# MUS vs. LOF; Pre-algebra vs. Algebra

## Recommended Posts

We use both MUS and LOF. (I know. But we like them both.) Both MUS and LOF have Fractions, then Decimals. But at that point, MUS spends a year in Pre-algebra while LOF goes on to Algebra.

I'm curious -- if the kids have mastered fractions, then decimals, do they or do they not need a year in pre-algebra before going on to algebra? "It depends on what's covered in Pre-algebra and Algebra," you say! Right. So, I have a list of those topics, which I will post below.

However, I'm not a math person. The topic lists mean nothing to me. Can somebody who understands algebra compare and contrast these topic lists, and comment on the two paths.

We're currently on Decimals in both programs. But at the end of Decimals, I'm wondering how to carry on. How do these three classes fit together? Is MUS's Pre-algebra really a year simpler than LOF's algebra? Why and when do they split apart? Where do they come back together? Which would you use in the same semester? Which topics are simplest, and which are the most advanced?

Thank you if you can enlighten me.

OK, topic lists:

LOF Algebra

1. Numbers and Sets (finite & infinite sets, natural numbers, whole numbers, integers, set notation, negative numbers, ratios, the empty set)

2. Integers (less than, the number line, multiplication, proportion, Pi, coefficients)

3. Equations (solving equations with ratio, formulas from geometry, order of operations, consecutive numbers, rational numbers, set builder notation, distance = rate x time, distributive property, proof that negative x negative = positive)

4. Motion and Mixture (proof of the distributive property, price and quantity problems, mixture problems, age problems

5. Two Unknowns (solving two equations, two unknowns by elimination, union of sets, graphing of points, mean, mode, and median averages, graphing linear equations, graphing any equation)

6. Exponents (solving two equations, two unknowns by graphing, solving two equations, two unknowns by substitution, inconsistent and dependent equations, factorials, commutative laws, negative exponents)

7. Factoring (multiplying binomials, solving quadratic equations by factoring, common factors, factoring a difference of squares, factoring by grouping)

8. Fractions (solving equations containing fractions, simplifying fractions, adding and subtracting fractions, multiplying and dividing fractions, complex fractions)

9. Square Roots (solving pure quadratic equations, principal square roots, Pythagorean theorem, the real numbers, the irrational numbers, cube roots and indexes, solving radical equations, rationalizing the denominator, extraneous roots)

10. Quadratic Equations (solving quadratic equations by completing the square, the quadratic formula, long division of a polynomial by a binomial)

11. Functions and Slope (definition of a function, domain, codomain, image, six definitions of slope, range of a function)

12. Inequalities and Absolute Value (graphing inequalities in two dimensions, division by zero, algebraically solving linear inequalities with one unknown)

MUS Pre-algebra

Lesson 2 Negative Numbers, Subtraction

Lesson 3 Negative Numbers, Multiplication

Lesson 4 Negative Numbers, Division and Integers, Number Line

Lesson 5 Exponents

Lesson 6 Place Value with Expanded and Exponential Notation

Lesson 7 Negative Numbers, Exponents

Lesson 9 Solve for an Unknown with the Additive Inverse

Lesson 10 Pythagorean Theorem

Lesson 11 Associative and Commutative Property

Lesson 12 Distributive Property

Lesson 13 Solve for an Unknown with Multiplicative Inverse

Lesson 14 Solve for an Unknown with Order of Operations

Lesson 15 Surface Area of Solids

Lesson 16 Transform Celsius to Fahrenheit

Lesson 17 Transform Fahrenheit to Celsius

Lesson 18 Absolute Value

Lesson 19 Ratio and Proportion

Lesson 20 Similar Polygons

Lesson 21 Least Common Multiple and Prime Factorization

Lesson 22 Greatest Common Factor

Lesson 24 Volume of a Cylinder

Lesson 25 Polynomials, Multiplication

Lesson 26 Adding and Subtracting Time and the Same Difference Theorem

Lesson 27 Volume of a Cone and a Pyramid

Lesson 28 Military Time, Addition and Subtraction

Lesson 29 Measurement, Addition and Subtraction

Lesson 30 Irrational Numbers and the Square Root Formula, Real Numbers

MUS Algebra

Lesson 1 Commutative and Associative Properties

Lesson 2 Order of Operations

Lesson 3 Solving for an Unknown with One Variable

Lesson 4 Distributive Property

Lesson 5 Cartesian Coordinates

Lesson 6 Graphing a Line

Lesson 7 Slope-Intercept Formula

Lesson 8 Graphing Parallel Lines and the Equation of a Line

Lesson 9 Graphing Perpendicular Lines

Lesson 10 Finding the Slope-Intercept Formula with Different Givens

Lesson 11 Graphing Inequalities

Lesson 12 Solving Simultaneous Equations by Graphing

Lesson 13 Solving Simultaneous Equations by Substitution

Lesson 14 Solving Simultaneous Equations by Elimination

Lesson 15 Coin Problems

Lesson 16 Consecutive Integers

Lesson 17 Multiplication and Division with Exponents

Lesson 18 Negative Exponents and Raising Exponents to a Power

Lesson 19 Addition and Multiplication of Polynomials

Lesson 20 Factor Polynomials

Lesson 21 Factor Trinomials with Coefficients (LOF 1)

Lesson 22 Factor Trinomials with Negative Numbers

Lesson 23 Square Roots and Dividing Polynomials

Lesson 24 Difference of Two Squares and Oriental Squares

Lesson 25 Repeated Factoring of Polynomials

Lesson 26 Solving Equations with Factoring

Lesson 27 Unit Multipliers

Lesson 28 Square Unit Multipliers

Lesson 29 Metric Conversions

Lesson 30 Fractional Exponents

Lesson 31 Significant Digits and Scientific Notation

Lesson 32 Bases Other Than Ten

Lesson 33 Graphing a Circle and an Ellipse

Lesson 34 Graphing a Parabola and a Hyperbola

:lurk5:

##### Share on other sites

Not sure if I have the answer. We currently doing a year of prealgebra with various resources. Next year we move on the Algebra, probably Chalkdust.

My ds finished up Singapore 6B more than a year ago. We've bumping along doing "enrichment" and "prealgebra" simply because I felt there were so many more topics that could be covered in significantly more depth than Singapore did in 6B. We've been using NEM, CWP and Lials BCM.

You can understand fractions and decimiles at differing depths. The proof is in the word problems.

Check out some of the placement tests for Saxon, Singapore, MUS and Chalkdust. See where your dc places in them. That should give you a good idea of areas she may need to firm up on or review.

##### Share on other sites

What about Math: a Human Endeavor, just for something different? Not sure how old your kids are, if they need another yr of maturing.

##### Share on other sites

I haven't seen LOF algebra yet, but for what its worth, my 7th grade son is using MUS pre-algebra with Right Start geometry right now and I am finding they go together quite well. We have used MUS all the way through, as well as LOF fractions and decimals. After pre-algebra I will go back to LOF, probably continuing with MUS also.

Amy

##### Share on other sites

Hi Cindy,

We have used MUS Pre-Algebra and are currently about 2/3 thru MUS Algebra and LoF Algebra. I also have a degree in math. That said, what do I know? My best suggestion is to write to LoF author and ask his opinion about how important the MUS Pre-Algebra topics are. He probably knows better than me. Have any of these been covered in LoF Fractions/Decimals? LoF Algebra is the first we've used in the series. We've used MUS since K.

So far, I have found that the topics in the 2 Algebra programs are remarkably similar. I guess that shouldn't come as a surprise. I attempted to give my thoughts about the MUS Pre-Algebra topics below. But, what do I know? As I look through what I've written, I would say that MUS Pre-Algebra is full of baby steps to Algebra and Geometry and rounded out with miscellaneous topics whose value is not essential (converting F to C, military time, etc.). I think you could consider MUS Pre-Algebra optional. Two exceptions: Lesson 21&22. These I consider essential.

Covered earlier in MUS:

5,6

Covered in MUS and/or LoF Algebra:

1-4,7,11,12,14,19,23,25

Generally covered in Geometry (Please consider that I took Geometry 30+ years ago, haven't covered it yet with ds, and have a bad memory :tongue_smilie:):

8,9,10,13,15,20,24,27

Not essential and/or can be covered lightly:

16,17,18,26,28,29,30

HTH! But, remember I'm no expert.

MUS Pre-algebra

Lesson 2 Negative Numbers, Subtraction

Lesson 3 Negative Numbers, Multiplication

Lesson 4 Negative Numbers, Division and Integers, Number Line

Lesson 5 Exponents

Lesson 6 Place Value with Expanded and Exponential Notation

Lesson 7 Negative Numbers, Exponents

Lesson 9 Solve for an Unknown with the Additive Inverse

Lesson 10 Pythagorean Theorem

Lesson 11 Associative and Commutative Property

Lesson 12 Distributive Property

Lesson 13 Solve for an Unknown with Multiplicative Inverse

Lesson 14 Solve for an Unknown with Order of Operations

Lesson 15 Surface Area of Solids

Lesson 16 Transform Celsius to Fahrenheit

Lesson 17 Transform Fahrenheit to Celsius

Lesson 18 Absolute Value

Lesson 19 Ratio and Proportion

Lesson 20 Similar Polygons

Lesson 21 Least Common Multiple and Prime Factorization

Lesson 22 Greatest Common Factor

Lesson 24 Volume of a Cylinder

Lesson 25 Polynomials, Multiplication

Lesson 26 Adding and Subtracting Time and the Same Difference Theorem

Lesson 27 Volume of a Cone and a Pyramid

Lesson 28 Military Time, Addition and Subtraction

Lesson 29 Measurement, Addition and Subtraction

Lesson 30 Irrational Numbers and the Square Root Formula, Real Numbers

##### Share on other sites

We use both MUS and LOF. (I know. But we like them both.) Both MUS and LOF have Fractions, then Decimals. But at that point, MUS spends a year in Pre-algebra while LOF goes on to Algebra.

I am curious about this too. My kids worked through LOF Fractions and Decimals and Percents so I bought Beginning Algebra. I started to work through it and decided they needed some more practice so I got MUS Pre-Algebra used. I think it will be a gentle transtition and I wanted to have some hands on, concrete learning to supplement LOF. We hs year round and I also wanted more "stuff" to work through. My kids have found it too demeaning to start a book over and do it again :bored:. DH would just prefer them doing LOF all over again, but they all groaned and wanted to move onto something new...so we got MUS.

So MUS Pre-Al is not really needed, but helpful for transition into LOF Beginning AL?

##### Share on other sites

There was a recent thread/post with a link to another thread/post in which the author of LOF says that he may eventually write a book or two to go between D&P and Beg. Alg. That would solve the problem of no "pre-algebra" in the LOF sequence.

Many students are ready to go into Beg. Algebra after mastering Fractions and then Decimals and Percents. And then many more are not. I plan to spend next year using a pre-algebra program (maybe Chalkdust, maybe BJU) with my older ds to help his mind mature a bit before we start Algebra. Most pre-algebra programs delve deeper into word problems and applications using already mastered concepts. This will be very useful in our particular situation (somewhat young age).

HTH!

##### Share on other sites

I have young-ish 6th grader who will finish CLE Math 6 in May or so. We do math year-round, so he's going to do LOF fractions and decimals this summer, and then MUS Pre-Algebra in the fall, probably at a faster pace that most.

He's a kid who needs a lot of review and this our first time with MUS, so that's reasonable in my scheme of things. Then he will go to MUS Algebra, and then LOF Algebra for review.

Time will tell!

##### Share on other sites

I am curious about this too. My kids worked through LOF Fractions and Decimals and Percents so I bought Beginning Algebra. I started to work through it and decided they needed some more practice so I got MUS Pre-Algebra used. I think it will be a gentle transtition and I wanted to have some hands on, concrete learning to supplement LOF. We hs year round and I also wanted more "stuff" to work through. My kids have found it too demeaning to start a book over and do it again :bored:. DH would just prefer them doing LOF all over again, but they all groaned and wanted to move onto something new...so we got MUS.

So MUS Pre-Al is not really needed, but helpful for transition into LOF Beginning AL?

I think you have it exactly right. MUS Pre-Algebra is a gentle transition into Algebra & Geometry. Kind of a sneak peek. Since the OP had used both MUS and LoF and planned to continue with both, I think it could be considered optional. It could also be done very quickly.

##### Share on other sites

Thanks everybody. I really appreciate the discussion. And, Sue, thanks especially for the details. That was just the kind of info I was looking for.

It's neat that Stan is considering an in-between (in between LOF Decimals and LOF Algebra) book; but it sounds like it won't be ready by the time we get there.

The linked thread commented on Stan's great customer service. I gotta agree. My son and I called him once with a problem we didn't understand. He was delighted to hear from us, understood our question immediately, and explained the answer simply. My son was most impressed!

Another program to consider as an in-between if you want a gentle intro to Algebra is Hands On Equations. I started this with my son when he was in the 3rd grade. We've moved very slowly and steadily, but it has produced amazing results. It's very effective and simple, and would have been perfect just before "real" algebra. As a result of this study, my son thinks he loves algebra and thinks he's great at it.

##### Share on other sites

• 1 month later...
I think you could consider MUS Pre-Algebra optional. Two exceptions: Lesson 21&22. These I consider essential.

Covered earlier in MUS:

5,6

Covered in MUS and/or LoF Algebra:

1-4,7,11,12,14,19,23,25

Generally covered in Geometry (Please consider that I took Geometry 30+ years ago, haven't covered it yet with ds, and have a bad memory :tongue_smilie:):

8,9,10,13,15,20,24,27

Not essential and/or can be covered lightly:

16,17,18,26,28,29,30

I had to correct this. Lesson 21 & 22 are actually covered in Epsilon. Not a bad idea to reinforce them before Algebra though.

##### Share on other sites

What about Math: a Human Endeavor, just for something different? Not sure how old your kids are, if they need another yr of maturing.

I tried this with my dd(12) this year (after both fractions and decimals) and found that, really, she needed algebra first.

##### Share on other sites

I have been struggling with this same decision. My ds is going through LOF Fractions very quickly right now and will then do Decimals/Percents. These are mostly review for him, but I haven't been all that happy with the math he has been doing and I wanted to make sure we had mastery before we went on. He really enjoys LOF so it seemed a great way to review. My problem was what to go on TO.

I had originally thought MUS pre-algebra, but my son likes LOF and I wondered if we should just go onto LOF Algebra. He isn't that strong in math though and is just in sixth grade. The more I think about it, and the more I read other people's experiences, I think we'll go ahead and slip MUS pre-algebra in there. It may be a quick study and be easy for him, but thats ok. I'd prefer it was easy and he really had it nailed down than to get into algebra and get lost.

Debbie

##### Share on other sites

I know the OP's sticking with MUS, but I thought I'd put in something I think I'm going to try before Algebra and haven't seen mentioned (in case anyone else reading the thread is pondering this and is weighing options), which is Singapore's Discovering Mathematics - I'm thinking just the first year of it, then switching to Algebra.

I think it's roughly equivalent to NEM, but I like the presentation better - it reminds me more of the way Primary's laid out (we've been using Singapore all along), so I think that might be a good transition year for us. It includes neg. numbers, coordinate graphing, and beginning linear equations, lots of geometry, and lots of other stuff.

##### Share on other sites

• 2 months later...

My dd did Saxon 76 in 4th, TT Pre-Algebra in 5th and LoF Dec. & Percents and Fractions books this year (she's still finishing up the D&P book). I'm thinking she has enough base now and could move on. She loves LoF, and feels she's ready to move to Algebra next year, where she did NOT want to move to Algebra after last year.

Based on what she's used, and her age (just turned 12), do you think she's ready for Regular Algebra? She understands Maths well, but doesn't like it---except for LoF. Should she take more than LoF? Can someone jump into MUS at this level? She's not sure she'd want to do MUS....

Cindy, I'm going to look at that link you put up. Thanks!

##### Share on other sites

It's neat that Stan is considering an in-between (in between LOF Decimals and LOF Algebra) book; but it sounds like it won't be ready by the time we get there.
I've started a write-in campaign to get him to consider Life of Fred: Logic after he's done the middle school series... well, if emailing him once constitutes starting a write-in campaign. Feel free to join me. :)
##### Share on other sites

Based on what she's used, and her age (just turned 12), do you think she's ready for Regular Algebra? She understands Maths well, but doesn't like it---except for LoF. Should she take more than LoF? Can someone jump into MUS at this level? She's not sure she'd want to do MUS....

It sounds like she's ready. If she likes LoF and does well with it, I'd stick with it.

##### Share on other sites

I've started a write-in campaign to get him to consider Life of Fred: Logic after he's done the middle school series... well, if emailing him once constitutes starting a write-in campaign. Feel free to join me. :)

Gosh, yes, I'd love LOF logic! Great idea. I'll e-mail him too. Here's his e-mail address: stan@stanleyschmidt.com

##### Share on other sites

I just heard back from Stan regarding the write-in campaign for a logic class. He told me he is keeping track of the requests, and so far there have been two. LOL! Write him, you guys! stan@stanleyschmidt.com

Also, on his pre-algebra class: He says he hopes it will be ready by the end of summer.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.