Grade 6 Math Test Review Representing Numbers, Place Value, Decomposing Numbers, Comparing Numbers, Rounding Numbers, Multiplying 3-Digits by 2-Digits, Exponential Notation

Hundred Thousand (HTh) Representing Numbers Millions Thousands Units Position Million (M) Hundred Thousand (HTh) Ten Thousand (TTh) Thousand (Th) Hundred (H) Ten (T) Unit (U) Value 1 000 000 100 000 10 000 1 000 100 10 1 Numbers can be expressed in 3 different forms: Standard form: 38 972 Word form: thirty-eight thousand nine hundred seventy two Expanded form: 30 000 + 8 000 + 900 + 70 + 2 Numbers can be represented using a place value chart (above), symbols, money, etc.

Place Value If you are asked how many HTh, TTh, Th, H, T, or U there are, you: Find the digit in that place Take that digit and all the other digits to the left of it 320 451 3 204 hundreds

Place Value If you are asked to the find the value of a specific digit: Find the digit in the number and what place it’s in Determine the value of the digit 320 450 The 4 is in the hundreds spot: 4 x 100 = 400

Decomposing a Number What does it mean to decompose something? Break something down Take something apart To successfully decompose a number, it is important that it is represented in an equivalent form.

How Can We Decompose a Number? Expanded Form 8 512 = 8 000 + 500 + 10 + 2 8 512 = 8 500 + 10 + 2 8 512 = 8 500 + 12 Using Place Value Symbols 8 512 = 8Th + 5H + 1T + 2U Using Order of Operations 8 512 = (8 x 1 000) + (5 x 100) + (1 x 10) + (2 x 1)

Decomposing a Number Using a Place Value Table POSITION Thousands (Th) Hundreds (H) Tens (T) Units (U) VALUE 1 000 100 10 1 NUMBER 8 5 2 8 512 = (8 x 1 000) + (5 x 100) + (1 x 10) + (2 x 1) 8 000 + 500 + 10 + 2

Decomposing Also Makes Multiplication Easier! 8 512 x 7 (8 000 x 7) + (500 x 7) + (10 x 7) + (2 x 7) 56 000 + 3 500 + 70 + 14 59 584 Remember: when multiplying numbers by a multiple of 10, 100, 1 000 etc., multiply the first factor without any zeroes, then add the zeroes to the end result. For example: In 8 000 x 7, first multiply 8 x 7 = 56, then add the zeroes: 56 000

Why Compare Numbers? Two tools to help us compare numbers: Place value chart Number line

Comparing Numbers Using a Place Value Chart HTh TTh Th H T U 1 3 5 6 9 7 M HTh TTh Th H T U 1 3 7 9 Start by comparing the digit with the highest value. If they are equal, compare the digits in the next position to the right.

Comparing Numbers Using a Number Line A number line is made up of evenly spaces points The space between points is called an interval Intervals are constant. They have the same difference Number lines help arrange numbers in increasing or decreasing order

Rounding Natural Numbers When you round a number, you replace it with one of approximate value Rounding numbers helps you estimate operations and makes mental calculation easier

Rounding 542 329 to the Nearest Thousand Step Example 1. Circle the digit in the position to which the number will be rounded. 542 329 2. Look at the digit to the right of the circled digit. -If less than 5, the digit to be rounded does not change -If greater than or equal to 5, the digit is rounded by 1 3. Replace all the digits to the right of the circled digit with 0 542 000 542 329 is closer to 542 000 than to 543 000

Multiplying 3-Digit Numbers by 2-Digit Numbers Understanding a multiplication question: 829 x 74 = 61 346 1st Factor multiplied by 2nd Factor equals the Product

Multiplying 3-Digit Numbers by 2-Digit Numbers Multiply each digit in the number 829 by 4 (units). Don’t forget to carry! 1 3 Th H T U 8 2 9 7 4 6 x

Multiplying 3-Digit Numbers by 2-Digit Numbers Place a 0 in the units column. Multiply each digit in the number 829 by 7 (tens). 2 6 TTh Th H T U 8 9 7 4 3 1 5 x

Multiplying 3-Digit Numbers by 2-Digit Numbers Add the 2 products to find the final product of the multiplication 2 6 TTh Th H T U 8 9 7 4 3 1 5 x +

What Does Exponential Notation Look Like? 25 Remember: the exponent means you are multiplying the base by itself a certain number of times The power is calculated by making a repeated multiplication “Two to the power of five” Exponent Base

Some Rules to Remember The exponent 2 represents a square number The exponent 3 represents a cubed number A base raised to the power of 0 always equals 1 80 = 1 100 = 1 A based raised to the power of 1 always equals itself 81 = 8 101 = 10

Powers of Base 10 Represent Place Values Position M HTh TTh Th H T U Value 1 000 000 100 000 10 000 1 000 100 10 1 Power of 10 106 105 104 103 102 101 A base 10 exponent refers to the number of zeroes