Math 6, Unit 1 Notes: Whole Numbers Estimating, and Patterns

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1 Math 6, Unit 1 Notes: Whole Numbers Estimating, and Patterns Objectives: (1.2) The student will estimate by rounding to a given place value. (1.5) The student will use a variety of methods to estimate. (2.5) The student will find missing terms in a sequence. (1.3) The student will use the order of operations to evaluate expressions with whole numbers. Whole Numbers The following is the set of numbers on the number line called Whole Numbers: {0, 1, 2, 3, 4, } All numbers in base 10 are made up of 10 digits; 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The value of a digit depends on its placement within a number, also known as Place Value. In base 10, we have columns; 100,000 10,000, 1000, 100, 10, ,000's 10,000's 1000's 100's 10's 1's The digit s value is determined by the specific column in which it is located. The 5 in the following two examples have different values. In 53, the 5 has the value of 5 tens or 50 In 1,548, the 5 has the value of 5 hundreds or 500 Writing a Number in Expanded Notation To write a number in expanded notation, you write each digit as a product of that digit and its place value and find their sum. Write 73 in expanded notation. 7(10) + 3(1) Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 1 of 6

2 Ex Write 543 in expanded notation 5(100) + 4(10) + 3(1) Write 1,207 in expanded notation 1(1000) +2(100) + 0(10) + 7(1) Writing a Number in Word Form Write 73 in word form: Write 705 in word form: Write 2356 in word form: Seventy-three Seven hundred five Two thousand three hundred fifty-six Rounding Whole Numbers To round a number, look at the digit immediately to the right of the place you are rounding. If that digit is 5 or more, round up. If that digit is less than 5, round down Round 4,321 to the nearest hundred. 4, Hundred s place This digit is less than 5. Round down. 4,321 rounded to the nearest hundred is 4,300. Round 58,786 to the nearest , s place This digit is more than 5. Round up. 58,786 rounded to the nearest 1000 is 59,000. Use Rounding to Estimate Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 2 of 6

3 Rounding is an effective way to estimate the sum or difference of a group of numbers. Estimate the sum to the nearest hundreds = 412 rounded to the nearest hundred is rounded to the nearest hundred is rounded to the nearest hundred is 100. Add the rounded values: = Sam is collecting aluminum cans to recycle. The following shows the number of cans he collected last week. About how many cans did Sam collect last week? Mon Tues Wed Thrs Fri 81 cans 48 cans 12 cans 75 cans 132 cans First choose the best place value to round each number. Since most of the numbers are under 100, round each number to the nearest tens. 81 rounds to rounds to rounds to rounds to rounds to 130 Add the rounded values: Sam collected approximately 350 cans last week. Properties of Real Numbers The properties of real numbers are rules used to simplify expressions and compute numbers more readily. Commutative Property of Addition Commutative Property of Multiplication a + b = b + a a b = b a Order does not matter!! = Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 3 of 6

4 10 7 = 7 10 Associative Property of Addition ( a+ b) + c= a+ ( b+ c) Associative Property of Multiplication ( a b) c= a ( b c) (7 + 8) + 2 = 7 + (8 + 2) Ex (13 25) 4 = 13 (25 4) Distributive Property a ( b + c) = a b + a c Distribute OVER-add/sub 5 23 = 5 (20 + 3) = = = = 25 (10 + 2) = = = 300 Arithmetic Sequence A sequence is a set of numbers in a particular order. Each number is called a term of the sequence. {8, 12, 0, 8, 105} is a sequence with 5 terms. An Arithmetic Sequence is a sequence in which every term after the first is obtained by adding a fixed number. {5, 10, 15, 20, 25, } This arithmetic sequence has an infinite number of terms. The terms are obtained by adding 5 to the previous term. {2, 5, 8, 11, 14, 17 } This arithmetic sequence has 6 terms. The first term is 2 and you must add 3 to obtain the next term. To find the next term in an arithmetic sequence, subtract any two consecutive terms, then add that difference to the last term to find the next term. Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 4 of 6

5 Find the next term in the following arithmetic sequence: {8, 19, 30, 41, } o Choose two consecutive terms (19, 30) and find their difference: = 11. o Add the difference (11) to the last term = is the next term in the sequence. Order of Operations The Order of Operations is just an agreement to compute problems the same way so everyone gets the same result. The following is the order that is followed when evaluating a numeric expression: 1. Parentheses 2. Exponents 3. Multiply/Divide from left to right 4. Add/Subtract from left to right Evaluate the following expressions. a) = = 18 b) = = = 13 Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 5 of 6

6 c) 8 (1 + 3) (1 + 3) = = = = 50 2 = 48 CRT example: Math 6 Notes Unit 1: Whole Numbers, Estimating, and Patterns Page 6 of 6