10 more/less and MORE!

Standards Progression

1st Grade

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

2nd Grade

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900

*Supporting Standard 

 2nd grade-Count within 1000; skip-count by 5s, 10s, and 100s.

This one sounds so simple, yet encompasses so much number sense and understanding!  Where to begin...same place as always, with some math manipulatives of course.

This standard states to "mentally find 10 more/less, without having to count" but that doesn't just happen without some serious instruction and practice where the students do count. They count over and over again until they see and understand the pattern of adding 10 more or subtracting to get 10 less. 

 In 1st grade, the 10 more begins early as the kiddos are adding 10 more to those groups of 10.  This is closely related to the place value standard that has the kiddos counting 10 and some more for teen numbers and multiples of 10 and some more for larger numbers.  When you're doing those activities, it's simple to throw some in tasks where you have the children continue counting past 9 more.  Then that opens the door to "regroup" to make a new group of 10.  It all just goes hand in hand and these place value activities make a smooth transition into the world of 10 more/less. Voila!  Sounds so easy, right? 

Those little firsties can do this in so many forms-using all kinds of counters and tens frames will help to build the understanding of 10 more/less but remember to not just stop there.  Counting is only the first step.  After that, the kiddos have to see the pattern which can be accomplished by pairing those concrete manipulatives with some representational recording of the numbers they are making.  A good way to start is with them doing the counting and the teacher recording the numbers-it's a little neater at first when you record.  So, record a number pattern on the board as your kiddos keep counting those counters.  After a few numbers, call them to the carpet and have them look at the numbers.  Remind them that good mathematicians stop and look for patterns to see if they can be repeated (ding, ding, ding...there's one of the Mathematical Practice Standards). I usually ask them some questions like, 

-What do you see?

-Do you notice a pattern in any of the numbers?

-Can you see something that changed?

-Can you see something that stayed the same?

Some students will see that the number in the tens place changed right away, while others will need to count it, record it and see it many more times before they finally "see" and understand that the number in the tens place changes when you add or subtract 10 (aka, 10 more/less). That's all there is to it right?  You're almost there, but not quite...

So once my kiddos start seeing the pattern then we continue to practice it, with guidance, in small groups and independently. I also make sure MY STUDENTS have plenty of opportunities to practice writing those number patterns themselves.  We practice skip counting by 10's (even though skip counting isn't an actual 1st grade standard I still do it to help solidify the pattern of the numbers) from any given number 23, 33, 43.... 

Finally when I think they've got the pattern down pat, we discuss the different ways this might look.  I show them some skip counting patterns with 10 more/less. I relate it to some +10/ -10 equations, and finally give it to them in chart form for the true mental test! 

Confession of a place value geek...no base 10 blocks were used in the building of this understanding for those little 1st graders.  It seems like it would be so much easier (I know), but I have to remind myself that I must build number sense and understanding of quantity of numbers for those little kiddos and the best practice for building that understanding is counting  all those individual little counters up and down, over and over again.

Now, onto those 2nd graders...hopefully they come to you with the complete understanding from those wonderful 1st grade teachers; however, in all reality we know stuff just slips out of their little brains over that summer break and as much as we try to convince them that they "did learn it in 1st grade," somehow we sometimes have to do some review and then it all starts coming back to them :)

So in 2nd grade, I know it's going to surprise you...but I still don't start with base 10 blocks (insert eye roll 🙄) so once again even though we are doing larger numbers, I still have them count 10 more/less with individual little counters but that doesn't always involve building the WHOLE big, huge 3 digit number.  We might just say the number, then count on 10 more/less like say 346 then use counters and count 347, 348, 349, 350, 351...until we have added/subtracted 10.  In the beginning, I record the number pattern for them as we practice just counting on 10 more/less from several numbers.  Then we have the same discussion as mentioned above.  In 2nd grade this concept usually comes much quicker and some kiddos already have it thanks to those wonderful 1st grade teachers doing such a thorough job (thank you 1st grade teachers). After that we do finally break out the base 10 blocks and practice adding/subtracting those tens rods and eventually move onto the hundreds flats.  We practice skip counting number sequences, adding 10/100 more/less with equations and finally in a chart form for the true mental test!  

                                             

We're almost there...one common issue for the 2nd graders is not being able to cross the hundred.  Now, you might have noticed that I didn't mention the good ole hundreds chart in my above description and that's because it's just not my tool of choice.  While completely acceptable and I do use it, it's just not the first tool I pull from my tool belt.  It is especially helpful when you have some kiddos that just can't seem to "see" the pattern. It's a very tactile tool that allows the kiddos to move up and down to see how the numbers get larger/smaller.  Now in 2nd grade, we use a 1000's chart to help cross over to the next hundred. Some kiddos just need to touch, say and move from the first hundred to the next in order to help them understand how to cross over when learning 10/100 more/less.

And there you have it, fellow teacher friends...mentally finding 10 more/less than a number without having to count! Easy as pie!

Place Value

Ahhhh...place value-the basis for our whole number system!  What a FUN thing to teach!  I love teaching place value in 1st and 2nd grade because there's so much to do with it...build number sense, use lots of manipulatives, explore expanded form, read and write word form, compare quantities, the list goes on and on.

Standards Progression:

1st Grade: Understand that the two digits of a two-digit number represent amounts of tens and ones. 

2nd Grade: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

Here's a glimpse into the way I choose to teach place value in my own classroom.  I begin with building number sense for my little kiddos.  This is SUCH an important step in their understanding, especially in 1st grade.  It's so easy to jump straight to the base 10 blocks but I have found that is not enough. Some math gurus even suggest that base 10 blocks should not be used in 1st grade at all because of their abstract nature.  My little kiddos need to UNDERSTAND what those base 10 blocks represent and they need to understand the quantity represented by the numbers being discussed in both 1st and 2nd grade.

To build this number sense in 1st grade, I've used lots of different objects and representations to build the understanding of ten and some more or groups of ten and some more.  We use counters, unifix cubes, and any other manipulative that is easy to count with tens frames (concrete), and circling groups of 10 and some more in pictures (representational) before EVER moving into base 10 blocks (abstract).  To some this may seem like a waste of time but for me I want to be sure my students understand the CONCEPT behind those base 10 blocks and have good number sense so I choose to spend a good amount of time on this first step before moving into blocks and for some kids that doesn't happen in 1st grade at all.  While doing all this counting, we practice relating the number we say to the written form to start building the actual place value understanding.

I do the same thing with my 2nd graders only with larger numbers. We review groups of 10 and some more with those same items (counters, unifix cubes, tens frames, pics of objects) and then move into 100 and some more.  Yes, this is messy!  Yes, it's a little crazy with all those manipulatives going every which way!  Yes, it's necessary to build the concept and number sense of a hundred and some more. Here's a picture of our cubes right before we were getting ready to move into base 10 blocks.

I started by giving my 2nd graders 2 handful of cubes then we worked together to make groups of 10. We discussed how it was more efficient to count by 10's than 1's to get our total number. I also intentionally slide the groups of 10 together to make 100, so they could begin to understand recognize a hundreds flat.

If you have students struggling with place value, you might try going back to this step.  It is often the missing link to their understanding and some kids need a LOT of time with this step in order to build their number sense and to learn to "trust" the pattern of numbers.  Grab those counters, bears, beans, cubes, etc. and have them count and group and write the numerals so they will build that number sense and true understanding of how numbers and place value works.  Your students will reap the benefits for years to come.

So 1st and 2nd grade teachers, I hope you will join me in taking a step back and building number sense before jumping straight to those beloved base 10 blocks 😉

Flexible Seating-Getting Started

Flexible seating is one of those things that a teacher has to WANT to do in his/her classroom in order for it to work. For many like me, it's a leap of faith.  There's so many things to think about and consider before making this change in your classroom. Here's the list that I used when considering whether or not to "take the leap."

1-Why are you considering it?
2-What will you do with the kids stuff?
3-How will you manage it?
4-How do you get the seating options?

1-Why are you considering it?
Are you looking to spice things up a bit for your students? Do feel there is a need in your classroom to change some seating options to help students perform or behave better?  Does it look really cool when you walk into teacher's classrooms that do flexible seating? These are just a few of the questions to consider when trying to decide whether or not to give flexible seating a try.

If you feel your students just need a change, then you could try just rotating a few seating options through your whole class.  I often do this early in the year when getting my kiddos ready for the most extreme seating options (aka-the yoga ball).  I just keep a checklist up front on my board or easel and choose 1 student before lunch and 1 student after lunch so everyone can give it a try. As a class we discuss and practice how to use the seat correctly and I  follow up with the students after everyone has had a chance to try it out to get their thoughts.  Surprisingly enough, I've had children pass on their chance to even try some seats.  I've also had kids who loved the special seats but are able to tell me it was a distraction to them. So letting everyone try it out is one way of introducing flexible seating into your classroom in small doses.

Another way to introduce it in small doses is to place the flexible seating options around the room for use during centers, group work or partner activities. I have several colleagues that choose this method of incorporating flexible seating into their classrooms because they just aren't comfortable with the controlled chaos of having all those seating choices everywhere for the entire day.  This helps get the kids used to it, while not causing a huge change in your classroom set up. Then you can go ALL IN a little later.

Finally, you can do like me and go ALL IN!  I'm an ALL IN or not kind of girl anyway, but my purpose was and is to help my little wigglers to stay focused in any way possible so they will listen to me, so I ditched my desks (not all, just most) and did a major rearrange.  If you're willing to take the plunge then go for it but if not please feel reassured that it's okay to start on a smaller scale and work up from there. You can see an updated panoramic shot of my classroom below.

2-What will you do with their stuff?
This is a very important question to think through before going ALL IN with flexible seating. Before flexible seating, all my students had a desk of their own and that is where they stored all of their notebooks, journals, etc.  When I made the switch to flexible seating, I got rid of most of my desks which meant now I had to find somewhere to put all that stuff.  Just the thought of it gave me butterflies!  Luckily, my classroom was designed with lockers that included cubbies on the top for each student.  I chose to clean out all of the rarely used stuff and make room for the necessities in the cubbies.  After all, my old way of thinking didn't want that much up and down in my classroom going to get stuff every time we switched subjects but I knew I was going to have to make a change.  Now pencil boxes, journals, folders, etc. all stay in the cubbies. This can be daunting but dig in and you'll figure it out. Think like one of those fancy home organizers that gets paid the big bucks and just think about 1)What do your students need daily? 2)Where is the convenient place to store it?  Teachers are terrific at organizing so think outside the box and you'll have it figured out in no time!

3-How will you manage it?
It's decision time...Do you want to assign seats? Do you want students to stay in the same place all week? Do you want your students to pick new seats daily? Is it important to you for them to have a "home base?"  To be honest, I've done all of the above.  In my current classroom, the students choose a new seat each day and that is their "home base" but for me it changes throughout the year.  At BOY I often have mostly chairs and tables, then I introduce the more "fun" choices by using the checklist system mentioned above.  Sometimes I have students who aren't making good choices about where they sit and who they sit with, so I assign them a seat (at least temporarily) after a discussion with them about whether they think their choices have been good/not so good and why.

 I feel that it's important for my students to have a "home base" for the day so they know where to leave their pencil boxes, coats, etc. I still say "Go to your seats..." and they know where to go.  However, unless we are taking tests, my students spend very little time at their "home base" seats.  Nearly all of my mini-lessons are at the carpet, then group/partner work is usually an opportunity for them to spread out in places they choose around the room (which includes some of those seats that other students picked for the day as their "home base").  They only time my kiddos are usually at their "home base" is during independent work or if they choose to go to their "home base" during group/partner work.

Another thing to remember is that there will be a lot of movement throughout the day if you go ALL IN with flexible seating.  I must admit some days it still drives me CRAZY but I have to take a breath and remind myself that I'm doing the flexible seating to help the kids!  I have  a hard time sitting at the same table, in the same chair, listening to the same person at professional development sessions and I have to remember that my students feel the same way!  Here's an overview of the movement in a typical lesson for my classroom..."Bring your word list (from your cubby) and your clipboard (from a class bin) and pencil (from your seat) to the carpet."  I teach the lesson, then..."Now you may choose a partner spot to work together."  They work together, then..."Now complete the independent practice at your seat." Yes, it's a lot of movement but that's a win-win. Not only are you giving your students the opportunity to work in places that are most comfortable for them but they are given a lot of chance for movement.  Remember those little wigglers?  That's exactly what they need and you are the awesome teacher giving them that chance to move and wiggle.

Something else to consider is what your "rules" will be for flexible seating.  There are lots of good resources out there if you need ideas.  This is where you have to be willing to set aside some class time to teach the kiddos in your class HOW to make good seating choices and work in some follow up and accountability. One thing I do is check in with my kids from time to time with a Student Seating Inventory.  I have them think about where they work best and who they can be around to do their best work.  I use a google form but you can see a PDF version below.

4-How do you get the seating options?
Start by looking around your house or storage building. Are there some bar stools you haven't used in years? If so, add them to your classroom.  You can talk to your custodian and ask them to show you some of the unwanted items they have in their secret hiding places. Local discount stores have a lot of the items (stools, yoga balls, etc) that are reasonably priced.  Especially if you have to start with the cheap stuff (like me) be sure one of your rules is to use the seats appropriately and keep tools (pencils, scissors) away because these items aren't meant to last forever with day to day kid use.  Once you get your feet wet, then you can begin to talk to your principal or PTO to see if they would help you purchase some "school quality" items.  Plus, if you're good with data, you could have some behavior data to present them as you make your case for flexible seating. Most items aren't very expensive. You can find Yoga balls for $5-$10.  Wiggle seats are less than $20 online.  Stools can be $5ish. I'm currently still trying to get funding for a stand up table (I have one meant for older grades that is raised but it gets wobbly quite often) and those durable cushions (that are about $50 a set) for floor cushions.

 

One word of caution, please don't talk it up and get your kiddos all excited about flexible seating,  let them try it out and then take it away completely.  Remember the point isn't to be a reward or punishment. It's about HELPING the children who need it. It has been my experience that if you're having management problems, then it would be more appropriate to take away the seating choice that is causing the problem, address it with the student(s) having the problem or spend a little morning meeting time reteaching your procedures for making seating choices and using them correctly.  Once the kids have experienced the freedom and independence of choice, they will not be fond of giving it up.

I hope this list has helped you in thinking about and planning for flexible seating in your classroom so you'll be all set to go ALL IN!

Word Problems-Now What?

The first step in TEACHING your kiddos word problems is making sure you are familiar with the different types so you can help your students understand them.  Here's a quick review of the types.

Add To-have an action that adds something (ex. friends at a table and more join)

Take From-have an action where something is taken away (ex. birds in a tree and some fly away)

Put Together/Take Apart-Add or take away parts from a whole (ex.boys and girls in a class)

Compare-Compares the difference between 2 given sets (chocolate chip vs. peanut butter)

Now, how to teach these to your students.  Pick a type and start familiarizing them with the language of the problem type. Yes, I said use the names of the problem types with them. Now I know this can be scary at first when the kiddos look at you like you've grown 3 heads (especially in kindergarten) but don't give up!  Over time, they will become familiar with the vocabulary of the different types and the problem type is what actually helps them to understand the words in the problems.

Before jumping into word problems, I always make sure I've already been working on the concepts of adding, subtracting, part-part-whole and comparing (more about that later). Also, I make sure we've used a part-part-whole model with bars with basic computation since it's my personal model of choice for working with word problems. You can use number bonds and other models, but I choose to stick with the bar model for my students because it works with all the primary problem types and can be used for upper grades problems too-so to me it's the universal model for word problems.

Here's how I teach each problem type.

1) Teach the concept behind the problem type (K/1/2).

2) Practice the problem type with numberless word problems using labels and a model (1/2 grade)

3) Practice the problem type with the unknown in each position (as stated by your standards).

Let me explain...

Teach the Concept

In other words, they have to understand what happens to numbers when you add or take things away. This is where the manipulatives come out.  I read aloud several word problems and have the kiddos really act them out using cubes, counters, etc.  In 2nd grade this helps my students make the connection between the concrete and the representational form. I did this same thing in 1st but spent more time on the concrete before moving to the representational (on paper) form.  

It might look like this for an add to problem.  I read aloud, "There were 7 cubes on the desk.  The teacher walks by and puts 3 more cubes on the desk.  How many cubes are on the desk now?"  As I read the problem aloud, the kids count out the cubes and act out the problem.  I usually show them the problem on the board and they practice listening to me read it, then they practice trying to read it themselves. As a class we discuss the important information in the word problems and practice marking it to show what is important.

Practice with Numberless Problems

If you've never used numberless word problems then I cannot begin to explain to you how powerful they are when teaching the problem types.  This is my "go to" strategy for those kiddos who struggle with word problems.  A numberless problem is just what it sounds like, you take a word problem and leave out the numbers.  I show the word problems on the projector screen then just delete the numbers. On some problems you'll need to adjust the wording a little bit so that it makes sense but oh my goodness, this forces the kiddos to make sense of  THE WORDS!  

Here's an example for a take from problem.  I read aloud, "There were some oranges on the kitchen counter. Mom came by and threw some of the oranges in the trash. How many oranges are left?" I have the children practice drawing a bar model and putting the labels in the correct place with NO NUMBERS.

Once they get good at no numbers, then we are ready to add in the numbers for the next step.

Practice Finding the Unknown

According to the state standards, in 2nd grade we teach the unknown in ALL positions for each type. This differs depending on your grade level so dig deep in your standards to know what is appropriate for your grade level.  Here's the breakdown based on the state standards for my area.

Kindergarten-Add To/Take From result unknown, Put Together/Take Apart total unknown and 2 addends unknown

1st Grade-Add To/Take From change unknown, Put Together/Take Apart addend unknown, Compare difference unknown

2nd Grade-Add To/Take From start unknown, Compare bigger unknown, compare smaller unknown

Here are some examples of what the final product might look like for each problem type.

So there you go!  This is how I teach the word problem types in my classroom and it works for me and my kiddos.