Manipulatives for algebra - Victoria?

http://www.homespun4homeschoolers.com/index.htm

I ordered two videos and the CD Rom from this web site….I need something that he can see visually. Have not received it yet.

Lori

Obviously I’m not Victoria, but I thought I’d pass this along. Math-U-See has a nice set of fraction overlays that is used in their intermediate and advanced (pre-algebra) programs. They have some other manipulatives to use for algebra. I haven’t used them personally, but a friend has enjoyed the program, and I thought the fraction overlays were a neat idea. Their web site is http://www.mathusee.com.

Jean

Until victoria comes to the rescue you can check out the following:

On Cloud Nine Math by LMB uses manipulatives. The manual is really easy to follow as well. In regards to Algebra Hands on Equations uses manipulatives and has a video that teaches the students and the teacher at the same time.. Harry Borgeson is the one that makes Hands on Equations..

In the teachers supply stores you can get lots of manipulatives. There is one book I find that involves lots of games and hands on activities for $13.95. It is called the Middle School Mathematician…empowering students to achieve success in Algebra and Geometry by Terri Breeden and Kathryn Dillard and published by Incentive Publications.

The advice given by all the other friends you have on the board looks good.

If you have the money to spend on these books and programs, get the first book/video/whatever in a series that looks good to you, and investigate it. Don’t go by publishers’ or sellers’ marketing, but get the actual book.

First, read the first chapter of the book yourself and see if it seems reasonable to you. If it seems too complicated to you, look over the introductory material again, and if it still looks bad, send it back. (If at all possible buy from people who have return policies.) If it looks good to you, then have the tutor try it. More suggestions on tutoring below.

As well as the above suggestions, many good people on this board are very positive about Singapore Math. I have not worked with it, but it is said to have very good visual and concrete demonstrations, so would go well with a hands-on learner. The level you describe (OK multiplication, little division or fractions) is standard beginning Grade 5 in traditional math suystems, so would be 4 to 5 in Singapore.

What to do in tutoring: a tutor who knows no algebra at all is obviously at a disadvantage teaching it. If she knew something, I could suggest a lot of do-it-yourself approaches that are cheap and simple, and because they are simple, very effective. However if your tutor doesn’t know the scope and sequence, she will be uncertain where to go. She can still do a good job, but she will be better with the scaffolding of a good text or program.

The idea of fraction overlays is excellent; try to get them. Also, what you really need to do at your present stage is to get into graphing and number lines. These are concrete and visual ways of working with numbers, and since they are used and stressed all through algebra, they don’t seem too babyish.

Number lines, in the form of rulers with fractional parts, are excellent for doing concrete work with fractions. Some time ago I posted a very long outline of how to do this, and I’ll try to dig up a copy and re-post it.

Many teachers, themselves very verbal and trained verbally, tend to ignore the visual and concrete lessons in the pre-algebra and algebra texts and to jump straight to verbal rules and formulas. This is bad for *every* student, because visualization and concretizing numbers is important to doing math in the real world, and of course it is especially bad in your case. Try to sit down with the tutor and the book or books you decide to use for a scaffolding, and do just the opposite; pick out all the concrete and visual material in the lesson and the exercises, all the graphing, number lines to draw, paper folding to try, etc., and *do* it. In any decent text there is far more graphing than there is time to do in a regular class, and you will find lots of work.[if it isn’t a decent text, that’s another problem — I suggest used book stores, and texts pre-1955 are best although some post 1995 are coming back] Once the tutor sees what works, she should (hopefully) be able to get over her own verbal tendencies and continue on.

Speaking again of text or texts, it’s sometimes a good idea to work in parallel: half an hour on “review” in something like Singapore 4 or 5, and half an hour with a good Grade 8 or pre-algebra text. The two lines will reinforce each other, and the student sees real progress.

Your request is a little global, so the above is some global getting-started advice. Ask me again for more particulars. I’ll try to get the long fractions post back soon.

Oh Victoria! I’m so glad you’re here! I thought I had gotten the wrong place.
Your help is very much appreciated.
Sorry for being so general with my request for advice. But you hit the nail on the head and if you are able to locate the fraction info, I can use it.
I’ll get together with the tutor and see what’s what. I haven’t even met her yet. Today was her second day with him and he tells me she seemed to understand it a little better. He is only with her for 30 min.
Lori

>>Victoria said: “Number lines, in the form of rulers with fractional parts, are excellent for
doing concrete work with fractions. Some time ago I posted a very long
outline of how to do this, and I’ll try to dig up a copy and re-post it.”>>

I tried to look for the post you refer to - but came up with nothing.
Victoria…if you have the time (- :
it would be great to get this information about fractions and using rulers.
I am asking for a meeting with the tutor so I can finally get things organized with her. She has only been helping him with his daily homeowrk and I need to get her going on these other areas.
In the mean time, I’m going to tell her what you said and get the other materials you suggested.
Appreciate your help and advice.
SO much.
Lori

Nothing to do with math, just life; after two years, my divorce is final; I plan to return home to Montreal and went to look for a place to live but there is a huge housing shortage and we found nothing in a week there; my daughter’s boyfriend’s father is having marital troubles of his own and came to stay in the spare room here; he took my car apart for me and we lost another week trying to get the head gasket loose; meanwhile daughter’s boyfriend helped me get a laptop so I can stay online and tutor while in a peripatetic lifestyle, but he hasn’t yet helped me transfer the files — is that enough excuses? Haven’t forgotten you, honest!! Will get it reposted ASAP.

My daughter transferred all my files to the laptop today and took her computer back; I’m still not finding the long concrete treatment of fractions yet. I’ll look a bit more and write it up nagain if not found — email me if you see nothing in a week or so.

Victoria,
With all you’ve got going on, I really appreciate that
you are trying.
I managed to get a different tutor for my son and we are
trying to figure out how much time she should spend in
each session doing the homework from that days class and
how much time on other stuff - money skills, fractions
etc…
It is a 45 minute period, so I said 20 or so minutes
with class/home work, and the rest on filling in the
gaps. Essentially, splitting the class time in half.
They said the school has some manipulatives in the LD
resource room that can be used, but I’m willing to buy
some to add.
I am hoping the tutor will attend our IEP meeting on
Monday the 17th….any advice you can give me or
questions I should ask her ??
The Pre Algebra Teacher told me that they will be using
*some* manipulatives in class during the year….blocks
I think. He said that we can use things that are
pictured in the book, like the little bags with two
blocks etc. I asked him if the “Lab Gear” manipulatives
would work and he said not really. He said he will be
covering much of the basics all year such as fractions
etc - this class only prepares them for the Algebra
class.
So, that’s where I’m at and I really have no idea what
to ask this tutor or what to tell her she should use to
fill in the gaps with division, fractions, decimals and
even tricks on teaching him to count money back for
functional math skills. (I have shown him at home, but
he isn’t mastering it .)
Sorry for going on and on, just want you to know what
we’ve got to work with.
The schools’ Pre Algebra text book is called: Impact
Mathematics, Algebra and More for the Middle Grades,
Course 2, Everyday Learning Corporation, Developed by
Education Development Center Inc. Copywrite 2000 - “The
algebra content of this book was adapted from the
series, Access to Algebra, by Ian Lowe, Jayne Johnston,
Barry Kissane, Sue Willis and Neville Grace.”
(just in case you have an opinion about it)
Thanks so much,
Lori

It’s from 3-14-00. I just copied it here instead of trying to figure out how to link you to the post. Now I’m going to make another copy for my math notebook (I know it’s supposed to be in there, but I can’t find it- aargh!)

Jean

I’m doing my student teaching in an LD middle school classroom. I
: need to start a fractions unit with very low level student’s any
: ideas?Yes, be concrete, be real, be applied.But please — Beware the food approach: Allergies, sometimes deadly Diabetes, possibly deadly Religious deitary rules Cultural dietary rules Diets to reduce hyperactivity VegetarianismThere will be at least one kid, and usually two or three, in every class, for whom the food “treat” is big trouble and stress and possible illness and a situation of conflict between parental rules and teacher rules. Just not worth it. Yes, this applies to every food. I and my daughter cannot have chocolate or M&M’s or ice cream or cream-filled cake (four big teacher favourites) due to serious milk allergies. I can’t have pizza either (celiac disease). Peanut candies, and even food with peanut oil including maybe that pizza, could kill my landlord’s kid in five minutes. And my diabetic five-year-old student cannot anything at all not on her dietary balance plan (and she’s too young to figure out exchanges)and the sugary “treats” will send her to the hospital in a coma. And my vegetarian student’s family won’t thank you for any of these junk foods.Also, once you get the class to think that math will be rewarded with treats, be prepared to bribe them with treats forever after.OK, back to fractions. Start with dividing something into equal parts. Make sure they understand the parts have to be (as close as possible) exactly the same size. Pies are OK but get really hard to divide equally for numbers other than 2, 4, and 8. Better to use a bar 12 or 24 inches long (make bars out of construction paper)(or if you can get Cuisenaire rods, use all the parts that add up to 12, 12 ones, 6 twos, etc.) or for students on their paper, make dittos with bars 12 centimeters long. 12 and 24 divide easily. Show that 1/2 means 1 part out of 2 (equal), 1/3 means one part out of 3 (equal) etc. Also show the fractions on a standard measuring cup. Draw diagrams with a bunch of bars the same length and colour in 1/2 of first, 1/3 of second, etc. Compare and see that 1/3 is less than 1/2. Note the pattern that bigger number on the bottom means smaller unit fraction. Spend a couple of days on just this. Then introduce different numerators. Explain that we know the bottom number means how many equal parts in one bar; the top means how many of those parts to take. Draw diagrams of 1/4, 2/4, 3/4, 4/4. Note that 4/4 means 4 out of 4 so 4/4 must equal one whole bar. Do the same with other denominators. Again, a few days just on the meaning concept. Practice measuring fractions of a cup, fractions of a yard, fractions of an inch, just as we do in real life in cooking, sewing, and carpentry. Do fractions of a group: If there are 6 girls in the class and two of them hagve red sweaters, what fraction of the group is wearing red sweaters? (No simplifying yet) Draw dots and colour them in to represent the group anmd parts of the group, and draw loops around equal sub-groups. Introduce mixed numbers and measure them — how much is 2 1/2 cup? 1 2/3 yards? 4 3/8 inches? Draw and diagram and measure everything. Once we have a good idea what fractions are, introduce equivalent fractions meaning EXACTLY THE SAME SIZE. We measure and count up. We saw that 4/4 has to be 1. Now we see that 2/4 is the same as (in the sense of exactly the same size as) 1/2, 3/12 as 1/4, and so on.We can show this by drawing circles around equal-sized groups; we have 12 sections of 1/12 each in one unit; if we take a different colour and draw a box around every set of 3 of these, we get four equal groups, and 3e/12 colours exactly one of these four. NOTE THAT I HAVE NOT MENTIONED A SINGLE COMPUTATION SO FAR. Computation is the enemy of thinking in this area. Give a student a simple, short recipe, tell him to hurry up or he will be punished for not finishing the page, and he will use it in panic forever after whether or not the results are in any way meaningful or sensible. After the students are well aware of what fractions are and how to use them to measure and how two different ways of counting (lots of little pieces versus fewer bigger pieces) can get to the same measurement, *then* you can start introducing some computational rules. The system of multiply or divide top and bottom by the same thing can be made sensible by drawing pictures and splitting up parts or re-grouping, as above. By the way, if you want students to actually learn math, avoid computational shortcuts until the students have earned the right to use them by showing they understand what is going on. The usual system of simplifying by crossing out is a magical mystery trip to most kids, and this is the point where many develop a math phobia — they are told to do things that defy logic and common sense, so of course they resist. You’ll get far better results in the long run if you first have diagrams to show that 2/6 = 1/3, then show computationally that 2/6 divide by 2 BOTH top and bottom (2 divide by 2 over 6 divide by 2) comes out to 1/3. Addition/subtraction is best learned on some form of number line (large ruler, bar model). If you start with same denominator, such as 3/4 - 1/4, and point out that “fourths” is the name of the pieces, then you are just taking one piece away from three pieces, all the same size, so you have two pieces left. (Easy to illustrate this) When you get to different denominators, if you have been diagramming/modelling all along, it is easy to see that thirds and halves are different spieces, and to add them is to add apples and oranges. So you work out an “exchange” of both of them for an equal amount in sixths. Use similar “exchanges” to do improper fractions and mixed numbers; 2 = 8/4 (draw it and look at it; one whole bar is 4 parts so two make 8 parts) so 2 + 3/4 is 8/4 + 3/4 or 11/4. And the same in reverse, 11/4 = 8/4 + 3/4 = 2 + 3/4 = 2 3/4. Be warned: if you introduce the recipe computation of multiply this numner here by that number there and add on this one over here and shove it all on top of this other one down here, knowthat you will speed up your students’ computations for two or three days and then stall them out in confusion for a long time after that. To do this all properly will take months, don’t forget. Be patient with the students and yourself. For multiplication, if you get that far this year, use an area model; a mile by a mile makes a square mile. Cut in two equal parts one way for 1/2 and three equal parts on the other side for 1/3 or 2/3. Then it’s easy tio see that 1/2 of 1/3 is 1/6, and so on. For division, use the question “How many ___s in ___?” How many 1/3 cups in 1 cup? 3. So 1 divide by 1/3 = 3. How many 1/3 cups in 2 cups? 6, because 2 = 6/3. So 2 divide by 1/3 = 6. You can lead up to the “multiply by the reciprocal of the divisor” rule this way, but don’t rush it.I have an excellent old textbook that covers much of this, and will mail you photocopies if you are seriously interested. It costs money and time, so only if you really intend to use it, please; but if you do, just email and ask.

Lori,

Just thought I’d pass along some info about some of the commercial math manipulatives.

Hands On Equations that Pattim suggested is a neat program- my son used it last year (age 9) and it made perfect sense to him. He doesn’t have trouble with math, but he’s not a math whiz either, just an average kid. We stopped about halfway through when the program started working with negative numbers (I hadn’t introduced those yet). This program uses pawns to represent x or -x and red and green die to represent positive and negative numbers. By “balancing” the pieces on both sides of a scale (just a picture, not the real thing) kids learn to solve linear equations in a single variable.

There are various commercial manipulatives for algebra. “Lab Gear” by Henry Picciotto is one, “AlgeBlocks” and “Algebra Tiles” are two others I’ve heard of. They share a lot in common, but there are some differences that might be confusing if your son had to switch back and forth from class to tutor. Try to pin down the pre-algebra teacher to find out exactly what they are going to be using in class, then you can choose something compatible for the tutor to use. Of course, you can make similar materials from centimeter graph paper and scissors, but they don’t hold up as long as the plastic commercial ones.

Jean

Thanks for saving this — I feared I had lost all that typing.

www.borenson.com :)