Introduction to Vertical Addition and Subtraction

When I introduce vertical addition and subtraction (done on different days because it's too much for one day!) I do it very concretely. We actually make the problem with base ten blocks and break apart our problem by place value. When we borrow a ten for the ones place, we actually take a rod out and replace it with ten units. Or when we carry a ten from the ones, we take ten units and turn them into a rod. It doesn't take long for the kids to understand why we're doing what we're doing. Soon we move to a written version with the place value broken apart. Finally, some students will move to the standard algorithm. They only make this move when they're successful with the broken-apart method. We continue practice with the vertical method until we've reached mastery. It's important to have these concepts mastered before we begin multiplication and addition! 

Tables and Measurement Conversions

This week we spent lots of time looking at sets of data in a table, and finding the relationship. It's often easy for students to find the pattern and fill in missing information. What can be difficult is trying to use number sentences to describe the pattern. Often our kids are shown a table, then given words that describe it to determine which descriptions are correct and which aren't. We spend time practicing actually plugging in the data to check the description.
This week your child was given a picture of a vehicle. They had to determine how many wheels the vehicle had, then create a table to prove how many of their vehicles were needed to reach 24 wheels. After we finished, we describe the table in many ways, then determined which of our descriptions were correct and which weren't.

Next we discussed how tables could help us with measurement conversions. The students figured out they are a great tool in keeping our conversion work organized!

Rounding

Rounding numbers is often taught in a very rule-based way, not conceptually.
"Just look at the next door neighbor and if it's 5 or higher, the number goes up. If it's 4 or less, the number goes down."
That probably sound really familiar to most adults. There are even a ton of cute sayings to help us remember this idea.
I like to focus on a couple of things when teaching rounding. Firstly, I ditch the phrase, "goes down" and replace it with "stays the same." The number in the position you're rounding never goes down. It either goes up or stays the same. This can be confusing for some. Secondly, and most importantly, we start rounding by placing numbers on a number line. This helps us determine if the number rounds up, or stays the same.
For example, if we're rounding 437,284 to the nearest hundred, we would make a number line. One end of the number line will be labeled with the hundred thousand the number is already in - 400,000. The high end of the number line will be labeled with the next hundred thousand - 500,000. Next we find the middle of the number line - 450,000. Finally we determine if the number falls to the left of 450,000 or to the right of 450,000. We do this by focusing on the ten thousands place (this is where the whole "look next door" idea originates.)

After we practiced this MANY times, rounding to MANY different places, we moved to the shortcut.

Relationship of Numbers in our Place Value System

One of the most important concepts a child can learn is number sense. This week we spent a lot of time investigating what happens as we move left or right in our number system, and comparing numbers in different places in our place value system. We related them to each other by describing their relationship. Using equations to describe the relationship is a pretty big concept for 4th graders to grasp. We spent lots of time writing equations to describe them. I tried to color code my journal examples so it makes sense.

Place Value, Expanded Form, and Number Line

This week has been all about place value. We started our discussion with the importance between the words "place" and "value". We practiced writing numbers in word and expanded form, and spent lots of time practicing saying numbers correctly. In 4th grade, the expanded form changes a bit so that we focus more on the multiplication involved. For example, 28,437 would look like (2 x 10,000) + (8 x 1,000) + (4 x 100) + (3 x 10) + (7 x 1). Today, we focused on putting these numbers on a number line and correctly identifying the intervals of the number lines.

Frequency Tables, Dot Plots, and Stem and Leaf Plots

This week we focused on ways to collect and organize data. We began by making frequency charts and dot plots, which aren't new for 4th graders. We simply reviewed their set-up and purpose. We then moved to stem and leaf plots. These are new for 4th graders, so we spent a whole math block just creating them with made-up data. The next day we brought in some already-made stem and leaf plots so that we could really evaluate them to determine what they represented.