Math Notebook and Compositions
This blog post we are covering keeping a math notebook and writing compositions by way of equivalent expressions. If you've managed to land on this page from some link on the internet, welcome. You will want to right click the book image to access a free copy of the textbook in another window, then come back and follow along. We're at the bottom of page 48, exercise 42.
You can find my entire series on Gattegno's Mathematics Textbook 1 here.
Multiple Operations at Once
Before we touch on compositions, I want to briefly talk a bit about exercises 42 and 43. Just as Gattegno has done in the past, he combines the operations we've been working on together in one statement. You may think your students cannot do this, but if you've been following Gattegno this whole time, there is no reason a child in k/1 can't work these out mentally.
P. worked through these in his head and asked for harder problems. What is 2/3 of (4-1)? Easy peasy.
What is two halves of two plus three quarters of four? That was a bit harder for P. it took him about 2 seconds and then he had his answer.
What if the student isn't able to come up with an answer? Then that probably means you didn't spend enough time on the previous work. Unless, of course, your student is refusing to answer, which may mean the student is bored. In that case, provide some problems with higher numbers to increase difficulty. Best bet, put it away for today and come back at it tomorrow.
If the student is still having trouble, back up a bit. Work on the fractions. If that doesn't seem to be an issue, spend some time working on mental math. But start with easier problems and work your way up. Mental math is a skill that takes time. Students need time to take the language of the operations and move it from short-term memory to long-term memory.
Exercise 43 is the same as 42 but instead of two operations done verbally, there are three operations and they are written symbolically. I usually write these expressions on a personal white board for P. to solve. We want the students to understand oral and written math expressions and we want them to be able to write math expressions. The students need practice at all forms of communication.
Math Notebook and Compositions
In exercise 44, Gattegno states several different ways we can write the number one. We can write it as: 1, 3 - 2, 5 - 4, 1/2(2), and so on. He calls these other ways to write one equivalent expressions. 3 minus 2 doesn't make 1 it IS one. It is another way to write 1. Another way to say that is 3 - 2 = 1. The equal there doesn't mean 'write the answer here' or 'magically becomes'. 3 - 2 is the same as, is equivalent, IS 1.
Equivalent expressions will form the foundation of your student's exploration in their math notebook. An example from P.'s notebook for the number 2. We call these math compositions. If you are familiar with Charlotte Mason, then you are already familiar with the concept behind the composition.
We can determine what a child understands about math based on how well they can generate math on their own, not from what blanks they can fill in or how they answer multiple choice questions. I can tell by P.'s compositions how much of a grasp he has on the material we are working with. If he uses fractions easily, I know he has them down. If he isn't using them, I know he isn't comfortable and we should do more work with fractions.
P.'s big sticking point is subtraction. He can do it, but for him it's work. So, I require that the provide some subtraction in his compositions. He usually gives me a string of subtraction expressions in a systematic way.
How To Keep A Math Notebook
First, let's distinguish between an interactive math notebook and a math notebook or journal.
Interactive math notebooks are all the rage right now. If you are familiar with homeschool notebooking, then you will find the same kinds of elements in interactive math notebooking. I don't think an interactive math notebook is the best way to document your child's math journey. We keep games and activities in our interactive notebook that P. can do when he is bored or when I am busy. We think of that notebook as a giant task card. Most of the things in our interactive notebook came from Lacy at Play, Discover, Learn's TpT Store. She made the task cards to go with Module 1 of the Hands-on Learning with Gattegno manual.
When we do compositions we keep them in the graph paper composition notebook that from the stuff-mart for $1.29. The graph paper allows us to recreate 2 dimensional Cuisenaire Rod structures easily and to scale. It also helps me write in a straight line.
What Goes Into The Math Notebook?
The nice thing about notebooking any subject is that you have an on-going written record of your student's learning. Math notebooks are the same. Here's what we keep in ours:
- Starting Points: Starting Points are open ended problems, that I created, that give P. the opportunity to make observations and create questions. Questions are either based on constraints that I give him or whatever he feels like creating, and sometimes we stop at observation s.
- Rod Structure Studies
How Much Should My Student Write?
When a child is first starting compositions or a structure study, a line or two is sufficient. Ideally, we want the student writing in their math notebook without looking at the rods. We don't stick to that when we are studying a rod structure, but I do when we write compositions.
In the beginning, a line or two was about all I would get. We are well into 2nd year with Gattegno and I expect more. P. is still an emerging writer, therefore I am still writing for him. Often, the amount we write has much to do with how much I want to write for him. He is always free to add more verbally than I will write, and he often does.
This post concludes our study of the section on the number 5 from Gattegno's Mathematics Textbook 1. In the next post, we begin the study of the number 6. The rest of this chapter goes very quickly as the foundation has already been laid.
Housekeeping . . .
If you are interested in learning more about teaching math with Cuisenaire Rods, hang around a bit and look through this site. Get Gattegno's Textbook online, it's free. And you might want the Module 1 of my teacher's manual to go with it. You can get that here. The Resources section is chock full of stuff - most of it free.
You can also join us in our Facebook Group for base-ten block users. We're a motley crew of teachers, parents and tutors who are learning to use base-ten blocks to teach math. Some of us know what we're doing. Most of us don't. We never bite. And we're always helpful.