Third Grade EOG Math Review Goal 1: Numbers and Operations

Most of the EOG focuses on Goal 1! Goal 1 covers: –Place value –Addition –Subtraction –Estimation –Multiplication –Division –Fractions This slideshow will help review important concepts that you need to KNOW for the EOG!

Know it...about place value! Our number system is based on groups of 10. This is a one.This is a tens rod. 10 ones= 1 tens rod This is a hundred flat. 10 tens= 1 hundred 10 x 10 = 100 This is a thousands cube. 10 hundreds= 1 thousand 10 x 100 = 1000 Numbers can be represented using these base ten blocks.

Numbers can be represented in different ways: = 231 expanded form 231 standard form two hundred thirty-one word form What is the value of the underlined digit? 231 Ask yourself: What place does the digit hold? 3 tens = 30 The value of the 3 is 30.

Place value can help us compare and order numbers! < less than> greater than= equal The more places a number has, the greater the number ,000 These are symbols we use to help us compare numbers: You can order numbers from least to greatest and from greatest to least!

Know it…about addition! Fact fluency is a MUST! Know your addition facts! = 15 addends sum You will need to be able to add two-, three-, and four- digit numbers together. When adding numbers, make sure you are lining up place values together!

Addition Properties Identity Property of Addition : The sum of any number and 0 is that number = 5 Commutative Property of Addition: Numbers can be added in any order and the sum remains the same = Associative Property of Addition: Addends can be regrouped and the sum remains the same. (2 + 3) + 4 = 4 + (2 + 3)

Know it…about subtraction! Fact fluency is a MUST! Know your subtraction facts! You will need to be able to subtract two-, three-, and four- digit numbers = 7 When subtracting numbers, make sure you are lining up place values together and regroup as necessary! difference

How are addition and subtraction related? Addition and subtraction are inverse, or opposite, operations! They can be used to check each other = = – 3 = 9 12 – 9 = 3 Addition and subtraction facts that use the same numbers belong to a fact family.

Know it…about rounding! Read questions carefully! You may be asked to round to the nearest ten, hundred, or thousand. example: Round 564 to the nearest ten. Underline the digit in the place you are rounding to Look at the digit to the right of the underlined digit. 0-4 Circle it to drop it down! 5-9 Box it up nice and tight! This number would round down to 560.

Know it…about estimation! Estimating is NOT giving an exact answer! The word about is used in story problems to let you know that an exact answer is not needed. You need to estimate! Estimating means rounding to the greatest place value!

Know it…about multiplication! The multiplication symbol “x” can mean: – groups of - rows of There are a couple of different strategies you can use to help you multiply! Circles and Stars Draw a picture Make an Array Make a Table (look for patterns!) Skip Counting Repeated addition

What is an array? An array is an orderly arrangement of objects in rows. REMEMBER: Rows go across! There are 2 rows. There are 4 hearts in each row. This array can be represented in 2 ways. 2 x 4 = 88 ÷ 2 = 4

Multiplication Properties Zero Property: The product of any number and 0 is 0. 3 x 0 = 0 “Zeroes clear it out!” Commutative Property: Numbers can be multiplied in any order and the product remains the same. 3 x 4 = 4 x 3 Associative Property: Factors can be regrouped and the product remains the same. (2 x 3) x 4 = 4 x (2 x 3) Identity Property: The product of any number and 1 is that number. 8 x 1 = 8

Division is the inverse, or opposite, of multiplication. Division is the inverse, or opposite, of multiplication. Division is an operation that tells how many groups there are and how many are in each group. Division is an operation that tells how many groups there are and how many are in each group. subtraction addition division multiplication is the opposite of.. j u s t a s … Know it…about division!

What does division look like? 24 ÷ 6 = 4 A division problem can be written horizontally using the division symbol A division problem can be written in a division box A division problem can be written as a fraction.

Know the Division Lingo! 24 ÷ 6 = 4 – dividend – the number being divided (total number of items) – divisor – the number by which another number is divided (# of groups) - quotient - the answer to a division problem (# of items in each group)

Let’s review strategies for division! We can solve problems by thinking of division as: We can solve problems by thinking of division as: – dividing a number into equal groups – sharing equally – repeated subtraction Fact fluency is a must! Knowing your multiplication facts will help you master division!

How are multiplication and division related? Multiplication and division are inverse, or opposite, operations! A fact family can show how multiplication and division are related. Remember that fact families are groups of number sentences that use the same numbers. Here is a fact family for 7, 3, and x 3 = 21 3 x 7 = ÷ 3 = 7 21 ÷ 7 = 3

What is the Order of Operations? This is a special math rule that tells you what ORDER to compute numbers in when you have more than one operation. It helps you solve problems like this: 3 + (4 x 2) - 7

Parantheses ( ) Multiplication & Division Addition & Subtraction We can use a flow map to help us remember the ORDER of OPERATIONS. Pass My Drink And Snack

Know it…about fractions! A fraction is a symbol that is used to name equal parts of a whole The number up NORTH is the Numerator! The number that is DOWN south is the Denominator!

Naming Parts of a Whole

Naming Fractional Parts

Know it..about parts of a set! A set is a group of objects. 4 of the set are pears 5

When a picture is given, put the items into groups based on the number in the denominator. 1 of 9 books = 3 books in each group 3 Know it..about finding the fractional part of a set!

1 of 64 = 8 ? x = 8 times what = 64?

Know it..about equivalent fractions! Equivalent fractions are equal fractions; fractions that show the SAME amount! There are 3 strategies for finding equivalent fractions: Draw a congruent model! Look for a pattern. Use “Bottoms Up”!

Equivalent Fraction Models ==

Equivalent Fraction Patterns To find equivalent fractions… LOOK FOR A PATTERN The numerator tells you to count by 1’s. The denominator tells you to count by 2’s.

Equivalent Fractions with Bottoms Up To find equivalent fractions… USE BOTTOMS UP! =

Know it..about comparing and ordering fractions! As the size of the denominator increases, the size of the piece decreases. When drawing models, be sure to make them CONGRUENT! Same size, same shape..CONGRUENT!

Ordering Fractions with Drawing A Picture Least to greatest:

Ordering Fractions with Bottoms Up Compare 1 and Compare 1 and Compare 1 and > > > Since 1/3 was largest 2 times, it is the largest fraction! 1/6 is next, followed by 1/9.

These are fraction strips. 1 Whole

In an improper fraction, the numerator is larger than the denominator. How would you name this fraction? Just like you would name a proper fraction, count the number of parts that are shaded. 5 How many equal parts are the squares divided into? 4 Know it..about improper fractions!

Improper Fractions We could name this fraction as 5 4. There is another way to describe this fraction. You can describe it using a mixed number. 1 whole square is shaded, plus ¼ of the other square is shaded. 1 ¼ is shaded. 1 ¼ and 5/4 are equivalent fractions

Know it..about mixed numbers! A mixed number is a whole number and a fraction combined.

Mixed Numbers Count the WHOLEs first Then find the FRACTIONal part

Know it about fractions on a number line!

We can ZOOM IN between whole numbers! Let’s zoom in between 1 and 2 on a number line! There are spaces in between whole numbers. 12 Count the spaces, or jumps, between the whole numbers to determine the denominator