Hudson Valley Parent

HVP - March 2014

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Page 30 of 45 n Hudson Valley Parent 29 Conceptually, addi- tion involves joining two groups of things together to make one single group. For example, if you have 5 apples in one box, and 3 apples in another, when you put the apples togeth- er, you have 8 apples. The blue circles show how the numbers are linked together in a group called a "number bond." The most useful number bonds are those that add to 10. Take 7 + 3 = 10, we have the number bond pictured in the blue circles at right: Now we're ready to add 8 + 7 by making 10 with num- ber bonds. Our work will look like the image below. Let's go through the steps one at a time. First, since one of the numbers we are adding is 7, we can complete 7 to make 10. That is, we can figure out which number when added to 7 will give us 10. A famil- iarity with the number bonds of 10 should cause us to remember 10 = 7 + 3. What this means is that if we could find a 3 somewhere, we could add the 3 to the 7 "completing it" to 10. What's more, the number bonds of 8 tell us that there is a 3 embed- ded in the 8 (that is, the 8 can be broken down into a set of numbers that includes 3, the number we are Dear Jeff, What the heck is a number bond? If you're like me, you learned arithmetic shortly after the number "1" was invented — at least, it feels that way, especially when you look over your child's math homework. And while you might not be able to add 375 + 298 in your head, you probably feel that you could do 8 + 7 without reaching for the calculator. But then your child brings home a problem like the following, from a 2nd grade worksheet: Solve 8 + 7 by recording make 10 solutions with num- ber bonds. You may wonder if they just discovered that 1 + 1 = 3, and you missed the podcast. Fear not, for 1 + 1 is still 2, and the new math is still the old math. The important change is that in addition to being asked questions like "What is 8 + 7?" new ques- tions are being asked that rely on a conceptual understanding of mathe- matics, to prepare students for more advanced work. Thus, in addition to being asked to find a numerical value, your child (and indirectly, you) might be asked to elaborate on your answer: How did you obtain it? Why did you do it that way? looking for). So instead of simply knowing that 8+7=15, we can do it this way: First, break 8 into 5 and 3. So now we are no longer just add- ing 8+7, we are adding 7+3+5. Now we know that 7+3 makes 10, and 10+5 makes 15, our total. You may ask your- self, why all this extra fuss? Why don't students just memorize 8 + 7 = 15. One reason is this: When students memorize 8 + 7 = 15 before they understand the mechanics that make up this addition, it leaves teachers with a choice: wait until all their students have memorized this fact before proceeding to more advanced topics; or forging ahead, letting the students who haven't memorized the fact fall behind. Neither option is palatable. In- stead, if students can develop their own ways of finding 8 + 7 = 15, then all students have the same solid foundation to reach higher levels of mathematics. And, just as you eventually remember how to drive to work without a map, students will eventually remember 8 + 7 = 15. Jeff Suzuki teaches mathematics at Brooklyn College, and is one of the founders of the Mid-Hudson Valley Math Teachers Circle. Email your Common Core questions to our editor at JEFF SUZUKI Mathematics Common Core @ Home Answers from Common Core experts Part One of a continuing series 5 3 8 3 7 10 8 + 7 = 15 5 3 On the web: Our expert answers your questions about the Com- mon Core English Language Arts standards at

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