# Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10.

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 0 Different signs: Subtract & take sign of larger value = = - 5 Keep Change-Opposite = = = = = - 2 Same signs: Positive product ( + 7) ( + 8) = + 56 ( - 2) ( - 6) = + 2 Different signs: Negative product ( + ) ( - 9) = - 27 ( - 5) ( + 4) = - 20 Same signs: Positive quotient + 42 / + 6 = / - 8 = + Different signs: Negative quotient + 56 / - 7 = / + 2 = - 25 Recall the order of operations: Parentheses (or grouping symbols) 2 - Exponents - Multiplication / Division (left to right) 4 - Addition/Subtraction (left to right) Find each answer ( - 7) = =. 2 + ( - 25) = ( - 8) = 5. - ( - 5) = = 7. ( - 9)( - 8) = 8. (2)( - 2) = / - 7 = / + 8 =. ( - 2)( + 6)(- 5) = ( 2) = ( 8) 4 = 4. -( 8) + 2 = Answers:

2 Topic: Rationals page 4 Multiplying Fractions and Mixed Numbers ) Change any mixed numbers to improper fractions 2) Cross cancel any numerator with any denominator by dividing each by a common factor ) Multiply numerator by numerator and denominator by denominator 4) Simplify your answer (make it a mixed number if you can) Dividing Fractions and Mixed Numbers ) Change any mixed numbers to improper fractions 2) Remember Keep-Change-Flip: keep the first fraction, change the division sign to a multiplication sign, and flip the second fraction ) Multiply numerator by numerator and denominator by denominator 4) Simplify your answer (make it a mixed number if you can) Adding and Subtracting Fractions and Mixed Numbers ) Check to see if the denominators are the same; if not, find a common denominator 2) Now add or subtract the fractions remember, keep the denominator! ) Add or subtract the whole numbers 4) Simplify the fraction 5) Rewrite the sum or difference 5 2) 84 2 ) ) Answers:. 2. 4) ) 2 5 6) ) 7) )

3 Topic: Combining Like Terms and Applying the Distributive Property In algebraic expressions, like terms are terms that contain the same variables raised to the same power. Only the coefficients of like terms may be different. In order to combine like terms, we add or subtract the numerical coefficients of the like terms using the Distributive Property: ax + bx = (a + b)x. Examples:. 2x + 9x = (2 + 9) x = x 2. 2y - 7y = (2 7) y = 5y. 5x + 8-2x + 7 = x + 5 Here, the like terms are: 5x and -2x = x and: = 5 The Distributive Property of multiplication over addition/subtraction is frequently used in Algebra: Examples:. 7 (2x + 9) = 7 2x = 4x (6 5x) = 4 (6) - 4(5x) = 24-20x Simplify each expression by combining like terms.. 8y + 2y y + 4y + 9 =. x + 7 2x = 4. 8n 7y 2n + 5 y = Answers: Apply the distributive property and write your answer in simplest form. 5. 7(x 4) = 6. 5(4n ) = 7. -6(y + 5) = 8. -4(8 9x) = (n + 7) 0n = (5 + 7y) + 6(2y 9) = 0.

4 Topic: Algebra Solving equations by using the Addition, Subtraction or Multiplication Property of Equality. Check the solution. Ex : x Ex 2: 7x 6 - x = x 6 x x 4x 6 4 x Check: x 4x x = 2 ( ) = 9 9 = 9 Check: 7x x = - 4 Translate and evaluate the following equations. Ex : The product of 4 and a number is n 28 4n n 7 Addition: sum, more than Multiplication: product 7(2) - 6 -(2) = = = -4-4 = -4 Ex 4. The quotient of a number and is 5. n 5 n 45 Subtraction: difference, less than Division: quotient Solve the following equations. Show your work and check your solution.. 2x x. 5x + 8 = - 2 Check: Check: Check: 4

5 Apply the distributive property first. 4. 4x x (x 7) = 8 4 Check: Check: Check: Apply the distributive property first. 7. 8x 5 6x = 7 8. = 4x 0x x ( + 8x) = - Check: Check: Check: Translate each sentence to an algebraic equation. Then use mental math to find the solution. Equation Solution 0. One-half of a number is more than 7 times a number is less than three times a number is increased by twice a number is 24. 5

6 Topic: Angle Relationships and Algebra Notation: m means the" measure of angle" means congruent or equal in measure Vertical Angles Complementary Angles Supplementary Angles Angles that are opposite each other across two intersecting lines. m m and m 2 m 4 Two angles whose sum is 90 o. m m Two angles whose sum is 80 o. m m State how the angle labeled x is related to the angle with the given measurement. Find the value of x in each figure. ) 49º x º ) x = 2) 2) x º x = 62º ) 6 xº 2º ) x =

7 4) Find the missing angles. Note: the angles are not drawn to scale. Given: 4 = 50 Find each angle and write your reasoning. = = = 5) 5) (x - 4) 2 (x + 0) Relationship x = m = m 2 = m = 7

8 Topic: Geometry You should know the following formulas and be able to use them to find the area or perimeter of a geometric figure. Perimeter of a polygon = the sum of the sides Rectangle: P = 2l + 2w A = lw Square: P = 4s A = s 2 Parallelogram: P = s + s2 + s + s4 A = bh Triangle: P = s + s2 + s A = ½ bh Trapezoid: P = s + s2 + s + s4 A = ½ (b + b2)h Circle: Circumference = πd A = πr 2 Find the perimeter/circumference and area of each figure. Express #6 in terms of pi (π). Show your work. (Use and attach a separate work page if space is needed.) cm 4.5 cm 7 cm cm 8 cm 20 cm 5 in 4 in 9 in 7 ½ in 5. 5 cm 6. 5 ft 5 cm 4 cm 5 cm cm 8

9 9) Name each figure. Find the volume or surface area of each. (Use the reference sheet at the back!) a) Name: b) Name: Volume: Surface Area: (in terms of pi) 2 in. 4 in. 0 in. 0 in. 5 in. c) Name: d) Name: Volume: Volume: (in terms of pi) in. in. 9 in. 0) A storage tank shaped like a rectangular prism is being manufactured to hold 00,000 cubic feet of natural gas. It has a length of 0 feet and a width of 25 feet. Use algebra to find out what height the tank should be. 9

10 Topic: Ratio & Proprtion ) Buck drove 220 miles in 5 hours. What was his average rate of speed? 2) Horace read 60 pages in 4 hours. How many pages can he read in 6 hours? ) Pasha bought pounds of onions for \$2.67. Which ratio is proportional to pounds at \$2.67? A. B. C. D. 0

11 8 th Grade Summer Math Packet Unit: Knowledge of Algebra, Patterns, and Functions Objective: Write an algebraic expression to represent unknown quantities with one unknown and or 2 operations. Examples: The tables below show phrases written as mathematical expressions. Phrases Expression Phrases Expression 9 more than a number the sum of 9 and a number a number plus 9 X subtracted from a number a number minus 4 4 less than a number h - 4 a number increased by 9 a number decreased by 4 the total of x and 9 the difference of h and 4 Phrases Expression Phrases Expression 6 multiplied by g 6 times a number the product of g and 6 6g a number divided by 5 t the quotient of t and 5 divide a number by 5 5 Write each phrase as an algebraic expression..) 7 less than m 2.) The quotient of and y.) 7 years younger than Jessica 4.) times as many marbles as Bob has 5.) Let t = the number of tomatoes Tye planted last year. This year she planted times as many. Write an algebraic expression to show how many tomatoes Tye planted this year. 6.) Last week Jason sold x number of hot dogs at the football game. This week he sold twice as many as last week, and then he sold 0 more. Write an expression to show how many hot dogs Jason sold this week.

12 8 th Grade Summer Math Packet Unit: Knowledge of Algebra, Patterns, and Functions Objective: Evaluate an algebraic expression using one unknown and no more than 2 operations. Example : Evaluate 6x 7 if x = 8. Example 2: Evaluate 5m 5 if m = 6. 6x 7 = 6(8) 7 Replace x with 8. 5m 5 = 5(6) 5 Replace m with 6.. = 48 7 Use order of operations. = 0 5 Use order of operations. = 4 Subtract 7 from 48. = 5 Subtract 5 from 0. Example : Evaluate 7b ( 7 ) ( 6 ) = 42 = 7b if b = 6. Example 4: Evaluate x + 4 if x =. Replace b with 6. x + 4 = + 4 Replace x with. Multiply 6 by 7. = Use order of operations. = 4 Divide. = Add 27 and 4. Evaluate the following expressions using the given values for a, b, and c. Show each step!.) Evaluate 6 + b if b = 7 2.) Evaluate 6a 2 if a = 4.) Evaluate 5(6) c if c = 7 4.) Evaluate b 4 if b = ) Evaluate 7. 5 m 6.) Evaluate (n ) 2 if n = 9 if m =

13 8 th Grade Summer Math Packet Unit: Knowledge of Algebra, Patterns, and Functions Objective: Evaluate numeric expressions using order of operations with no more than 4 operations. Use the order of operations to evaluate numerical expressions.. Do all operations within grouping symbols first. 2. Evaluate all powers before other operations.. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. Example : Evaluate 4 + (7 2) 2! 5 Example 2: 8 + ( + 5) (7 2) 2! ( + 5) 2 4 = 4 + (5) 2! 5 Subtract first since 7 2 is in parentheses = 8 + (6) 2 4 Add first since + 5 is in parentheses = ! 5 Multiply left to right,! 5 = 5 = Find the value of 6 2 = Multiply left to right, 2! 5 = 0 = Divide 6 by 4 = 29 0 Add left to right, = 29 = 7 Add 8 and 9 = 9 Subtract 0 from 29 Evaluate each of the following. Show each step!.) (2 + 0) ) (6 + 5)! (8 6).) 72 5(2.8) )! 4(0 8) 60 5.) The perimeter of a hexagon is found by adding the lengths of all six sides of the hexagon. For the hexagon below write a numerical expression to find the perimeter. Then evaluate the expression. 6.) Without parentheses, the expression equals 27. Place parentheses in the expression so that it equals ; then 2. 5

14 8 th Grade Summer Math Packet Unit: Knowledge of Algebra, Patterns, and Functions Objective: Determine the unknown in a linear equation with or 2 operations Remember, equations must always remain balanced. If you add or subtract the same number from each side of an equation, the two sides remain equal. If you multiply or divide the same number from each side of an equation, the two sides remain equal. Example : Solve x + 5 = x + 5 = Write the equation x + 5 = Write the equation - 5 = - 5 Subtract 5 from both sides Check = Replace x with 6 x = 6 Simplify =! The sentence is true Example 2: Solve - 2 = - y - 2 = - y Write the equation - 2 = - y Write the equation - = - Divide each side by Check - 2 = - (7) Replace the y with 7 7 = y Simplify -2 = - 2? Multiply is the sentence true? Example : Solve x + 2 = 2 x + 2 = 2 Write the equation x + 2 = 2 Write the equation - 2 = - 2 Subtract 2 from each side (7) + 2 = 2? Replace x with 7 x = 2 Simplify Check = 2? Multiply Divide each side by 2 = 2? Add is the sentence true? x = 7 Simplify.) Solve x 9 = -2 2.) Solve 48 = - 6r.) Solve 2t + 7 = - 4.) Solve 4t +.5 = ) It costs \$2 to attend a golf clinic with a local pro. Buckets of balls for practice during the clinic cost \$ each. How many buckets can you buy at the clinic if you have \$0 to spend? 6.) An online retailer charges \$6.99 plus \$0.55 per pound to ship electronics purchases. How many pounds is a DVD player for which the shipping charge is \$.94? 8 4

15 Unit: Knowledge of Algebra, Patterns, and Functions Objective: Graph rational numbers on a number line. 8 th Grade Summer Math Packet Rational Numbers are numbers that can be written as fractions. Some examples of rational numbers are ½, 5 ¾, 0.8, and Example: Graph and label the following numbers on the number line: A: 2 B: 4 4 C: D: 2.5 C A D B " " " ".) Graph and label the following numbers on the number line. 2.) Graph and label the following numbers on the number line. A: 5 B: C: 2 D: 5 A: 0 B: 2 C: 5 2 D: 4.) Graph and label the following numbers on the number line. 4.) Graph and label the following numbers on the number line. A:.5 B: 0.5 C:.5 D:.5 A: 9 B: 2 C: 9 4 D: 2 5.) Jonah recorded the temperature for 5 days on a chart. Draw a number line and graph the temperatures. Where do the numbers on the line need to begin and end? Label the points to 5. Day Day 2 Day Day 4 Day ) Graphing numbers on a number line can help you put them in order from smallest to greatest. Draw a number line and graph the numbers in the chart below. Label the points. Which number is the smallest? V W X Y Z

17 Unit: Knowledge of Geometry Objective: Determine the congruent parts of polygons. 8 th Grade Summer Math Packet Congruent Polygons Non Congruent Polygons Congruent Polygons Congruent Segments Congruent Angles Corresponding Sides of a Polygon Corresponding Angles of a Polygon ABC DEF A D cm cm B 7cm C E 7cm F Polygons that have exactly the same size and the same shape Segments that have the same length Angles that have the same measure Sides of a polygon that are matched up with sides of another congruent or similar polygon Angles of a polygon that match up with angles of another congruent or similar polygon Corresponding sides and angles of congruent polygons are congruent: AB DE BC EF AC DF A D B E C F.) G 5cm H 4cm F 45 8cm J K z L 8cm y M x N 2.) Use the figures in problem # to complete the following congruence statements. G K Polygon FGHJ polygon NMLK Complete the following congruence statements. H F GH KL IJ.) Look at the figures in problem #. Determine the measure of each segment or angle. 4.) Polygon HJKLMNPQ is congruent to polygon RSTUVXYZ. What is the length, in units, of RZ? (Note: Figures are not drawn to scale.) x = y = z = 9 7

18 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Determine equivalent forms of rational numbers expressed as fractions, decimals, percents, and ratios. - A Examples: To write a decimal as a fraction, divide the numerator of the fraction by the denominator. Use a power of ten in the denominator to change a decimal to a fraction Write as a decimal = 0. 5 because 5 repeats forever Write 0.2 as a fraction in simplest form. 0.2 = = = ) Write using bar notation to represent the repeating decimal. 2.) Write 5 as a decimal..) Write 5 4 as a decimal. 8 4.) Write 0.94 as a fraction in simplest form. 5.) Write 0.48 as a fraction in simplest form. 6.) There were 6 girls and 8 boys in Mrs. Johnson s math class. Write a ratio of the # of girls to the # of boys in fraction form. Then write the fraction as a repeating decimal. 8 8

19 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Determine equivalent forms of rational numbers expressed as fractions, decimals, percents, and ratios.- B Examples: A RATIO is a comparison of two numbers by division. When a ratio compares a number to 00, it can be written as a PERCENT. To write a ratio or fraction as a percent, find an equivalent fraction with a denominator of 00. You can also use the meaning of percent to change percents to fractions. 9 Write as a percent = = 95% Since = 5, multiply the numerator and denominator by 5. Write 92% as a fraction in simplest form = = Write 92% as a decimal. Move decimal two places to the left. Add zeros if needed. 92.0% = 0.92 Write 0.4 as a percent. Move decimal two places to the right. Add zeros if needed. 0.4 = 40% 7 2.) Write 9% as a decimal and fraction in simplest form..) Write as a percent and decimal ) Write 75% as a decimal and fraction in simplest form..) Write as a percent and decimal ) Ms. Crest surveyed her class and found that 5 out of 0 students brushed their teeth more than twice a day. Write this ratio as a fraction in simplest form, then write it as a % and a decimal. 6.) A local retail store was having a sale and offered all their merchandise as a 25% discount. Write this percent as a fraction in simplest form, then write it as a decimal. 9 9

20 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Compare, order, and describe rational numbers. Examples: RATIONAL numbers include fractions, decimal, and percents. To COMPARE or ORDER rational numbers, they must be in the same form (all fraction or all decimals, or all %s) Example: Order 0.6, 48%, and 2 from least to greatest. Step Change all to decimals % = 0.48 Step 2 Compare decimals & Order. 0.48, 0.5, 0.6 = Step Write using original form. 48%,, ) Order from least to greatest. 22%, 0., 5 2.) Order from least to greatest. 0.74, 4, 70%.) Replace with <, >, or = % 4.) Which is the largest? ) According to the Pet Food Manufacturer s Association, out of 25 people own large dogs and out of 50 medium dogs. Do more people own large or medium dogs? 6.) Your PE teacher asked you to run for specific time period. You ran 0.6 of the time. Two of your friends ran 7 and 72% of the time. Order the amount of time you 0 and your friends ran from least to greatest

21 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Add, subtract, multiply and divide integers. - A Examples: ADDITION INTEGER RULES: For integers with the same sign: The sum of two positive integers is POSITIVE. The sum of two negative integers is NEGATIVE. For integers with different signs, subtract their absolute value. The sum is: Positive IF the positive integer has the greater absolute value. Negative IF the negative integers has the greater absolute value. Examples: (- ) = add keep the sign = (- 2) = add keep the sign = (- 7) = subtract keep the sign of the higher = = subtract keep the sign of the higher = - SUBTRACTION INTEGER RULES: Keep the first number the same Switch the subtraction sign to ADDITION Change the second number to it s opposite. Opposite: - 6 to 6 Follow Addition rules above. Examples: 6 9 = 6 + (- 9) = (- 2) = = 2-7 = - + (- 7) = - 0 ( - 2) = + 2 =.) Add: 2 + (- 7) 2.) Subtract: ) Evaluate a b if a = - 2 and b = ) Evaluate x + y + z if x =, y = - 5, and z = ) In Mongolia the temperature can dip down to 45 o C in January. The temperature in July may reach 40 o C. What is the temperature range in Mongolia? 6.) Write an addition expression to describe skateboarding situation. Then determine the sum. Hank starts at the bottom of a half pipe 6 feet below street level. He rises 4 feet at the top of his kickturn. 4 2

22 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Add, subtract, multiply and divide integers. - B Examples: MULTIPLYING & DIVIDING INTEGER RULES: Two integers with DIFFERENT signs the answer is NEGATIVE. Two integers with SAME signs the answer is POSITIVE. Examples: 5 (- 2) = 5 times 2, the signs are different so the answer will be negative = - 0 (- 6) (- 9) = the signs are the same so the answer will be positive = 54 0 (- 5) = the signs are different so the answer will be negative = (- 5) = the signs are the same so the answer will be positive = 20.) Mulitply: - 4 (- 7) 2.) Divide: 50 (- 25).) Evaluate if a = - and c = 5 4.) Evaluate if d = - 24, e = - 4, and f = 8 - ac de f 5.) A computer stock decreased 2 points each hour for 6 hours. Determine the total change in the stock value over the 6 hours. 6.) A submarine descends at a rate of 60 feet each minute. How long will it take it to descend to a depth of 660 feet below the surface? 42 22

23 8 th Grade Summer Math Packet Unit: Knowledge of Number Relationships & Computation Objective: Add, subtract, and multiply positive fractions and mixed numbers. - A Examples: To add unlike fractions (fractions with different denominators), rename the fractions so there is a common denominator. 2 Add: + = x5 = = 6 x x6 = = 5 x = Add: = 2 2 x = x = x2 = 8 x2 = = is improper so we must change it to proper. 7 divided by 6 = = ) Add: ) Add: ) Add: ) Add: ) A quiche recipe calls for A recipe for quesadillas requires 2 cups of grated cheese. 4 cups of grated cheese. What is the total amount of grated cheese needed for both recipes? 6.) You want to make a scarf and matching hat. The 7 pattern calls for yards of fabric for the scarf and 8 2 yards of fabric for the hat. How much fabric do you 2 need in all? 4 2

24 *** Mathematical websites that would be most helpful are:

### Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10.

Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = + 11-8 + - 2 = - 10 Different signs: Subtract & take sign of larger value + 9 + - 5 = + 4-6

Sierra Verde STEM Academy 8 th Grade Summer Math Packet Dear Incoming 8 th Graders, Please complete this summer math packet prior to the beginning of the 2015-2016 school year. The purpose of the math

### Eustis Middle School Summer Packet. Students Entering 7 th Grade

Eustis Middle School Summer Packet Students Entering 7 th Grade Eustis Middle School Math Department Dear Parents and Students, We are assigning this work in an effort to prepare our students for a successful

### 7 th Grade Pre Algebra A Vocabulary Chronological List

SUM sum the answer to an addition problem Ex. 4 + 5 = 9 The sum is 9. DIFFERENCE difference the answer to a subtraction problem Ex. 8 2 = 6 The difference is 6. PRODUCT product the answer to a multiplication

### 100 Math Facts 6 th Grade

100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### MAT 0950 Course Objectives

MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify

### EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

### ascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.

SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom

### T. H. Rogers School Summer Math Assignment

T. H. Rogers School Summer Math Assignment Mastery of all these skills is extremely important in order to develop a solid math foundation. I believe each year builds upon the previous year s skills in

### Sixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B

Sixth Grade Math Pacing Guide MATH 6/7 1 st Nine Weeks: Unit: Decimals 6.4 Compare and order whole numbers and decimals using concrete materials, drawings, pictures and mathematical symbols. 6.6B Find

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### EXAMPLES. Objective: Write an algebraic expression to represent unknown quantities with one unknown and 1 or 2 operations

PRE-ALGEBRA Summer Packet VANDEBLT CATHOLC HGH SCHOOL ncoming 8th Grade EXAMPLES Section Objective: Write an algebraic expression to represent unknown quantities with one unknown and 1 or 2 operations

### ALGEBRA READINESS DIAGNOSTIC TEST PRACTICE

1 ALGEBRA READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the examples, work the problems, then check your answers at the end of each topic. If you don t get the answer given, check your work and

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### Math Foundations IIA Grade Levels 9-12

Math Foundations IIA Grade Levels 9-12 Math Foundations IIA introduces students to the following concepts: order of operations squares and square root multiplying decimals organizing and graphing data

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### Fractions Associate a fraction with division to calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3/8).

: Autumn 1 Numeracy Curriculum Objectives Number, Place Value and Rounding Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit. Round any whole number to a required

### exponents order of operations expression base scientific notation SOL 8.1 Represents repeated multiplication of the number.

SOL 8.1 exponents order of operations expression base scientific notation Represents repeated multiplication of the number. 10 4 Defines the order in which operations are performed to simplify an expression.

### 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B. Whole Numbers

Whole Numbers Scope and Sequence for Primary Mathematics, U.S. Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced or specifically addressed. Understand

### Galena Park ISD. Friday, September 9, 2016 (Due Date) Summer Assignment. Pre-AP Geometry. (Name)

Summer Assignment (Name) Friday, September 9, 2016 (Due Date) Pre-AP Geometry Summer Assignment: Pre-AP Geometry This assignment should serve as a review of the skills necessary for success in Pre-AP Geometry.

### Unit 1, Review Transitioning from Previous Mathematics Instructional Resources: McDougal Littell: Course 1

Unit 1, Review Transitioning from Previous Mathematics Transitioning from previous mathematics to Sixth Grade Mathematics Understand the relationship between decimals, fractions and percents and demonstrate

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

### SIXTH GRADE MATH. Quarter 1

Quarter 1 SIXTH GRADE MATH Numeration - Place value - Comparing and ordering whole numbers - Place value of exponents - place value of decimals - multiplication and division by 10, 100, 1,000 - comparing

### Texas Success Initiative (TSI) MATH REVIEW

Texas Success Initiative (TSI) MATH REVIEW Algebra Review ALGEBRA & FUNCTIONS Variables and Algebraic Expressions The sum of a number and 5 means: m + 5 or 5 + m The number diminished or subtracted by

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

### Algorithm set of steps used to solve a mathematical computation. Area The number of square units that covers a shape or figure

Fifth Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students need to learn the concept but not necessarily the term. Addend Any number being added Algorithm

### Whole Numbers and Integers (44 topics, no due date)

Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKU-KPMR9 ALEKS Course: Pre-Algebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole

### Combined Operations 150 UNIT 5 COMBINED OPERATIONS. This yacht is propelled by a sail, a motor, or both.

UNIT 5 Combined Operations This yacht is propelled by a sail, a motor, or both. 150 UNIT 5 COMBINED OPERATIONS Many yachts can be powered by the wind, by a gas engine, or both. A hybrid automobile can

### Common Core State Standards for Mathematics Accelerated 7th Grade

A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting

### Illinois State Standards Alignments Grades Three through Eleven

Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other

### Course: Math 7. engage in problem solving, communicating, reasoning, connecting, and representing

Course: Math 7 Decimals and Integers 1-1 Estimation Strategies. Estimate by rounding, front-end estimation, and compatible numbers. Prentice Hall Textbook - Course 2 7.M.0 ~ Measurement Strand ~ Students

### Domain Essential Question Common Core Standards Resources

Middle School Math 2016-2017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How

### Pre-Algebra - MA1100. Topic Lesson Objectives. Variables and Expressions

Variables and Expressions Problem Solving: Using a Problem-Solving Plan Use a four-step plan to solve problems. Choose an appropriate method of computation. Numbers and Expressions Use the order of operations

### Greater Nanticoke Area School District Math Standards: Grade 6

Greater Nanticoke Area School District Math Standards: Grade 6 Standard 2.1 Numbers, Number Systems and Number Relationships CS2.1.8A. Represent and use numbers in equivalent forms 43. Recognize place

### Placement Test Review Materials for

Placement Test Review Materials for 1 To The Student This workbook will provide a review of some of the skills tested on the COMPASS placement test. Skills covered in this workbook will be used on the

### Study Guide For use with pages 5 9

1.1 GOAL For use with pages 5 9 Evaluate and write variable expressions. VOCABULARY A numerical expression consists of numbers and operations. For example, the expression 10 4 is a numerical expression.

### Pearson Scott Foresman "envision" Grade 4

Pearson Scott Foresman "envision" Grade 4 KEY Number Sense Algebra & Functions Measurement & Geometry Statistics, Data Analysis & Probability Problem Solving ** Key Standard Testing & All Lessons are listed

### ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### 6.1 NUMBER SENSE 3-week sequence

Year 6 6.1 NUMBER SENSE 3-week sequence Pupils can represent and explain the multiplicative nature of the number system, understanding how to multiply and divide by 10, 100 and 1000. Pupils make appropriate

### RIT scores between 191 and 200

Measures of Academic Progress for Mathematics RIT scores between 191 and 200 Number Sense and Operations Whole Numbers Solve simple addition word problems Find and extend patterns Demonstrate the associative,

### Archdiocese of Newark Catholic Schools. Curriculum Mapping

Curriculum Mapping Curriculum mapping is a process that helps schools and districts/dioceses determine the agreed-upon learning for all students. Curriculum mapping was undertaken in the Archdiocese of

### Text: Scott Foresman CA Mathematics

Grade 6 Mathematics 008-009 3 Course Introduction 7 Segment I: Algebra and Decimals -0 Variables and Expressions NS.0 AF. -9 Orders of Operation AF. 4- Powers and Exponents - Comparing and Ordering Decimals

### Math 0306 Final Exam Review

Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### Year 6 Maths Objectives

Year 6 Maths Objectives Place Value COUNTING COMPARING NUMBERS IDENTIFYING, REPRESENTING & ESTIMATING NUMBERS READING & WRITING NUMBERS UNDERSTANDING PLACE VALUE ROUNDING PROBLEM SOLVING use negative numbers

### Contents. PART 1 Unit 1: Ratios and Proportional Relationships: Fractions and Ratios

Contents PART 1 Unit 1: Ratios and Proportional Relationships: Fractions and Ratios RP7-1 Patterns 1 RP7-2 T-tables 3 RP7-3 Lowest Common Multiples 5 RP7-4 Models of Fractions 7 RP7-5 Comparing Fractions

### Florida Math Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper

Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Whole Numbers MDECL1: Perform operations on whole numbers (with applications,

### CARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM

GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write

### Grade 5 Math Curriculum Guide

Grade 5 Math Curriculum Guide Lesson 1 1 st Nine Weeks Unit 1: Number and Operations in Base Ten Understand Place Value 5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents

### Campbellsport School District Understanding by Design (UbD) Template

Campbellsport School District Understanding by Design (UbD) Template Class Curriculum/Content Area: Math Course Length: 1 year Course Title: 6 th Grade Math Date last reviewed: April 24, 2015 Prerequisites:

### First Six Weeks (29 Days)

Mathematics Scope & Sequence Grade 6 Revised: May 2010 Topic Title Unit 1: Compare and Order, Estimate, Exponents, and Order of Operations Lesson 1-1: Comparing and Ordering Whole Numbers Lesson 1-2: Estimating

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Describe as a mixed number where the arrow is pointing to on the number line. Explain how the base 10 system relates to place value.

Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop

### Pre-Algebra IA Grade Level 8

Pre-Algebra IA Pre-Algebra IA introduces students to the following concepts and functions: number notation decimals operational symbols inverse operations of multiplication and division rules for solving

### Utah Core Curriculum for Mathematics

Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

### Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

### Grade 4 Math Expressions Vocabulary Words

Grade 4 Math Expressions Vocabulary Words Link to Math Expression Online Glossary for some definitions: http://wwwk6.thinkcentral.com/content/hsp/math/hspmathmx/na/gr4/se_9780547153131_/eglos sary/eg_popup.html?grade=4

### Mathematics Placement

Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

### Name Period Date MATHLINKS: GRADE 7 STUDENT PACKET 1 FRACTIONS AND DECIMALS

Name Period Date 7- STUDENT PACKET MATHLINKS: GRADE 7 STUDENT PACKET FRACTIONS AND DECIMALS. Terminating Decimals Convert between fractions and terminating decimals. Compute with simple fractions.. Repeating

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

### Lesson 7: Using Formulas

Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with

### Archdiocese of Washington Catholic Schools Academic Standards Mathematics

5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

### FIFTH GRADE Mathematics Standards for the Archdiocese of Detroit

FIFTH GRADE Mathematics Standards for the Archdiocese of Detroit *Provide 3 dates for each standard Initial Date(s) Operations and Algebraic Thinking Write and interpret numerical expressions. 5.OA.A.1

### Assessment For The California Mathematics Standards Grade 7

Introduction: Summary of Goals GRADE SEVEN By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use

### Fifth Grade. Scope & Sequence of Lessons. by lesson number

Scope & Sequence of Lessons by lesson number PLACE VALUE AND COUNTING Place value 1 Recognizing numbers less than a million 65 Recognizing tenths and hundredths places 80 Recognizing numbers up through

### Math Foundations IIB Grade Levels 9-12

Math Foundations IIB Grade Levels 9-12 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multi-step equations and inequalities points,

### Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic

### Bedford Public Schools

Bedford Public Schools Grade 7 Math In 7 th grade, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding

### Unit 1, Concept 1 Number Sense, Fractions, and Algebraic Thinking Instructional Resources: Carnegie Learning: Bridge to Algebra

Unit 1, 1 Number Sense, Fractions, and Algebraic Thinking 7NS 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

### LESSON 4 Missing Numbers in Multiplication Missing Numbers in Division LESSON 5 Order of Operations, Part 1 LESSON 6 Fractional Parts LESSON 7 Lines,

Saxon Math 7/6 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### Mathematics VI Grade Level 6

Mathematics VI The Mathematics VI course includes topics such as: geometric measurements using scales coordinate planes formulas and pi 1 Teachers' Guide COURSE DESCRIPTION: The Anywhere Learning System

### Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

1. sum the answer when you add Ex: 3 + 9 = 12 12 is the sum 2. difference the answer when you subtract Ex: 17-9 = 8 difference 8 is the 3. the answer when you multiply Ex: 7 x 8 = 56 56 is the 4. quotient

### Study Guide and Intervention Workbook

Study Guide and Intervention Workbook To the Student This Workbook gives you additional examples and problems for the concept exercises in each lesson. The exercises are designed to aid your study of mathematics

### Algebra 1 Chapter 3 Vocabulary. equivalent - Equations with the same solutions as the original equation are called.

Chapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate

### troduction to Algebra

Chapter Three Solving Equations and Problem Solving Section 3.1 Simplifying Algebraic Expressions In algebra letters called variables represent numbers. The addends of an algebraic expression are called

### Name Date Time. STUDY LINK 8 13 Unit 9: Family Letter. Please keep this Family Letter for reference as your child works through Unit 9.

Name Date Time STUDY LINK Unit 9: Family Letter More about Variables, Formulas, and Graphs You may be surprised at some of the topics that are covered in Unit 9. Several of them would be traditionally

### EVERY DAY COUNTS CALENDAR MATH 2005 correlated to

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:

### New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator

### MATHEMATICS GRADE LEVEL VOCABULARY DRAWN FROM SBAC ITEM SPECIFICATIONS VERSION 1.1 JUNE 18, 2014

VERSION 1.1 JUNE 18, 2014 MATHEMATICS GRADE LEVEL VOCABULARY DRAWN FROM SBAC ITEM SPECIFICATIONS PRESENTED BY: WASHINGTON STATE REGIONAL MATH COORDINATORS Smarter Balanced Vocabulary - From SBAC test/item

### Number & Place Value. Addition & Subtraction. Digit Value: determine the value of each digit. determine the value of each digit

Number & Place Value Addition & Subtraction UKS2 The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value

### Introduction to the Practice Exams

Introduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra

### Key Stage Two Maths Overview

Crick Primary School The lists of objectives shown are the core objectives in Mathematics for each year group and will be taught at some stage over the academic year at an appropriate level. Your child

### Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.

Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM

7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in

### Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW

Name Period Date 8-1 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW 1.1 Integer Operations: Patterns Explore the meaning of integer addition, subtraction, multiplication, and division.

### MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

### CURRENT RESOURCES THAT SUPPORT TEACHING AND LEARNING OF THE COMMON CORE STATE STANDARDS IN MATHEMATICS

CURRENT RESOURCES THAT SUPPORT TEACHING AND LEARNING OF THE COMMON CORE STATE STANDARDS IN MATHEMATICS GRADE 5 Operations & Algebraic Thinking Write and interpret numerical expressions. 1. Use parentheses,

### An arrangement that shows objects in rows and columns Example:

1. acute angle : An angle that measures less than a right angle (90 ). 2. addend : Any of the numbers that are added 2 + 3 = 5 The addends are 2 and 3. 3. angle : A figure formed by two rays that meet