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Family Math The Middle School Years Algebraic Reasoning and Number Sense (a book review) Re


Family Math: The Middle School Years, Algebraic Reasoning and Number Sense (a book review)

Family Math: The Middle School Years, Algebraic Reasoning and Number Sense (a book review)


With great success, I have used the ideas in this book to tutor students who struggle in math.


My favorite section is the part that teaches “Number sense”. As educators, we force too many of our math students to memorize various methods for solving equations, but we often do not take the time to explain the reasoning behind these methods. Many of the activities in the “Number sense” section effectively deconstruct the logic behind common mathematical procedures that we have all taken for granted since grammar school.


"Digit Directives: Maximizing Multiplication”, for example, is a great way to help students understand the importance of the place values present in a large number. Many of my elementary-aged students have a difficult time understanding the concept that 1,000 is a bigger number than 999. They see all of the nines in 999, and then they look at the zeroes in 1,000, and conclude (incorrectly) that 999 must be the bigger of the two. In this game, though, students must think critically about place values, or they lose the game.


A worksheet provides us with exactly five blank place values (*Space* *Space* *Space* multiplied by *Space* *Space*) and then gives us a “reject box” to the side. In the game, you simply roll a dice and plug random digits into the empty boxes in any order to create the largest possible product. Your child will quickly realize that large numbers like six should go into the 100’s place value of the first number, and smaller digits like one should go straight to the reject box.


The book itself has illustrations throughout, and sidebars with neat tricks that you can try on your calculator.


Every chapter also includes some sort of “hands-on” activity that you can try at home with your child. For instance, you might want to fill large a jar full of pretzels, Goldfish Crackers and marshmallows. Then, you could tell your child that you have three times as many pretzels as crackers, and two times as many marshmallows as crackers. You can now ask questions like, “If there are a total of 120 snack items in the jar, then how many Goldfish Crackers are there?” You could even go an extra step and have the student write algebraic equations for finding the two values. Activities like these, I believe, are much more effective than sitting a student down and having them figure out “x + 2x + 3x = 120”.


If your middle school child is struggling in math class, or you understand the importance of your kids possessing superior quantitative skills in college and beyond, then this book is certainly for you.


Nashua Math Tutors


Blog Posts by Tim





13.10.17 16:45

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