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Meaning of factors in multiplication: four groups of 2, or 4 taken two times?
Someone asked me about the interpretation or meaning of the two numbers in multiplication, such as 4 × 2. Do you view it as four groups of 2 , or as four, taken two times ? Here's their question: "...I noticed that your explanation about how to interpret a math phrase, such as 4 × 2, is different from how I have understood it and taught it to my older daughter who was using RightStart Math at this level. Let me explain: I see that you are using the first factor to denote number of groups and the second factor tells how many are in each group (4 × 2 would be interpreted 4 groups of 2). On the other hand, I have taught and thought of it reversed, with the first factor telling how many are in each group and the second factor telling you how many groups (4 × 2 would be 4 taken 2 times). I know that the difference in explanations does not ultimately change the product, but I am wondering what you thoughts are. When I conceptually picture what I'm doing I see i...
Saxon Math is not for everyone
(Updated in 2018) People sometimes ask me of my opinion or review of Saxon math. What I've written here applies in particular to Saxon Math's high school courses and middle grade levels. (The grades K-3 are by a different author and are quite different; more on that below.) Saxon Math uses an "incremental approach" where math concepts are studied in little pieces over several lessons, and those lessons are strawed over a long period of time, intermixed with lessons about other topics. In other words, if one lesson is on some particular topic (say, percentages or inequalities), it's almost guaranteed that the NEXT lesson is NOT on that topic . It jumps around from topic to topic constantly, and this is by design. Saxon's method also includes a feature where after a lesson is taught, there are very few practice problems about the topic of the lesson. Most of the problems are mixed review problems, and they practice concepts from earlier lessons, not th...
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http://www.youtube.com/watch?v=ZFDTcasgHK4
I read it is also very good.