Comparison Problems: Using Tape Diagrams to Represent Math Thinking

Word problems are a key part of rigorous standards everywhere, but teachers and students alike often dread tackling them.  Even textbooks sometimes save them for the bottom few problems on a page or a separate lesson toward the end of a chapter.  The thing is--word problems (at least good ones!) are the "real world" part of math.  One type of word problems, comparison problems, can be particularly challenging for students.  Let's look at some teaching tips that might make them more accessible!
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1.  Critical Reading of Math Problems


As teachers, we should always be striving to help our students understand that the skills we are teaching are them are FOREVER...not just to complete a math page or worksheet.  One skill that we really want to make sure our students understand is the need to critically read math problems to figure out what is being asked, what information is given, and to make a plan for solving.  So often we do the thinking for our students.  Just look at how many of our math books are organized.

A lesson entitled "Solving Addition Stories" doesn't leave much room for student thinking, does it?  Providing students with a constantly spiraling variety of problems forces them to think for themselves, learn to look for key information in problems, and make solution decisions accordingly.

One idea?  Use highlighters to find important information.  Underline the question.  One thing I do NOT recommend? Looking for key words like "fewer" or "total".  These words may seem like a quick fix for students...but they can lead them down the wrong path.  How?  How about this problem...

"Larry has 14 baseball cards.  This is 25 fewer than his sister Becca has.  How many cards does Becca have?"  By teaching "fewer" as a signal to subtract, a student will certainly not think through this problem correctly!
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems

2. Visualization and Modeling

One strategy that can really help students make sense of problems is to be able to visualize and draw models of different problem types.  Comparison problems--sometimes represented with "tape" or "strip" diagrams are a GREAT way to help students visualize the math!  I thought I'd share a few ways that these can be super helpful for students--whether used as whole class lessons or for intervention groups.  

Using a blank "template" of a tape diagram with manipulatives can really help students see the comparison that appears in a problem.  This diagram shows a visual representation of the following problem:

"Bill has 13 candies.  If Sarah has 5 more than Bill, how many candies will Sarah have?"

Now...this is a VERY simple example and is perfect to use with intermediate students who really need to back up and see the actual manipulation of the numbers.

comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems
 As students get more adept at these problems, you might see that a sketch with only numbers placed in the diagram is appropriate.  Check out this lesson where we "filled" a diagram and then brainstormed a ton of different questions that could work with this problem.  Again, part of making sense of problems is realizing that the QUESTION matters...and we need to always be looking for what that question is!
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems
Another strategy to get students really visualizing is to take a blank diagram and create different stories to go along with them...help students get flexible with their thinking.
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems
Once you have worked with the class on this--send them loose to try some on their own!  Share with partners or put some great examples under the document camera to look at all the different ways that students found to visualize this math situation.
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems

3.  Tips for Additive Comparison Problems

The beauty of comparison problems is that they actually get students thinking about all FOUR operations--and how addition and subtraction are related and how multiplication and division are related--and even how those inverse operations can be used in solving.  Although we may call some problems "additive" comparison, the reality is that the information can often be represented by subtraction as well.  These problems really form the foundation for later work in algebra, so it's so important that we help students recognize what is happening in these problems--and to find different ways to model them.
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems

4.  Tips for Multiplicative Problems

As students develop their math skills, we know they need to be able to deal with "groups of" and division problems as well.  This also ties directly to fraction work ("1/3 of ..." as opposed to "3 groups of...").  Helping students SEE the difference between 3 groups of five and 3 MORE than five is such a valuable exercise.

comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems

Interested in trying the activities pictured above?  Here you go!

Want to pin this for later?
comparison problems, word problems, tape diagrams, strip diagrams, problem solving, teaching comparison problems, grade 3 math, grade 4 math, grade 5 math, comparison word problems

How To Organize Your Classroom


Chances are, when you first started dreaming of becoming a teacher, your vision did not include excessive meetings, lots of data collection, and a clutter-filled classroom that caused you even more stress.

Even if you were not picturing yourself as the proud owner of a space that looked like something Martha Stewart, Pinterest and Joanna Gaines collaboratively created, I would put money on the fact that you didn’t imagine frantically trying to find your students’ homework packets under the stack of assessments you didn’t have time to correct because you were too busy looking for the lesson plans you had placed down…somewhere. 

And you certainly didn’t imagine you would be repeating this same scene every. single. day. for the better part of the school year.

Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.

Are you finding yourself…
  • A) staying later than you would prefer each afternoon (or let’s be honest, each evening)?
  • B) walking into school each morning and feeling defeated by the site of your classroom before the day even begins?
  • C) feeling frustrated and embarrassed by the condition of your classroom? 
  • D) not enjoying the time with your students as much as you should?
  • E) all of the above
You certainly are not alone. The majority of teachers I speak with all report feeling overwhelmed, and more often than not, a cluttered and disorganized classroom is a huge factor weighing into their stressful days.

Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.

I’ve been running workshops, presenting at conferences and consulting with teachers 1:1 for over a decade (you can read about that here) on the topics of Classroom Organization and Management. When working with teachers to get their classrooms decluttered and organized I always advice them to follow these ten systematic steps. 
Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.

1. Take before pictures. 
2. Create an action plan. 
3. Enlist the help of others. 
4. Know where your clutter will go. 
5. Gather supplies. 
6. Make a clean sweep. 
7. Schedule time to work on the space. 
8. Work through the decluttering process. 
9. Organize the items that remain. 
10. Create systems to maintain your new clutter-free classroom.
Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.


Each of those steps are explained in detail in my recently updated eBook, A Clutter-Free Guide to Classroom Organization. The guide also comes with lots of printables to help you get and stay organized. 

Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.

In addition to that resource, I am excited to announce that for the first time since 2012, I will once again be offering free coaching on how to declutter your entire classroom and would love to have you join me. Just text the word "CLASSROOM" to 428-28 and follow the prompt to receive lots of tips, ideas, and free printables to take your classroom from cluttered to organized. 

Classroom Organization and Storage Ideas for Busy Teachers on a Budget - This tip filled post shares how to declutter and organize an elementary classroom. Supply labels, baskets, bins, crates and boxes are all you need to store centers, games, manipulatives and more.


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A Simple Way to Give Independent Reading a Boost

Try this simple idea to inject some new life in your students' independent reading and classroom library interactions. Free editable "Favorites" sign included!It's difficult to keep students' "reading life" energized through the entire year.

The beginning of the school year is the easiest, with bright eyes gazing into your newly introduced classroom library with excitement, hands barely able to hold back from grabbing books here and there. But after a few months, it's easy for students to slide into indifference toward their independent reading, especially if the contents of the classroom library and the routines surrounding it never change.

In my (epic!) series of blog posts on how to make the most of your classroom library, I share gobs of practical ideas to keep your classroom library thriving, which in turn pumps life into students' independent reading.

One of these ideas is to use a "Current Favorites" shelf. A "Current Favorites" shelf is a spot in your classroom where you keep your own personal favorite children's books.

An important part of the idea is that the books change. You periodically add or swap out a book or two so that the handful of books you have on the shelf are your favorites at that moment.

The concept directly contributes to a healthy, growing reading atmosphere. It shows that (1) you read, (2) you have read enough books to distinguish some of them as your favorites, (3) you continue to read more and more, and (4) you enjoy reading because you continue to gain new favorites. And when YOU model fun, positive reading behaviors, students' own interactions with books follow.

There's lots of ways to create a your favorites shelf. Below is what I used in my third grade classroom. It's a rain gutter screwed into the wall with a sign hanging nearby.


A rain gutter might seem a little extreme, but a small section of your whiteboard tray with a sign above would do the trick, or the top of a bookcase or bit of counter space. Take the metal parts out of a large binder clip and it doubles as a nice sign stand, like below.


Students love getting to know you on a more personal level, and what better vehicle to draw back the curtain a bit than with books? Think about adding books to your "Current Favorites" shelf that jive with an approaching holiday, that might surprise your students, that hint at an upcoming unit of study, or that beg conversation or questions from the class. But also feel free to leave an all-time-favorite or two on the shelf for the whole year!

Don't be surprised when students begin asking to borrow one of the books on your shelf. I like to ask them to just be sure to return the book by the end of the day, and they can always borrow it again tomorrow, or look for it in the school library.

After a few weeks, experiment with some variations... maybe try choosing a student to curate the shelf with their own current favorites. Change students each week, and the class has a unique way to get to know each other better as readers, and pick up some new book ideas for themselves.

You can grab a free editable PowerPoint template of my Favorite Books sign to make your own. Just click HERE or the picture below:

http://bit.ly/2kB1cu0

And for a bonus idea, you can give your independent reading another shot of caffeine with the Tower of Books Challenge. It's a reading challenge that encourages students to read a wide variety of genres and uses a fresh and motivating way to keep track of their reading. You can find it in my TpT store HERE.

https://www.teacherspayteachers.com/Product/Reading-Log-Alternative-Tower-of-Books-An-Independent-Reading-Challenge-684824

Come visit me at my blog, The Thinker Builder. And while you're there, be sure to sign up for my FREE newsletter, and receive a mini-pack of my response pages as my gift to you!

www.thethinkerbuilder.com




How to Engage Students Before Break


Teaching before a break or vacation is always difficult. We have came up with some strategies and activities on how to engage students before a vacation. We hope that you will be able to use some or all of the ideas!

Journaling
For most students a break from school is exciting. There are probably lots of things that they are looking forward to. Take this opportunity to have them journal about what they are looking forward to. Here would be some journal starters:


  • Over break, one thing I am looking forward to is... because...
  • During vacation, I plan on playing... because...
  • I am excited to be able to.... over break because....
  • If there is one thing that I wish I could do over break, it would be... because...
This activity could be as short as five to ten minutes, or you could turn it into thirty minutes or longer by adding some cool stationery for them to write on, or giving them to draw and color a picture about their break. You could also play some music in the background. We like to use some stations on Pandora such as: Classical Goes Pop, Yoga Sanctuary, or the Piano Guys.

Class Reflection Meeting
Before leaving for break, it is a good idea to have students reflect on how the school year has gone up to this point. We have created a FREE sheet that you could pass out to your students before the class meeting. It includes self-reflection questions, working in group questions, and whole class questions as well. 

We have created some questions for students to answers on a 1-10 scale. Some questions included are: 
-How would you rate your overall behavior this year?
-How well have you worked in groups so far this year?
-How well have you participated in class discussions this year?
-How well have you treated other classmates this year?
-Overall, how hard have you tried to reach a goal this year?

We also included some open-ended questions on the second page:
-What is one thing you know you are doing well in school and how do you know?
-What is one area that you want to improve in school and why?
-What can your teacher do to help you be the best you can be for the rest of the year?

After students answer these questions you have many options as to what you can do:
-review them yourself
-have a class meeting where students bring their sheets and share responses
-have them partner up or get in small groups and discuss
-use them as a self-reflection tool and share at the next parent/teacher conference
-or any other option that you see fit for your classroom.


This activity is a great way to see where your students think they are in terms of behavior and goal achievement.

Allow Choice
If you are doing an activity in reading, writing, math, science or social studies, instead of a customary worksheet or routine activity that you usually use why not try adding choice to liven things up? In reading class, if students have just finished a guided reading book, allow them to choose their understanding of the book through choice. They could write how the story would be different from another character's point of view. They could make a book review news show where they get up in front of the class and try to "sell" the book. Students could make a game board that relates to the story and create questions that need to be answered. The possibilities are endless. If you are on a specific math concept and students have finished learning about it, allow them to show you what they know. They could: create a poster/diagram of the concept learned, teach it to the class/small group in their own way, make up problems and solve them on their own, create a PowerPoint/Google Slides/Prezi on the concept. Whatever you decide, allowing choice may be a great motivator for students heading into a break.

Engagement Activities
We have created 25 student engagement task cards. Each card includes an activity overview and examples of how to use the activity in your classroom. Some examples are: jigsaw, paper basketball, knowledge parade, penny for your thoughts and so much more. You can find them by clicking here.


Student Engagement Task Cards
Another resource is our winter engagement activities. This resource includes 10 engaging activities that come with specific directions and materials needed: Cotton Ball Snowmen, Candy Cane Toss, Cut the Tree, Snowball Fight, Ornament Hang, Christmas Tree Building, Snowball Scoop, Snowball Toss, Snow Fort, and Candy Cane Relay. Your students will love it. Click here to find out more!
Christmas Winter Challenge Engagement Activities
Just remember, kids are going to be naturally excited before a break. Make the most of it by including some or all of the ideas and activities mentioned above to make it a smoother transition into break!

Make sure to subscribe to our newsletter for more great ideas! 







Writing SMART Resolutions for the New Year


As soon as school resumes after the new year, teachers everywhere will be asking their students to write New Year's Resolutions!! I know this is something that I ask my students to do each and every year. For us, the new year is the start of our second semester. It is the perfect time to encourage students to set goals for the remainder of the school year!!

This year when you are asking your students to write goals and resolutions, make sure that they are writing SMART resolutions. You can have students use this FREE organizer to make sure that their resolutions are Specific, Measurable, Attainable, Relevant, and Timely.
When given the task to write resolutions for the New Year, students tend to stick with the same generic goals: Get better grades, work harder in school, improve my behavior, and so on! Using the SMART format encourages students to come up with resolutions that they can use to hold themselves accountable.

Specific
Students should be sure to come up with goals or resolutions that are specific. Ask them to be specific about what they hope to accomplish, and what their goal will look like once it's achieved. Have students really reflect on what's challenging for them and where they hope to see themselves at the end of the school year.

Measurable
When writing their goals or resolutions, students should keep in mind how they will measure their progress. For instance, if students want to improve their grades, they will want to be specific about what grade they are shooting for. If a student is working below grade level in math, he or she may set a goal to have at least a B- in math by the end of the school year. Then this student could use progress on math assignments, quizzes, tests, and assessments to track his or her progress.

Attainable
As they are building their resolutions and making sure they are specific and measurable, students should remember that their goals need to be realistic and attainable. On one hand, we want to challenge students and help them to make progress. But on the other hand, we need to make sure they aren't setting themselves up for failure. Students should choose goals that are not too easy to achieve, but also not too difficult to achieve.

Relevant
Encourage your students to choose goals that are relevant to their own strengths and weaknesses. They should also avoid choosing a goal just because it's what a friend is choosing. They need to be sure to connect their goals to their own educational needs.

Timely
Students should decide how long it will take them to achieve their goals. They should also have an end time in mind: By the end of the year, by the end of the quarter, by the start of the next school year, etc. They might also want to build in some benchmarks. At my school, students use Accelerated Reader and earn points by taking tests on the books they read. All students have their own point goals, and I often encourage them to break it up into smaller chunks to make it more manageable and to help hold themselves accountable for meeting their final goal in a timely manner.

All of these steps work together to help students craft resolutions that will encourage their growth in the areas of their choice. SMART goals give students a chance to set themselves up for success, and the New Year is the perfect time to get students back on track for the second half of the school year!!

If you are having students write resolutions this year, please feel free to download this FREE organizer to help them organize their goals!! Click on the picture below to visit my shop and download this FREEBIE!!



Once students use the organizer to write their SMART resolutions, they should publish them to make them official!! This New Year's Tab Book is the perfect place for students to reflect on the previous year, look forward to the next, and record their RESOLUTIONS!!

Click on the pic to learn more!!


          

SAVE TIME - Review Basic Computer Skills

Review Basic Computer Skills, Technology in the Classroom, Keyboard shortcuts printable and cursor icon printable

Technology can be awesome. It can help bring excitement to any subject, but it can also bring frustration if you don't take the time to review basic computer skills. In this blog post I will go over some basic skills that you should review before sending off students to complete digital assignments. I hope you find the free printables helpful.



The problems:
  • Students accidentally delete text boxes
  • Students take too long copying and pasting images

The solutions: 
  • Students may not be aware of the 'magical' undo shortcut. If they accidentally delete an item, students can quickly use the undo shortcut or click the undo icon.
  • Students can use the copy/paste shortcuts to quickly make copies of images.
Click the image below to download a free printable with keyboard shortcuts. It includes both a Mac and Windows version. 


basic computer skills, keyboard shortcuts



Help students understand what their computer is doing by reviewing the many faces of a cursor icon. The cursor icon tells a student...
  • when a page is loading
  • when a text or image is a hyperlink
  • when they can resize an image
  • when an image is moveable 
  • when they can enter text
Click the image to download a free printable. 
basic computer skills, cursor icons free printable

I hope you find the printables helpful as you integrate technology in your classroom. 





5 Easy to Implement Multiplication Games

The drill and kill of multiplication facts can get old very quickly for students.  Especially those that struggle memorizing them.  Adding games into your math block will not only excite them, but provide great learning opportunities.  

Here is a list of 5 multiplication games that are super easy to implement and require very little prep.  A win for both the teacher and the students!



Games with Dominoes


Ordering Products

  1. Students choose five dominoes, turn them over, and multiply each side together.  
  2. Order the products from least to greatest or greatest to least.
  3. Want to make it a game?  Partners order their dominos then find the difference between their greatest number and least number.  The partner with the greatest (or least) difference wins.



Multiplication War

  1. Students begin with dominoes face down.  
  2. Each student chooses a domino.
  3. On the count of three, students turn over their domino and multiply the dots on one side by the dots on the other side.  The student with the highest product wins the dominoes.


You can download the free printable with these two games and more HERE.

Multiplication War With a Deck of Cards

Do you have a deck of cards?  With a simple deck of cards you will have an instant multiplication game that is a hit!  The directions for playing with a deck of cards is the same as with dominoes, students just use two cards to multiply together.


You can download the above digit cards for free HERE.

Around the World

Using a set of flashcards, play a whole class game of around the world.  How does this work?  All students stand in a circle.  The teacher chooses one student to begin.  That student stands next to another.  The teacher shows the flashcard, and the first student to say the product stays standing and moves to the next student.  This continues until there is one student left.  The one left standing is ultimately the winner.  Students love this!

Multiplication Beach Ball

Take a cheap dollar store beach ball, write some multiplication facts on it, and you have multiplication beach ball.  I have my students stand around the room, and they toss the ball to each other.  To keep order in the room, they have to say the person's name that they are throwing it to before they throw the ball.  When the student catches the beach ball, they have to solve the multiplication fact that their right thumb lands on.  After finding the product, they toss it to another classmate.  


Printable Partner Games

Roll-a-Product, Tic-Tac-Toe, and Roll and Solve to name a few.  You can download a sample of each of these games and more HERE.




If you are looking for more multiplication ideas, be sure to check out the following!

10 Ways to Practice Multiplication Facts


Operation Math Facts






Exploring Complex Sentences

When it comes to complex sentences, things quickly become... well... complex. At the mere mention of independent clauses, dependent clauses, and subordinating conjunctions, many young eyes immediately glaze over.

One year, when I was about to introduce the topic of complex sentences to my fifth graders, I decided on a whim to use an image of a nurse helping a patient walk. I was amazed by how much this simple image helped my students. I told them that the nurse in the picture was like the independent clause. Just as the nurse can stand alone, so also can an independent clause "stand alone" as a complete sentence. Then I told my students that the patient with the crutch leaning against the nurse was like the dependent clause. The patient could clearly not stand on his own, just as a dependent clause cannot stand alone, either. A dependent clause depends on the independent clause to help it be part of a complete sentence.

This idea resonated so well with my students that I've used this explanation ever since. As you can see, I discarded the nurse/patient image I had previously used. (Although it did the trick, it wasn't very visually appealing.) When I ran across the image below when I purchased a clip art set by Educlips, I upgraded my image to this one.

Complex Sentences Anchor Chart! This blog post also features a FREE activity where students write their own complex sentences.

A FREE PARTNER ACTIVITY

As you can see, there is a lot of information on this anchor chart. Students will only retain these concepts if they get an opportunity to interact with the various elements of complex sentences. Therefore, I created an interactive exercise where students can manipulate each clause and then write complex sentences using the clauses. Personally, I would have students complete this activity with a partner, but students can also do it independently, if you wish. (CLICK HERE if you would like to download this free activity to use with your students.)

First, give each student the two worksheets and the writing mat. (This photo shows only the first worksheet, and the writing mat printed on yellow paper.) They follow the instructions written at the top of the worksheet:
1.  Read the clauses in each pair.
2. Underline the dependent clause with a green marker.
3. Underline the independent clause with a red marker.
4. Circle the subordinating conjunction with a blue marker.

Exploring Complex Sentences: This blog post features a FREE writing activity, plus an anchor chart that focuses on complex sentences.

5. Use the two clauses to write a complex sentence that starts with a dependent clause in the first box of the writing mat.
6. Use the two clauses to write a complex sentence that starts with an independent clause in the adjacent box.
**Don't forget to use capital letters and punctuation!

Exploring Complex Sentences: This blog post features a FREE writing activity, plus an anchor chart that focuses on complex sentences.

Although it's not written in the directions, if you want, you can add a step between Step 4 and Step 5 where students cut out the strips. This might be helpful for students who would benefit from physically moving the dependent clause directly in front of the independent clause before they write the first sentence on their mat. Then, students can move the independent clause to the front before they write the second sentence.

Once students are done, they will have eight complex sentences written in both formats. I recommend checking all of the sentences to make sure students used commas in the first column, and that they refrained from using commas in the second column.


If you are looking for additional resources for teaching about compound and complex sentences to your upper elementary students, feel free to check out the following resource. I have placed my bundle image here, but all of these items are also available for individual purchase in my TpT store.


Simple, Compound, and Complex Sentences Activities- a PowerPoint, task cards, a game, a craftivity, and more!



Finally, I wrote a related blog post at my own blog about compound sentences. Click HERE to check it out!

Thanks for stopping by today! 




Pin for future reference:
Exploring Complex Sentences: This blog post features a FREE writing activity, plus an anchor chart that focuses on complex sentences.