Helping Students Solve Math Problems

Are your students struggling to understand, work through and correctly solve word problems? Does the method you are currently using fall short of actually finishing the problem or only get your students to understand parts of the problem but not actually how to solve it.

This was the problem that I was facing with my students.

There are many problem-solving strategies out there but I found that they simply dealt with comprehending the problem.   Sort of like a finding Waldo within a word problem.  But one of the biggest problems was not finding the information but in communicating ideas and making a plan on how to solve the problem.  I needed more than simply circle….underline…and box some words inside a word problem.

Circle the Question

This is a key step was defining what the actual problem was and what it was asking a student to do.  This step was still important to me as I wanted students to understand what the question was asking them to do.

Hunt for the Clues

Unlike previous strategies I had used, I didn’t want students just to look for specific things within the story I wanted them to pull them out and list these out.  Moving beyond keyword hunts and other shortcut strategies.  I didn’t want students to just memorize the patterns that most problems follow but I wanted them to think critically about the facts that were presented inside the question.

This is also important as you begin to add irrelevant details to the questions being asked.

When real life problems are presented they are ways so nicely organized in a way that can be easily solved by looking for key words on a nice neat package.

Now this is where most solutions finish.

Assemble An Action Plan

One of the biggest difficulties is not identifying the first two steps but that students don’t know how to choose a strategy or make an action plan.

In this stage student combine two things.

First they need to ask themselves a few questions.

– How will the facts help me answer the question

– What do I not know

– What do I need to do first…second…etc

– What strategy do I need to use

I often find students get easily overwhelmed thinking they need to do everything at once. I often ask them “If you had a pool party would you grab a sandwich and jump in the pool at the same time?” This idea grosses them out. This works for this example. Students need to realize that there be multiple steps to solving a problem and that they should do these things one at a time.

It is important for them to make a plan of action to solve the problem one step at a time.

Solve the Problem

Another decision they need to make is how they will solve it.

Clearly and explicitly showing students different ways to solve problems is important to help them better understand strategies to use when solving problems.

  • Students will choose what operation to use
  • Students will also have to decide which strategy or algorithm they will use.
  • Finally students will need to show

This is also the time where the dreaded debate with students on showing work. This year I am not using the phrase “show your work” instead I am using “make your thinking visible”. I am finding that this is helping students to realize that I want all of the great math being done in their heads somehow represented or explained on paper.

Justify Your Answer

Finally students will summarize what they have done and answer the word problem by explaining what their answer is in the context of the problem.

This is a statement of their answer using the keywords from the question.

I use this strategy regularly in my classroom with students to remind them of the steps they can follow when solving a problem.

Want to try it for yourself?

Try it here

Gradual Release of Responsibility

How do you get kids to learn?

Learning happens gradually over time. We know that content that is revisited over time has a much larger impact over content that is delivered in a ‘one and done’ style.

So what does it mean to gradually release responsibility.

This means that we are moving students from needing us to not needing us. We are moving them to independent tasks.

So what does this look like in the classroom.

Well it looks at 4 different levels of support that you move students through to teach a concept.

It means that we don’t expect students to do anything independently before we get them to do it with us. Now that doesn’t mean they don’t try. But it does mean that we don’t assess them until we can get work them through the learning.

The four different levels are

  1. Modelled teaching
  2. Shared learning
  3. Guided learning
  4. Independent learning.

So what does this look like in the classroom?

Modelled Teaching

In this phase students are introduced to learning about something.

The teacher is teaching the students are watching. There is a lot of talking through what you are doing to make your thinking visible. This is like show and tell of teaching.

The teacher has 90% of the control over the learning.

In Writing – you are walking them through how you do something. You show them and talk them through your thought process.

In reading you are doing the reading. You are sharing the thinking. You are the only one with the book.

In math – you are showing students how you do something you are making your thinking visible. Say it, show it, do it live.

Shared Learning

In this type of learning you are learning along side your students the teacher is less in control.

You may lead the learning but the students have all of the materials in front of them.

They are starting to use this as a way to follow along as you do it with them. You ask them for more input as this is less of a passive experience.

Think of this as a 60/40 split. Where the teacher is still doing most of the heavy lifting. Teachers create anchor charts and learning objectives here for students to follow.

In Writing – you may write together. Whole group teacher asks for input but leads the discussion. More interactive with students.

In reading – everyone has a copy of the text and you work though it together. You ask questions and get answers but the teacher is still leading.

In math – you may work through a problem together. Students share what they learned and you help to walk them through the learning.

Guided Learning

This is small group learning

Targeted instruction

Easy assessment opportunities.

More work done here by student.

Teacher as a guide not a leader.

Independent Learning

Student on their own without support.

Students lean on examples and previous support

Use anchor charts from previous lessons.

Here is where you assess

Can they apply what they have learned to do as you ask.

Students also do not pass through this in a straight path. Sometimes it is two steps forward and one step back.

This is why time is your friends and revisiting concepts over and over helps

Give small goals and take baby steps.

What is driving you crazy focus on that. Do that. Fix that. Show them how, do it together, let them try.

Just don’t do too much for them.

Students will not do it all all at once. It will be one step at a time.

But It’s Boring: Using Inquiry to make dull topics interesting

So sometimes we have to teach things to our students that are heavy topics that cover a lot and to get through it is a drag.

How do we get our students excited about a topic if we are not very excited about it either.

One of the subjects that I need to teach is government. A topic that is typically dry and many teachers complain that it is hard to get through and tedious to teach.

So how can Inquiry be used to invigorate this traditionally dry topic?

Use Controversy

One of the easiest things to do to make students interested in something is to add a dose of controversy.

Students are often by nature focused on fairness and being fair. If you can find an example of people not being fair and use it as a jumping off point you can hook them quickly.

In a government unit I like to focus on the Canadian charter of rights and freedoms. We talk about what is fair and just and what is something all people have a right to?

“Does everyone have the right to leave the country when they want?”

“Should your boss be able to fire you if they think you are too old to work”

Take some right out of the news

“Should a bakery be able to refuse to bake a cake for a gay/homosexual wedding?”

“Should a women be allowed to wear a niquib/hijab/turban/cross at work?”

“Should only a indigenous people be allowed to hunt on ancestral lands?”

These issues lead to hard discussions with strong opinions and as a teacher you have to be prepared for these difficult conversations with an open mind and open heart.

However there is not much that peaks interest like a little controversy.

Provocation

Wonderwall

Curiosity

Questions

Ask For Student Input

If the topic is boring then ask about what they want to know about it.

Perhaps initially they won’t know very much so introduce them to a few concepts and a broad survey to give them some background knowledge.

Then ask them what they need to know more about.

When you do this you can have student share what they wonder about or want to know more about.

Take their questions and sort them and group them into guiding questions.

This will help you to find key points that students can learn about.

From there students can design their own learning project that answers these questions. Think of it like a design your own test activity. You give students the test questions and they come up with the way that they are going to answer the question.

It is a backwards approach to assessment but one that increases engagement and learning for students.

Make A Game Of It

There are so many ways to turn a learning objective into a game. And a game that can include a traditional board game format but is not limited to this challenge.

Try an escape activity with students where they have to uncover the information through a series of steps. While they try to break free they can also learn about their topic in a fun way.

When learning about biodiversity students are challenged to learn about all of the various ways to classify vertebrates and invertebrates.

This content is large and getting through it can be long and tedious.

Using a breakout with a foldable for student to create through a series of challenges creates a visual display of learning and classification that also covers a great deal of information in a small amount of time.

Hands on Learning

6 Routines You Need For Inquiry

6 Routines You Need For Inquiry

As we think ahead to back to school we begin to plan out the rules, routines that are essential to set us all up for success.

But what routines are essential to teach at the beginning of the year that will set you up for success if you plan to use inquiry in your classroom.

Calls For Action

Throughout our day we need to get the attention of our class. These type of routines are signals. Some of the signals I need to establish include

  • Signal for attention
  • Transition signal
  • Gathering space
  • End of day signal
  • Signal for Attention

  • These are words, sounds or phrases that signal to my class with little input from me what to do next.
  • For years I have used the call and response routine of CLASS-YES. When I need the attention of my whole class and I need them to stop, look, and listen I use this call out.
  • When I say CLASS CLASS my student s respond with YES YES. Now however I say class class is how they respond yes yes so to keep it interesting I say it in a variety of ways….like underwater.
  • There are so many phrases that can be used. So use what works for you and your personality. What matters is that you are consistent that when you call out students stop, look and listen quietly. This routine is practiced very often in my first weeks of school.
  • Honestly it is a routine that is constantly reviewed.
  • Transition Signal

  • Sometimes this one is overlooked and the previous call and response is used for both.
  • What I have found is that having separate signals for these events is important.
  • Think of the main transitions that you may have in a day. If you have daily tasks that require a series of steps to complete using a separate transition signal will help with this often chaotic time.
    Get to work quickly
    Join me on the carpet
    Move between centres
    Line up at the door
    Home time

All of these transitions happen daily in my classroom so to have a plan on how we transition and what I expect makes these times more structured.

To get my students to get to work quickly I will often use a key phrase that is recognizable with my students. We discuss this signal and practice this over and over. This phrase is never the same year to year.

  • Minds on? Go on
  • And go…
  • 5…4…3…2…1…go!
  • Whatever you use it really doesn’t matter. Just practice and consistency.
  • To get my students to gather I love setting a timer for their work period. At the end of the timer I love to play an alarm that is usually meant to help people wake up. A sound that starts softly and builds is a great way to ease people into this transition.
  • When the sound is done all students should be on the carpet or gathering space. Because we have knowledge building circles frequently having a gathering place routine is essential.
  • Plus it save me a lot of instructional time not having to explain what I want done every single time.
  • Sometimes we are working in centres or different learning tasks. When I want student to move from one to another it is helpful to have another sound for this too. A quick beep signal works great here.
  • Finally home time is another routine that we need to have a routine to make sure we get it all done.
  • Come up with a little saying for your students that reminds them of what to do. Or even try an acronym. What are the tasks they need to do.
    Agenda
    Chairs
    Table
    Floor

Well that spells out FACT so try to come up with a cute saying. “It’s home time that’s a FACT” when they hear this they know what to do.

Another phrase that could work is “Tidy, Tools, Table, Chairs”

They practice it, you review it, you rehearse it, you time it, you do it again.

These routines are tedious but so worth your sanity in the end.

Teachers Busy Routine

Other routines you can practice involve planning with your students what to do when the teacher is busy.

You could use cups to signal that help is needed.

You could use a clip system that students sign up for help and you will get to them.

Or you could implement an ask 3 before me system with student leaders helping out.

I personally use the ask three before me. I want them first to solve their own problems followed by asking me for help.

Many teachers signal to students that they are off limits with a light or sign. This is a great idea if you have a class that regularity lines up wherever you are.

Make sure however that you talk to students about this and explain that you want them to build their own problem solving skills. Explain to them why you are unavailable and be aware of certain personalities that will struggle with this. Being too black and white or rigid with this rule can be quite problematic.

Movement

Movement is chaos! Students need to be still and quiet….

Well we are all recovering control freaks so let’s work together to let this one go a bit.

Movement is okay

But let’s teach them how.

When should you move, why should you move, and how you should move.

These are all important questions to ask students when planning out this routine.

I like to start by playing the what-if game. You know the “but what if I have to…?

Well work through these questions. Lay it all out there.

  • Think about how students enter the classroom
  • Where do they sharpen pencils
  • Where do they grab and plug in their tech
  • How do the get from one place to another.
  • All major traffic areas should have 2-3 feet in between them for a walkway. Try to avoid the bottle neck that happens in classroom where you have placed things in inconvenient places.
  • Also try to avoid placing high traffic areas in the centre of your classroom.
  • In the first month of school you want to start with a plan but also assess along the way of your placement of things gets in the way.
  • If so move it.
  • If you want a more detailed walk through and plan to help you plan through your routines grab this freebie here.
Flexible Seating

Flexible Seating

Have you heard if it?

Well unless you have been under a rock how could you not see this as a wave that is slowly taking over Pinterest.

Everywhere teachers are proclaiming they are using flexible seating.

But without repurchasing brand new furniture for your classroom how can you dip your toe into this idea. Or how can you jump right in?

I have been slowly moving towards flexible seating.

It all started with a girl named… well let’s call her ‘Ava.’

Ava was a great student one of my best. But Ava always stood when she worked. In fact, Ava did her best work while standing at her desk.

Now I could have told her to sit down, the line I had told countless other students throughout my career.

But I didn’t.

And that changed the game for me.

It was that realization that some kids, even our good kids want flexibility and choice in how they work.

Not every student works best sitting in a chair in front of a desk.

Well after this experience with Ava it grew.

I began to let more students sit or stand at their desk while working. I let some stand at the back counter. I let others sit or lie down on the carpet. I let one student sit under my desk.

With every new “can I work here??” question that I was asked I kept saying she’s to most of them.

Always with the response “will you work best there?”

And for the most part, they did.

It didn’t take new tables, yoga balls, fancy chairs…

all it took was my ability to say yes to alternative workspaces within my classroom.

Now jump ahead, and I now have a few alternate spaces for students. A few new chairs and options for seating.

I add a few more each year (and take some away if they don’t fit)

So let me walk you through what flexible seating looks like in my classroom.

Tables

I wanted more alternative spaces for student work. I didn’t need or have extra room for desks. So I swapped the desks for tables.

Tables seat 6 per table group and each person in my room does have a home base. A place to call their own.

I am also not concerned about “seeing the board” from these tables. This means they can be placed anywhere. All of my whole group instruction is done from the carpet in my room, so the layout of tables is less of a concern.

My students eat in my classroom for lunch so since I find it grow to have food on my carpet or other soft furniture. Food is only consumed at tables.

All my tables are the same height.

I am lucky that I have a back counter that is standing height, so I do not need any standing height tables.

Carpet

I teach 10 – 11-year-olds

Some think that they are too old for the carpet.

But they are not.

If I don’t baby then when they are on the carpet then they are okay with it. I also am not concerned if they don’t like it. It is expected you join us there for whole group instruction.

It’s non-negotiable.

The carpet also serves as the main location for flexible seating. Students sit together, share ideas, work and read in comfort.

It does become the hub of the classroom.

Hiding

For some students, they like to work in isolation.

For these students providing locations for them to hide is essential. Hiding under a table covered in a tablecloth. Hiding under the teacher’s desk, or making a fort out of finding objects.

All of these easy makeshift ways are options in my room. Options that don’t cost me more than a few dollars for tablecloths and picnic clips.

For these students, you do need to check in on their work completion more than others, and if they take advantage then they lose the privilege (and return to their desk)

Chairs

Over the years I have collected a few chairs for my room.

I have two ottomans that I picked up at the second-hand store value village. I also picked up some shower curtains and sewed two covers for them. The ottomans don’t match in colour, but they are the same size. When covered the ottoman looks the same. I also threw in a bed bug cover in between the layers and the sheets themselves are removable and washable. I am not great a sewing, but I figured it out.

I also picked up two Muskoka chairs at Value Village. I guess someone messed up when trying to put them together because

 

there were pre-drilled holes in the wrong spots.

But that didn’t matter to me. I grabbed them for $12, and my friend Sarah put them together with me one August. They have stood up well to all of the wear and tear kids can put them through.

Finally, I picked up some kids white plastic outdoor chairs from IKEA.

These chairs are stackable and easy to move around the room.

They wipe easily and are the perfect size for a junior student.

Rules

To start flexible seating you need to have rules.

And routines

To start, I never start the year with flexible seating open and available. This is something we work our way up to.

We start by talking about the rules

#1 Wherever you sit. You need to work.

We review what this looks like

  • Stay in one place
  • Avoid distractions
  • Work the whole time

We then look at the four different areas in our classroom for flexible seating. We discuss the benefits and negative attributes of each step.

We look at what needs each student has as a learner.

  • Is it a quiet workspace
  • Are they easily distracted
  • Do they work better sitting or standing
  • We then choose two spots for each student to try out. They then try each place and rotate through the list we made. We evaluate what works and what didn’t.
  • We review the list and make a final one that we use.
  • However, this isn’t the only way we have organized this.
  • Other years I have numbered the table groups and simply rotated each group through the flexible areas.
  • Both ways worked for each group of students. Sometimes some rules work better than others.
  • Flexible seating doesn’t have to be fancy. But it is worth it.
  • Give it a try, dip your toe in.
  • Let Ava remind you that some students work better with a bit more choice and flexibility. It might even make management in your classroom easier.
Planning your Time Table

Planning your Time Table

Well that is another year in the books. As I close the door on my 11th year teaching I look forward

First to enjoying my summer

Second to planning for next year!

So recently I was asked what do I do to get ready for next year. I thought that this was a great question to answer in a blog post.

So this month I will talk about organization here on the blog and in my Facebook live show.

First up is creating my time table.

It is one of the first things I do and often is the foundation for establishing routines and other systems I will have in my classroom.

I am lucky in that I get my timetable quite early One of the first things I do is plan out what my schedule looks like.

Things like french, library, phys. ed, music. Etc are all pre determined for me so I need to be able to work around this.

I also have guidelines for timing

  • Language – 500 min/week
  • Math – 300 min/week
  • Science/Social Studies – 150 – 200 min/week
  • Arts – 150 – 200 min/week
  • Physical education – 150 min / week (prep)
  • DPA 40 min/ week
  • French 200 min/week (prep)
  • Library 50min/week

If you are quick with math you will see that I am over my weekly min of 1500 instructional minutes.

So some of this gets integrated and I teach multiple subjects during the same period.

Math is integrated with science and social studies especially when looking at data management, measurement, location and movement, number sense.

Dance is integrated with physical education, drama and art are also integrated.

I do stick to my 100 min of uninterrupted language per day and 60min of math.

So does it really matter what you do when??

Yes!!

Here is my own methodology for how I create my weekly time table.

Language Arts

I start with language arts. I look for blocks of time where I can put 100 minutes of uninterrupted time for literacy instruction. (We are on a balanced day so it is generally easy to do)

I like consistency more than time period. I look for the most consistent time in the day where I have these.

I have no preference for morning or afternoon for language. My language program is pretty laid back and independent so I can get away with putting this anywhere in my schedule.

Math

Next I schedule math. I make sure to put this in the first half of the day and always right after a break or transition period. For example it is great after they have Physical Education.

I try to never schedule math where it is the second subject I teach them in a block of time. I find it easier to transition into math this way without losing time.

Visual Arts

Next is visual arts. I look for two periods of this together preferably at the end of the day.

This year I couldn’t find them together so instead I had one art scheduled for period 6 one day followed by period one the next day. This actually worked out amazingly well. Since my instruction could be period 6 and their working period right away the next day period one.

However I still prefer art to be at the end of the day. I also integrate this with drama and throw that in there throughout the year every third or fourth art period or so.

Physical Education / DPA

My students have physical education three times a week so this means that on those off days I find time to do Daily Physical Activity (DPA). Normally I will put this in a period that I do not have a tonne of reporting. This is great for a prep coverage teacher that isn’t reporting like during library, or computers (if you still have that)

I never take DPA time out of language, math, or social studies time.

I teach a split so things take longer.

I cannot afford to steal from these areas. So this is an important consideration when creating your time table.

Science and Social Studies

For these subject areas I teach them in blocks of time.

I will teach science for a month then social studies for two months.

Because I teach a split I need more time to cover the material. So while using a flip flop method between the two grades I focus on one subject state and at a time each week.

I terms of my time table I am running out of room so these subjects need to fit in wherever I have room.

I look for 3-4 periods a week that these fit into my schedule.

If I had lots of space I would try these for close to a math or language period.

Most often though these get pushed to the end of the day and 10 min is relegated to math to make up our full 60 min math requirement.

Notes and Considerations

Many times we are given a prep period where our classes are covered by a teacher that has lots of time but not a lot of reporting.

If you teach a split I highly recommend you try to negotiate your way out of this predicament.

You need as much time as possible to teach your core subjects so moving things off your plate will be important.

  • Ask your Phys. Ed teachers to also teach dance and health
  • Ask your librarian to cover media, oral communication, drama or DPA
  • Ask your drama teacher to also do dance or DPA.
  • Ask your computers teacher to cover a math strand, science, media or drama.

Grated some of these asks can be refused by the teacher. But if you have a supportive admin perhaps they can help. If not this year then next.

Most admins want all time to be instructional time so don’t be embarrassed to leverage that when you advocate for your time table.

However it is always better to approach admin with solutions that you have solved. Then you are simply asking if they can approve them. This is always a better approach then going to them with a problem you are putting on their shoulders to solve for you.

Want to know more about what I do now to get ready for September.

Stay tuned for the next post coming soon.