A Guide to Understanding 3rd-4th Grade Math

Place Value

Hundred Thousands

Ten Thousands

Thousands Hundreds Tens Ones . Ones Tenths Hundredths

Writing Whole Numbers Place value tells you how much each digit stands for.

Use a hyphen when you use words to write 2-digit numbers

greater than 20 that have a digit other than zero in the ones place. Example: Write 57 in words. Answer: fifty-seven Example: Write 80 in words. Answer: eighty

A place-value chart tells you how many hundreds, tens, & ones to use. Example: A supermarket has 258 boxes of cereal on its shelves. Answer:

Hundreds Tens Ones 2 5 8

Or use a base ten model:

2 hundred 5 tens 8 ones

Zeros may stand for nothing, but that doesn’t mean you can leave

them out. They keep other digits in the correct places.

Thousands Hundreds Tens Ones 1 0 3 0

Think: 1 thousand + 0 hundred + 3 tens + 0 ones Write: 1,030 Say: One thousand thirty

Place Value Through the Millions

Millions Period Thousands Period Ones Period

Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 9 1 4 0 2 6 0 0

The digits in large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods. Write: 91,402,600 Example: What is the value of the digit 4 in 91,402,600? Answer: the digit 4 is in the hundred thousands place. Its value is 4 hundred thousand or 400,000.

Reading Large Numbers Reading large numbers is easier than it looks. You only need to know

How to read 3-digit numbers, and The names of the periods.

Example: How do you read 2,469,600? 1. Start at the left. Read the first comma. Say the name of the period.two million 2. Read to the 2nd comma. Say the name of the next period.four hundred sixty-nine thousand. 3. Read the three-digit number in the ones period. six hundred

You don’t say the name of the ones period.

Answer: Say: two million, four hundred sixty-nine thousand, six hundred.

“AND” is for Decimals – Not Whole Numbers

When you read a whole number, don’t say the word and. Use and only when you read a decimal point. Write: 905 Write: 900.5 Say: nine hundred five Say: nine hundred and five tenths (not nine hundred and five)

Comparing Whole Numbers 1. Line up the place values by lining up the ones. 563 521 2. Begin with the greatest place. Find the first place where the digits are different. 563 521 different same 3. Compare the value of the digits in that place. 60 is greater than 20 So, 563>521

BE careful when you compare numbers that don’t have the same number of digits. Make sure you line up the ones places.

Suppose you want to compare 1246 and 896. Lined up correctly at the ones place Lined up incorrectly 1246 1246 896 896 * When one whole number has more digits than another, it is greater.

So, 1246> 896 (the hungry alligator always eats the bigger portion, the mouth of the symbol is open to the greater number)

Ordering Whole Numbers

It is easier to work with a group of numbers it they are in order: Order can be from greatest to least, or from least to greatest. If you know how to compare numbers, you know how to put a group of numbers in order. 1. Line up the numbers at the ones place. 1127 841 1483 2. Begin to compare at the greatest place. 841 is the least because it has the fewest digits. 3. Compare the remaining numbers. Find the first place where the digits are different. 1127 1483 different same Answer: The order from least to greatest is 841, 1127,1483

Money U. S. coins and bills are based on ones, fives, and tens, which make them easy to count. The dollar is the basic unit. Penny Nickel Dine Quarter Half dollar 1¢ 5¢ 10¢ 25¢ 50¢ $0.01 $0.05 $0.10 $0.25 $0.50 $1 bill $5 bill $10 bill $20 bill $1.00 $5.00 $10.00 $20.00 Write: 25¢ or $0.25 Write: $5.00 Say: twenty-five cents Say: five dollars

Frank has $9.24 Write $9.24 Say: nine dollars and twenty-four cents (remember to say “and”

when you read the decimal point) *$ and ¢ do not go together Don’t write $ when you mean ¢, and don’t write¢ when you mean $ Correct Not Correct 47¢ $0.47¢ or or $0.47 0.47¢