How Can You Teach Subtraction Regrouping with Understanding?
Our third and fourth grades have been making the uphill trek to teach subtraction regrouping. We have taught kids to first use expanded form/decomposing numbers so that understanding may accompany all of the crossing out/regrouping that occurs. I started out calling it expanded form, but then I realized that having the plus signs in the expanded form would cause confusion when kids are actuallysubtracting. More accurate language would be “decomposing the numbers”. Anyhow, we used the method of decomposing numbers after students had lots of experience with base ten block subtracting. Some students are still using the base ten blocks to subtract because their understanding of the number decomposition isn’t there yet.
Subtraction Regrouping with Number Decomposition
Subtraction regrouping takes at least two weeks to perfect in my experience. After the students have had ample experience decomposing numbers with subtraction regrouping, then we move to the traditional algorithm using the same language we did when the numbers were decomposed–that is we make sure that we call the tens we are marking out tens etc. For example, if we cross out a seven in the tens place to write a six above it, we call it six tens NOT six. To help students’ understanding, it is important that the teacher language is precise and that the students are held accountable to use precise language as well.
One last side note: This week when I was working with an intervention group, I noticed that some students looked confused when I said the word regroup, so I changed my language. I called regrouping exchanging. They still looked confused so I changed my vocabulary again to the word trade. Students seemed to understand that better. I think that is something that kids are familiar with. They are always talking about trading a baseball card, something on their lunch plate, a piece of candy etc.
Happy teaching!
Use These in Your Classroom for Addition Fact Fluency
I have to share two great videos one of our teachers found for teaching doubles math facts. She also inspired me to find a video for bonds of ten. This year our district opened up the You Tube site for us to use. Previously You Tube had been blocked. The kids absolutely L-O-V-E the doubles videos! They are great if kids are restless or need a moment to move since they have a fun beat. See for yourself!
Now, in my head when I’m going home, I’m singing, “Doubles, Doubles I can Add Doubles.”
Have You Tried This Simple Idea to Ensure Serious Test Takers?
So often I see students blow off a test, rush through it, make careless errors, and become too lazy to show their work. Because of this, I have to share what this 5th grade teacher did whenever her students did horribly on a test. Many of the grades were failing. Now regardless of whether the grades were failing or not, she will have them do this–student test reflections. I love how she is holding the students accountable for their work by reflecting their test performance. Just take a look below at their writing prompt. (I am sharing this with her permission.)
Have You Taught Multi Digit Even and Odd Numbers Like This?
I thought I KNEW how to teach even and odd numbers until I saw this! Knowing that our third graders always miss the simple skill of even and odd numbers with two and three digits, I thought I would target this misconception. I told them that even numbers have partners and odd numbers have a lonely someone left out. To teach even and odd numbers,I asked if several small numbers like 4, 5, 6, 7, 8 were even or odd and drew pictures of counters to ask if they had a partner. With this idea, I asked if 227 was even or odd. I told the kids to write this down on a scrap of paper and cover it over with their hand so no one could see what they wrote. The teacher and I surveyed the room as kids secretly moved their hand. Just about half of the class thought it was even and half thought it was odd. Thinking of the 8 Mathematical Practices, I didn’t want to spill the beans. I wanted the students to really think about whether this number would come out with an even number of partners. I told them to start drawing 227 counters on their paper to see if each counter would come out with a partner. I knew this could be a tedious task, but to my astonishment, I saw a few kids actually drawing base ten blocks….WOW! I couldn’t believe they had thought of this. I had never thought of drawing base ten blocks!!!
Even and Odd with Base Ten Illustrations
This student started drawing counters but when he realized this would take way too long, he drew base ten blocks.
This is my favorite illustration of student work because the student drew the place value chart and plainly matched up each block with a partner
Through all of their work building numbers in second grade, they were so comfortable and flexible with base ten blocks, they actually saw them as tools!! After we did this little exercise, which took about 15 minutes, we resurveyed the class and only 3 of the 25 students still thought the number was even. Success through taking the time for students thinking!
How Do you Teach Regrouping with Understanding?
If kids aren’t building with base ten blocks to add and problem solve FOR WEEKS initially, they will get no where with their number sense understanding for regrouping. Under common core standards, we are heading towards the understanding of the traditional algorithm in the 4th grade standard–not just being quick at a procedure of crossing out numbers and writing new ones above them. Mistakenly 2 years ago we tried to rush the traditional algorithm with our second graders. As a result they are still struggling with this in 4th grade. So here is the success story of what we did in second grade last year. Nearing the end of the year, there were several skills that hadn’t been taught to the degree that they needed to be such as geometry etc. I knew without the foundation of addition, counting, and problem solving we would be up against a wall again in 3rd grade, so we focused on these skills. Throughout the year we spent a lot of time filling out number charts and discussing pattens on the hundreds chart above 100 using these:
Counting you ask? Yes, we spent time counting and looking at patterns in numbers. I know it is in the standard so that is part of why we counted, but counting is so much more important than teaching because it is the standard. How can students reason about whether their answer makes sense if they can’t count? Reasoning about math is in the mathematical practices several times. Students who can’t count, can’t estimate and can’t round because they have NO idea about where the number comes in the whole sequence of numbers.
Second graders last year solved a CGI word problem each day while they were learning addition and subtraction. Students spent several weeks using base ten blocks to solve their addition and subtraction regrouping problems. When students weren’t permitted to use the actual blocks, we prompted them to draw illustrations of the blocks to help them solve their problems. Even after students were shown how the traditional algorithm worked with their blocks, most of them tended towards drawing a picture of the blocks to solve the problem. Most were successful doing this. I was satisfied with this progress because I knew in 3rd and 4th grade that they would again have an opportunity to learn the traditional algorithm and other addition/subtraction strategies.
So here is how we are beginning with the kiddos in 3rd and 4th grades this year to teach addition regrouping. The kids are still given the opportunity to use blocks if needed to formulate understanding. Now I know that in showing them how to regroup the kids aren’t really “discovering” or “constructing” the algorithm themselves, but they are gaining an understanding. I just don’t think we have enough time in the year for the kids to discover everything and they must be shown some things. I haven’t arrived at that place yet where I think in CGI utopia…maybe I will get there someday?? (Don’t get me wrong, I find value in CGI) For right now the kids are getting this method of teaching addition regrouping and making sense of it. I’m happy and the kids are learning.
Traditional Algorithm Behind the Scenes
Now what I’m about to show you is the students’ first experience with regrouping like is pictured above. It isn’t cute at all…not worthy of for sale anywhere…but it is real and handwritten. To make it on a handwritten page was just so much faster than doing it on computer so it is what it is. I wanted to create columns so the students wouldn’t get their numbers confused. This worked well. I didn’t have the kids put pluses between the numbers like true expanded form to keep them from confusion later on when we do subtraction regrouping similar to this.
We discovered that students had a difficult time in the hundreds column when they had a number regroup to the thousands place. They weren’t used to putting two numbers together that weren’t zeros so this seemed to confuse them. If we had three digit adding to do over, we would have the kids include a thousands column so that they could regroup their thousands there at first until they made the connection that they could put two digits other than zeros in the left hand column. In other words, we would have them add one column more than the number of digits that there were in the number. For example…
Later on last week, we taught the kids to regroup without the columns drawn and without the numbers being decomposed into hundreds, tens, and ones. We continued to have the kids draw the arrows and to estimate their answer. It was rocky at first and about half of the class got regrouping with numbers written in standard form (just normal). They will be working on regrouping again early next week.
Wouldn’t This Make a Great Gift for a Teacher?!
This kind retired airforce veteran named Ray crafts beautiful handmade teacher name plaques, and he made one for me. He’s given them to many teachers in his hometown. I was thinking they would make great gifts for a new teacher during Christmas time, for birthdays, or if you are a mentor. I know when I have mentored teachers, I am always trying to think about a perfect gift! Nothing says I thought about you more than a personalized gift with your name. Take a visit to his Etsy storeif you would like to have one of these beautiful name plaques for your desk or for someone you know.
You’ll Love These Practice Pages at Your Fingertips
This week I have tried out Super Teacher Worksheetssite for the first time. This site has helped me so much when I’ve been in a rush. They have worksheets and activities for just about EVERYTHING! I have been struggling to find decimal activities for 5th grade, but just look at some of the things I found! Decimal Number line practice and ordering decimal card sorts. There are several of each of this type of practice so kids have time to perfect the skill.
Decimal Number Lines–A Freebie!
Ordering Decimals Card Sort
I was also needing some counting resources for kindergarten, and I found this card sort for them…just when I was thinking of making one, Super Teacher Worksheets came to the rescue!
Not only that, but I also found some ten frame practice worksheets. I LOVE ten frames and these will work out great for 1st and 2nd grade to practice their math facts.
Ten Frames Practice
I love how the site has their resources listed on the side of the screen so that you can quickly find the topic you need. They even had a file cabinet for you to store all of your resources as long as you have an account with them.
See the “My Filing Cabinet Button” in red in the middle.
Then I taught a lesson about fact families in first grade and I was thinking I sure do need a smart board lesson with a fact family house. Guess what? Super Teacher Worksheets had one of those, too, through their sister site Modern Chalkboard. I just adapted it for addition/subtraction instead of multiplication.
Fact Family Smart Boards
I’m a just a little biased because I teach math all the time, but Super Teacher Worksheets also has science, math, literacy, social studies, seasonal, and math (oh, did I say math again??) resources! I know we all need some grammar worksheets since we (my district) don’t even have grammar books anymore. Super Teacher Worksheets also boasts some fun puzzle generators and math drill worksheet generators, too! Not only that, Super Teacher Worksheets has some teacher helpers such as desk name tags, award certificates, sticker charts, calendars and more. Many of these items are free, so make sure you check it out! SEE…
Sticker Chart
Super Teacher Worksheets only charges $19.95 for an entire year’s subscription which is only about $1.67 a month–a great value. Many of their worksheets are FREE and Modern Chalkboard’s resources are ALL FREE! 
More Common Core Test Items
Apparently, the Smarter Balanced Consortium IS smarter or at least busier! They definitely have more sample test items posted than the eastern side of the U.S. We have only a sprinkling of sample test items with PARCC. If you go to Smarter Balanced’s website they have printable PDF’s of test questions available to download as well as some others which are animated to view. Directly below is one of the test questions from the printable PDF’s. Clicking on this items will take you to the page where there are links to other grade level’s test questions.
The following two test questions are from the interactive animated sample items. Clicking on either of these will take you to the site where more of these are available.
I’m totally printing those so at least we know what we will be aiming towards next year. One thing I have noticed is that the Smarter Balanced consortium’s test did include a multiple choice item (when I say multiple choice, I mean an A,B,C, or D response). I have not seen any of those with the PARCC assessment’s sample items. I wonder if they will be different when it all comes down to test time?
Use This New, Free, Quick, and Easy Classroom Management Tool
If you haven’t already heard of Class Dojo, a cutting edge classroom management tool, let me fill you in.
Our fourth and fifth grade teachers are using it and they absolutely L-O-V-E it!! Class Dojo is a website which allows you to load all of your students and keep up with their behaviors, positive or negative, based on a point system. You can upload the behaviors you want that match your classroom rules and expectations. For example, you can include behaviors such as “off task”, “participating”, “showing respect” etc. The entire system is on a website and/or it can be used as an app on an ipad or iphone (and android).
The marvelous thing about this is there is no walking over to a behavior chart to change a card or clip etc. You can carry the ipad around with you and immediately respond to behaviors. Then when you want to reward or use a consequence, you simply click/touch the child’s name. Each child has a cute colorful avatar beside their name.
They also have a little red bubble that shows their points accumulated. Students avatars can be projected onto a screen or smart board so that they can see their avatars and points. A whole classroom can be given a point at one time too–say for example all of the students walked quietly in the hall or all students were working hard on an assignment. I also really like the “random” button. You can push the random button and different names will flash on the screen until the program finally lands on one name. Then when it stops on that one name, you can look to see if that student is using appropriate behavior and record his/her point accordingly. This especially keeps the kids sitting up straight if the names are projected on a screen.
What’s even better is that there can be instant parent communication. Parents can have a code to view their child’s behavior and see how they are behaving. Students can even change and decorate their avatar to look like they want it to. The best part about Class Dojo–it is totally FREE!!
Another Cute Door {or Bulletin Board} Decoration!
Here it is… FINALLY! My new door decoration for this year. I named my room the “Math Cave” since my room is so small and huddled behind a bunch of bookshelves. I feel sort of like my room IS a cave! All of the eyeballs you see are like imaginary creatures in the cave. The comments in speech bubbles around the door suggest that the creatures are afraid of the dark. To bring in some mathematical thinking, the purple poster in the center prompts the children to count the creatures’ eyeballs in groups of two to find out how many creatures are in the dark math cave. You can download the bulletin board speech bubbles and sign for free right here if you want to recreate the door idea. I made most of the eyeballs out of leftover cutouts from the cricut cutter when various letters were cut out. It really bothers me that the words “Math Cave” are off center, but I glued them down and couldn’t very well rip them off without destroying the background. Oh, well, there are more important things to worry about at this time of the school year! The leafy green border is like vines growing around the cave.
Below are posted two pictures of my door. The second one is closer up so you can see the words more easily.
