Week Three Blog

Adding and Subtracting Integers Using a Number Line

First we learned that -8 - 7 = -8 + -7  -if you switch the sign from a subtraction to an addition problem, then you must change the sign of the second number from a positive number to a negative number.




if the problem is -3+4 you start at zero move to the left 3 so you are into the negatives then when adding 4 you go up 4 to the right and see where that puts you. Which is at 1.

• If you are doing a subtraction problem on a number line you place the two numbers in their correct place and starting from the second number draw an arrow towards the first number. Find the distance between the two and that is the answer, if the arrow is pointing towards the right its a positive number and if the arrow is pointing to the left it's a negative number.

Multiplication on a number line

5 x 2

showing five times two on a number line means there are five hops of two. When you write this out you can see that the answer is 10.

if the problem is -5 X 2 then you still do 5 hops of two except you make the hops on the negative side of the number line but hte arrow points to the right.

If it is 5 x -2 it's the same thing as the problem explained above but the arrow points to the left.

Multiplication using Chips

3 x -2 =?    This means three sets of negative two

= -6

-2 x 3

If you have 6 positive and 6 negative chips you are then able to take out two groups of 3. the answer is then -6

The same thing occurs when the problem is -2 x -3 =? you have six positive and six negative chips and then take out two groups of -3 and the answer is positive 6.




                     

 

Week two of Multiplication and Division

Multiplication and Division

This week we focused more on division. We were given the following problem: A middle school will hold 609 students. Each class will have 29 students, how many classrooms will the school have?

I started with

290 Students                                580 Students                        29 Students
in 10 Classrooms         X 2          in 20 Classrooms      +            1 classroom      =   21 Classrooms

Then I thought about the way I did this and realized this is very similar to a Ratio Table.

1             10           20           21
-------/-----------/-----------/------------
29          290        580         609


We then learned about PARTIAL QUOTIENTS



If you start with the problem 384/3 you think what can I multiply by 3 that will go into 384. If you do 100x3 you get 300. Subtract that from 384. Then see what will go into 84. If you multiply 3x10 you get 30 and subtract that from 84 and get 54. Then subtract another 30 and put 10 on the side because that is what you multiply 3 by. You are left over with 24 and 3 goes into 24 8 times so you put that on the side too .You then add all the side numbers up and get 128 and that is your answer.

AREA MODEL-DIVISION

Finally we learned about NUMBER BONDS- DIVISION
You can decompose the number to make it friendlier to divide.

4816/4  -break up 4816 to make it easier to divide into 4

4000+800+16 /4 - You divide 4 into each number

1000+200+4=1,204

2642 / 3 -when the numbers aren't so friendly you have to see what 3 goes into that is close to 2642

2400+240+2 / 3  -Now divide 3 into each number

800+80 R2
=880 R 2

Week 1 Post

Multiplication and Division

When we first walked into class we were given two problems to write a story problems on. One was a multiplication problem the other a division problem. Like everyone else I wrote my story problem based on Repeated Addition. This is the most common way to write story problems.

Repeated Addition

Ryan has four plates of cookies with seven cookies on each plate. How many cookies does he have all together?

This is called repeated addition because you are basically adding up each plate four times. This isn't a very effective way to teach kids how to multiply because they are still stuck adding things.


Array/Area

In a classroom there are desks lined up in 4 rows with 7 desks in each row. How many desks total?


This is an easier way to solve because kids are able to break this problem up easier and use their derived facts.

A trick that I learned this week was breaking up a multiplication problem that deals with doubles.

ex) 4 x 36= ?
      2 x 36=72
      72 x 2= 144
      72 x 2= 4 x 36

Properties of Multiplication

 The properties of addition are the same ones we use for multiplication.

Commutative Property

A x B=B x A

Associative Property

(A x B) x C= A x (B x C)

Identity Property- This means how does the number keep its identity

A x 1= A

Distributive Property

 A x (B+C)= (A x B) + (A x C)

You carry  A into the parenthesis and multiply it both by B and C, then add the two together.

Learning these facts about multiplication really helps in the overall understanding of how to teach it. Also learning different ways to solve a problem helps us get a grasp of what our students thought process might be.

Repeated Subtraction
Megan has $48. She wants to give $6 to needy kids for school supplies. How many kids can she give money to?

-This is repeated subtraction because everytime you give a kid $6 you just subtract it from the starting total until you get to zero.

Partition
Megan has $48. She wants to give an equal amout to 6 kids. How much can she give each kid?

-This is harder for kids to understand because you don't know how much to give each kid from the start.

Partial Products

  17
x 14
--------
28 ______4x7
40_______4x10
70_______7x10
100______10x10
+--------------------
238

-You multiply each number once, and the numbers that you find are the same numbers that appear in the area model that I talked about above.
 Ratio Table