Monday, March 31, 2014

Monday Math Literature Volume 37

Last week, I showed you a lesson out of this book based on a great story about the number 1000.  Today I want to share with you another favorite out of this book.


This is a great resource that will help you get even more out of your math literature collection.


This book is full of activities that go along with 20 different books at the grade 3-5 level.  They also have similar books for grades K-2 and grades 6-8.

This lesson is based on this great story


This book is part of a series of animal math books written by Ann Whitehead Nagda.  My other favorites in this series include Polar Bear Math and Chimp Math.


This book is all about a baby tiger named T.J. who was born in a Zoo and has a hard time gaining weight and growing at a steady rate.  On the right hand pages, it tells the story of T.J. and shows some very cute pictures.  On the left hand pages, it shows graphs that support the data found in the story.  The graphs include bar graphs, line graphs and pictographs.  I did this lesson with a class of third graders but it would also work well in grades 2-5.

The lesson from the Math And Nonfiction books starts by having you read the story to the kids.  The lesson plan has you just read the right hand pages and not even show the left hand pages, but my students were so into the data and so engaged by the story, that I did show some of the graphs on the left.  While we were reading the story and looking at some of the graphs we had a very rich discussion about how the slope of the graph reflected weight gain and loss and how the steepness corresponded to how quickly or slowly his weight was changing.

After reading the story, the kids we so into the story of T.J.  I knew I had them hooked.  The lesson from the Math and Nonfiction book did some really creative things from here.

First, I showed a pictograph from the beginning of the story.  This is one graph I made sure I didn't show them when reading the story.  I covered much of it up with sticky notes.

A peak at part of the graph.  
Students had to think about what the graph was showing and what other information we were missing.  As they thought of something else on the graph, I removed another sticky note.  Once the graph was revealed in its entirety, I had 13 kids represent the different kinds of tigers and we made a human pictograph in the middle of the classroom.  Each kid represented 500 tigers just like each tiger picture in the pictograph represents 500 tigers.

Kids graph themselves by tiger type.  Extra kids got to be tiger wranglers and help me line everyone up

Here is where I was super impressed with this lesson.  The kids moved into one long line and then closed the line into a circle to make a circle graph.  I had never thought about making this connection for kids between a pictograph and a circle graph.  It worked very well and the kids were so impressed.

After the kids moved from a line into a circle, I had them stand shoulder to shoulder and then sit down. We used meter sticks to make the partitions between the different groups of tigers.    
We had a quick discussion about how the graphs were similar and which one showed the data better.  Kids had great insights to share like noticing how it was easier to see that more than half the tigers were Bengal tigers in the circle graph than the pictograph.

How do you use your math literature collection to enhance and enrich your students' mathematical understanding?

Friday, March 28, 2014

Multiply Like an Egyptian

As we get to this point in the school year, I have more and more students who are achieving standards and are ready for a challenge.  Of course, I also have students who need intervention and much more support to get the big ideas they need to be successful in the next grade.  Because of this, I do more and more groupings as the year goes on.  I write about ideas for interventions all the time but I also think about the kids on the other end and how to keep them engaged when they are understanding all they are supposed to be learning.

I have turned to several books to challenge students and get them excited about math.  Math Detectives is one I wrote about several months ago that I use to challenge K-3 students.  Cool Math is another one I have written about that I use to challenge students in grades 3-6.

Today I want to share with you a new favorite book and a lesson I did with a group of students based on one of the ideas in the book.


Near the beginning of the book, there is a history of some of the ways numbers have been written in the past.  If you know any Egyptian or mathematical history,  you know the Egyptian numbers were quite complicated and required quite a few symbols to write each number.  

Because of this, multiplication was challenging for the Egyptians so they developed this great strategy for multi-digit multiplication based on the idea of doubling.  I showed their strategy to my students and they worked together to see if it always seems to work and to figure out why it works. 

Check out some of the problems

Look at the number on the left.  Start with the number 1 and double it until you get to the point where the next doubling would be bigger than the number on the left.  Take the number on the right and double it just as many times as you doubled on the left.  Find the numbers in the left hand column that add up to the number on the top left.  Cross out any numbers you did not use and the numbers across from them.  Add up the numbers left on the right.  
 Here is another one
This one made for easy doubling and easy addition!
Now that they had the process down, we started thinking about why it works
Here kids made the connection that the 188 across from the 4 represented 4 groups of 188.  The 752 across from the 16 represents 16 groups of 47.  
Now they pull it all together
Here is where students REALLY got what was happening and were able to write it out and talk about how it represented the distributive property.  I also had a student who was able to show how it connected to using an array.  
This lesson led to a great discussion about multiple strategies for multi-digit multiplication and how some strategies are more efficient than others and how the numbers in the problem change the efficiency of some strategies.  

How do you challenge kids who are ready for it? 

Looking for a great book on teaching multiplication?  Check out this post!

Here is a fun way to practice double digit multiplication.

Thursday, March 27, 2014

Common Core Standards for Telling Time: Grade 1

Have your first graders started working on time?  I just introduced time to my first graders a week ago and they are already doing a great job!

The Common Core standard for telling time can be found in the Measurement & Data section.

CCSS.MATH.CONTENT.1.MD.B.3
Tell and write time in hours and half-hours using analog and digital clocks.

It is short and to the point.  First graders need to tell time to the hour and half hour.  Here are a few quick and easy ways I get my students to meet this standard



Introducing the Floor Clock (Time Mat)

I have several Judy clocks and they are great for whole group instruction.  However, when I really want to get little kids engaged in talking about the clock, I pull out my Time Mat.  This is a huge clock that folds conveniently in a box but is big and kids can gather around it.

I start by laying the clock on the floor and asking kids what they notice.  (I do not attache the hands prior to doing this.)  I have them share their idea with a partner and then we share as a whole group.

I ask kids what they notice about this clock.  They point out the numbers and the dots.  They might talk about the colors or other non mathematical ideas as well.  
Next I put the hour hand on the clock or have one of the students do it.

A student attaches the hour hand to the time mat
Next we talk about what the hour hand looks like at 6:00, 11:00 5:00, etc.  We get to the big idea that when it is something o'clock, the hour hand is pointing right at the number.

Next, I show them that sometimes the hour hand is right between two numbers.  We talk about this being half an hour and being half way between two numbers.  My students have a good conceptual understanding of half at this point in the year because we have already done our fraction unit.

Students see just the hour hand and it is pointing in the middle of two numbers

Next we attach the minute hand and use both hands to show what time to the hour and half an hour look like.

First I make times and the student tells or writes the time.  Then I say show me a time and the students make it on the time mat

Next we do the same think with time to the half hour
This lesson up to this point takes about 20 minutes.  Then we work on other things or go to our math stations.

Moving from Whole Group Practice to Independent or Partner Practice

Over the next few days, I might use the Judy clock or the time mat again to model times or have students model times.  After several days of this as whole group instruction, I give each student their own mini geared Judy clock and I have them build times as I name them.  The geared mini clocks are more expensive than the non-geared one but I think they are completely worth it!  They work like a real clock and really help students understand that the hands move together.

Practicing at Math Stations

After I feel kids are getting proficient with this, I introduce a telling time number puzzle that becomes one of our math stations.  Kids are given digital and analog times and asked to match them.  The puzzles are great because they are self-checking.  If they don't fit together, the student does not have the right answer.

Students work on telling time number puzzles during math stations
A student completes all the puzzles at the telling time work station

Checking in

After a day or two of kids having the chance to play with the time puzzles and practice alone and with a partner, I give them this quick formative assessment that comes with the time puzzles.  It lets me see who has the concept and who needs to be pulled to my table during math stations for some extra instruction and practice.  It is very easy for me to sort these into piles of kids who get it and kids who don't.  The kids who don't get it are added to my list of intervention groups and get extra instruction during math station time over the next few days.

Here is a student who seems to understand time to the half hour but has some major confusion over time to the hour.  This student will be part of my intervention group!

This student clearly needs more instruction! 

Most of the students' papers look like this.  A quick and easy way for me to see that they are getting the big ideas and their practice is paying off.
A few other things about telling time



If you are looking for some great activities for telling time to the five minutes, check out this new product from the Math Coach's Corner.

A great book for telling time to the hour is Bats Around the Clock

What are your favorite activities for teaching time?  





Wednesday, March 26, 2014

My Favorite Classroom Supplies: Pencil Sharpener

As a math teacher, I am a big fan of kids using pencils for most of their work.  As a math student in college, I got exposed to many different ideas about the best pencils out there.  I like really sharp pencils and for a while was all about mechanical pencils.  However, I work primarily with elementary students.  Mechanical pencils do not work well with kids under 12.  The push to hard to they just play with the pencil constantly.  As such, I have good back to my roots and the original old pencil as my primary writing utensil.  I still like my pencils to be VERY sharp.

Also as I have spent a great deal of time co-teaching and being in other teachers' classrooms, I have discovered how much time gets wasted by kids looking for pencils, sharpening pencils and trying to fix the pencil sharpener.  Because of this, I always have a huge mug full of sharp pencils ready to go for my students.  Since I spend my own time sharpening pencils, I have been on a quest to find the perfect pencil sharpener.  I have tried hand crank ones and electric ones and have found that nothing seems to last long.

I was very happy when I saw a few posts on Facebook about a small company making great pencil sharpeners for classrooms.  I love that it is a small company run by a teacher as a side business.  It is called Classroom Friendly Supplies.  Here are some pictures of my students using the pencil sharpener and some thing we have discovered about it.

You don't have to hold the pencil!  This eliminates students' pushing to hard and keeps the pencil held exactly where it needs to be!  It comes with a clamp to attach it to a table or shelf but works great without it as well.
 
Before and after shot.  The pencil on the left was sharpened using the electric pencil sharpener I bought at the beginning of this school year.  The one on the right is from the Classroom Friendly Supply sharpener. 

A shot at the inside of the sharpener.  I have a group of sixth graders who think a great STEM task would be to take this sharpener and a few others apart and see why this one works so much better.  It is a great idea and think of all they would learn!  However, it isn't happening to my new pencil sharpener!  

Here is the collection drawer after sharpening 5 new pencils.  Not much gets wasted!  My students can sharpen a new pencil in 7 seconds.  It takes me about 10.
What are your favorite classroom supplies?  Please respond in the comments below!

Tuesday, March 25, 2014

Scoop Em Up!



Does your school use Responsive Classroom?  Mine does and that means morning meeting time each day.  Last year, I purchased this great book for the teachers in my school.



This book is full of great ideas that are quick and easy and some that are a little more involved.  It ranges from grades K-5 and has ideas for adding math into your morning message or morning meeting.  

I have seen this book used greatly in some classrooms and less so in others.  To encourage more use and to get more math into morning meeting time, I have been visiting different classrooms during their morning meeting to demonstrate an activity from this book.  Check out this post about how I used an activity from this book  to work on counting money with third graders or this post to see how I used an activity to work on coin recognition with first graders or this post where I combined addition fact practice with counting quarters.

Today I want to share with you an activity called Scoop Em Up.  It is from the first grade section but I made adaptions to it and did it during a second grade morning meeting.  It is the PERFECT follow up to the counting and estimating routines I do in grades K-4.  It takes what they have learned in a whole group setting during a counting and estimating routine and asks them to do it more efficiently and to work with a partner instead of the whole group.  It was also a great way to get kids to generate their own strategies for 3 digit addition.

Here is the morning message they saw upon entering the classroom

Each student was paired up with another student as they came in.  I have several large buckets of buttons and gave kids a fairly large scoop.  I wanted each pair to have more than 100 buttons. 

A student gets ready to scoop buttons
Second graders need to be comfortable with numbers to 1000 so I chose a small object and a large scoop.  If I was doing this with younger children, I would choose bigger objects and/or a smaller scoop.  If I was doing this in grade 3 or 4, I would choose very small items like popcorn kernels or elbow macaroni noodles and give them a big scoop.  

Each pair dumped their scoop on the floor and figured out how many they had in all.  There was a lot of arranging into groups of ten and one hundred.

Here a group has two piles of 100, several piles of 10 and some ones left over
As students finished counting, we erased the morning message and had kids write the amount they had on the white board.  Amounts ranged from about 180 up to 290.  We talked about why if everyone used the same scoop we got different answers.  Kids who scooped from the bottom of the bucket definitely got more.  

We only had about 6 minutes left at this point and I wanted to review a few concepts with them so I choose two numbers, 188 and 270 to focus on for our discussion.

Here we found which number was larger and used the less than and greater than symbols to compare the numbers

Then we wrote the numbers in expanded notation and discussed how expanded notation matched their piles of hundreds, tens and ones

I finished the meeting with this BIG idea question about putting the two groups of buttons together.  Kids had about two minutes to think and then we discussed strategies.  There were several ways but most involved starting by adding the hundreds and then the tens.  I took some quick notes above on one of the strategies.  The student added the 70 and 80 by taking 30 out of the 80 to put with the 70 (because it makes 100!).  This is a great illustration of why knowing combinations of 100 is so important for a second grader!
This morning meeting was so much fun and we squeezed so much extra math out of the morning!  This book is giving me so many new ideas!