Beginning of Unit One:

The Number System and Addition

Number System

We are working with place value and being able to think flexibly with numbers. In fourth grade, we will be looking at numbers all the way to the hundred millions place value. There are many different ways to show a number.

  • 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 is a great way to build flexibility with numbers. We will be estimating before solving almost every problem and students will be expected to estimate throughout the year. Estimation is not just rounding. There are different ways to estimate.

  • 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

Adding by Place

Students separate numbers into place values and then add each section together. This strategy allows students to visualize the value of the numbers, instead of just the digits.

U.S. Standard Algorithm - Addition

This is the traditional way we see addition. Stack up the numbers and make sure place values are lined up. Regroup if necessary.

Breaking One Number Apart

Start at with one number (typically the largest one) and add on. Break up the second number into easier, more manageable pieces. Students can break up the number in a way that works for them. Different students may break up the number differently.

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

Thinking Blocks is a great resource for practicing word problems as well as strip diagrams (which we will be learning about soon). It is available as an app and as an online website.



**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:

**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?

I love family game nights so here's a game you can play with a deck of playing cards.


  • 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

My name is Maggie Nelson and this is my 2nd year teaching 4th grade Math at Sheffield. I hope this helps fill you in on some of the strategies we are practicing in class. Please let me know if you have any questions, comments, or concerns. Feel free to message me on ClassDojo. ClassDojo has just added a "Class Story" section which I am taking advantage of to upload some of our anchor charts detailing strategies as well.

I look forward to a great year!