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5th Grade Algebra and Candy


If you’ve read the recent article My Daughter’s Homework is Killing Me, then you know that parents all over our country are scratching their heads, wondering when homework got so dang hard. 

I think that part of the reason is that complex concepts (like algebra) are being introduced  in earlier grades.

In an ideal world, an early introduction to algebra would help prepare students to master advanced math in middle school and high school.  It’s scaffolding for the future.

In the meantime, parents look at their kids’ homework and go “Whoa.”

Here’s a trick that might make homework easier.  Add candy to the equation!

To show how this can work, I’m using an example similar to what you would find in the 5th grade Houghton Mifflin Math Expressions textbook, which the Edmonds School District uses.

Problem: Mrs. Garcia’s neighborhood has 28 pets.  There are twice as many cats as hamsters and four times as many dogs as hamsters.  How many of each pet are there?

You could use guess and check to figure this out, which would take forever.  Or you could use algebra.  Or you could use algebra and candy…even better!


One piece of candy corn equals the number of hamsters.  Two pieces of candy corn equals the number of cats, which is twice the number of hamsters.  Four pieces of candy corn equals the number of dogs, which is four times the number of hamsters.  In all, the total number of pets is 28.  That would mean 4 hamsters, 8 cats, and 16 dogs in the neighborhood.


Once you introduce candy into the equation, math homework becomes more fun.  Just don’t forget to have toothbrushes on the ready.

Hougton Mifflin Math Expressions, A Review

Those of you familiar with my blog will know that I am a former K-4 teacher who believes in teaching math from a Constructivist perspective. This review of Houghton Mifflin’s Math Expression is based on what I have seen as a parent with my “teacher glasses on”, so to say. I do not have any association with Houghton Mifflin whatsoever.

As a parent, I have had the opportunity to help my son complete the second grade Houghton Mifflin Math Expressions curriculum in a home-study way last year when he was in Kindergarten. Now my role has been simplified (yeah!) to only helping him with his third grade homework. I have also volunteered in my son’s Kindergarten classroom and helped lead many of the small group Kindergarten activities. This gave me a chance to see how the teacher’s guide was written and laid out. I also volunteered to tutor a Kindergartener through my church a few years back, so I got to witness firsthand how an English Language Learner responded to this program.

In general, I am favorably impressed with Math Expressions, but only because as a teacher I have witnessed, and been forced to use, some really awful math programs in the past. (Anyone familiar with Math Their Way?) Houghton Mifflin seems to be trying to strike a balance between Constructivism and traditional algorithm based approaches. This reminds me of the phonics vs. Whole Language debate that resulted in Balanced Literacy Instruction. Math Expressions encourages children to learn to solve arithmetic problems using multiple strategies, but often spoon-feeds the children what these strategies should be.

Pure Constructivists would be very unhappy with Math Expressions because of the way the program directly tells children how to solve problems. This is also a curriculum that usually insists that children “stack” problems (write them vertically) in order to solve equations. Pure Constructivists can sometimes advocate the opposite, and insist that children write problems horizontally. I personally, think children should be able to write problems however they want. On the other hand, Constructivists would be happy with Math Expressions in that it goes beyond borrowing and carrying, as the only way to solve problems.

As a former Kindergarten teacher, I feel very strongly that the Kindergarten curriculum moves way too slowly. The English Language Learner boy I tutored was capable of a lot more than what Math Expressions was having him do. This is also a horrible program for school districts who use the Alternate Day Kindergarten schedule. There is no way you could cover the whole year’s program and only teach math two days a week. On the plus side, the Kindergarten curriculum did include lots of hands-on games and activities to reinforce conceptual learning.

I think  my son’s school district has now been using Math Expressions for three or four years.  If I recall corectly, they were using Dale Seymour’s Investigations before that.  In the past five years, the district’s standardized math scores have gone up 19%, which does not surprise me.  Math Expressions seems to be a very “teacher proof” program (although I had that expression!). The teacher guide tells you exactly what to do. It is up to the intelligence and intuition of the teacher herself however, to make this program really great. As with any subject, good teaching is still essential with Math Expressions. Although if your child was stuck with a “bum teacher” (another expression I detest!), they would probably be better off with that teacher using Math Expressions, then a lot of other programs out there.

Finally, I have to mention one thing that is currently bugging me about the third grade program. My son’s homework keeps requiring him to write down his answer numerically and then make a proof drawing of his work. The problem is, my son often solves three digit problems in his head. This is really just a minor annoyance with the program. It is after all, important for mathematicians to be able to explain their thinking and show their work. Unfortunately for Bruce, a proof drawing has nothing to do whatsoever with how he is solving the problem!

If you are a parent reading this whose school district has adopted Math Expressions I would say “Relax! It could be a lot worse.” But if you are looking for ways to support math learning at home, please take a look around my blog because I have lots of ideas for you.