what pre-algebra for this kid?

[silver]

My upcoming 6th grader has finished Beast Academy back in December. We moved onto AoPS Pre-A, and she hates it (we got about halfway through chapter 5 before deciding it was a bad fit). We've tried a little bit of Singapore Dimensions 6A (just the textbook). The more interesting problems have not been doable, because we didn't do any Singapore math before this, so we don't know how to use bar diagrams to solve some of the trickier problems. This is especially noticeable in the fractions chapter.

She's good at math, but she doesn't like it. Rote problems bore her; she much prefers puzzles over doing the same sort of procedural problem over and over. Any ideas for an interesting pre-algebra for this kid? 

[EmilyGF]

Hi Silver,

I talked about the math book I'm using with DD11 called Algebra: Themes, Tools, Concepts that I like in this thread 

One plus is that you can access the whole book and teacher book online to check it out. The problems are definitely not rote and there are plenty of puzzles. The first 4 chapters are pre-algebra.

Emily

[silver]

2 hours ago, square_25 said:

 

Did she enjoy Beast Academy? What was a bad fit about AoPS Pre-A? 

She enjoyed the fact that there were puzzle problems in BA. The word problems and the more rote problems she disliked. But the ones that were maze like or other similar puzzles, she enjoyed. 

I'm not sure what made AoPS Pre-A such a bad fit, but I think it was that a lot of the problems were hard just for the sake of hard and there were no puzzles. There aren't very many straight out rote problems, but she didn't enjoy the ones that required her to see some special insight or that took a long time to solve.

[silver]

Does MEP 7-9 have as many puzzle type problems as levels 1-6? If so, what years would be a good pre-algebra equivalent?

In doing searches on the forum, I found the Russian Mathematics 6 book by Nurk mentioned as a good pre-algebra. But I also saw mention that it may not be available anymore. Has anyone had success in purchasing that recently? Did the answer key ever get completed?

[silver]

1 hour ago, HeighHo said:

Grab the Dolciani Pre Algebra: An Accelerated Course textbook.  Have her do the B problems and attempt C. This will painlessly get her word problem where they need to be. 

In the meantime, have you considered having her understand the bar diagrams?  They are handy and a powerful tool for mental math....you can go to mathplayground.com's Thinking Blocks section and find all the tutorials and the puzzles to practice with. 

 

She can do the basic bar diagrams, as they're similar enough to cuisenaire rods, which she's used. She can even muddle her way through slightly more complicated ones. But the book has some where it's not clear how to even set it up.

Here's an example of one she couldn't do:

Quote

David bought some canned drinks. 2/5 of them were cherry soda and 1/4 of them were root beer. The remaining 28 cans were fruit juice. How many more cans of cherry soda than root beer did he buy?

She was able to solve it by using equations and variables, but had no clue how to even begin for the bar diagram.  

[mathmarm]

1 hour ago, silver said:

She can do the basic bar diagrams, as they're similar enough to cuisenaire rods, which she's used. She can even muddle her way through slightly more complicated ones. But the book has some where it's not clear how to even set it up.

Here's an example of one she couldn't do:

She was able to solve it by using equations and variables, but had no clue how to even begin for the bar diagram.  

Process Skills in Problem Solving (aka FAN-Math) is a supplemental book that teaches how to use bar models to represent the scenarios in word problems.

Level 4 is the book that introduces Fractions. If she can do the basic bar models, then she could jump right in at level 4.

However, since she is able to solve problems easily with variables and properties, you will have to make a judgement call if she even needs to learn how to model with bars.

[forty-two]

46 minutes ago, silver said:

She can do the basic bar diagrams, as they're similar enough to cuisenaire rods, which she's used. She can even muddle her way through slightly more complicated ones. But the book has some where it's not clear how to even set it up.

Here's an example of one she couldn't do: David bought some canned drinks. 2/5 of them were cherry soda and 1/4 of them were root beer. The remaining 28 cans were fruit juice. How many more cans of cherry soda than root beer did he buy?

She was able to solve it by using equations and variables, but had no clue how to even begin for the bar diagram.  

It's a basic part-whole diagram, but what makes it hard is dealing with the fractions of differing denominators - figuring out how to draw it without basically solving it first to be able to accurately draw it.  You can first find your LCM and make 2/5 and 1/4 into equivalent fractions (8/20 and 5/20), and then you'd know just how to draw everything. 

But you don't have to.  The way I deal with the practical issue of drawing unlike fractions accurately but without making equivalent fractions first is to:
*draw my bar,
*draw lines for fifths on the top and mark the 2/5 cherry soda on one end,
*draw lines for fourths on the bottom and mark the 1/4 root beer on the other end, and
*mark what's left in the middle as the 28 cans. 

It would look like this:

Then the equation set-up is pretty straightforward:
1 - 2/5 - 1/4 = 7/20 (fraction that are juice cans);
7/20 of the total cans = 28 cans, so total cans = 80 cans;
2/5 of the total cans = 32 cans (of cherry soda);
1/4 of the total cans = 20 cans (of root beer);
32 cans (cherry soda) - 20 cans (root beer) = 12 more cherry sodas

~*~

That said, if she is capable of reliably setting up and solving problems with variables and equations, and you both otherwise like SM7 - is there any reason she can't just do the SM problems that way instead of doing bar diagrams?  I mean, I do like bar diagrams for helping to see what's going on, but they are just one tool among many.

~*~

FWIW, I'm finishing up Dolciani Pre-Alg with my oldest and I do like it.

[forty-two]

I will say, if you understand the problem and can solve it another way, it *is* a fun puzzle to then try to figure out how you'd do the bar diagram.

Pretty much all bar diagrams fall into two categories: part-whole and comparison.  Part-whole is usually one bar subdivided into parts (like the above soda problem), while comparison usually has each part gets its own bar (and you figure out how each bar relates to each other and the total).  (And problems can combine elements of both: individual comparison bars being subdivided into parts, or comparing parts of a whole (like the end of the soda problem).)  Figuring out which one to draw is the first decision you make with bar diagrams.  Some problems can be drawn effectively either way, but some definitely prefer one or the other - if you choose wrong you'll run into trouble at some point.

Once you get past the four operations and into fractions, ratios, and percentages, then another element comes into play: that of a unit.  Generally speaking, in diagramming a fraction/ratio/percentage problem, you want to define some quantity as your base unit and draw everything in relation to it.  Really, it's very comparable to choosing a variable.  (Although if you bring algebraic thinking to figuring out your diagram, sometimes you'll end up with a less elegant unit than if you were thinking in diagrams - the diagram becomes more of an appendage or visual showing of your algebra than a genuine tool for solving the problem.)  So, in the soda problem, the first bit of work you do is to find your LCM for your unlike fractions, and that's your unit - 1/20 of the total number of cans - and everything sorts out very nicely from there.

So, in terms of trying to puzzle out bar diagrams, it helps to think in terms of part/whole versus comparison, and (in fractions/etc.) to seek a common unit to subdivide your bars into.

Edited May 4, 2020 by forty-two

[forty-two]

Here's a more elegant way of solving the soda problem than I did before, one that takes better advantage of 1/20 cans as your common unit:

Having found your LCM=20, you draw your diagram, dividing your bar into 20 equal units: |-----*****-----*****|

Then mark the parts on your bar (2/5 of 20 is 8 units of cherry; 1/4 of 20 is 5 units of root beer; the remaining 7 units are the 28 cans of fruit juice): |-----***|**---|--*****|

1 unit = 28 cans / 7 units = 4 cans

8 units (of cherry) - 5 units (of root beer) = 3 units difference 

3 units * 4 cans/unit = 12 cans difference

Edited May 4, 2020 by forty-two