tag:blogger.com,1999:blog-8017698507183263684.post4596636945166387529..comments2024-03-14T08:13:40.103-05:00Comments on Tales of Frogs and Cupcakes: Think About It!: The Equals SignJanayehttp://www.blogger.com/profile/02255030091299082258noreply@blogger.comBlogger30125tag:blogger.com,1999:blog-8017698507183263684.post-9793110262818483142014-10-25T11:54:48.788-05:002014-10-25T11:54:48.788-05:00Thank you for the great resources! I am trying to...Thank you for the great resources! I am trying to figure out how to help my kiddos understand the Engaged New York lesson and this really helped. I love the book you suggested, I just ordered it and the website to the interactive math manipulatives is amazing. Shona Earlyhttps://www.blogger.com/profile/16933831650881688571noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-35905317483738896212013-10-05T16:04:41.841-05:002013-10-05T16:04:41.841-05:00I'm an intern in a first grade classroom, and ...I'm an intern in a first grade classroom, and we are strting to explain to the kids that "equals" means "the same as". Thank you for this post and great ideas, including the book Equal Shmequal!Anonymoushttps://www.blogger.com/profile/05772275463794546631noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-34556110371270821342012-01-21T12:20:44.388-06:002012-01-21T12:20:44.388-06:00I'm back. I just wanted to share with your so...I'm back. I just wanted to share with your some of the learning from our class this week. I even had one of my kinders say the equal sign means equality! :) Can't wait for your next Think about It Series post.<br />http://learningwithmrsparker.blogspot.com/2012/01/balancing-act.htmlLearning with Mrs. Parkerhttps://www.blogger.com/profile/17531829108247730123noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-76180719774554236812012-01-02T22:36:46.522-06:002012-01-02T22:36:46.522-06:00Great post. I know exactly what you mean about 4th...Great post. I know exactly what you mean about 4th graders and number sense. I spend a great deal of time working on this in my 4th grade class. I cannot wait to read your next post. You always have great ideas.Leanne Helumshttps://www.blogger.com/profile/12587182084555690939noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-82548407075370487742012-01-02T20:34:49.790-06:002012-01-02T20:34:49.790-06:00I do teach that -whatever is on the left side of t...I do teach that -whatever is on the left side of the equals sign must have the same value as what is on the right side, and am amazed to see 3rd graders actually try to FIGURE OUT the answer to (ex) 4+3=3+ __ . I like the idea of using pennies on a balance scale to get this across conceptually. In Washington, 3+4=7+5=12 is called a run-on equation. If you're asked to write an equation to show the solution to a problem and use a run-on equation, you will not earn the highest possible score even if the answer is correct. Thanks for pointing out/reminding us to review this with our kids.Liz B.noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-34019029751351845822012-01-02T20:10:03.664-06:002012-01-02T20:10:03.664-06:00Great post! I really enjoyed reading your explanat...Great post! I really enjoyed reading your explanation. After 2 decades in 1st grade before moving to 4th 4 years ago, I find it helpful to move from the concrete to abstract with 4th graders too. When teaching about equality, I talk about how a see-saw works. The students always discuss without my prompting them how you have to get both sides the same or someone always stays up in the air. (If your school has a see-saw, I'd recommend starting your lesson there.) The analogy of balancing people on a see-saw really helps some students understand that both sides of a math equation have to balance too. After the discussion about making both sides the same or equal, we use scales for balance equations with objects and then move on to equations. (Of course, some students don't need all of this so you can move on to the actual written equations.) My students are much better at thinking of the equal sign as showing balance or equality and not "it means the answer comes next" thanks to the visual image of a see-saw.Marthahttps://www.blogger.com/profile/08389747095442084900noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-76896091647899192422012-01-02T20:04:39.230-06:002012-01-02T20:04:39.230-06:00This comment has been removed by the author.Marthahttps://www.blogger.com/profile/08389747095442084900noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-63677382884248248772012-01-02T19:31:46.097-06:002012-01-02T19:31:46.097-06:00As a second grade teacher, I have this conversatio...As a second grade teacher, I have this conversation with my students when I teach finding the missing values for number sentences such as 50+10= __+40. They automatically want to put 60 in the blank. We have to go through the motions and use the vocabulary over and over again. Some get it, some don't. But I did not realize the misconception until I started teaching this concept in 2nd grade. Thanks for sharing your thoughts!Ms. Akinhttps://www.blogger.com/profile/12834745424698802085noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-83035542766719284452012-01-01T22:20:56.449-06:002012-01-01T22:20:56.449-06:00We talk a lot about "balance" in my clas...We talk a lot about "balance" in my class. Math, like many things in life, is all about balance. If you don't have balance in an equation (the two sides don't equal each other), math won't work. I use concept lessons and "Two Problems" a lot, which help with this idea of balance. <br /><br />On a related note, have you used Hands-On Equations? It is perfect for teaching this idea of balance and equality. <br /><br />I look forward to the the next installment.<br />~Stephanie<br /><a href="http://teachinginroom6.blogspot.com" rel="nofollow">Teaching in Room 6</a>~Stephanie https://www.blogger.com/profile/00302695374678919562noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-47544566791142736432011-12-30T06:57:35.632-06:002011-12-30T06:57:35.632-06:00I LOVE THIS POST!! I have been reading your blog f...I LOVE THIS POST!! I have been reading your blog for a while (and bought a few AWESOME activities from your store)! Last year I was shocked at how difficult it was to do checks for algebraic equations because the students had NO IDEA that = meant that both sides were the same. We are still working on it now, even with my smarty Algebra kids! <br /><br />Kate<br />http://tothesquareinch.wordpress.comKatehttps://www.blogger.com/profile/00769217636041844512noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-73537320051201594602011-12-29T22:20:04.934-06:002011-12-29T22:20:04.934-06:00I loved this post. Thanks so much for your hard wo...I loved this post. Thanks so much for your hard work. <br /><br />Tanya<br /><a href="http://msvs3rdgradeclass.blogspot.com/" rel="nofollow">A Class Act</a>Tanya V.https://www.blogger.com/profile/12252780991358392486noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-32675277353112069162011-12-29T18:06:37.456-06:002011-12-29T18:06:37.456-06:00As a 7th grade math teacher I deal with the miscon...As a 7th grade math teacher I deal with the misconception of the running equal sign. I have seen this misconception perpetuated by teachers (and I have probably been guilty of it myself) while teaching order of operations.<br /><br />It is amazing how hard it is to break these types of misconceptions that my students have by the time they get to middle school.<br /><br />Great post!Sherriehttps://www.blogger.com/profile/16110420412281024292noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-28993889712002723802011-12-29T17:36:46.092-06:002011-12-29T17:36:46.092-06:00Loved this post! Sometimes I think the sad truth ...Loved this post! Sometimes I think the sad truth is that many teachers are uncomfortable with math themselves! So the kids walk away at times not knowing the basics and whys of math. Thanks for starting the conversation. I just love it.<br />Adrianne<br />www.kidscogworks.comAnonymoushttps://www.blogger.com/profile/17784224284761467528noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-68085392814569797572011-12-29T13:54:19.334-06:002011-12-29T13:54:19.334-06:00When I started teaching 4th grade 7 years ago, I r...When I started teaching 4th grade 7 years ago, I ran into the same thing you did with your students. Both districts I have worked in use inquiry based math, and we have taught more of the why behind math than I ever learned growing up. Through the years, less of my students come to my class thinking that it means the answer comes next, and most understand that it means the two sides are equal. It is great to see this change, and I do attribute it to the way we are teaching math. The algebra that I am able to do with my class just because they understand the concept of the two sides being equal is well beyond what other fourth graders are doing. It is so much fun!<br />I love math, and it is so much fun to teach now that I understand how kids learn math concepts. I teach in Utah, where we have an Elementary Math Endorsement, which makes us "math specialists." It was such an eye opening experience to learn about the research on how kids learn math differently and at different times, just like they learn to read. I love that you have started this conversation, and look forward to reading some more of your ideas!annzitohttps://www.blogger.com/profile/00707032634102770623noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-58094691611289066392011-12-29T12:32:51.743-06:002011-12-29T12:32:51.743-06:00Yes!! The Balancing Act equations are THE hardest....Yes!! The Balancing Act equations are THE hardest...why?! lol...and also - another "equal" that's difficult, for my 2nd graders especially, is the line that you draw under a vertical math problem...I don't know why, but they DON'T want to put that when writing out their math problems...<br />Jen ROss<br /><b><i><a href="http://theteacherscauldron.blogspot.com/" rel="nofollow">The Teachers’ Cauldron</a></i></b>Jen Rhttps://www.blogger.com/profile/17632307261949996727noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-48159337895594639362011-12-29T11:52:38.923-06:002011-12-29T11:52:38.923-06:00I totally agree! I teach 5th grade and I posed thi...I totally agree! I teach 5th grade and I posed this problem a few weeks ago: 5 + x = 12 + 8<br /><br />The most common response was: 7. I guess they just ignored the 8? They were thinking 5 + 7 =12<br /><br />The second most common response was: "That's not right. Why are there two numbers on both sides of the equation?" That's when I realized that this error was a mistake on my part. We've got to show students multiple representations of content knowledge.<br /><br />Oh, some students were correct with their answer, which made feel a little better about myself.Katiehttps://www.blogger.com/profile/05199727073486635335noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-22934493611802653112011-12-29T08:54:37.726-06:002011-12-29T08:54:37.726-06:00I LOVED this post and can't wait to read more ...I LOVED this post and can't wait to read more like this!! And I really loved your freebie from TN--thank you so much for sharing all of this Janaye!<br />Kristen<br /><a href="http://ladybugsteacherfiles.blogspot.com/" rel="nofollow">Ladybug's Teacher Files</a>Kristenhttps://www.blogger.com/profile/10502794638519071800noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-71153189749691673832011-12-28T23:33:56.777-06:002011-12-28T23:33:56.777-06:00Did you read my mind?! After observing the mid yea...Did you read my mind?! After observing the mid year state test my students took in December, it is SO important for [3rd grade] students to understand this concept. I've been thinking about how to present the concept, and the balance is perfect. I never thought, until recently, to explicitly teach the concept of a "balanced" equation in elementary school. Thanks for you post, and I can't wait fo more!<br /><br /><br />Meg<br /><a href="http://thirdgrade-firststate.blogspot.com/" rel="nofollow">Third Grade in the First State</a>meghanhttps://www.blogger.com/profile/07601059640778499239noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-42105204047113747652011-12-28T23:33:07.618-06:002011-12-28T23:33:07.618-06:00Great post! I am a member of a math lesson study ...Great post! I am a member of a math lesson study that includes teachers from grades K/1 (ME!) to 8th grade. We discussed this concept this year and so I have changed my way of doing "Number of the Day". Number of the Day is when I give my kiddos a number like 10 and they have to think of equations that will equal ten - for example, 8+2=10. Now I list some of the equations in this format: 10=2+8 so that the children get used to the equals sign meaning "the same as" rather than "the answer is coming now".<br /><br />I love math and am so glad you are taking the time to reflect on it! This is so good for all of us! Thank you!<br />Camille<br /><a href="http://camillesopendoor.blogspot.com/" rel="nofollow">An Open Door</a>Camillehttps://www.blogger.com/profile/15944280556679586400noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-66463612305135206742011-12-28T22:33:25.290-06:002011-12-28T22:33:25.290-06:00We use Bridges math in my district {not sure if yo...We use Bridges math in my district {not sure if you're familiar with it} but that is a concept I taught for the first time using this new math resource...= means "the same as". My firsties were thrilled with this piece of information and it really made sense to them...<br /><br />Great post!<br /><br />Holly<br /><b><a href="http://crisscrossapplesauceinfirstgrade.blogspot.com/" rel="nofollow">Crisscross Applesauce in First Grade</a></b>Hollyhttps://www.blogger.com/profile/10861143488616582042noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-1913908384647509192011-12-28T22:03:52.258-06:002011-12-28T22:03:52.258-06:00Love this! I actually had this discussion a couple...Love this! I actually had this discussion a couple of weeks ago - my 9 year old is gifted mathmatically and he understood that the equals sign means "the same as" but my 12 year old daughter had no real concept of what the equals sign meant! My district is actively working on this, but there solution is to just ban the word "equals" altogether. Now we're supposed to call it "the same as sign" so an addition sentence would be read as "4 added to 3 is the same as 7" for "4+3=7". Not a bad concept entirely, but I have a problem with not teaching "plus" "minus" and "equals" because that is what the rest of the country is still going to say. So I think we do a disservice by not teaching the CONCEPT instead of just replacing vocabulary. <br /><br />By the way, I have a little monkey scale from Lakeshore and you hang bananas on either end. Thus children can see that 2 and 3 bananas on one side is the same as hanging the 5 bananas on the other side. Kind of hard to explain it, but it works and it's just cute enough to motivate the students to want to explore it!<br /><br />Can't wait to read more, good job!<br /><br />Jennifer @ <a href="http://herdingkats.blogspot.com/" rel="nofollow">Herding Kats In Kindergarten</a>Jennifer K.https://www.blogger.com/profile/15114666136412667718noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-59719720502501913902011-12-28T22:03:42.935-06:002011-12-28T22:03:42.935-06:00I'm so glad you're addressing these issues...I'm so glad you're addressing these issues. Number sense is a huge issue with our kids, and I think a lot of it has to do with the drive toward testing at such early grades. Kids aren't given enough opportunity to manipulate numbers and values within a structure and see what happens! <br /><br />There are ways we can integrate these kinds of experiences into kids' math instruction starting at an early age. If we can do this, kids will actually understand what they're doing when they are performing operations! <br /><br />Keep up the great posting!<br /><br /><a href="http://buzzingwithmsb.blogspot.com" rel="nofollow">Buzzing with Ms. B</a>Ms. Chrissy Bhttps://www.blogger.com/profile/18269577180650924790noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-65270162621983921322011-12-28T21:44:03.151-06:002011-12-28T21:44:03.151-06:00Great post!!! I teach 4th & 5th grade Math an...Great post!!! I teach 4th & 5th grade Math and am looking forward to more posts! Thank you.agarciahttps://www.blogger.com/profile/18430428236837198953noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-20774954237841437592011-12-28T21:39:19.116-06:002011-12-28T21:39:19.116-06:00Here! Here! We do our kids such a disservice by ...Here! Here! We do our kids such a disservice by teaching them incorrectly on this simple matter. I took a math workshop a couple summers ago that highlighted this misconception. Love this post. Keep it up!<br /><i><b><a href="http://2bhoneybunch.blogspot.com/" rel="nofollow">2B Honey Bunch</a></b></i>Erikahttps://www.blogger.com/profile/01535929124900144607noreply@blogger.comtag:blogger.com,1999:blog-8017698507183263684.post-46564316399781970452011-12-28T21:33:44.656-06:002011-12-28T21:33:44.656-06:00Not sure how old you are, but as a kid we had this...Not sure how old you are, but as a kid we had this game where we would put numbers on one side and the other side had different numbers. Ifnthey wer of the same value, then the balance would be level. There is great merit in everyone teaching this to their students and modeling a balance scale to show this process.Patty Rutenbarhttps://www.blogger.com/profile/01326196976806184546noreply@blogger.com