Wednesday, October 19, 2016

Multiplication Area Model

We finally got to begin 2-digit by 2-digit multiplication this week! I began by reviewing with them the area model we used when multiplying by 1 digit. Then the kids self-discovered (with my prompting and questioning) that they could create an area model for 2x2 multiplication. They referred to it as the "double-decker couch." Ha! The kids are absolutely loving the 2x2 area model!! They love it because it's super easy. I love is because it shows them the place value involved in 2x2 multiplication. They can actually see the process of multiplying the ones and tens of one number by the ones and tens of the second number. When they finally move to vertical multiplication, they'll actually understand why it works! There's nothing better than actually understanding WHY you do something!!!

The area model can actually be formatted to fit more than 2x2 multiplication. We played around with differently-sized numbers and made our matrix box fit those problems as well.

Our class anchor chart
Close-up of the box itself

An example

Friday, October 14, 2016

Breaking Apart Multiplication

As we move to multiplying larger numbers, I like to guide them into the algorithm. We start by investigating the pattern when multiplying by multiples of 10. We look at the problems 2 x 3 = 6, 2 x 30 =60, and 2 x 300 = 600. We discuss what is the same/different about each problem, then we look at several other similar examples. Eventually the kids see the pattern of just "adding a zero" each time. Patterns are a great shortcut, but it's important the kids understand why they work.
Next we move to breaking apart larger multiplication problems, such as 18 x 5. We can break the 18 into 10 and 8 to help us multiply easier.

We practice this with many numbers, also looking at the array model for each. We slowly get to larger numbers like this one...
This will lead us into the multiplication algorithm next week.

Monday, October 10, 2016

Finding the Factors of 12

We begin our lesson on finding the factors of a number by making all the arrays we can think of for the number 12. The kids usually do a really good job finding them all. When I question if we've found them all, however, the kids start to second-guess themselves. This moves us into the discussion of what we're actually finding when we're making these arrays. I lead them to discover they're finding the factors (number that are multiplied to make a number) of 12.

But how can we keep our factors organized so we can make sure we've found all the factors? This leads us to making our T-Chart. We always start with 1 and the number itself. Then we move to the next number in the number line, 2. We know 2 is a factor because 12 is even, so we then find the partner for 2 which is 6. Then we move to 3, which has a partner of 4. The next number in the number line is 4, which we've already used, so we know we're done. Once numbers start to repeat, we've found all our factors. This lesson is followed by lots of practice finding the factors of many different numbers. As we're making our factor lists, we discuss the definition of prime, composite, and square numbers. 

Thursday, October 6, 2016

Elapsed Time

Elapsed time can be a challenge for kiddos because they like to try to find the difference between two times by lining them up vertically and subtracting for the difference. In a whole-group discussion, we talk about why this won't always work. Our number system is base-10, which means when we reach 10 in a place, we must move it over to the place to the left. For example, when we get 10 ones, we turn it into 1 ten. We also borrow in groups of ten. Time does not follow these rules, so we cannot always successfully borrow or carry vertically.

Monday, September 26, 2016

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! 

Friday, September 23, 2016

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!

Monday, September 19, 2016


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.