Fractions
Fractions are consist of two things.... A numerator which is on top / the denominator.. The N means the # of pieces / D means size of pieces. It is crucial to understand what they mean. Fractions are comparisons, now we see a problem such as 18 5/6 - 10 3/8 well we have two whole numbers. 18-10 which gives us 8 now we are left with the 5/6 - 3/8 notice they do not have the same common denominator. well we have to look for a common denominator, LCF now we have 2*3 gives us the 6 and 2*4 gives us the 8 now we have to see what each has and multiply what they don't have. and we multiply both top and bottom on both fractions we will end up getting 20/24 and 9/24 now we subtract that gives us 11/24, and our final result is 8 11/24.
Adding/Subtracting Integers
Now this is a new way of solving pos and neg numbers. We will start with -14 + (-30), which is the bigger number? -30 is the larger number. So we will give it two - - and -14 will get one - this means that the signs are the same so which is where we add, when the signs are different we subtract. Example 2: 19+(-10), 19 will have + + and -10 will have - . The signs are the opposite so we will subtract. 19-10 is +9.
Multiplying Integers
Multiplying Integers : what does 3(-2) mean? 3 tells you how many groups you have and -2 tells you what we have inside those groups (--) (--) (--) there are our 3 groups of -2 inside. using the integer tiles we must focus on what we have and what we need such as zero banks they do not change the problem its like magic zeros.
Ploya's 4 Step
1.Understand the problem ( Read out loud)
2. Develop a plan
3. Test plan/ Carry out
4. Ask and look back and see if the answer makes sense (UnDevCarLo)
Early Number Sense
What are the first number skills needed?
Counting numbers, kids get praised from counting
numbers 1-10, but kids need to find a true connections
with numbers.
Divison
There are two new forms of showing how to do long division it An example : 872 divided by 6 putting the 6 outside of the "box" was the old way... NOW THE NEW way requires you to put the numbers outside the box but instead creating a line straight down and using it to solve by using numbers to keep on subtracting, for instance it is like subtracting every single time by this it will become the number smaller and smaller.
Upwards divison
This form is using the subtraction up hill and counting to subtract every single time this will only allow the number to decrease
Integers
Integers are numbers, they can be positive or negative numbers but still all numbers. It is important to know when numbers have connections. An example is using ++++ and the ------- meaning positive and negative numbers. showing 5 using 11 means we have +++++ 5 positive and +-, +-,+-. These are called zero pairs. Zero pairs do not change the value of the problem we are just showing 5 while using 11. Each of the + and - is equal to one, we must count each one. It is like a bank account positives and negatives.
How to show with problems ? -4+3 what do we know? We know that there is 4 negatives, - - - - , and we are adding 3 positives, so we are trying to cancel out what we have which is + + + - - - they cancel out and we are left with -1.
Base Ten Blocks
What are they?
Base Ten blocks are 1 Log made up of 10 units.
Each Log is made by units that are equal to 1.
1 Log is equal to 10 units. That creates a base ten block.
Base Ten Examples
Place Value
Examples :
23
using our ten base blocks we know that 1 Log is ten units which would be 2 Logs equals 20. We still have 3 left which would convert to 3 units, the result is 2 Logs and 3 units.
174
This problem because more complex, but we already know 1 Log equal 10, we also know if we add 10 Logs gives us 100. Therefore, 1. We are now left with 74, the 7 turns to 7 Logs and finally 3 turns into 3 units.
Base in other bases
45 seven
What does this mean? Means we are in base seven. The logs will now be equal to 7. Now this will consists of 4 Logs of 7 which gives us the value of 28. We still have 5 which will we will add on to and our new value is 33.
27nine
We know that we are in base 9. Which means our Logs are equal to 9. We will need to convert 27 to base 9. 9+9 which gives us 18. We are left with 7 units, now we add our 9+9+7=25 that is our new result.
Understanding How
To Add and Subtract Alternative Algorithms
What are easy to add together?
Is there an easier way to add? Well in some cases
we have the numbers 33-12 we would have to manually figure this out. The numbers are not as easy when they come across in our heads. We could say we have 33 dollars but you decided to go to target and spend 12 dollars how much is there left. Using our base ten blocks we will have 3 logs and 2 units. Remember we spent 12 which we can convert it to 1 Log and two units. We will be left with 21 left over.
Trade offs
Trade offs are when we use "friendly numbers"
Friendly numbers are when we use the method trade off and make our numbers to a zero which makes them friendly.
37 + 88
1. What is the problem asking us to do.
2. How can we make this friendlier?
3.Well we can make the 88 to a 90 if we take 2 from the 37.
Our new problem is now
35+90
Now we just add and our result is 120.
Now we will focus on subtracting numbers
We know that trade offs work great for adding, now we want to know if it will work for subtraction.
Lets do 30-12
The old method would make us take away/barrow from our neighbor, but we no longer need to do that. Using our trade off method we will be able to figure out how to subtract these two digit numbers.
First the goal is to keep the 2nd digit number to end in a zero referred to as a friendly number.
Lets take make our 12 to equal 20. We must take away 8 from our 30.
30 will turn into a 22 and 12 to a 20.
New problem: 22-20
The result is now 2, by using friendly numbers.
Expanded Form
What is Expanded form?
Exapanded for is a different way of adding and making all our numbers into zeros.
325 + 297 + 145 = ?
expanded method
300+ 20 +5
200+ 90 +7
100+ 40+5 We did the numbers from up and down
Then you would add straight down
600 + 150 + 17
final result 767
Multiplication
Is there any difference when multipling?
There are many ways to indicate when two numbers
are being multiplied such as
3*2
3(2)
3x2
3 groups of 2
In many cases we are able to miss understand what the problem is asking such as the dot and be easily missed as a decimal.
Scratch Method
This method allows individuals to add
their numbers all the way up to 10. Then use the to turn into
1 Log, (remembering that 1 log is 10 units)
426 + 385 + 107
This method requires to it to be up and down
4 2 6
3 8 5
1 0 7
starting from the right side you will add the 6 + 5 which will turn into 1 log , then you would do the method again
Lattice
Lattice Addition
is based putting the numbers up and down
Order does not matter!
You are able to add the numbers in any order.
We would create a box under the line.
256 + 897
2 5 6
8 9 7
_____
The 6 + 7 would go in its own section box
along with the rest of them
after you would be able to add them wherever you want.
Benefits are that it is no messy and no carrying.