Posted in Math, Misc. Ramblings

Fact Fact Off!

Who couldn’t use a quick and easy new game to practice addition and multiplication facts that is fun and involves a little bit of strategy?  My eleven year old son, Ben, and I dreamed up this little game this evening.  This is a game that you could use in your classroom OR played at home and can be adapted in lots of different ways.

Materials:  You will need a standard deck of cards with jokers.

Card Values:  For this game we designated the Joker as a wild card, meaning you could make it any number you want when it is played.  We made all of the Aces = 1, Jacks = 10, and Queens and Kings = 11.

Directions:

  1. Shuffle all of the cards and place them face down in a pile.
  2. Each person takes 3 cards (and hides them so that no one, but themselves, can see them).
  3. When each round begins, each player chooses a card from their hand and lays it face down in front of them.
  4. After both players have a face down card each player takes one of the remaining cards from their hand and places it face up beside their opponent’s face down card, as shown below.  So, in fact you are giving your opponent a card which they will use to make an equation in the next round.
  5. Both players turn over their original card and multiply the card they were given by the card they had placed face down.
  6. The players both state their equation and product.  For the hand show above Ben had 6 x 11 = 66 and I had 8 x 10 = 80 so I would win all 4 cards.
  7. The player with the highest product wins the round and takes all of the cards on the table (4).
  8. At the end of the round each player will have 1 card left in their hand.  They will save this card for the next round.
  9. At the beginning of each round players take 2 more cards so that they have a total of 3 cards in their hand (this gives players some choice in what they play) and repeat steps 3-8 until all the cards from the face down pile are gone.
  10. When all rounds are complete players count the cards they won and the player with the most cards wins.

Special notes:

  • If a player places a joker on the table they will state the number they want it to be when they state their equation and product.
  • If the product is the same, play a second round and the player with the highest product will win all 8 cards instead of 4.

Variations:

  • For younger grades use addition.  Players will find the sum of the two cards.
  • To make the addition more difficult you could have players take 4 cards and lay 2 face down in addition to the one their opponent gives them.  Then players would find the sum of 3 addends.  In this variation, the player with the highest sum would take the 6 cards on the table instead of 4.
  • You can always change up the value of the face cards.  For example Jacks could be 10, Queen could be 11, and King could be 12.

The possibilities are endless!  We made a little video to help explain the rules.  We hope you enjoy the game and share it with your students!

Posted in Math

Number Chart Routine…FRACTION STYLE!

Wow, isn’t it amazing how something that can start out as a small idea can explode into something much bigger than you ever anticipated.  That is how my Number Chart Routine has become for me.  I started small, modeling this routine in a few primary classes and coaching teachers on using this routine to build number sense with students.  Now, this has transitioned into my intermediate classrooms as a way to help students develop their decimal, and now fraction sense.

For those of you who are reading about my Number Chart routine for the first time, I would suggest that you go back and read my first post and watch a sample video of how the original routine works.

After modeling the whole number routines in various classrooms I felt like it was time to “take it up a notch” and use this routine to build fraction sense.  We know it is important to learn to count whole numbers before we compute with them.  Students who can count forward and back by numbers can more easily compute those numbers.  So…why don’t we do this with fractions.  We seem to just jump from representing fractions to adding and subtracting.  The Common Core emphasizes the use of the number line to help students bridge this gap.  With this thinking in mind I created the fractional Number Charts.  Each one counting up by fractional units.  Keep in mind that routine works the same way as the whole numbers.

So, Mr. Jeremy Wood, another one of my fabulous fifth grade teachers agreed to try the fraction routine out with his students.  Much to my delight his students did well with the routine and didn’t want him to stop (there’s a win!).  He felt like it really helped students see patterns and be able to count forward and back in fractional units.

After Mr. Wood tried out the first board we felt like it might be helpful to create boards the counted by fractions like 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, etc…  as well as a board with eighths but also equivalent forms of numbers.  For example this board has 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, etc… as shown below.

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If you are interested in trying out the fraction boards they can be found here:  Fraction Number Chart Routines.  These would be great for classrooms from grades 3-5+.  I will continue to add more fraction variations as time allows and as my teachers request them (lol…things always get done faster when someone asks me to create them for a lesson they are doing).

If you would like links to all of my Number Chart Routines be sure to check them out on the Number Chart Routine Page.  Be sure to download the PowerPoint and click the present button so that the animations work on the third slide.  Note, the first 2 slides for just for teaching background and information.

Posted in Math

Upside Down and All Around: The Hundreds Chart 3.0

It seems that my first two posts on turning the hundreds charts (grid) upside down has generated a good bit of buzz.  I really appreciated all the feedback from teachers across the country and from the teachers in my own building (special thanks to Andrew Stadel and John SanGiovanni)!  What I thought was going to be a one shot blog post deal has taken on a life of its own.

The great part about being a lead teacher is being in a large elementary school (750 students) with lots of teachers who love to volunteer their classrooms up to me to model and try things out with their students.  So when I pitched this idea to my grade 1 team they were eager to have me try it out.  At that same meeting I came up with the idea of using Steve Wyborney’s digital hundreds chart version to make this into a math routine.  I was able to modify his original hundreds chart into several different upside down versions to use in my routine.

So, the very next day I went off, ipad and tripod in hand, to video myself on my first attempt to Spencer Taylor’s first grade classroom.  Spencer has a group of first graders who have many special needs (a quarter of them already have an IEP) as well as 1 or 2 students who are English Language Learners.   I knew that in our first grade classrooms had spent a good amount of instructional time with place value and using the hundreds chart early in the year.  From our planning the teachers decided to again revisit and expand on their instruction in place value to addition and subtraction in this upcoming marking period (we are really going to focus on those 1.NBT standards).  Spencer warned me that he wasn’t sure how they might respond but, undeterred I forged ahead!

I began by exposing only the 1 and the 100 on the board.  These are what I call the “anchor numbers”; numbers that help students make sense of the board and the arrangement without showing them the entire board.  Then I turned 9 other squares white.  With the students I first just had them simply NOTICE and WONDER about what they saw.  The students quickly able to see that these numbers were in a different place then they were used to but, as you will see in the video, they adapted quickly and were not phased by the change.  Next, for the routine we played a game of the class against me.  I told them that for every  number on the marked spaces, that they could identify correctly they would get a point and for every number that they incorrectly identified I would get the point.  Throughout the idea was that the student identifying the number had to explain to the class how they used their math thinking to determined the solution.

Side note….the video quality is not fabulous (sorry) as the lights had to be off to see the blue outline of the boxes on Steve’s chart.  

What I saw from these students during the short routine was a tremendous amount of thinking and reasoning!  I also saw how easily they could reason through the changes given their knowledge of numbers and patterns. This has spurred me on to think about creating lots of different number charts (with numbers in different locations) and building routines around them to build number sense through reasoning with patterns.

Side note…I would love to create a program where you could have a board with 100 or 120 spaces, fill the smallest number you want into one cell and the largest number into the last cell and then the board would automatically populate so you could use it like the board I modified from Steve or this Classworks board. If this is a skills you have contact me so we can make this happen!  In the meantime I’ll create some different boards on this page and start posting them for teachers.

Something else you might notice from the video is that you will see me try to redirect them to talk to their classmates instead of just me.  Students tend to just respond to the teacher but it is very important for them to communicate with each other instead of just the teacher.  This is something that could easily be built in this classroom through routines and activities.

Even after a successful routine with this group of first graders, I realized that this journey was taking on a life of its own.   First, I’m going to call change the routine name to Number Chart Routine.  My plan is that the boards will have many different configurations.  They may be right side up or upside down, sometimes they will end with 100 and sometimes they will go way beyond that into digits in the thousands or even start below 1 with decimals, fractions, negative number (yes even elementary students can understand that concept), etc…   For now, until I can figure out a way to automate the chart as I mentioned above, I will just begin by creating more variations on the board for teachers use and archiving them here on my blog (and on my school’s google page) for anyone to use and modify for FREE.

Here is the link to the folder that I’m going to continue to add versions of the Number Chart Routine.  I created 10 number charts to start with (5 regular and 5 upside down).  I will be adding more over the next few weeks.  Be sure to drop in again and make suggestions of other variations that you would like to see created!  This post will also be added to a new Math Resources page titled Number Chart Routine.

So…after all of this I hope you will dive in with me and try out this routine and share your experiences, thoughts, and feedback!

Posted in Math

Turning Your Math World Upside Down!

UPDATED!! After this post went live last night, I had some fantastic feedback and thought I would make a few revisions.  Andrew Stadel (Divisible by 3) suggested that I reverse the direction so that 1 is in the right hand column more like a coordinate plane.  What a fabulous idea!!  SO…below you will now find those links instead of my original ones!  

I bet you are wondering what this post is all about!  How could I possibly turn your math world upside down?  As elementary math teachers we tend to use hundreds charts  to help students see patterns as well as a math tool.  Most of you probably use a traditional 1 to 100 chart or a 0 to 99 chart.  My complaint about the hundreds chart has always been that when you start using as a tool to teach patterns in adding and subtracting, well it seems to be visually backwards…

Think about it…on a hundreds chart if you add 29 + 10 you start on 29 and go DOWN one line to find a sum of 39.  Moving down feels like taking something away not adding to something.   The same is true when you subtract you are actually physically moving UP!  No wonder our kids are so confused!!!  Think about this…on a graph 0 is at the bottom of the graph or on a coordinate grid and the scales moves up.  The same is true for a thermometer.

So, why do we do this to kids.  Why not turn that chart upside down????  Check out the image below…now add 29 + 10 again.  Notice that now you move up, just like a graph, or a thermometer.  I just ask you to think about it.  I know that you’ve probably been using that traditional chart forever but maybe this might help our students.

To get you started I am giving you some links to some basic Upside Down Hundreds Charts I have made.

1-100 Basic Upside Down Hundreds Chart LR 2.0

0-99 Basic Upside Down Hundreds Chart LR 2.0

1-120 Upside Down Chart (Grade 1 CCSS) LR 2.0

1-200 Upside Down Chart LR 2.0

Decimal Hundredths Chart LR 2.0

Let me know what you think of this!   I’d love some feedback…do you like this idea, not like this idea, or if you try it out I’d love to hear how it worked!

Posted in Math

Try out a Silent Sort Routine!

When I started teaching math, 22 years ago we always started math with a “warm-up”;  a small set of problems to get kids to review material from previous days or units.  Over the years my thinking on this practice has gone through some radical transformations.  Now the first few minutes of my math time with students is spent using one of many different math routines not just to spiral back to material but to also activate prior knowledge, build number sense, and build thinking skills.

There are many routines that I use on a regular basis; number talks, math strings, Which One Doesn’t Belong, Splat!, Cube Conversations, Geometric Subitizing, Reveal a Graph, Which Would you rather as well as the routine I’m going to share with you today…Silent Sorts!

Silent Sorts are a twist on the “Guess My Rule” type of activity.  This can be adapted for just about any topic in math (or even other subjects).  First the teacher decides on something that could be sorted for math.  One example that was used in my building to introduce first graders to fractions this week involved the sorting of representations of halves, fourths, and wholes.  I created enough representations so that each student would receive at least card.  The teacher divides a piece of chart paper into the number of categories that they will sort into (for this example we divided the page into 3 sections) and then hangs the paper in a place where the class can see and reach it.

Click on this link for the Fraction Sort used in Grade 1.

On the day of the routine the teacher tells the class that they will be given an object on a card.  They will be silently sorting their objects; meaning they will be sorting without talking.  Each student’s job is to look at their card, and based on what they see on the sort, decide where they think their card should go.  One at a time students come up and place their card.  If the card is not placed correctly, the teacher immediately moves the card to the correct location without saying anything.  I make sure that before we begin I tell them that it is ok if I need to move their card.  As each student comes up and places their card they tap another student to come up before returning to their seat.  I tell them that their job is to continually look for what they notice, wonder, and think about what they see.  When we are done, the class will try to beat the teacher by coming up with the rule for each section of the sort.  Before we finish we also name each section.

Today I was able to video tape myself doing this routine (click here to see the sort).  These students in grade 1 and on Monday will be starting to add and subtract within 100 (starting with adding and subtracting tens) next week.  The teacher, Mrs. Hahn, and I thought it would be good to see what they remember about place value and numbers greater than 20 to get them ready for their new unit.  So, I created a sort with 4 sections – numbers with ones, number with zero ones, place value representations of numbers with ones, and place value representations of numbers with zero ones.   We were not sure how well they would do but, if you watch the video you will see that had to move very few cards.  Most students were able to quickly notice the pattern.

Keep in mind that silent sorts can also be used in other subjects.  For example you can sort types of words and particular sounds in reading as well as sorting science or social studies concepts.  The most important part is that students are doing the thinking.  You as the teacher only need to encourage them and give them opportunities to collaborate in their thinking.

Here is a link to the folder in which I will be keeping my Silent Sorts as I create them.  Keep checking back as I will be adding more.  I’ll also add this link to the math page of my blog for future reference.

 

Posted in Math

Need to jump start your math the day after the Super Bowl? Then read this…

I’m sure if your reading this then either the Super Bowl is over and your are waiting for This is Us to come on or… you are passing time during the commercials surfing your ipad!  If you are like me…I’m always in search of a way to get my students “into learning” after a late night watching the Super Bowl by incorporating some of the game into our learning.

I have created a new math routine called, Reveal a Graph to help teach students how to really “read” graphs and data and peak their interest in numbers and math.  Tonight I created 2 additional Reveal a Graph routines that incorporate the Super Bowl.

The concept behind my routine comes from a Dan Meyer video I watched on ways to get kids really engaged in mathematics.  Dan suggested taking a graph, covering parts of the graph and having students notice and wonder with it before giving them the entire graph and a question.

In my 22 years of teaching I have noticed that students do not really “read” graphs.  They simply read the question and start searching for the answer.  This routine will force your students to really “read” all the information on the graph and think about it before answering a question.  Better yet…with each routine I ask kids to come up with questions they can ask and answer about the graph BEFORE I give them a question.  Most of the time my kids will come up with the question I was going to ask without me even posing it!

Know that these graphs can be used across the grade levels as long as your students can understand the information in the graph.  I am often intrigued to hear how the responses differ when I use the same graph with students in primary grades and then use the same graph in the upper grades!

So…if I have peaked your curiosity go to my Reveal a Graph Routine page to watch my short video and access the files.

PS… Here is a direct link to the the 1st Super Bowl Reveal a Graph and the 2nd Reveal a Graph that includes the Super Bowl!

 

Posted in Math

3 Act Math Lessons Added and UPDATED!

Many of you are familiar with 3 Act Math Lessons.  I have written as well as collected many 3 Act lessons over the years.  One of my former Lead Teacher partners asked if I would be willing to share my collection so that his teachers in his West Virginia Elementary school would have access to them.  I thought this was the perfect place to link them so that everyone had access to them again.  So…if you want to learn more about Dan Meyer’s 3 Act Lessons for Math check out this page on my blog that is dedicated to this fabulous instructional structure/strategy!