Last year, that is, back in the 2011-2012 school year, my building principal became aware of the lack of fluency in fundamental math facts throughout our building. We began a school-wide initiative to emphasise these facts. For the students in the primary grades, they focused on the addition facts. In the intermediate grades, we placed emphasis on multiplication facts.
Throughout the year and then on into this year, the emphasis has continued. From the first week of school, we have been practicing these facts. Whether we are rolling 12-sided dice to generate facts, playing “around-the-world,” taking quizzes online, taking timed tests, and just practicing when there is a spare moment or two, my students have been working on mastering these 144 basic facts. (169 if we include the zeros.)
And it has all been leading up to this.
Multiplying a multi-digit whole number by another multi-digit whole number. We started with the multi-digit by one digit problems last week. Then we started in on two-digit by two-digit yesterday. Today was originally going to be a continuation of this process but, as so very often happens in teaching, the students’ own queries moved us ahead.
It started when I gave this problem: If the 26 students in our classroom each read for 45 minutes each night, how many minutes would they read in one week? First we multiplied 26 by 45 and got 1,170. Then we multiplied that by 7 and got 8,190. Someone wanted to know how many minutes they would read in a month. Each month has an average of 4.2 weeks, so we multiplied 8,190 by 4.2 and got a product of 34,398. Pretty impressive, right?
Then someone in the class wanted to know how many minutes we’d get if they each read for an hour! So I cleared the whiteboard and we started again: 26 x 60 x 7 x 4.2. Of course, we did it step by step:
26 x 60 = 1,560
1,560 x 7 = 10,920
10,920 x 4.2 = 45,864
I paused in the middle of the calculations to point out that I didn’t want them to freak out when they saw a decimal point in the problem. Then someone expressed that these problems were difficult and confusing because the numbers were so big. I put the kibosh on that right away!
I reminded the students that all we were doing was single-digit multiplication over and over and over again. And then I pointed out that we have been practicing these facts since the beginning of the year and they are all doing a great job with them!
Yes, multi-digit multiplication requires remembering where to write the products of all the single-digit problems, but beyond that, it is something they are all exceptionally skilled at doing. Once I finished pointing this out, it seemed like the entire room changed. Instead of complaining that the problems were hard, they started asking for harder problems!
After finishing our practice, I gave the class fifteen minutes to partner up and come up with as many two-digit by two-digit multiplication problems based on situations in our classroom. For example, one of my bookshelves contains 21 compartments and each compartments holds on average 16 books. By multiplying, we know that my shelf holds approximately 336 books. I was expecting the students to come up with maybe a dozen, tops. Several found at least a dozen; a few found considerably more! It was awesome, especially because they then solved the problems they had identified, giving them a sense of the usefulness of what we have been doing.
What a wonderful way to wrap up another short week in fourth grade!
Fourth grade is difficult year. There are dozens and dozens of standards for mathematics, English/language arts, social studies, science, physical education, health, social/emotional learning, and fine arts. When I contemplate all of these standards, I often think about ways I can make them more interesting and relevant to my students. I love it when I come up with an idea completely out of the blue!
That happened this morning while I was getting ready for work. One of the standards for my students states that they will be able to discuss the differences between prose, poetry, and drama. We have been reading and discussing prose all year long, will be doing a unit on poetry next week, and started a unit on drama yesterday. The idea I got this morning was simple: the best way for my students to learn about the distinctive aspects of dramatic storytelling is by creating their own dramatic stories.
I decided to utilise my reading groups this afternoon to start this process. The students are writing brief plays based on one or two scenes from the books they are reading for their groups. It took a few minutes for them to settle into the process and start working together, but once they did, they really got into the task! They were discussing characters, setting, lines, dialogue, and even assigned roles. It was awesome! I am excited to see what comes of this project. The goal is for them to finish by next Tuesday so that they can share their plays with their reading buddies in first grade. We’ll see how it goes!
Of all the things I have written about on my blogs since I first started recording my adventures, the one topic that has received the single most search queries has been ISAT test prep. (The second most common topic is my review of Gloria Ladson-Billings’ book The Dreamkeepers.)
I find this rather amusing, since I try not to place too much emphasis on preparing for the Illinois Standard Achievement Test. It is a series of high-stakes test administered during the third quarter, and the results are taken very seriously as the higher levels of our public education system. But at the lowest level, that is, at the classroom level? Well, yes and no. I take the test results seriously, but since they don’t get released until the summer, and parents don’t get to see them until the next school year starts, the tests don’t do much to help me guide my instruction. And if I am not guiding instruction based on the assessment itself, I am going to focus on more important data, such as my formative assessments and benchmarks.
All that being said, I do see the value in state-wide standardized testing and I don’t want any of my students to shrug them off as unimportant. Just because I feel something else is more important does not mean that I don’t think that the tests have no value. They do. And so I want my students to be able to perform at their best.
We all behave differently in different situations. It is appropriate to do so. When I am at home watching a movie with my friends, my behaviour is different than when I am at school working with a reading group. The way our kindergarten teachers talk to their students is very different from the way they talk to our principal! And the way we take a test in my classroom, often short, open response tests that students have as much time as needed to take, is different from the more strictly controlled series of tests we are going to take before Spring Break.
Which is why we have started our ISAT test prep today. It isn’t because I don’t think my students will be prepared for the content. I believe they will be. It isn’t because I think they need to be taught “to the test.” My regular teaching already does that. It is because the ISAT test is nothing like we do in my classroom. Three 45-minute sessions with a 10-minute buffer for those still working, with a combination of multiple choice, short response, and extended response questions for reading, the same for math, and two for science, for a total of eight tests to be administered over the course of four days. Our test prep is beautifully simple: we will read short passages and examine the format of the questions. The students practice responding and learn strategies for communicating with the test graders in a way that is both effective and appropriate. I often see this picture floating around on social networking sites:
(There is a quote related to this that is often attributed to Albert Einstein, but my brief online research has indicated that the attribution is dubious.)
I want all of my students to be able to climb the tree. That means they need to be taught how to do so. The only way it can be fair to administer the same test to every student is to teach every student how to take the test. So we will be doing ISAT test prep in my classroom over the next few weeks. It won’t dominate what we do, and it won’t be a high-pressure event. But my students will know what is expected on the test and how best to respond in a way that will convey their understanding of the questions given them!
After spending several days looking at multi-digit multiplication problems that were purely numberic, such as 358 x 9, we started working on some math word problems today. The problems involved multiplication, but I’ve found that it is always a challenge for students to read a problem, unravel the information, and then solve the problem.
The first problems we looked at today dealt with the kind that provide far too much information. For example, I gave the students this problem:
There are 275 students in our elementary school. We are going to have a school family movie night to help raise money for new interactive whiteboards. Each person who attends will be asked to make suggested donation of $4.00. If 337 people attend the two-hour movie and each person gets two bags of popcorn, how much money will be raised?
One student thought you would solve by multiplying 275 by 4, and someone else said we needed to know how much the popcorn cost. We were able to determine, though, that the real problem was the number of attendees (337) times the cost per person ($4.00). All of the other information is just extra. (I used this example because one, it involves a situation that the students could identify with and two, we are going to have a family move night in a few weeks. However, I don’t know what the suggested donation amount actually is.)
Then we looked at the problem that don’t give enough information. The example I gave also used our own school:
There are 275 students in our school. For the Wiley Walk-a-thon, each student was able to find a business sponsor who agreed to donate $2.00 for every lap. How much money was raised?
Most of the students easily figured out that they needed to know how many laps each student walked to solve this. But one student said, “Can’t we just assume each student walked one lap?” I complimented his creative approach, but made sure he knew that you can just fill in the gaps if they aren’t there.
We will continue with word problems on Monday when we start tackling multi-step problems. While our math curriculum only gives one lesson on this topic, I plan on spending a few days on them, as they are a fairly big focus of the Common Core State Standards and, as mentioned before, fourth graders tend to struggle with unraveling word problems anyway, and I want my students to be able to do more than just compute; I want them to think!