Reading and Building Equivalencies

Want to keep this for reference? Click here, I'll send this to you as a PDF.

We are still working our way through Gattegno Mathematics Textbook 1. We're on chapter 3, activities eight and nine which cover reading and building equivalencies. The gist of these two exercises is to have the student learn to read addition and subtraction statements, check those statements for accuracy by building them with the rods, and lastly, students will build patterns and create their own equivalencies based on what they can see in the rods. Reading math symbols and creating the patterns based on those symbols is the next step to fluency.

Reading The Symbols

The first activity in this section provides us with numerous math expressions related to addition and subtraction. Each expression contains 2 rods which are equal to a single rod. The student will be reading those expressions using the correct words for the signs.

After the student reads the equivalency, she is asked to build it to make sure the expression is correct.

The next group of exercises is addition-only activities containing more than one rod equal to a single rod. Again, the student must read the equivalency, build what the rods say and check for accuracy.

Building and Reading Original Patterns

As the final step in exercise eight, the student will make his own pattern or patterns and say (or write) whatever equivalencies he can see in the patterns.

Fluency with Variations of the Same Expression

The point of exercise nine is to make sure that students are flexible with math expressions.  While we can use the order of the variables and numbers to communicate certain ideas, most of the time it doesn't matter and math expressions can be written in various forms without changing the meaning. We know that r + w = g is the same as g = r + w is the same as w + r = g, g = w + r.  We want to make sure the student can express addition in all of these forms.

If you student is not writing, you have several options. The easiest is for the teacher/parent to take dictation for the student. The other option is to use cards or some other means that will allow the student work out the exercise without writing them down. I usually take dictation, but we've used the cards that you find in these images as well. You can download a copy of the cards here.

For awhile now, I've been telling people that I don't come up with math games to play anymore. For my 5-year-old the blocks and math are the game. I wasn't sure when this happened, I just knew it happened. It wasn't until writing this blog post that I realized when the transition came. For him, it was when he was fluent enough in mathematics that he was able to create his own patterns and make his own expressions based on his created work.

It's the creation of original math work that seems to motivate P. He is willing to make crazy long trains for the fun of it. He will dictate the expression if he does it. He likes to find an equivalent train to go with it. If I were to give him expressions of that sort to work, I don't think he would find near the joy in it. Beyond that, it is in this kind of play/work that he is figuring out how it all fits together. I am not in his head, so I don't know what kinds of ideas interest or puzzle him. If I pay attention to his math compositions, whether we document them or not, I can get a feel for what he is thinking about.

Creating original math work is one one of the things that appeals to me about Gattegno. His believes that children must do the hard work of learning and letting them be responsible for it, which means the teacher must learn to talk less. As soon as is reasonable, Gattegno has the students creating their math work, which will eventually lead to math compositions. This kind of engagement with the material is another reason that Gattegno's students were able to accomplish so much in a short amount of time.

If you missed it above, you can get the cards by clicking here.