Numberless Word Problems

I started using Numberless Word Problems in my math classes late last year, and immediately, I was hooked.  I loved how it made my students look at work problems in a different way - they really had to think about what the problem was asking ... and develop a plan to solve it - without being distracted by the actual numbers in the problem, or just taking the numbers in the problem and adding or multiplying them together.  The conversations that were happening between my students were fascinating - they were far more willing to take risks with their partners or small groups because the numbers were eliminated at first - students weren't worried about their math skills, or getting the "answer" wrong.  Engagement was definitely high and students were eager to share what strategies they used to "solve" the numberless problems.

Numberless word problems are an excellent way to get your students thinking about WHAT the word problem is actually asking them to do and developing strategies for solving the problem.  Using these kinds of word problems provides the essential scaffolding that helps students develop a stronger understanding of how the numbers work together and how to make a plan to solve the problem.

 I would use these problems as a mini-ish lesson (takes a little longer than the 10 minute lesson) when beginning a particular concept (operations, measurement, fractions, etc.), when teaching a problem-solving strategy (using smaller numbers, simpler problem, identifying the operation, etc.), or when practicing algorithms or strategies for multiplication and division. These are great for differentiation when practicing these strategies because students are working with "their own" numbers for the first problems; encourage students to use numbers that are reasonable, but that they are comfortable working with.

   

I would do these activities as a whole class - projecting the problems so everyone could see.  I would display the first slide - a chosen problem with all numbers removed like the example on the right.  You can make up a problem or use any word problem you have that fits your learning goal for numberless word problems (grab a textbook or worksheet) - just remove the numbers - and make sure you separate the problems (don't have all 3 on one page - students shouldn't see the third problem until the very end). 

After I displayed the slide I would them let my students talk (or use whiteboards or their journals) with their elbow buddy or small group, asking: 

• "What do you know about the problem?" (here I would look for answers like numbers are increasing per day)
• "What do you need to know?" (what are the points? is there a pattern? how many points on Thursday?)
• "What is a possible solution?" (here I ask the students to try to come up with an equation related to the learning goal (in this case - adding and subtracting large numbers) using their own set of reasonable numbers - they may come up with something like 100 + 200 + 300 + _____ + 500 = 1500, or 250 + 300 = 500, or something completely different.)  At this point I ask students to share some of their equations with the class and we discuss if the answer makes sense and if it is reasonable. This is a great time to check for misconceptions, too - make sure students understand the importance of the word increasing ... and that we are looking for a specific answer for a specific day.

     

I would then show the second problem - same problem, same question, with some information added to it.  This time students discuss:

• "What changed in the problem?"  "Does this change your equation?"  How?" 
• By asking them again, "What do you need to know?" they narrow down what information is still missing and realize that the actual question they need to solve did not change, but HOW they go about solving the problem may change - they may need to change their equation (here I would look for students realizing this was a multi-step problem - that they would probably have to add points together and subtract from the total to find Thursday - reminding students of the learning goal while they work through these questions often helps them with choosing the correct steps).
• Students work with their partners to change their original equation (either by substituting in the new information for their number and re-evaluating, or by using a new equation altogether.  Again, students are asked to share how their thinking evolved or what made them change their thinking.

     

The third problem I show has all the information they need to solve the problem.  But instead of having students work with their partner or small group, I have them work independently for the first few minutes ... then I usually allow them to partner up - making sure they "prove" their solution to each other.  That independent part is important to help them become risk-takers and attempt difficult things and use their problem-solving strategies and make a plan to start ... and all those great things we want them to do when working independently. I choose one or two pairs or groups to share their work at the end and model how they solved the problem.   

I've been making some Numberless Word Problem resources to use in my classroom.  Each resource contains 10 different scaffolded problems, plus an extra "challenge" page that has 3 - 4 more word problems (not numberless) that review other math concepts related to the word problem.  There are also problem-solving templates, learning goal and success criteria to display, and an answer key.  Each resource also contains a self-reflection form, as well as peer and teacher feedback forms for formative assessment opportunities, and a rubric for more formal assessments.  Having students actively use the feedback forms to make improvements on their next problems by explaining how they used the feedback on their self-reflection forms makes these word problems an excellent portfolio piece or piece of assessment evidence.





You can take a peek at these resources by clicking HERE:

Quick Writing Reflection

This super easy "Don't Stop Until You're Proud" chart may be the best thing that happens to your writing program.  Seriously.  Student self-reflection, goal-setting, peer feedback, writing collaborating, teacher evidence, portfolio piece ... all in a 5 - 10 minute activity.  And the very best one - student pride. 

I'm lucky in that most of my students love writing every year.  They really do.  A definite credit to my fantastic coworkers who built this into our students.  We do a lot of formal writing all the time, but we also make the time to do a lot of "free writing" in my class.  Any writing style.  Any genre.  Any topic.  Just write.  10 - 15 minutes.  But ... be prepared to share your writing with a friend at the end of the time.  (You can read more about this time in my blog post - Just Let Them Write).

About every 2 - 3 weeks, I quickly title a piece of chart, "Don't Stop Until You're Proud - The Line I'm Most Proud of Today is ..." and hand out sticky notes.  The chart isn't instagram pretty, but it's easy and crazy effective.  Which makes it way better than instagram pretty in my books.  I usually have this set up before they begin writing, so they're working just a little harder while they're crafting their pieces ... knowing they will share their best at the end. 

This chart works for any kind of writing - after formal writing lessons, or after fun free writing time.  I try to do a combination of both.  Sometimes I relate the writing to a particular goal we're working on from our writing units which focus on the traits of writing, or from our independent writing goal clip chart, or I ask them to include a kind of punctuation and circle it (comma, apostrophe, etc.), and sometimes there are no rules at all.

When our writing time is up, I ask the students to read through their work, focusing on their very, very best line or sentence from their work - the sentence they are most proud of (I really play this part up).  They then buddy up to read each other what they have.  Working together, they need to make at least two improvements to their line (improve a word, fix spelling, add a phrase, etc.).  When this is done, they write their sentences on a sticky note and add them to the chart paper.  That's it.  My students are always anxious to read what others have written - and their compliments to each other are so genuine.  I love it.

So ... chart done - now what?  You could leave the activity at that - writing revision, self-reflection, peer feedback, peer collaboration ... 10 minutes ... check.  Or you could use the stickies for:

• students add them to a portfolio page where they can track the growth in their writing over a term or year
• teacher can add them to assessment binders for writing evidence - especially at the end of units or near the end of the term
• use them in student teacher conferences to set new writing goals or provide quick oral feedback
• use them as exemplars of great writing and share (can be anonymous) with the class
• use them as story starters for a quick writing activity - read the student's sentence and have the class write the next sentence (or finish the paragraph) (my classes LOVE this one)

And this chart doesn't have to be for writing - I'm going to try, "The proudest math moment I had today was ..." next year.  :)  

Writing resources in this blog post:

Donut You Know ... A Fast No-Prep Math Game

Looking for more fun ways to incorporate a little extra math facts practice into your day?  This super fun, no prep math game is a huge hit in my classroom.  I've seen the idea floating around instagram and pinterest a few times, and decided to try it out.  My crews always love a little competition, and actually, practicing their math facts too, so this game became an instant winner.  They seriously love it.

You start out by drawing a donut (hence the name - "Donut You Know".  We use whiteboards, but any surface can be used.

Then you write your numbers around the donut (be intentional with the numbers depending on the skill you are practicing).  *These numbers can stay the same for all the rounds you play.*

Then ... with dramatic flair ... announce the donut hole number and skill ... and watch the students go crazy as they try to solve all the facts first.  *No calculator allowed - mental math only.

We don't use a time limit - the first person, or pair, or group to solve all facts correctly wins.  When a group has finished, they yell, "check" and all groups pause - markers in the air.  I run over, do a quick check, and if all are correct, the game is done and we start again with a new number.  If they have an incorrect fact I hand the board back to them and say, "game on" - meaning they need to find their error and correct it and all other groups can go back to work, too.  It literally takes one minute to complete a round.

To play a second round, just erase the numbers around the donut and in the donut hole - leaving the numbers on the donut.  Just change the skill and number in the middle of the donut hole and students solve all the facts again.

This game can be used to practice all kinds of math skills:

• adding, subtracting, multiplying, dividing
• whole numbers and decimals
• adding or subtracting fractions
• doubling and halving
• tripling and thirding
• multiplying by powers of 10
• mental math strategies
• number talk strategies

Check out these other fun ways to help your students master those tricky math facts:

• Speed Dating Math Facts 

• Math Facts Math Circle

Back to School Graphing Activity

Are you looking for a new idea for a math back to school activity?  These back to school Pop-Up Bar Graphs might be just what you need!  I needed something new this year because I will have most of my class for a second time (I taught them in 4th, and will now have them for 6th).  They are a fantastic bunch and I'm looking so forward to another great year with them.

One activity they particularly enjoyed was our Pop-Up Bar Graphs, so I thought I could incorporate that idea into our first day of school this year.

This Back to School 3D Pop-Up Bar Graph activity contains an ice breaker activity students will use as they survey questions.  The object is for each student to find out how many classmates have the same answers as them.  They will then use this data to complete a graphing organizer, graphing reflection, and an interactive 3D bar graph that will WOW!  A learning goal and success criteria poster is also included, along with full lesson and assembly instructions.

You can take a peek at these bar graphs by clicking HERE or on any of the pictures in this post.

Math Scavenger Hunts

One of my favorite ways to use task cards in the classroom is to hide them around the classroom, so students have to hunt for the cards before they can complete each task.  Cards are numbered, so students can complete the tasks in any order.  It's just a little way to get them out of their seats and moving around the room, and it's a super easy way to add a little more fun to the activity.  It only takes a couple of minutes to do - I'll hide the cards in the morning or during a break - when the kids aren't in the room - in the bookshelf, behind cupboard doors, under a desk top, on the back of a chair ... anywhere except inside desks or books.

This way of hiding task cards led to me creating these Math Scavenger Hunt Task Cards.  One of our school goals is to continue to integrate more technology into our activities, so I made these cards as more of a "digital scavenger hunt" - students will collect pictures of the objects or numbers they need to find according to the task cards, rather than collect the actual object or number.  Students can take pictures of the objects on any device - depending on the number of devices you have available, you could have students complete this activity individually, in pairs, or in groups.  I only have 5 iPads in my room, so we'll definitely be working in groups.  You can have students work only in your classroom to complete the tasks (or find the objects), or they can work in a larger area of the school if you have access to one.  Students should hunt through books, magazines, classroom walls and resources, newspapers, anywhere and everywhere, while trying to find the different objects.

Students could use the pictures they collect as evidence they have completed the tasks.  They could also display their picture galleries to other groups during a "gallery walk" activity.  You could also take it a step further and have students create a quick slideshow of their scavenger finds.  There are many possibilities.  Pictures could also be printed and added to students journal responses as a reflective bulletin board.

This Scavenger Hunt Task Card Bundle contains 4 different scavenger hunt resources - Place Value, Math in Real Life (a good overall review of math terms), Classroom Geometry, and Classroom Measurement (two versions of this resource are included - one with metric units and one with customary).  Each resource makes a great diagnostic activity at the beginning of the unit, or a review before a summative task.  They are also an easy low-prep activity, perfect for your sub tub, or math station resources.

Each resource contains a Minds-On Task I like to use whole group to introduce the activity, 12 task cards, a journal prompt (this is optional - it could also be a good discussion question or activity at the end of the task), and a student answer page.

You can take a peek at my Math Scavenger Hunt Bundle by clicking HERE or on any of the images in this post.

5 Activities for Teaching Problem-Solving

This "5 Activities for Teaching" post (click the link for more 5 Activity Ideas) is all about Problem-Solving in Math (and there just may be 6 activities in this one).  As our testing relies heavily on our students' ability to problem-solve and analyze and solve word problems, we have a heavy focus on problem-solving all year long.  This post aims to give you some new ideas to get your students digging deep into word problems, on their way to becoming problem-solving masters.  

1.  Go Numberless - 

I recently started using Numberless Word Problems in my classroom and it has changed the way we look at word problems.  By taking the numbers out of the question, students work with the actual problem itself - deepening their understanding of what the problem actually means and how to go about solving it.  It is fantastic for differentiation because students start to substitute their own numbers into the problem (working with numbers they are comfortable with using) as a way of scaffolding the process.  You can read more about Numberless Word Problems and see exactly how I use them in my classroom in my blog post HERE.

2.  Use CUBES to help students analyze the problem before they begin solving - 

Before I began using CUBES with problem-solving, I would watch in frustration as my students plucked numbers from the question and began solving without really thinking about WHAT they needed to solve.  Sometimes they would miss some of the steps in a multi-step question, and other times their answers weren't actually answering what the question asked.  By introducing CUBES, my students now actually slow down and examine the question fully first ... leading to much greater success in problem-solving activities.  I introduce CUBES very early in the school year.  I hang an anchor chart in the classroom, and we complete an entry in our Interactive Math Journals (click HERE to see this resource in greater detail).

I also created sets of concept-related Word Problem Activities using CUBES.  These resources contain a checklist for CUBES right on the page that students need to complete before they begin solving the problem.  I LOVE using these pages for quick formative assessments in the classroom - and they make a great portfolio piece to keep parents informed of what we are doing in the classroom, and how their child is progressing.  There are 2 different versions of each word problem so you can easily provide differentiation for your students or provide some extra practice for students who need some reinforcement with the concepts.

3.  Establish a set of success criteria for the steps to solving the problem - 

Once my students know how to analyze the word problem, it's time to start talking about how to SOLVE the problem.  Because we have a HUGE focus on communicating HOW the students solve the problem, just showing their work isn't enough - they have to show their thinking, too.  Using my Building Better Responses in Math has been the key to this in my classroom.  This resource breaks down the problem-solving process step-by-step and creates a set of easy-to-follow success criteria for students, ensuring that they have not only solved the problem, but also communicated their thinking during the process.  We start out with our first success criteria, and every time we master a criteria (usually every two to three weeks), we add another criteria to our board (there are 9 criteria in all).  I also post EVIDENCE (a student-created exemplar) alongside the criteria each time we add a new one.  This gives the students a model to reference.  This resource also comes with printables for students to practice each criteria in isolation, as well as pages for scaffolding the steps each time they add a new one.  All pages contain a checklist for students so they can be sure they are completing each step.  

4.  Work Backwards - 

I LOVE this open-ended activity for getting students to think about word problems.  I start with an answer, and get each student to write a word problem for the answer on a sticky note.  They quickly check in with me before they post their question.  When we first started this activity, students were including the answer IN their question, but with more practice, they are now thinking more about writing the word problem with the answer in mind.  To extend this activity, students can choose a word problem written by a peer, and work to solve it - PROVING the answer is correct.

5.  Work Together - 

Students can be a GREAT reference for each other.  I love letting my students explore word problems together.  They often have different ideas and strategies for how to solve a problem, which leads to awesome conversations about justifying their answers.  I always make them responsible for completing their own pages, but they can work together on the solutions.  My favorite resource for this is my Stick-It-Together Math Resources.  These resources have students working together in groups of 4.  Each students is responsible for solving the problem independently first (on a sticky note), then working together with the success criteria to build the best response they can from each other's responses.  I hear the BEST math talk when using this resource, and I watch them go back into their notes to help them with their solutions, which makes my teacher heart smile.  Each of these resources also contains an editable template, so you can add in any word problem you want to work on - better yet, give your students the opportunity to come up with the problem themselves.

You can also have them work together on large chart paper, or just give them some clip boards for their paper and let them work anywhere they wish within the room.  This is my students' favorite way to problem solve.

6.  Let them be the experts - 

Lastly, let your students be the experts.  Allow them plenty of time to see other solutions, and comment on the work (their own, and other's work).  I do a lot of peer and self-evaluation with problem-solving.  After problem solving activities, we do gallery walks - where students' work is displayed, and the students are asked to go around and view all the work, giving "stars and wishes" to their peers.  This makes them really think about what is needed in the solution to fully answer the problem.

I also like to post all the responses on the board, and allow students time to present their solutions - explaining what they did and how they know they are correct, or what they would do differently next time.

To help them differentiate between explaining HOW they solved the problem, and WHY they chose the steps they did, I also like to do an activity where I give the students two different colors of stickers or sticky notes.  They walk around the gallery of math, examining all the solutions, and place the one color where they see students explaining HOW, and the other color for WHY.  This really helps them see the difference between the two.  I then allow them time to go back to their own solutions, to see if they have completed both steps, and improve upon their communication.

These are just a few ideas.  I'd love to hear some of your fabulous ideas for helping your students dig deeper into word problems - just leave a comment below to share your ideas.

Your Try / My Try Spelling Chart

This Your Try / My Try Spelling Chart is one of the best additions I've recently made to my classroom.  Within 3 days, it completed eliminated the "How do you spell ...?" questions that brought my students to a halt during the writing process, made my students actually think about and attempt to spell the word instead of just shooting their hands up, and freed up my time to meet with more students and provide more meaningful feedback and comments while working on writing.  And the best part ... it literally takes absolutely no time or prep to implement in the classroom.  And that's a win in my books.

I set up this chart on a chart stand that didn't get a lot of use in the room so it could be a permanent fixture in the room.  The instructions are simple - during the writing process, if a student has a question about how to spell a word, they can check a dictionary (online or in print) or write the word on the chart under "your try".  As soon as I get a chance, usually within a few minutes, I will write the correct spelling beside it on the "my try" side.  I've also started to put a checkmark beside correct attempts by students, and I still rewrite the word on the my try side.  And that's it.  I started this chart mid November, and by the end of December, we were already onto our 4th page of chart paper - so it's definitely getting used by the students.  I've also seen them go back and check previous sheets when they know the word was on the chart before.

I do a lot of free writing in my room, and that is when the chart is getting used the most, but I've also seen students using it when writing responses during other subjects, so I've encouraged its use for that, too.  My friend, Tina, from Tina's Teaching Treasures, has a great little freebie if you want to do this on an individual basis with your students.  You can check it out HERE.

Check out some of my other writing resources:

Mad Scientist Day

Mad Scientist Day!  This is seriously one of the best days of the year in my classroom!  As a class, my students have the opportunity to earn points for excellent behaviour and excellent learning - with the points going towards earning extra excellent learning days!!!  Mad Scientist Day is our first one of the year.

This is my second year doing Mad Scientist Day.  This year I switched up the activities a bit. Last year we had Mad Scientist Day the day before Halloween, so our activities were very Halloween based.  This year, that wouldn't have worked.  All of our activities are aligned with the science strands we study during the year, so they have a little information to draw from when we get to the particular units.

I "set the stage to engage" first.  A fun costume and a few props did the trick - something quick and easy to set up.  Students were also invited to dress up as Mad Scientists for the day.

Our first activity was a STEM activity for making catapults (tie in to Simple Machines - levers).  I divided my class into small groups and gave each group a plastic spoon, two popsicle sticks and masking tape.  They were also allowed to use anything in their desks.  Last year, before Halloween, I had small plastic rats to use as the load and we called our catapults, "ratapults".  This year we used hershey kisses and "chucked chocolate".  I gave them around 15 minutes to build their catapults.  Once we were done, we had a chucking chocolate competition.  Students had to measure the distance they could "chuck their chocolate" in metres and centimetres.  Each group had 3 attempts, and then we compared and ordered the distances (YAY for a math tie-in!!!).

Next, the little Mad Scientists got to smash some rocks - cracking open geodes for our tie-in to Rocks and Minerals.  I bought some geode kits from Amazon (affiliate link to the product below).  This was definitely the WOW activity for the students.  It definitely took some time to get through the whole class, so I used the time to take some awesome pictures of my students dressed as mad scientists sitting behind the prop desk.

As we completed each activity, students worked in a little Mad Scientist booklet I made for the day (the AWESOME clip art was part of the Mad Scientist Set by Melonheadz Illustrating - you can see it HERE).  For each activity we had to fill in "What we Did" and "What we Learned".  You can download a copy of this booklet I made HERE (just a note - it's not editable if you are doing different activities, but it can definitely serve as inspiration).

Next up was Making Blood Models (tie in to Human Body unit).  I've blogged about this as a full lesson before - you can see this blog post HERE.  Each student had a water bottle.  We added a drop of yellow food coloring to the water for the plasma.  Then we added cheerios (dyed red with a full bottle of food dye) for the red blood cells.  Mini marshmallows were added for the white blood cells, and we used small circles of paper from the hole punch for platelets.  We watched a Brainpop video on blood before we made our models to further our learning.  The students LOVE this one!

For our last activity, we had to blow something up!  Mentos and coke fit the bill - and was a fun tie-in to Matter and Materials.  I have wanted to do this FOREVER!  So much fun!  We added 7 mentos to a bottle of coke (I read online that 7 is the perfect number) and watched the fun!

Mad Scientist Day was a perfect way to reward students with an awesome day of learning they will be sure to remember.  Engaged students LEARN.  Period.