5th, 6th, 7th, and 8th Grades

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Visit the TeacherWeb® videos to learn about the features, modifications, and customizations available on your website. Click here to learn more. 5th Grade Math Notes small medium large Section 1-2 Divisibility Patterns A whole number is divisible by another number if the remainder is 0 when the first number is divided by the second. Divisibility Rules A whole number is divisible by Examples 2 if the ones digit is divisible by 2 2,4,6,8,10,12... 3 if the sum of the digits is divisible by 3 3,6,9,12,15,18 ( 1+8)=9 4 if the number formed by the last two digits is divisible by 4 112, 684.... 5 if the ones digit is 0 or 5 10, 20, 55... 6 if the number is divisible by both 2 and 3 6,12,18... 9 if the sum of the digits is divisible by 9 27, 36, 45 ( 4+5)=9 10 if the ones digit is 0 20,30,40... A whole number is even if it is divisible by 2. It is odd if it is not divisible by 2. 1-3 PRIME FACTORS When two or more numbers are multiplied, each number is called a factor of the product. 7 6 1x7 1x6 2x3 So the factors of 7 are:1 and 7 So the factors of 6 are:1,2,3,6 A whole number that has exactly two unique factors, 1 and the number itself is called a prime number. A number greater than 1 with more than two factors is a composite number. Every composite number can be expressed as a product of prime numbers. This is called a prime factorization of the number. A factor tree can be used. 1-4 Powers and Exponents A product of prime factors can be written using exponents and a base. 32=2x2x2x2x2= 25-exponent base Numbers expressed using exponents are called powers. Powers Words Expression Value 25 2 to the fifth power 2x2x2x2x2 32 32 3 to the second power or 3 squared 3x3 9 103 10 to the third power or 10 cubed 10x10x10 100 * The symbol . means miltiplication 1. Write 3.3.3.3 using ans exponent. Find the value 2. Write 45 as a product of the same factor. Then find the value. 3.Science The approximate daytime surface temperature on the moon can be written as 28 Farenheit. What is this temperature? 4. Write the prime factorization of 72 using exponents. 1-5 Order of Operations Order of Operations tells you which operation to perform first so that everyone gets the same final answer. PLEASE EXCUSE MY DEAR AUNT SALLY P=Parentheses E=Exponents M=Multiply or divide from left to right D=Divide or multiply from left to right A=Add or subtract from left to right S=Subtract or add from left to right Example 1 4+3 x 5= 10-2 + 8= 3 x 62 + 4= (27 +2) x 42= 1-6 ALGEBRA: Variables and Exponents Algebra is a language of symbols. One symbol that is often used is a variable. A variable is a symbol, usually a letter, used to represent a number. An algebraic expression are combinations of variables, numbers, and at least one operation. 1-7: Algebra: Solving Equations Objective: To solve equations by using mental math and guess and check strategy We looked at algebraic expressions, today we are going to solve algebraic equations. Equations contain an equals sign. Some equations can be solved mentally. Example: Solve 5 + h=12 mentally Your turn: 18- d =10 We can guess and check s + 49 = 61 Estimate= s+ 50=60, s should be about 10 Try 10 Try 11 Try 12 Or, would you like to view and optionally restore one of these previous versions? Password: Forgot your password?

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