All Things upper Elementary, a blog that I follow regularly recently had a post about teaching students to really develop problem-solving skills, rather than just learn rote algorithms. See her fantastic post here. This post really resonated with me as we are in the final days of our unit on subtraction. Most of the kids can use the algorithm successfully to subtract multi-digit numbers. Some cannot. But even those that can use the algorithm don't really understand what they are doing. To quote the ATUE:
"A written algorithm is meant to SHOW you have to think, NOT teach you how to think."
I realized that I needed to teach more thinking and less algorithm. So today's freebie lesson plan is designed to focus students on using rounding and estimation to help them with subtraction.
Materials: personal whiteboards, marker, and eraser for each child, the same for the teacher.
Duration: About 30 minutes (can be made longer or shorter) Grade Level: 3-5
1. Warm-Up: Pose some subtraction problems using multiples of ten. Start with problems like 90-70 = ? and end with problems like 8,000 - 5,000.
2. Write your final problem in the warm up on the board (let's say it's 8,000 - 5,000). Pose a related problem, leaving the first number the same, such as 8,000 - 4,875. Have the students estimate a solution and show their answer. If more than a few students get the answer wrong (it should still be 5,000), demonstrate how 4,875 rounds up to 5,000. So the answer will be about the same as the original problem. You can't just use the front of the number to estimate the answer. You need to look at the whole number.
Do several more examples, coaching after each one as needed. Once most of the class can successfully estimate the difference for each problem you pose, ask them to not end their estimates in zero. Pose problems in a sequence like this:
Ask students to tell how they decided if the difference was more or less than their estimate. If students do not come up with a method, show them how when the subtrahend is less than the estimate, the difference will be larger. Pose several problems using this method.
By using a lesson progression like this, you can help students think beyond the algorithm. Enjoy!
After a rough start, my leveled Math class is going smoothly at last. My students have gotten into a routine of a whole-class lesson on Monday (with pre-test), differentiated instruction based on the pre-test on Tuesday, Wednesday, and Thursday, finishing with another whole-class lesson on Friday with a final, standards-based quiz on that day. Most students are seeing growth as they graph their pre- and post-assessments. With this leveled group, I have often found that the class doesn't usually fall into three groups, like I have seen with heterogeneous groups in the past. Quite often, they only fall into two groups. This has lead to some changes in my I Love Math groups. Most of the time, I divide the class into two groups. One works with me while the other works on their Ten Marks or Manga High assignments on the computer. Then the switch. When there is a preponderance of students who have mastered the pre-test, I will often include Wednesday as an additional whole-class lesson.
This past week we worked on rounding. Rounding was one of those skills that no one in the class was even close to mastering, even after the first whole-class lesson. I had to dig deeper in order to meet my students' needs.
The first resources I used was Learn Zillion. Using the Quick Code LZ525 you can see a great lesson that uses a number line to show how to round. We used the following template:
For each number, they created an individual number line and place the original number as a dot on that number line. This was a time consuming process, but after doing several together, the light bulb went on for many struggling students who could finally SEE what it means to round.
After a differentiation day where I reinforced this method, I taught method number 2. This I introduced as a "game" I called "Slap! Trap!". I passed out a place value chart and a highlighter. (Kids always get excited when the highlighters come out!) Students used a pencil and the chart to write the number to round.
I announced: "Round to the nearest thousands!". Students repeated: "Thousands, thousands, thousands, slap, TRAP!" When they say slap, they use their left pointer finger to cover the digit in the given place.
When they say trap, they color the digit in the next place to the right with the highlighter. If the digit they "trapped" is 5 or more, the digit they "slapped" will go up by one. If not, it will stay the same.
All the digits to the right of the slapped/rounded digit turn into zeroes. Any digits to the left of the slapped/rounded digit stay the same. After the number line method, this seemed like a shortcut to many students.
After instruction, some students gravitated to one method; some to the other. In the end, all students benefitted from learning both methods.
Those of you that know me well know my passion for differentiated groupings that I call "I Love Math" groups. I Love Math is a structure that divides the class into a high, average, and low group and cycles those groups through three different stations. Once the students get the rotations (which are always in the same order no matter what group the child starts with), things run like clockwork. In the past I have always had an aide, Title One teacher, or special education teacher in my room to help ensure things go smoothly. That way two of the groups have adult supervision.
This year, for the first time, our grade has been required to level for Math. Since I was in the fifth grade at the time, I could not attend the meetings where they assigned teachers to the different levels. I have one of the average groups. Two of our classes (mine and the high group) do not have a support person in the classroom for Math. The other six specialist are divided among the bottom three classes. This is my first year trying I Love Math groups by myself. I knew it would be a real test of the structure that I love so much. If I can do it alone, then there is hope for other teachers who are solo practitioners. And yes, even a leveled Math group has enough differences in it to warrant differentiated instruction.
First of I decided that I needed to have I Love Math groups a lot more often. In the past I have done them regularly (once or twice a week), but only as needed. I know that the more I do them, the better the students get at it. I decided that this year I would have a whole class lesson on Monday which would end with an ungraded pre-test. This would be used to create differentiated groups Tuesday through Thursday. Friday will be another whole class lesson and post-test.
I also knew that I needed to use technology to help me keep track of the progress of my students in the same way that another person used to do. Luckily I found Ten Marks, a free site where I can assign specific skill lessons for my students.
After one week of following this plan the results have been fairly good. Technology has been the biggest challenge. Our wireless internet is not always reliable and the students are not used to logging in to the computers and finding websites in a timely manner. I hope that time and experience will help the students complete this part of the task more quickly and easily. If not, I may have to alter the activities or the order. I wish I had enough computers for all of the students to start on them and then move to other activities, but the most I can get are 8.
Great ideas are worth the time it takes to make them successful. I'm up for the challenge!
This summer I have embarked on a number of curriculum projects, mostly around the Common Core State Standards (CCSS). For Math I wanted to increase the amount of differentiation and technology as well as firmly ground my teaching in the Common Core. The first thing I noticed when I counted up the standards was that there was the same number of standards as full weeks in the school year. That means that my students will have to master one standard a week! At first that thought was quite daunting. My next thought was this is an opportunity to have a very organized curriculum based on a single standard each week. This is how I decided to organize and pace each week:
At the top of each week/page is the unit title, which part of the unit. vocabulary, skills, and the Common Core standard.
Monday will be a whole class, non-differentiated lesson straight from my Math program (Everyday Math). At the end of the Math lesson, I will give a short assessment on the standard of the week. For this part of the weekly plan I didn't reinvent the wheel. Teachers Pay Teachers has several short, one page per standard bundles that are specific to my grade level. I will use these to pre-test my students and put them in differentiated groups for the next three days of the week.
Tuesday, Wednesday, and Thursdays are differentiated instruction days. Students will participate in rotational groups I call "I Love Math" groups. For more information on I Love Math Groups, listen to this podcast or watch this video (the first of 5 parts) on Youtube. Technology will help make differentiation easier. I will use the Ten Marks website on Tuesdays and the Manga High website on Thursday. Both websites allow me to assign lessons/activities and also have fun games and activities for students who finish early. Scoot Pad is a similar website (click the names for links).
Friday we are back to another whole class lesson from Everyday Math. One Friday I will give the post-test (a different "one-pager" from TpT) and this will be graded.
So that's my curriculum pacing guide for next year. I haven't offered this as a product on TpT because it is personal to my situation- a labor of love, if you will. However, if you would like a free digital copy to tweak for you own use, email me at cjones@sau61.org.
Additional EDM/CCSS Alignment Resources:
First, the "official" CCSS alignment from EDM, then the more realistic version from New York.
I recently finished one of my professional books for the summer: Assessment in Perspective: Focusing on the Reader Behind the Numbers by Claire Landrigan and Tammy Mulligan.
In this book the authors talked about triangulating data. This means taking data from different sources and compare them side-by-side to build a complete profile of a student's strengths and weaknesses. I thought a nice way to do that would be in graph form. So I created a data triangulation form for my Math class. My form is specific to the grade level I teach and the assessments we use. For you, dear reader, I have created a generic form that you can use with any grade level and whatever assessments you use.
Teaching additive volume is certainly the most complex of the Common Core Core Measurement and Data standards. I first approached the task using hands-on activities and partner work. After two class periods of instruction, I wasn't getting the results I had hoped for. Time for Plan "B". I decided to try direct instruction.
I started preparing the way I often do nowadays- by going on You Tube and looking for a video on the subject. Using the term "additive volume", I found the following video:
The description had a link to a site. This is how I found Learn Zillion. Learn Zillion is a FREE site where registered teachers can find short, quality videos that directly correlate with the Common Core standards in Math or ELA for grades 3 through high school. Teachers can use the movies to introduce or reinforce a concept or they can download the slides and create a presentation on their own. Students can rewatch these videos to help with homework using a "quick code" that their teacher gives them.
I knew the class would need lots of examples for in-class practice and homework. My favorite site for creating lots of worksheets on the same subject is Worksheet Works. On this site you can set the parameters for the Math assignment and then the site will generate a worksheet and answer key using random numbers. You can generate as many worksheets as you want on a given topic. I printed five worksheets using only composite shapes:
1 to model using a document camera
2 to create a double-sided guided and independent practice worksheet
1 page for homework
1 sheet cut up to make a matching game
Here's how the two lessons went:
Day 1
Materials:
computer that can run PowerPoint or You Tube videos, document camera, 1 copy of the modeling worksheet and answer key, copies for students of double-sided worksheet and homework, two different colors of highlighters, markers, or colored pencils, calculators (optional)
Activity Flow:
1. Review the formula for volume of rectangular prisms using chant and actions. (15 minutes)
2. Show the Learn Zillion movie or slideshow on volume of composite figures. (15 minutes)
3. Project the modeling worksheet using a document camera. Show the students how to divide the shape and color each one a different color. Then go over how to use the "clues" (numbers on the sides) to determine the length, width, and height of each shape. Add the volumes together for the answer. Approach each shape like a puzzle. Watch for the common errors of not knowing that shapes are sometimes labeled on their parallel sides and that often you must use subtraction to find out the length of a side of only one shape. Use the gradual release of responsibility model as you work. (15 minutes)
4. Pass out the student worksheets, highlighters, markers, or colored pencils. Do the first several examples with the students. Then have the students try some on their own. To boost their confidence, I projected the answer key on the board. It told them the correct answer, but not how to get it. I encouraged students to work on their own, using the answers to check their work. If they got stuck, they could raise their hand. (15 minutes)
5. Tonight's homework: homework worksheet (send home Learn Zillion quick code for help) and bring in an empty cardboard box tomorrow
Day 2
Materials:
same as Day 1 (included extra blank copies of last night's homework), tape and glue, index cards (3 per box), cardboard boxes (teacher should bring extras from home)
Activity Flow:
1. Go over the homework with the students. (5 minutes)
2. Using the homework as a guide, divide the class into two groups. Those that did well on the homework will continue with yesterday's worksheets. Again, you will project the answers to act as support. Those that did not do well on the homework will go over it with you using a fresh copy. Allow them a few minutes to work on the in-class assignment, too. (15-20 minutes, as needed)
3. Cooperative Group Activity: Divide the class into pairs. Have each student pick a cardboard box from the ones that were brought in. Each pair will: 1) Decide on the same unit of measurement for their boxes. 2) Measure and find the volume of their boxes separately and label the measurements by taping the index cards on their box. 3) Add the volumes of their boxes together and tape them together. (About 30 minutes)
Frequent evaluation is the key to helping students not pick up bad habits, particularly in Math. It may seem counter-intuitive to evaluate student responses early in the process of learning a new skill, concept, or algorithm but it is vital in order to stop bad habits from developing. One way I do this is with peer partners.
One example is an exit slip I did at the beginning of a unit on volume. I had just introduced the algorithm of length X width X height, moving students away from the "counting cubes" concept. The front of the exit slip (shown) was all counting cubes. The back was rectangle prisms that did not have cubes, but had measurements instead. It was clear, looking at the front, that only 1/2 the class really mastered counting cubes. Never fear, half the class has mastered this skill. What to do? Partners, of course!
I divided the exit slips into two piles: those that mastered counting cubes and those that didn't. I randomly assigned partners by writing the same number on the top of their paper. The following day, I passed back the exit slips. I had the students meet with the person with the same number. When meeting together, they had two jobs: 1. Figure out what each person did wrong. Write it down on the index card attached to the exit slip. Sign each other's cards. 2. Fix the incorrect problems and pass the work back in.
Having students fix their own work is a powerful teaching opportunity. It teaches students perseverance and problem-solving. The more adept student learns as well. They get to take on the role of a teacher.
I was looking through my teacher files this week to try to come up with a fun games for my kids. It is still cold with lots of snow on the ground here in northern New England. Although Easter is around the corner, spring hasn't sprung yet. The kids are pretty anxious for that to happen. When it gets above freezing they try to ditch their winter coats. I know many of you are starting "test prep" season. Our high stakes test is in October, so I don't have to worry about that until the start of school. So maybe a fun game is good for all of us. :)
One of my favorites is Hollywood Squares. It combines two things kids love: competition and whiteboards. You can use this game to review anything, but it is particularly good for vocabulary,spelling and math computation because the answers will be short enough to write quickly on a whiteboard. Set up the front of your room with three student desks in a row and three chairs in front of them. Lay one whiteboard, marker and eraser on each desk, chair, and one in front of each chair. Having one child sit on each desk, one in each chair, and one on the floor in front of each chair gives you a three by three tic-tac-toe board.
Divide the rest of the class into two teams: X and O. Usually I do boys verses girls, just like Hollywood Squares. The teams take turns picking a person holding a whiteboard. I ask the question and the person with the whiteboard writes their answer and shows it. Now, here's the great part. The person with the whiteboard doesn't have to get the answer correct. The person who picked them has to decide if the answer is right or wrong. If they choose correctly, they "take" the square. If not, the other team gets it. Just like tic-tac-toe, the object is to get three in a row.
My students love this game, and I hope yours will, too.
I know I'm a bit of a dinosaur, but my supply closet still has lots of transparency film. Now that we're making the switch to document cameras as opposed to overhead projectors, we don't need that stuff anymore... or do we??? This week I have been contemplating how I could use this resource. It's cheap and a little out of the ordinary. And you know how kids get excited about something a little out of the ordinary!
One way to use transparency film is to reduce the amount of paper you use. Although I love me a good worksheet (read between the lines: addicted to Teachers Pay Teachers and Teacher's Notebook), I find copying off all those worksheet to be a waste of paper and my time. So if you are using a program where the students do the same thing each day (such as Decimal of the Day shown here), make only one blank copy for each child. Staple the film on one side of a file folder and slip the worksheet inside. Students can then use a dry erase marker and a piece of felt as an eraser. I was worried initially that the markers would not last, but most of my students have used the same marker since we started this in December. For Decimal of the Day, I write this on the board so the students can complete the worksheet:
7.308
+ 0.04
- 6.508
X .35
/ 9
_____ (this is the place to put the comparing symbol) 7.038
Another way to use transparency film is as part of a game or activity. This week we have been rounding. Rounding is very tricky for students because they have to know which place they need to start and what place they have to look at. Using transparency film, I created a fun rounding game I call "Slap! Trap!". To play the game, each student will need: a dry erase board, a dry erase marker, and a copy of the Slap! Trap! transparency (see pictures below).
Pass out the supplies and give your students a few minutes to use the transparency to practice making numbers that will fit inside. One digit should to in each box. After a few minutes of experimentation, write a number on the board, such as:
You can use any size numbers that you are working on. They can even be bigger than the two digit number shown in the example. In fact, the transparency works even better with numbers with many digits. Now yell, "Round to the nearest (place). (Place) SLAP!" The students yell back, "(Place) SLAP!" and slap transparency down so the box on the left with the question marks is surrounding the digit in the place you said. Check to see that everyone has placed their transparency correctly. For this example, I would have said, "Round to the nearest whole number! Whole number SLAP!"
Next I say (in a robot voice), "Engage eyeballs!" and the kids repeat with a shzzzzz sound after, and move their right index finger until they are pointing at the next place to the right. Then I say, "Five or more go up one floor." The students repeat and add, "Going up!" or "Stays the same!" depending on what they are supposed to do.
Finally I yell, "Remove trapper!" and the kids repeat. If they need to change the target place, they do that now and turn everything else into a zero.
I will be uploading a video to my You Tube mrsc4jones shortly that shows this lesson in action. In the meantime, can you think of another use for transparency film? Please share in the comments below.
I have really been inspired this week by my fellow bloggers out there. It just amazes me how one short post with a quick idea can get my creative juice flowing again! It made me realized I should post more often, even if I only have one small item to share.
My students are finishing up with adding and subtracting fractions this week with a little performance task making trail mix using fractional amounts. Next week we tackle multiplying fractions! I know that multiplying fractions is much easier than adding and subtracting them, but the Common Core standards are very clear and specific that students need to not just have computational accuracy, they need to understand the process. I had to do a lot of reading up on this because, quite frankly, I was only taught to multiply fractions using a rote algorithm, so I never learned this important step.
In books like Curriculum Based Assessment: Fractions by Michael Battista, the author uses squares to show the process of scaling. I wanted to create a manipulative that students could use over and over again to demonstrate the process of scaling and truly understand that multiplying a fraction by another fraction results in a smaller number than your started with (which is, frankly, counter-intuitive to students' experience multiplying whole numbers). The resulting do-it-yourself manipulative (which I called fraction squares) is explained in the You Tube video above.
One reason students do not develop strong computational skills is they start making errors and those errors are not corrected early on. Eventually they will think the wrong way is the right way, just because they got into a bad habit. Walking around the room and hoping you spot the errors and give enough feedback is not enough practice. Collecting work at the end of the period and grading it is not enough practice. I was inspired to come up with an idea to stop that error cycle right in its tracks. My idea is called Error Analysis Boxesand you can download the template by clicking on the words. It is appropriate to use with grades three and up. Generally, I wouldn't use this with an entire class. I designed it to work with a small group (say, intervention) that has not mastered a computational skill. Here's how to use the template: 1. Select any computation worksheet for any skill you want to teach. Copy the worksheet and the template on separate pieces of paper, so students will use them side by side. You will also need to give the students calculators to check their work. 2. Students calculate the answer to problem one. When they find the answer, they check it with their calculator. If they got the answer correct, they make a smiley face in the first error analysis box. 3. If they got the answer incorrect, they try to figure out why. Some common computational errors are listed at the bottom of the template. In the first box they write "I didn't _____________ ." Then they write "Next time, I will _______________ ." and fill in a computation strategy. Again, useful strategies are listed on the template. 4. Continue completing each problem in the same way. As I "work the room" and observe the students, if I see the same error pattern (for example, they are always writing "I didn't regroup."), I encourage them to dig deeper. Most students found out it was the little things they were forgetting. Seeing that right in front of them in the error analysis boxes was priceless. If you like this idea and want to see how I followed up with another just as clever, check out my Common Core Differentiated Math Activitieson Teacher Pay Teachers.
Me on the Web:
current class website: http://www.4mrsjones.weebly.com
I recently went to the supply closet to pick up a package of pencils for our high stakes state testing, which is next week. Yes, in their infinite wisdom, my state department of education decided to test students at the beginning of October. Guess they have never heard of summer learning loss! Anyway, imagine my chagrin when I saw the packaging:
I guess even the pencil companies know the destiny of their product! I refuse, however, to let this blog be about my beef with testing (a.k.a sucking the life out of my kids). I categorically refuse to let high stakes testing and its evil twin benchmarking become the new normal. I refuse to let mandatory test prep to put the damper on my students' spirit and fun, despite them being tested ad nauseum. This week we have been reviewing figurative language. To elicit some quality similes and metaphors, I showed some dazzling pictures of butterflies and caterpillars. Students came up with one simile and one metaphor. Then they met in groups to offer praises and deltas (the symbol for change). At the end of the session, they choose one simile and one metaphor to represent the best of the group. These bests were shown to the whole class who voted on the best of the best. They came up with some very creative figurative language: The caterpillar is like a gummy worm because he has bright colors. The butterfly is a model with its beautiful features. The butterfly is like an Indian because its wings look like eyes with face paint. The butterfly is an alien because it has so many eyes. In Math, we are working on estimating and problem-solving. As Professor Harold Hill from The Music Man said, "Think, men. Think!" I am hopeful that these two strategies will help steer students to the correct answers, even if they aren't exactly correct in their calculations. Yesterday we built arrays for multi-digit multiplication problems. My pre-test revealed that most students had forgotten everything they learned about multiplying by multi-digit numbers, including making magnitude estimates. Students are very familiar with building arrays for multiplication facts, however, so we built on that idea. Yesterday they learned why we don't generally use array-building as a strategy for multiplying larger numbers.
Here two students show 25 X 35 = 875. Many students were surprised at how big the arrays turned out to be. This activity showed them visually what is going on when we multiply multi-digit numbers.
One of my goals this year is to use more pre-tests to inform my instruction. My first experience with this was in Language Arts. As a fifth grade team, we identified vocabulary skills as a weakness in our students. Part of that is knowing how to use a dictionary. The first day of school, I gave my students a pre-test on the skills of using a dictionary to define multiple meaning words, using a pronunciation key, putting words in alphabetical order (to the third letter), and using guide words. Using their scores, I created a personalized packet for each student with just the skills they needed. Two students demonstrated mastery in the pre-test, so they had challenging activities which they completed as a team.
Three students did very poorly, so they worked with an aide in a small group on slightly easier skills.
The rest of the class participated in a mini-lesson each day on a different skill, then worked independently on their packets.
Today I gave the post-test and 90% of the class passed. Go kids! My second experience with pre-tests was did not go as smoothly. I pre-tested my Math class for the first unit. Most of the material should have been review, but clearly it wasn't. So I greatly reduced the scope of the unit, since I had only alloted two weeks for it. My original plans were to teach factors, multiples, arrays, prime, and composite numbers, prime factoring, multiplication properties, and divisibility rules. I decided to stick with factors, multiples, primes and composites. We spend a week on factors alone because it was so difficult for them. We did many activities: Venn diagrams, foldables with examples and rules, games from our Math series, and traditional worksheets. We even color-coded a hundreds chart with colors that represented the different multiples. Students were allowed to use their interactive Math notebooks, their student reference book, or the definition wall during the test. Despite all of this, many students failed the test. When I thought about why I had two very different outcomes, I came to the conclusion that my Language Arts students corrected their own pre-test. They knew what they needed to work on. I also used differentiated instruction with my Language Arts class where I didn't do as much of that with the Math class. For the Unit 2 pre-test, I came across a site called Mastery Connect. Mastery Connect is a site that links Common Core assessments in Reading and Math and tracks student progress.The basic service is free. I couldn't find an assessment that really matched the skills I will teach in Unit 2, so I made one and posted it to the site. It was easy to add the scores to my "tracker" and visually track what skills students have and need.
It's been two weeks since school has started. This year in fifth grade we have homogeneous groups created by the fourth grade team. Because of this, I have had to come up with a new Math routine/structure. I want to take advantage of every minute I have them for instruction, particularly because fifth graders have significantly less time for instruction than they do in fourth grade. In fourth grade they had two hours, including enrichment. In fifth it is down to one hour and fifteen minutes. 10:00-10:15: Agendas, Homework, and Fact Folders Students trickle in from the other five fifth grades (no bells at our school) and get out their Agendas with homework on top. This allows me to quickly check in homework and write in their agendas. They copy down the homework for the next day (which is already on their desks). After that, they set up their Math fact folders which is a blank worksheet under a clear sheet of plastic which they write on with a dry erase marker. Each child is on a different level of multiplication facts. This takes the most time, since they aren't used to creating their fact sheet and monitoring themselves. I hope this will take less time as the year progresses. If students finish all of this, they may start on their homework. I was going to have some type of Daily Math or Problem of the Day, but why go through the trouble of finding and copying all of that when they could start their homework? 10:15-10:30: Mini-Lesson: Review or Introducing a New Concept As my aide goes around to check their fact folders, I take the kids to the carpet to do a review activity. Often we use personal whiteboards that are in a basket in the middle of the carpet. 10:30-10:15: Back to Desks: Main Lesson Students come back to their desks and check the status of their Fact Folders. If they passed a level, they record it on the chart in the folder. This process is taking about five to ten minutes now. I hope we can cut this down significantly in the coming weeks. This is where and when I deliver the main content of the lesson. I am making good use of the students' interactive Math notebooks. After some challenges getting started (again, this class has difficulties following multi-step routines/directions) the students are already really enjoying them. Each Monday night's homework will be creating their weekly student reflection page in the notebook. Since their journals are so small (composition books cut in half) I decided to do this instead of the traditional left side-right side organizational structure. These journals are so new for them I don't want to overwhelm them with coming up with multiple pages. We usually fill one page a day in class.
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