## Thursday, November 29, 2012

### The Meaning of the Equal Sign

First, a little exciting news to share.  I was notified today that I'll be presenting at CAMT next July.  For those of you outside of Texas, that's our state mathematics conference.  I'm doing two sessions of a K-2 workshop on number sense routines--dot cards, 5- and 10-frames, rekenreks, etc.  If you're in the San Antonio area July 10-12, I hope to see you!

Now on to business.  Ask a kiddo who has just written 2 + 3 = 5 if it's okay to write it 5 = 2 + 3 and you're likely to get an emphatic NO!  Enter common core standard 1.OA.7:
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
A great hands-on way to introduce this concept is actually a pan or bucket balance.

Start by having students build two equations that both equal five using teddy bear counters.  For example 2 green bears and 3 red bears for the first equation and 1 yellow bear and 4 blue bears for the second equation.  Put the bears from the first equation on one side of the balance and the bears from the other equation on the other side of the balance.  You can even put a sticky note with an equal sign on the base of the balance.  The balance will, well, balance.  :)  Try this with other equations ("Hmmmm, I wonder if this would work for combinations for 6?").  Be sure to model some false statements, too.

When your kiddos are ready for a little practice, I made a mat and some cards they can use to explore different equations and determine if they are true or false.  Notice that you still want to have manipulatives to connect the concrete learning with the abstract equations.  The kiddos basically just take two cards, place them on either side of the equal sign on the mat, build the number, and determine if the equation is true or false.  Students can record their work in their math journal, and if they also draw a picture to represent their equation, you are bringing in representation.

UPDATE 12/27:  I expanded this idea into a complete unit on the meaning of the equal sign!  Check it out at my TpT store.  Check out this blog post to see all the activities from the unit in action!

1. Thank you for the cards!!! This year I used the scales!!! The kids loved the scales, but i think the cards are a good visual too!!!
Amy Burton

1. You're welcome, Amy! See, you were one step ahead of me with the scales. :)

2. I follow your site daily now! It's been very helpful to my team as we unpack the new CCLS! For some reason this link to the balance activity did not work-error popped up. I will try again tomorrow! Thanks for all you share! Kelly Syracuse, NY

1. Glad the blog is helpful to you, and I'm sorry for the trouble! Is it maybe being blocked by a school filter? I just checked the settings and it's shared to anyone with the link. If you still have trouble tomorrow email me! mathcoachcorner@gmail.com

3. Donna,
This is genius! O love it and can't wait to use it with my Firsties! Just found your blog recently and am now a faithful follower. I really look forward to your posts and have spent time looking into your older ones. I am a first grade teacher in Michigan and my district uses Investigations. Your stuff has been an awesome supplement to my math teaching. Thank you so much for creating and sharing!
Heather

1. Thanks so much, Heather! I'm glad you've found some useful stuff. :)

4. This year I have really started to LOVE using my balance for this exact activity with my second graders! Well, instead of bears I use unifix cubes). Nothing can make it more clear than this! But now I find myself on the lookout for a real scale so that I can do accurately this with bigger numbers. I find that my cheapo scale is not always accurate...I just put my pinky on the side that needs a little "push" :)

-Alyssha
Teaching and Tapas: 2nd Grade in Spain

1. Sure, unifix cubes are a great alternative. I love the little push thing. Ha ha. :)

5. Thank you so much for sharing this. We use EnVisions and the way the lesson was presented was complicated and confusing to the children. This will make it so much less complicated andconfusing! I can't wait to revisit this concept. Liz in South Dakota. P.S. Congrats on being chosen to present at the conferece! :)

1. I'm glad this was more clear! And, thanks, I'm looking forward to presenting!

Shibahn

1. My pleasure, Shibahn! :)

7. I love, Love, LOVE this idea!! I just did a similar game with my third graders. We started with introducing the balanced scale. Then 7 cards, face cards removed, were dealt face up. They were to choose cards that balanced the equation. Each card used counted as one point. So 5=5 was worth 2 pts, 2+3=5 was 3 pts...After finding the most valuable equation they record it on their balanced scale recording sheet. Used cards were replaced, then the partner had their turn. After 4 turns each they added up the points to see who the winner was. They loved the competition, but for most it was mainly cooperation! They were just excited to see how many ways they could balance the equation!

1. Very creative idea! Anytime you can make something into a game it's good. :)

8. We have been discussing this a lot in my district recently. We have really tried to make the equal sign equivalent (no pun intended) to a balance. Students really have a tough time saying an equation is correct when the answer is on the left on the right as they have typically seen it. Students tend to say it's incorrect.

A couple of other math coaches and I have been trying to stay away from "is the same as". The value on both sides of the equation are the same but visually, they aren't, as you can see with some of your pictures. 1 red + 4 yellow is not the same as 5 yellow. It can really be a matter of semantics but if students can start using math appropriate terminology such as equal, equivalent, has the same value as - it would only help them in the long run and it goes along perfectly with Standard of Mathematical Practice #6 Attend to precision...where using precise math vocabulary definitely fits! :)

1. Point taken. I really like 'has the same value as'! Just as we move our kiddos from concrete to abstract learning, I think we also need to connect formal math language to more kid-friendly wording initially. I definitely agree that they should read the equal sign as "is equal to", and I did not mean to imply that they wouldn't. The purpose of this activity and the verbiage was to help them connect the formal math vocabulary (equal) to words they were more familiar with. But I really do like 'has the same value as"... May have to make a little change there. :)

9. Thank you so much for the addition mat and numbers. We have been working with manipulatives and are just starting to add writing the numbers. This is an excellent intermediate step to writing it themselves. The equation step has been confusing for a few of my little cherubs. Am hopeful that these will allow them to see the form and internalize it. We too have used the balance previously. Thanks again for sharing!

1. I hope this helps your kiddos! It is a pretty abstract concept.

10. Donna, Your timing is great. I stumbled on an activity that mentioned the true/false concept. This gives more background to support it. Thanks so much! Elizabeth

1. I always love comments like yours, Elizabeth! It's so cool when something is right on time. :)

11. I love the idea of using the balance scale - I can't wait to try this with my students!

1. I'm sure they'll love it!

12. Thank you for supplying the tools I needed. I already had my lesson planned with the balance scale but I needed the materials to make the transition to numeral equations.

1. Yea! So glad it was useful to you, Jeannette! :)

13. Excellent idea! I would love to have cards for the larger numbers to 20 for my second graders. They seem to get stumped by larger numbers. Thanks so much!

1. Great idea, Christen! I sometimes get hyper-focused on numbers to ten. Ha ha.

14. I love all your ideas. I am a new teacher and you give me great ideas and ways to look at numbers and math than our math books does. Thank you and keep it up. You are an inspiration to me improving in how I look at math and teach!

1. What a sweet comment, Michelle!! I am so passionate about math, and it's always nice to hear that some of what I write is useful to others! Have a wonderful holiday! :)

15. This is such a great idea! Thank You for helping me to teach the kiddos in my classroom. I read your blog often and am always coming across something that I love! Thank You for sharing!

1. Thanks so much, Raley! Glad you're finding some of my ramblings useful. :)

2. Thanks so much, Raley! Glad you're finding some of my ramblings useful. :)

16. Great activity Donna!! My kiddos definitely need practice with this! Thanks for sharing! Where did you get the little button manipulative? I know I could use unifix cubes, but these look really fun!

Ali

1. I got those little counters when they were cleaning out a closet at our admin building a few years back! Never seen anything like it again. They actually stack on top of each other.

17. This is great! This helps make an abstract idea concrete for my first graders

1. Absolutely, Mini! It makes a whole lot more sense when they see each side "acted out".

2. Sorry, MinDi! Didn't mean to leave out your D. :)

18. I like to read what you explain here and I remember long time a go when my teacher tought me the meaning of multiplication that is the repetition of addition. 5 x 2 = there are five of number 2, isn't it?

19. Thank you so much for sharing this! I have just printed the cards and can't wait to use them.

1. Great! I hope it works well for you and the kiddos. :)

20. Hello Donna! I am SOOO glad you created this. It is hard to find various activities for this standard, but you took a simple concept and made it into action. Thanks again. My students are going to rock this standard, thanks to you!!! I can't wait to use them next week.

1. Thanks so much for the kind words, Lakisha! I hope your kiddos love the activities. :)