Algebraic thinking

I downloaded the "balance" worksheet freebie, and daughter liked it. We homeschool and she would be in fifth grade this year if she were in public school. ... My question is about the balance worksheets - where would there be more of that? Stuff that does groundwork for algebraic thinking?

It's not just balance problems that prepare a child for algebra. These are important factors also:
  • a good number sense (e.g. mental math)

  • understanding of the four basic operations, for example how the opposite operations work. Another example: understanding that a division with remainder such as 50 ÷ 6 = 8 R2 is "turned around" with multiplication and addition: 8 × 6 + 2 = 50.

  • a good command of fraction and decimal operations. Understanding the close connection between fractions and division.

  • understanding the concepts of ratio and percent.

You can also simply write her more problems with an unknown. For example:

Write 7 + x = 28 and similar ones, like 12 + x = 99 and harder numbers.

x − 9 = 9 and notice how this is "solved" by adding.

6 − x = 4 and then harder numbers.

The same with multiplication and division.

I would also add one more thing that prepares children for algebra: good word problems -- not such that only require one operation to solve.

Singapore math's word problem booklets are told to be good, and here are some other (free) word problem websites.

In fact, soon I want to talk a little more about good word problems based on a paper I'm currently reading.


Here's an instructive puzzle by Sam Lloyd: A milkman has two ten-gallon cans of milk. One cook has a five quart pail, and one cook has a three quart pail. Each cook wants two quarts of milk. There are no other containers around, and no way to mark any of the milk cans or pails. How does the milkman make this sale, without pouring milk away?

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