# Beginning of Unit One:

### The Number System and Addition

## Number System

**Standard form:**using numbers/digits*(521,708)***Word form (written form):**the way we say a number or write it using words*(five hundred twenty one thousand, seven hundred eight)***Expanded form:**breaking apart the number by place value*(500,000 + 20,000 + 1,000 + 700 + 8)***Expanded notation:**multiplying the digit and the place value and then adding each part together*[ (5 x 100,000) + (2 x 10,000) + (1 x 1,000) + (7 x 100) + (8 x 1) ]*

## Estimation

**Front-End Estimating**- we only look at the highest place value (3,223 + 779 goes to 3,000+200 = 3,200); not the closest estimate, but very fast in a pinch.**Rounding-**change the number to a "friendly" number--something easy for you to use (3,223 + 779 could round to 3,200+800= 4,000 or 3,220+780 = 4,000 or 3,225+800= 4,025, etc)**Compatible Numbers**- When I'm estimating an equation, I might see numbers that go well together. I can estimate those so that they fit together and make my problem easier. (ex: 3,723 + 279 .... I know 7+3=10 so 700+300 would equal 1,000. So I can just add that to 3,000 and get 4,000 as my estimate).

## Addition Strategies

## Breaking One Number Apart

Some prefer to use a number line model to visualize this strategy, but it can be done with simple equations as well.

## Changing a Number to Make an Easier Problem

These strategies may be a bit more challenging. Students who prefer mental math and feel comfortable manipulating numbers may find these strategies helpful shortcuts. Other students may not be ready to adopt them just yet.

**Creating an Equivalent Problem**

"Equivalent" reminds us that our problem needs to stay equal and balanced. Whatever I do to one addend, I need to do the equal, but opposite thing to the other number.

*Ex: 428 + 394 = _____*

*I see that 428 is almost 430. So I may want to take 2 ones from 394 and move it to 428. Since I'm adding 2 to 428, I need to take away 2 from 394. My new equation would be 430 + 392. This is more manageable for me to do mentally. 430 + 392 = 822. *

**Changing to a Landmark**

Here we start out similar to estimating, but in the end we want an exact answer. We want to find friendly numbers (landmark numbers) that are easy to work with. We change our number(s) to a landmark number and then after we solve it, we "undo" it by taking back whatever we added or took so that our answer is exact.

*Ex: 629 + 307 = ______*

*Since 629 is only 1 away from 630, I can add 1 to it. 307 is only 3 away, so I'll add 3 to 307. My new easier equation would be 630 + 310. That is an easier problem to do mentally. 630+310=940. But since I added 1 and 3 earlier, I must now "undo" what I did and do the opposite, which is subtracting. 940-1-3=936. *

*OR, I may find.... *

*Ex: 434 + 225 = _______*

*If I find 430 to be a friendlier number, I may want to take 4 away from 434. 430+225=655. Since I took away earlier, now I need to add it back. 655+4=659. *

## Game Time!

## Thinking Blocks

App: https://itunes.apple.com/us/app/thinking-blocks-addition/id668450919?mt=8

Website: http://thinkingblocks.com

****While this game is free at the time of this newsletter, please always make sure to check before purchasing. Also, be wary of in-app purchases or ads that many apps may have.*****

## Sushi Monster

One app that makes learning fun is Sushi Monster! This game requires kids to build equations to equal a number. Currently, it is available from the iTunes store. You may search "Sushi Monster" in iTunes or click the following link: https://itunes.apple.com/us/app/sushi-monster/id512651258?mt=8#

****While this game is free at the time of this newsletter, please always make sure to check before purchasing. Also, be wary of in-app purchases or ads that many apps may have.*****

## Have a deck of cards?

Materials:

- deck of playing cards
- paper
- pencils (or markers!)
- tape
- place markers (can be coins, beans, small pieces of paper, or old game tokens)

The link below will explain how to set up a thermometer board (or number line) and how to set up your deck of cards. Start everybody's token at 37 degrees Celsius (body temperature) on the "thermometer". Take turns drawing cards. If you draw red, you must subtract that many. If you draw black, you must add that many. If you reach zero degrees, you're out. The first to 100 degrees wins!

## Meet the Teacher

I look forward to a great year!