less than the number is greater than the number.(12 is an abundant number). Deficient – sum of factors is less than the number (10 is a deficient number). Prime – a number having only 2 factors, itself and 1. Composite – a number with more than two factors. Sieve of Erasiothenes – Using a hundreds’ chart, cross out all multiples of 2, 3, 5, 7..Remaining numbers are prime numbers. factor tree – 240 / \ 60x 4 /\ /\ 15x 4x 2 x 2 /\ /\ | | 5x3x2x2x2x2 The prime factorization of 240 is 2⁴ ·3·5		How many different ways can 4 dozen donuts be arranged on a tray? 2 rows of 24 3 rows of 16 4 rows of 12 6 rows of 8… Make a chart identifying the numbers from 25 – 40 as being deficient, abundant or perfect. Explain why 33 is considered a deficient number How many consecutive primes are there between 1 and 58 (Since 2 is the only even prime, there is only one set of consecutive primes).		Science: patterns in nature Social Studies: election years Real Life: Patterns in architecture, industry, sports Math: Geometry- Using blocks or cubes, have the students discover that prime numbers can only make one rectangular arrangement. With composite numbers, multiple arrangements are possible. (e.g. with 24 cubes the arrangement could be 2 x 12, 3 x 8, 6 x 4, etc.)

NUMBER CONCEPTS

SCOPE AND SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS, INTEGRATION

RESOURCES

M D - M

NUMBER PATTERNS (CONT’D) Relative primes Twin primes Prime factorization of negative numbers

M.8.10 The students will determine if numbers are relatively prime and will identify twin primes M.8.11 By re-expressing negative integers as the product of –1 and a whole number, the students will find the prime factorization of negative numbers…

Relatively prime numbers Twin primes

Relatively prime numbers are two numbers that have no common factor except 1. (13 and 14 are relatively prime numbers). Twin primes are prime numbers which are next to each other in the order of primes. (3, 5) and (5, 7) are twin primes. Find the prime factorization of -144 Re-express -144 as -1 · 144 | \ -1 · 12 · 12 | \ | \ -1 · 3 · 4 · 3 · 4 | | \ | | \ -1· 3· 2· 2 · 3 ·2·2 -1·2⁴·3²

Tell which sets of numbers are relatively prime: 24 and 32 23 and 32 14 and 20 67 and 45 (23 and 32) and (67 and 45) are relatively prime The prime factorization of –128 is -1·2⁷

Technology – programs which generate prime numbers Real life – Stock market, games which score with integers Research: Christian Goldbach’s conjectures about prime numbers

I

Figurate Numbers

M.8.12 The students will associate patterns of numbers with geometric figures.

figurate numbers triangular numbers square numbers pentagonal numbers hexagonal numbers

· · · · · · 3 · · · 6 · · · · · · · · · · · · · · · · · · · · 10 · · · · · 15

Find the fourth pentagonal number. 1, 5, 12, 22, 35, 51

Science: Patterns in nature

(A good illustration of this is seen in the film Donald in Mathmagicland produced by the Walt Disney Corp.

NUMBER CONCEPTS

SCOPE AND SEQUENCE			SKILL	OBJECTIVE		VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION		RESOURCES
	I – D – M I - D	Sequences Fibbonacci Sequence			M.8.13 The students will recognize and extend arithmetic and geometric sequences and will solve problems using these. M.8.14 The students will identify the pattern of the Fibbonacci sequence and will identify the relationship between successive terms.	sequence terms arithmetic sequence geometric sequence common difference common ratio Fibbonacci sequence	arithmetic sequence- next term found by adding . (e.g. 3, 7, 11, 15, 19,..next terms found by adding 4 to last term.) Geometric Sequence – next term found through multiplication . (e.g. 4, 8, 16, 32, 64, 128…next term found by multiplying previous term by two.) Sequences found through using a combination of operations are neither arithmetic or geometric. (e.g. 4, 8, 9, 18, 19, 38, 39…the pattern is x2 + 1) 1, 1, 2, 3, 5, 8…(add last two terms to get next term) F9 – 34 (the ninth Fibbonacci number is 34)	Bill’s father gave him a choice of payment plans for doing odd jobs at the family store during the month of July. Plan A: Starting with $4.81 on the first day of the month, he could double the amount each day. Plan B: $10. a day for each day he worked. If Bill worked 20 days out of the month which plan would Bill find most beneficial? (Under plan A, Bill would earn $10,485.75. Under plan B, he would earn only $200.00) Extend – How many days does Bill have to work in order for plan B to be more beneficial? (14) How much would Bill earn under each plan if he worked for 12 days? 15 Days? 25 days? Joan noticed that the new leaves on the branch of a tree appeared in the same order as the fibbonacci numbers. How many leaves will there be when the 11^th set of new leaves appears? (89)		Math: Problem solving—Make a Table Strategy Science: Patterns Language Arts: Prepare an oral presentation explaining the different types of sequences. Prepare a job interview simulating the problem situation. Technology: Use the calculator/computer in working on sequences. Research: Leonardo Fibbonacci Science, Music: Applications of the Fibbonacci sequence. Art, Architecture: Applications of the Golden Rectangle
	M I	GREATEST COMMON FACTOR Euclidean Algorithm			M.8.15 The students will find the greatest common factor of two or more numbers.	GCF	Methods A) list factors and identify common factors. Choose greatest. B) Write prime factorization of each number. Identify common prime factors and find their product. Use the Euclidean algorithm to determine the GCF of larger numbers.	The eighth grade has 30 students; the seventh, 36. What is the greatest number of students that can be put on a relay team if all participate?		Real-life problem solving: a detective searches for common factors in order to solve a crime. Research: Euclid
SCOPE AND SEQUENCE			SKILL	OBJECTIVE		VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION		RESOURCES

NUMBER CONCEPTS

I – D -M	READING AND WRITING MATHEMATICAL SYMBOLS	M.8.16 The students will read and write mathematical symbols	Symbol +, -, x, ÷ =, <, >, ≤, ≥, ≠, ≈, ~, ∅, ∩, ∪,⊂, ∈, ∉, ∠, ↔, —, → …, ∴, %, √36, @, ½-3½, p, ·, ( ), [], { }	Provide practice using symbols in context.	Mary’s favorite foods included pizza, hamburgers, fries, and ice cream. ( M Ɛ { pizza, hamburgers, fries, ice cream} )
M	COMPARING AND ORDERING NUMBERS Whole numbers Rational Numbers	M.8.17 Given real-life situations, the students will compare numbers	greater than less than equal equivalent	1. Compare on number line: number to the right is always the greater number. 2. Use place-value chart to compare numbers. 3. Using graph paper, create models of decimals to compare.	Items to compare: -sports’ statistics -gas mileage -barometric pressure -nutritional value of food -interest rates	Science: data for astronomy and meteorology. Social Studies: distances on maps Study Skills: Reading charts, tables, etc. Math: Use bar graphs and line graphs to visualize statistical data.
M	ORDERING NUMBERS FROM GREATEST TO LEAST AND VICE VERSA	M.8.18 Given a set of data, the students will order the data from least to greatest or from greatest to least.	Least / greatest	Order the following: from least to greatest: 5, 0.5, 0.55, 0.505, 50. (0.5, 0.505, 0.55, 5, 50) Order the following from greatest to least: 166, 16.6, 1.66, 1.6666. (166, 16.6, 1.6666, 1.66)	Compare the batting averages of the members of a major league baseball team. Obtain the barometric pressure from the daily weather report for five days. Order the readings from greatest to least. Compare the nutritional data of several brands of cereal.	Language Arts: Write a step-by-step plan for comparing decimals. Technology: Utilize software programs which compare decimals. Mathematics, Social Studies, Science: Compare data using bar and line graphs. (e.g. Stock market: Choose a stock. Chart its progress for a week.)

NUMBER CONCEPTS

SCOPE AND SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS, INTEGRATION

RESOURCES

NUMBER LINE

The students will use the number line as an aid in developing number sense. (The number line is referred to under various topics in these guidelines.

M

ROUNDING WHOLE NUMBERS AND DECIMALS

M.8.19 The students will round whole numbers and decimals to any place-value position.

Rounding

Round 53,769,211 to the nearest thousand. (The digit nine is in thousands place. The number immediately to the right is 2 which is less than 5, so 53,769,211 rounded to the nearest thousand is 53,769,000. Round 4.0695 to the nearest hundredth: (The digit 6 is in hundredths place. The digit to the right is a nine. 4.0695 rounded to the nearest hundredth is 4.07)

Locate the depths of the world oceans in an atlas or almanac. Round these numbers to the nearest thousand. Order these from greatest to least. Make a graph showing their relationships.

Mathematics: measurement, estimating. Real life Skills: rounding money to the nearest dollar.

D - M D - M

POWERS AND EXPONENTS POWERS OF TEN

M.8.20 The students will use powers and exponents in expressions. M.8.21 The students will identify the powers of ten.

factors exponent base powers cubed squared power of 10

Exponent ⇩ 100,000 = 10⁵ ⇧ base Write 2³ as a product. (2³=2·2·2) 3 factors Write 5·5·5·5 Using exponents ( 5⁴) Stress: Any number written to the zero power is equal to 1: 10²=.01 10¹=.1 10º=1 10¹=10 Use a number line to show the relationships between powers (patterns of multiplying and dividing by 10).

Which of the following statements is correct: A. 3²=2³ B. 4²=2⁴ ( B is correct.) A. 9 ≠ 8 B. 16=16 Express a billion as a power of ten. ( 10⁹ )

Science, Social Studies: Use of larger numbers

NUMBER CONCEPTS

SCOPE AND SEQUENCE	SKILL	OBJECTIVE	VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION		RESOURCES
I – D -M	SCIENTIFIC NOTATION	M.8.22 The students will express numbers as a product of a number ≥ 1 but less than 10 and a power of 10. M.8.23 Very large and very small numbers will be expressed in scientific notation. M.8.24 Numbers expressed in scientific notation will be translated to standard form.	scientific notation standard notation exponential notation	2369 = 2.369 X 10³ 1.25 X 10⁵ = 125,000 1.25 X 10ֿ² = 0.0125	Express the distances of the planets from the sun in scientific notation.		Science: astronomy Social Studies: Use of larger numbers in statistical data.
	ESTIMATING	This material is to be reviewed and maintained from material presented at earlier levels.
	RATIOS	This material is to be reviewed and maintained from material presented at earlier levels.
	PROPORTION	This material is to be reviewed and maintained from material presented at earlier levels.
	PERCENTAGE	This material is to be reviewed and maintained from material presented at earlier levels.

NUMBER CONCEPTS

SCOPE AND SEQUENCE	SKILL	OBJECTIVE	VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION	RESOURCES
I – D - M	NATURAL NUMBERS INTEGERS RATIONAL NUMBERS IRRATIONAL NUMBERS REAL NUMBERS	M.8.25 The students will identify and classify numbers in the real number system: Use a Venn Diagram to illustrate Real Numbers.				Classify the following numbers: +6, -2.3, /5, p, 0.16 Note the use of ≈ with irrational numbers. E.g. whenever p is used, the approximation sign is used rather than the = sign. Find the whole numbers whose square root is between 5 and 6. (26, 27, …….35) Logical Reasoning skills: Have the students explain the following statements: Every rational number is a real number. Every natural number is a whole number. Not all real numbers are integers. Some real numbers are rational numbers. All irrational numbers are real numbers.	It is very important that students have a clear understanding of this concept. Thorough development, extensive practice, and continued maintenance are necessary.

OTHER SETS OF NUMBERS

Note: The students should have continued practiced graphing Natural Numbers, Whole Numbers, Integers, Rationals and Reals on the real

number line as follows:

Natural numbers, whole numbers and integers are graphed with a dot at the number mark itself:

N > 3

ß------|------|------|-----|------|-----o---|------|-----------------à

-2 -1 0 1 2 3 4 5

H < 4

ß---|-------|------|------|-----|-- ----|--- --|------|------o-------|-------à

-4 -3 -2 -1 0 1 2 3 4 5

H < 2

ß------|------|-----|------|------o------|-- ----|------|-------à

-2 -1 0 1 2 3 4 5

Any number that is greater than or equal to or less than or equal to is graphed with a closed circle at the beginning of the arrow.

OPERATIONS

SKILL	OBJECTIVE	VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS, INTEGRATION	RESOURCES
USE CONCRETE OBJECTS TO MODEL OPERATIONS	Manipulative materials –connecting cubes, blocks centimeter cubes, beans, etc. should be used frequently when modeling concepts. Understanding is built when skills are presented following the concept continuum.
OPERATIONS INTRODUCED AND DEVELOPED IN PROBLEM SOLVING CONTEXT	When operations are presented, it is important to give purpose to the learning by presenting the material in a problem-solving / real life context. Equations should never be presented in isolation until mastery has occurred.
USE SYMBOLS FOR OPERATIONS	Refer to “symbols” in Readiness and Number Concepts section of these guidelines.
ADD SINGLE-DIGIT AND MULTI-DIGIT NUMBERS	Review and maintain material presented at earlier levels. Extend through millions. Students should make frequent use of the calculator to check material which they have already mastered.
PROPERTIES OF OPERATIONS	Review the following properties of operations: Properties + X Commutative a + b = b + a ab = ba Associative (a + b) + c = a + (b + c) (ab)c = a(bc) Identity a + 0 = a 1· a = a Distributive ab + ac = a (b + c) Apply these properties to each set of numbers: Natural, Whole, Integers, Rational and Real.
ESTIMATION SUMS DIFFERENCES PRODUCTS QUOTIENTS	Estimation in all operations and with all sets of numbers should be reviewed and maintained. Estimation is a key skill and should be interwoven into every lesson involving operations.

OPERATIONS

SCOPE AND SEQUENCE		SKILL		OBJECTIVE		VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE		CONNECTIONS, INTEGRATION	RESOURCES
I - D	OPERATIONS WITH POWERS AND EXPONENTS		M.8.26 The students will learn that when multiplying the same base number, the operation can be simplified by adding the exponents; when dividing by the same base number, the operation can be simplified by subtracting the exponents.		power exponent base		6²·6⁵=6⁷ 4⁹ = 4³ 4⁶		Technology Computer programs dealing with numbers and bases.
M	INTERPRET REMAINDERS		M.8.27 The students will interpret the remainder in a division problem and will decide whether the remainder should be written as a fraction or a decimal or whether the answer should be rounded up or rounded down.		remainder				Forty-seven computers are available for use in 15 classrooms. About how many computers will each classroom have? (Using a decimal or fraction does not make sense.) $63.00 was divided among five students. How much will each receive? Rounding the decimal to hundredths place makes the most sense.	Language Arts Have the students create their own original word problems requiring reasonable answers. Have them conduct a newspaper scavenger hunt for situations which require exact numbers.
D - M	SQUARE ROOT		M.8.28 After comprehending the concept of square root, the students will find the square root of a number in one of two ways: 1) Estimation 2) Calculator Recognize perfect squares		square root radical sign		Estimation: To find the square root of 2369: Calculator: Identify the radical symbol on the calculator. Teach the correct sequencing of keys for determining the square root. Note: It is important that the students make use of the calculator for problem-solving.		The Scouts packed 4096 cans of food in cartons. The number of cans in each carton equaled the number of cartons they packed. How many was this? Pythagorean Theorem: a² + b² = c²	Math: Pythagorean theorem, estimation, problem solving.

OPERATIONS

VOCABULARY OF OPERATIONS

Students should read, write, and speak using the correct mathematical vocabulary. Provide ample opportunity during each lesson for the students to become aware of the vocabulary and to use it. Avoid expressions such as “timesing numbers” instead of multiplying, etc.

APPLICATION OF OPERATIONS TO OTHER SETS OF NUMBERS

SCOPE AND SEQUENCE

TOPIC

OBJECTIVE

VOCABULARY

EXPLANATION/EXAMPLE

CONNECTIONS

RESOURCES

D - M

RATIONAL NUMBERS FRACTIONS DECIMALS INTEGERS

M.8.29 The students will apply previously learned skills to rational numbers and will extend these skills to larger and smaller numbers:

Operations Properties

Addition, Subtraction, multiplication and division applied to rational numbers. Apply properties to all sets of numbers.

Problem-solving with all operations and in all sets of numbers (except irrational).

Multiple applications in all content areas and in many aspects of real life.

PROBLEM SOLVING

SCOPE AND SEQUENCE	TOPIC	OBJECTIVE	VOCABULARY	EXPLANATION/EXAMPLE	CONNECTIONS	RESOURCES
M	USE A PLAN FOR PROBLEM SOLVING	M.8.30 The students will use a 4/5 – step plan for problem-solving	Understand Plan Do Check Answer Statement strategy	Understand: What is known? What must be found out? are there any hidden Questions? Do I need an estimate or an exact answer? Plan: Choose a strategy. (A procedure to follow in solving the problem.) Alert!!! Addition, Subtraction, Multiplication and Division are operations not strategies. An operation is not a plan in itself, but a means to carry out a plan. Do: Carry out the plan. Check: Is the answer reasonable? Does it answer the given question? If an operation was used to carry out a plan, use its complement to check the computation. Check using an alternate strategy. Answer Statement: Re-phrase the question in terms of an answer statement.	Language Arts Reading Comprehension Reading for main ideas and details Declarative and Interrogative sentences Study Skills Mapping, outlining Following directions Logical reasoning Decision making Critical thinking skills Science: Scientific Method Research: George Polya, Mathematician	A Problem Solving Chart listing the steps in the problem-solving method would benefit students.

PROBLEM SOLVING

SCOPE AND SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS, INTEGRATION

RESOURCES

M

USE VOCABULARY AS A CLUE

M.8.31 While using vocabulary as an aid in problem-solving, the students will be careful to understand the complete meaning of the problem and its question prior to finding a solution.

23,458 people were in attendance at the Phillies game. 2,347 started home when the rain began and another 4,541 went when a rain delay lasted over an hour. How many people left before the game was over?

Language Arts vocabulary development

M

USE PICTURES AND MAPS AS A CLUE

M.8.32 The students will continue to use pictures and maps as clues to problem-solving and will apply these skills at a higher level.

Use pictures and maps from Social Studies and Science texts to develop original problems.

Social Studies map reading skills

D – M

USE GRAPHS, CHARTS AND TABLES AS AIDS IN PROBLEM SOLVING

M.8.33 The students will use graphs, charts, and tables as aids in problem-solving.

circle graph bar graph line graph histogram time table scatter plot box-and-whisker plot

On a farm there are chickens and cows. There are 50 heads and 100 legs. How many of each animal are there? (10 chickens and 40 cows)

Math Statistics, Graphing

D – M

RECOGNIZE PROBLEMS WITH NOT ENOUGH INFORMATION OR TOO MUCH INFORMATION

M.8.34 The students will recognize too much / too little information in a problem.

Too little information: Mike bought three tapes on sale. How much did he spend? Too much information: Sally paid for the tapes she bought with a $20 bill. If she paid $7.98 for each of the two tapes she bought, how much did she spend?

Reading reading for details.

USE CONCRETE OBJECTS TO MODEL A PROBLEM

Whenever possible, concrete objects should be used to model problem-solving.

SCOPE AND SEQUENCE M M

SKILL USE PROBLEM-SOLVING STRATEGIES ACT OUT THE PROBLEM GUESS AND CHECK

OBJECTIVE M.8.35 By acting out a problem-solving situation, the students will reach a solution. M.8.36 The students will use the guess and check strategy to solve a problem.

VOCABULARY strategy guess and check

EXAMPLE PROBLEM SOLVING EXAMPLE Five children trade baseball cards once with each other. What is the total number of cards traded? (10) The sum of three consecutive odd numbers is 63. What are the numbers? ( 19, 21, 23 )

CONNECTIONS, INTEGRATION Real Life Find careers in which employees act out problem situations

RESOURCES

D - M

SELECT AN OPERATION

M.8.37 The students will solve problems using an equation; they will select an operation and will formulate an equation.

operation equation

25% of the chances for the Christmas Bazaar were sold. If 750 were sold, how many chances were available? 0.25n = 750 n = 3000

Math - percentage, pre-algebra

M

CHOOSE A CALCULATION METHOD

M.8.38 The students will decide whether to use mental math, pencil and paper or a calculator to solve an equation

Mr. Stolzer marked five notebooks each day. In a 20 day school month, how many notebooks did he mark? (Mental Math) Carol made 4 wreaths on Monday, 6 on Tuesday, 2 on Wednesday, none on Thursday, and 8 on Friday. How many wreaths did she have at the end of the week? (Mental math or pencil and paper). A plane traveling at a rate of 375 mph lands 17 hours and 30 minutes after takeoff. How far did it travel? ( 6562.5 miles) Calculator

Technology -- use of calculator

PROBLEM SOLVING

SCOPE AND SEQUENCE	SKILL		OBJECTIVE	VOCABULARY	EXAMPLE	PROBLEM SOLVING EXAMPLE	CONNECTIONS INTEGRATION	RESOURCES
D - M	USE MATH SENSE TO SOLVE A PROBLEM	M.8.39 After reading a problem, the students will decide what type of problem it is and will select an appropriate strategy		pattern working backward simplify	Mike caught 2 fish on Monday, 4 on Tuesday, 8 on Wednesday, etc. Following this pattern, how many did he catch on Saturday? (64) I am thinking of a number. If I increase it by 10 and then subtract 12, I get 12. What is the number? (14) How many cuts are needed to separate a board into 14 smaller parts? (13). Think: cut into 4 parts ▇ ▇ ▇ ▇ Always one less.		Math : Prime and composite numbers. Study Skills Classifying information
D - M	SOLVE PROBLEMS WITH MORE THAN ONE STEP	M.8.40 The students will solve multi-step problems			Mrs. Shopright made the following purchases at the local K-Mart during their recent 99 cents sale: 2 bottles of dish detergent, 4 jumbo-sized rolls of paper towels, 3 bags of potato chips and 2 cans of iced tea mix. How much did she spend? What was the amount of tax she paid? For what items did she pay tax?		Real-life skills: taxable items, rate of sales tax
D - M	USE LOGICAL REASONING	M.8.41 The students will use logical reasoning to solve a problem.		Logical reasoning	Solve the following: each letter stands for one digit and each digit has only one letter value. TA + T = AYY 91 + 9 = 100		Puzzles, games, logical reasoning puzzles
D - M	SOLVE PROCESS PROBLEMS	M.8.42 The students will understand that some problems can best be solved without writing an equation; they will use a variety of problem-solving strategies to solve problems.			Refer to problem solving strategies, logical reasoning, Use math sense for examples of non-routine problems.
D - M	CHECK REASONABLENESS OF ANSWER	M.8.43 The students will check for the reasonableness of an answer to a problem.		Refer to steps in Problem Solving – Check Answer
D	FORMULATE ORIGINAL WORD PROBLEMS	M.8.44 The students will formulate original word problems based on content of lesson.		Frequently ask students to write original word problems related to skills presented. This helps students to develop communications skills as well as to deepen understanding of the skill presented. It helps the teacher to determine students’ level of comprehension of the skill presented.

MENTAL MATHEMATICS

SCOPE AND SEQUENCE

TOPIC

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM-SOLVING EXAMPLE