There are many home schooling math curricula out there.

.......Some of them are so boring/repetitive that kids quickly forget anything they may have learned.

.......Some of them are mathematically light-weight.  The kids think that they have learned all of first-year algebra.  That is, until they hit their SATs or a college classroom.  At that point they find out that there are big gaps in their knowledge.

 

     With that in mind, let's see how much first-year algebra your child has learned. 

     Here are some representative questions to ask your child.  They are taken from Life of Fred: Beginning Algebra Expanded Edition.  Have them take out a piece of paper and play with these questions:

 

 

1.  What is the coefficient of 34.7abc?  (page 68)

2.  Army regulations require that their pickle relish use 10 pickles per pound of relish.  In one giant bowl, the cooks have relish that only used 8 pickles per pound (too weak).  In another bowl, they have relish that has 16 pickles per pound (too strong).  They need to make 200 pounds of relish.  How many pounds of each bowl should they use? 
(p. 170)

3.  The point (a, b) is directly below (4, 9).  What can you say about a?  What can you say about b? (p. 228)

4.   The cooks at the army camp have four different dinner menus.  In the next four days, how many ways could they serve them so every dinner will be different? (p. 273)

5.  Solve  1/(x-1)  + 1/2   =  2/(x² -1)   (p. 357)  

6.  Suppose there are two elements in the domain of some function and two elements in the range.  How many possible functions could there be?  (p. 492)

7.  Solve 48 - 3x > 36  (p. 520)