13 Rules That Expire Summary
“1. If you multiply a number by ten, just add a zero to the end of the number. This “rule” is often taught when students learn to multiply an integer by ten. However, this Directive shall not apply where the decimal places are multiplied (e.g. 0,25 × 10 = 2,5, not 0,250). Although this statement may reflect a regular pattern that students identify with integers, it is not generalizable to other types of numbers. Expiry date: Class 5 (5.NBT.2). This table shows some commonly used phrases that “expire” and more appropriate alternatives. How many of these “rules” did you say in class? While you`re at it, don`t forget to leave a review on iTunes. I`d like to hear what you think about it and how we can make sure we`re offering you content you`ll really like.
But another reason I don`t want to teach these tips and rules is that they don`t last. They are working for now. They work for the types of problems that students are working on right now, but when they move on to other types of problems, the rules no longer work. To address vocabulary, I talked about using descriptions rather than terminology. For example, the term “flip-flops” is often used in first-grade classes. We discuss the idea that if children can say Tyrannosaurus rex and Stegosaurus and know exactly what they mean, they can say “commutative property” with understanding. “Flip-flop facts” may be a good first-class description of commutative property, but do not replace the actual term. I am working through these stages in my own school district. Won`t you join me on this journey to abolish the rules that expire by engaging in professional discourse and making school-wide agreements? I also used the fact that we say “multiplication makes bigger and division always makes you smaller” as an example of how we accidentally teach misunderstandings. Hey, have you already subscribed to the Build Math Minds podcast? If not, be sure to do it today because I don`t want you to miss episodes! Click here to subscribe to the podcast in iTunes.
The mathematical conversations that emerged from this process were incredible. I hope you will try it! If you multiplied 3 x 1/3, would the product be larger than the factors? Many students learn that when you multiply, your product is always larger than your factors, but this rule only applies if you are working with positive integers. If fractions, decimal numbers, and negative numbers are introduced later, the rule is no longer true. It`s not a quick thing that happens to your students, but the quick answer is to teach them the value of space and how, if you multiply by ten, make the number ten times larger, thus moving the number to the next space value. How about sharing 2 and 1/2? Would the ratio be lower than the dividend and the divisor? When students first learn division, they focus on partially understanding that when you share a lot, you can`t have more than you started with. However, this rule expires when you start dividing integers and fractions/decimals and fractions by fractions or decimals by decimals. 13 Expiring Rules from Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty changed my teaching forever.
Not only do they share the 13 rules, but there is also a section on the expired mathematical language we use, and they give alternatives that can be used instead. This article is seriously a MUST-READ. To give you an overview of the article, I just want to share one of the rules with you today. Karp, Bush, and Dougherty explain, “The over-generalization of generally accepted strategies, the use of imprecise vocabulary, and the use of tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstandings later in students` mathematical careers.” Check out this article by Karp, Bush, and Dougherty on other rules that happen in math! www.scusd.edu/sites/main/files/file-attachments/13_rules_that_expire_0.pdf Thirteen rules that expire: 1. If you multiply a number by ten, simply add a zero to the end of the number. 2. Use keywords to solve word problems. 3.
You can`t take a larger number from a smaller number. 4. Addition and multiplication make numbers larger. 5. Subtraction and division reduce numbers. 6. You always divide the largest number by the smallest number. 7. Two negative points are a positive.
8. Multiply everything in parentheses by the number outside the parentheses. 9. Incorrect fractions should always be written as a mixed number. 10. The number you specify first when counting is always less than the number that comes next. Over-generalization of generally accepted strategies, the use of imprecise vocabulary, and the use of tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstandings later in students` mathematical careers.