It’s not often that Otter asks to do MORE math. However, after incorporating some recent hands-on pre-algebra activities into our summer studies, I’ve been hearing that quite a bit!
Transitioning from concrete math to the abstract can be a little tough for some kids. It doesn’t have to be though! Below are some of the resources I’ve used to help make pre-algebra not only tangible, but also fun.
Learning about integers while playing a game!
Exploring Algebra and Pre-Algebra with Manipulatives is one of Otter’s summer favorites. Chock full of lots of activities, this book even comes with tear-out tiles you can use for some of the games. You do need to copy some of the pages though for things like the algebra dominoes, game boards, and activity sheets.
Otter was having trouble solving equations like “40 – 2X = 6”. Looking at rows of problems like that in his math text just made his eyes glaze over. After playing a game with some math dominoes, he was solving these types of problems like a pro and then asking if he could do MORE. After I picked my jaw up off the floor we played for about an additional 45 minutes or so.
Matching up math domino cards with mom
Learning about integers the easy way
Playing a game with mom to learn about positive and negative integers
Another big hit is The Hands-On Equations Learning System. I honestly think this is Otter’s favorite math “program” he’s ever used. Every time I pull it out he’s enthusiastic and his math confidence soars.
Basically the program takes something that is usually thought of as abstract and makes it totally concrete, helping to lay a terrific foundation for algebra. I really wish I had had access to something like this when I was a kid.
UPDATE: You can now get the Hands-On Equations Learning System via a set of apps and save a TON of money:
Hands-On Equations 1
Hands-On Equations 2
Hands-On Equations 3
Learning how to solve a linear equation
Hands-on Equations is so easy to use and understand. In the above picture, Otter is solving the equation 5X – 3X + 2 = X + 5. In this particular lesson he is learning to take away pawns as part of the set-up process. So, the first thing he needs to do is get rid of 3 pawns from the left (that’s the 5X – 3X part). Once he’s done that, he has things set up and is ready to solve the equation.
The next thing he would do is subtract one blue pawn from each side (because it’s a balance whatever you do to one side you must do to the other!). Finally, he would subtract 2 from both sides (get rid of the red 2 cube and replace the 5 cube with a 3) and come up with the final answer of X=3.
Afterwards he has to check his work. He checks it by looking at the original physical setup, NOT the original abstract equation. This way he understands the concrete meaning of the abstract equation.
The program comes with 3 levels of books and each step is spelled out visually to help you easily teach each concept. There is also the option to purchase DVDs, but the books were enough guidance for me.
I also order the Verbal Problems book that goes with the program. Using this book, he’ll be able to solve problems like the following by using hands-on methods that really help make the meaning and problem solving clear:
Dave had one package of cookies in his bag. Ed received 4 cookies from a friend on the bus to add to the 2 packages that his mother had packed for him. Andy did not eat breakfast that morning, so he had already eaten 2 cookies from his one package of cookies. Each package of cookies had the same number of cookies at the start. When the boys were ready to eat the cookies, they counted a total of 10 cookies. How many cookies were originally in each package?
You can purchase Hands-on Equations from Amazon or Rainbow Resource for around 35.00. It’s one of the best supplementary math purchases I’ve made.
Another hands-on pre-algebra resource I bought is ETA’s Hands-On Standards Math Online for grades 7-8. You can order physical copies, but I found it easier to use the online version which is basically PDFs you can print out as needed.
“Home” screen for ETA’s Hands-On Standards Math Online
Each lesson has full-color lesson pages as well as black and white student pages to print out and work on. You can look at some of the sample lessons online for free. The only downside to the program is that you have to purchase a lot of manipulatives. Fortunately I already had some of the required items, but I had to search all over the ETA website for the rest of the ones I needed and the cost added up pretty quickly (over $100 bucks for the program and the manipulatives!). I also had to put in a special request for a single order of some algebra manipulatives as they only had a classroom sized set listed on the website. Because of this, I would recommend the other two previous resources, if you are looking for something that is inexpensive, quick and easy to implement your math studies. However, if you really need more, the ETA program is well put together with lots of different “things” to play with while you are learning math that help keep the interest level high.
ETA Hands-On Math: Using fraction towers to find percents
ETA Hands-On Math: Using fraction circles to figure out decimals and percents
ETA Hands-On Math: Figuring out decimals, fractions and percents using colored square tiles.
Just because you’ve got a middle schooler or a high schooler doesn’t mean you have to stop using manipulatives! In fact, for some kids (like Otter), they really help foster a true understanding of higher level math. Pre-algebra doesn’t have to be boring and it doesn’t have to be hard!