This is the place value chart we are using to manipulate numbers every day:
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
Addition and Multiplication Properties
Knowing the different addition and multiplication properties gives your child tools to not only understand basic math concepts, but also provides them with multiple choices for mentally solving math problems.
Zero Property or Identity Property: any number added to zero is that number. For example: 0+8=8
In class we discussed that any time we see 0 + another number, we know the sum will be the other number (or that number keeps it's identity). This property helps students to add quickly.
Commutative Property: when adding and multiplying, numbers can be moved around in any order and you will end up with the same solution. For example: 3+8 is the same as (or equal to) 8+3
In class we talked about "commuting" in cars to move from one place to another but you still end up at the same place. This property helps students to manipulate the order they compute numbers. Sometimes it's easier to move the greater number to the beginning and then add the smaller numbers.
Associative Property: when adding or multiplying, numbers can be grouped in any order and you will still end up with the same sum. For example: (3+8)+2 is the same as (or equal to) 3+(2+8)
In class we demonstrated groups of 3 students standing together. Two of the students "associated" by shaking hands. No matter how many different ways we "associated" or grouped the students, we still had the same group of three students. This property helps students to group numbers in a way that makes sense to them so they can add/multiply quickly when there are three or more numbers in the equation.
Rounding
Your child has been working on rounding numbers in places up to the 100 millions. Rounding helps us solve math problems mentally so we can check our answers. If the estimated answer is close to the actual answer, then great job! If the estimated answer is far off from the actual answer, then you know to double check your work.
Here's a quick refresher and what we have talked about in class:
1.) Look at the digit in the place you want to round: 1,234,567
2.) Underline that digit: 1,234,567
3.) Look to the digit to it's right. Ask yourself, "Is the digit 5 or greater?" If it is, then you round up. If the digit is 4 or less, you round down.
1,234,567
4.) Then rewrite the rounded number: 1,200,000
Regrouping in Subtraction
Your child uses place value to subtract multi-digit problems. They start from the ones place, and work their way over to the greatest place in the problem.
Example:
67,890
- 15,234
________
Starting with the ones place. There are 0 (or no) ones, and you have to take away 4 ones. There are not enough ones to take from, so you have to regroup a group of tens from the 9 in the tens place, and break that group of tens into 10 ones. Add those 10 ones to the 0 ones you already have, which leaves you with 10 ones. Now you can take away 4 ones. 10-4=6 ones. This is the value of the ones place in your answer.
Now we move on to the tens place. There are no longer 9 tens in the tens place. We regrouped a group of tens into 10 ones for the ones place. This means we are now starting out with 8 tens and subtracting 3 tens. 8-3= 5 tens. This is the value of the tens place in your answer.
67,88 10
- 15,23 4
________
You then work your way over the same way as you make your way to the ten thousands place.
Multiplication
Multiplication is simply repeated addition.
The numbers multiplied together are called factors. Ex: 23 x 86 The factors are 23 and 86
The answer to a multiplication problem is a product. Ex: 23 x 86 = 1,978
Students learn many strategies for multiplying large numbers. Here are the strategies we are learning in class:
Partial Product Method:
23 x 86
1.) Break each number down into expanded form: 23 x 86 = 20+3 x 80+6
2.) Write the expanded form around the boxes:
20 3
80
6
3.) Multiply each group of numbers together and write the product in the boxes:
20 x 80 = 1600
20 x 6 = 120
3 x 80 = 240
3 x 6 = 18
4.) Add the products together:
1,600
+ 120
______
1,720
240
+ 18
______
258
5.) Add the sums together:
1,720
+ 258
_____
1,978
Factors & Multiples
Factors are the numbers multiplied together to get a product.
Example: 5 x 3 = 15 5 and 3 are the factors multiplied together to get a product of 15.
Multiple is what you get when you multiply two factors.
Example: 5 x 3 = 15 15 is a multiple of both 3 and 5
Factoring Numbers:
To find the factors of a number, write out the multiplication sentences that result in that number.
Example:
15
15 x 1 = 15
5 x 3 = 15
So the factors of 15 are 1, 3, 5, and 15.
Prime & Composite Numbers
Prime numbers are numbers with only two factors. Those two factors are 1 and the number itself.
Example: 7
Write down the factors of 7:
7 x 1 = 7
The only way to get 7 as a product in a multiplication sentence is to multiply
7 x 1. The only factors of 7 are 7 and 1. Therefore, 7 is a prime number.
Composite numbers are numbers with more than two factors.
Division
Division is a quick way to do repeated subtraction. Students are taught the following terms: Divisor: This is the "bossy" number that tells the dividend how many groups to divide into. Dividend: The dividend is the "whole" group you have that needs to be divided into smaller parts. Quotient: The quotient is the answer to a division problem.
Example: I use donuts in my examples a lot in class. It's important for students to know the numbers represent a quantity of something. Let's say I'm talking about donuts for this problem.
I have 155 donuts that I have to split between 5 people. This is what the problem looks like:
155/5=31
The dividend is 155, meaning I have a total of 155 donuts.
The divisor is 5, meaning that it is "bossing" the dividend around and telling those 155 donuts to divide into 5 equal groups.
The quotient is 31 in this problem, meaning that if I take my 155 donuts, I can hand them out evenly to 4 people. Each person will get 31 donuts and I will not have any left over.
