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Saturday, November 30, 2013

Pengin Math

I have had penguins on the brain this weekend as I start planning ahead for my December and January math stations for first grade.  There is nothing like a fun theme to tie things together and make practicing math more fun.

Here is a peak at what I have been working on (and some FREEBIES!)
I have written a few times about the 12 problem types for addition and subtraction that primary kids are responsible for under the Common Core.  I have created a set of 12 full color picture problems for my first graders to solve that address all of these different types.  I have also released 2 of these picture problems as a freebie for those looking to try them out!  I know there are 4 of these problem types my students have not yet been exposed to using our math program so I excited to see them try them out!
 I have also done some re-formatting to a great penguin game that works on subtraction facts under 10.  I am finding my first graders are doing a very good job with addition facts and not so well with subtraction facts so during our penguin time, I will be focusing on this.
This simple game encourages counting back and the spinner includes dots for kids who need a lot of support.  There is also an optional record sheet where kids can record just answers or entire equations depending on their level.  This is also a freebie at my TPT store.

Help! An Orca is coming in action!

One of my favorite things to work on with first graders in numeral recognition and using the greater than and less than symbols to compare numbers.  I created one set of cards to work on both of these skills with my students.  I only had to copy and cut one set of cards and got 2 games out of it.  This saves me time which is always a good thing.

I use the cards with the pictures of base 10 pieces to play both of these games.  It is a great way to get kids thinking in tens and ones and using that knowledge to compare numbers.  It is available here!
Another great freebie that I often use as a formative assessment to assess my students' understanding of equality is this:
My penguin equality 2 worksheet set is available as a freebie in my TPT store and  is a great way to review, practice or assess your students' understanding of equality.  
Another favorite of my students' is the game I have, who has?  I created this cute penguin themed version of this game to give them another way to practice numeral recognition, especially the numbers between 100 and 120.

This is a quick and easy game and is currently only $1 in my Tpt store!

I also have been pulling together a collection of literature books around penguins to further spread my theme through the kids school day.  Here are a few of my favorites so far.

This is a great non-fiction picture book with a lot of facts that kids find interesting and some top quality National Geographic photos.  

A great book with cute pictures written in a poem format
I love Tacky the penguin, he is such as great character.  I have several of the Tacky the Penguin books and am working on getting all of them.  
I would love to hear what other penguin books (both fiction and non-fiction) people recommend   If you have a favorite please share in the comments below!

Friday, November 29, 2013

Student Generated Strategies for 3 digit Addition

I have spent a lot of time over the last few years thinking about how to develop lessons and problem strings to help students construct their own knowledge about multi-digit addition and subtraction rather than teaching them "how to do it."  I have written about some of my struggles, triumphs and amazing moments but I always find more I can talk about with teachers and students around teaching kids to think about math rather than just doing it.

Today I want to share with you 3 different solutions to a three digit addition problem that I posed this week to a group of third graders who are a bit behind where they should be but are working hard to construct their own knowledge about addition.

This idea is one I see many second and third graders try out.  It works on every problem and is fairly efficient.  They are adding numbers by place value and it is a strategy many students invent for themselves.  
This student used a strategy that is VERY efficient for this problem because 299 is so close to a VERY friendly number.  It is the idea of compensation or taking from one and giving to the other.  It is a great strategy for kids to have in their toolbox and it leads to a strong ability to calculate mentally.

This student did something similar to the last student but instead of compensating before doing the problem, he compensated after finding the sum.  He "pretended 299 was 300 and added 548 to it.  Then I took away 1 because I added one more than I had to."
I have been using problem strings to lead kids to making some of these big discoveries about multi-digit computation for the last few years with great success.  I have also read and applied much of what I have learned from reading this book which has really helped me out.  They really focus on the idea of students constructing their own knowledge and number sense.

I was surprised to learn a few weeks ago that another book by the same author existed that I did not know about.  I saw this book on a colleagues shelf and knew I had to have it.  It has a WEALTH of mini lessons for working on addition and subtraction and had I had this book a few years ago it would have made my journey to being a better math teacher much smoother!

What opportunities are you providing for your students' to develop their number sense?

Thursday, November 28, 2013

Double Digit Multiplication QR Code Scavenger Hunt

I have been working on 2 digit multiplication with my fourth graders over the last few weeks.  They have been doing a great job writing and solving story problems and developing strategies.  Their strategies have moved from modeling with base 10 pieces to sketching on base 10 paper and then finally using an open area model to solve these types of problems.  Last week, they were introduced to the idea of partial products and spent a lot of time examining how they connect to the open area model.  This week I wanted to give them one more chance to practice all they had learned before having 5 days off.  I designed a QR code scavenger hunt for them to get some extra practice with double digit multiplication.  I also used this same scavenger hunt with my fifth graders who have recently been introduced to the standard algorithm to help them become more fluent.

Here are the Common Core standards for multi-digit multiplication for grades 4 and 5
  • CCSS.Math.Content.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • CCSS.Math.Content.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm
To get started you just need a smartphone or tablet or almost any digital device with a camera. (Update: we love using this app on our Chromebooks) Students begin with the START card, scan the QR code and get the first problem.  They then figure out the answer and go find it on another card.  If they can't find their answer on any of the other cards they know they have an error and need to fix something.

A student uses a table to scan a card and solve a double digit multiplication problem
They had a great time working on this and were so engaged and excited.  I love how QR code scavenger hunts make routine practice feel like something fresh and exciting.

Here is a peak at a student record sheet.  This is from grade 4 and they are using partial products for some questions and an open area model for others.  
One student needs more space for their calculations so they made up their own record sheet!

When I make or purchase a new product like a QR code scavenger hunt I like to put it all together in a folder so it is ready to use when I need it!
Here is peak inside the folder.  I have the scavenger hunt cards printed on cardstock, cut apart and put in a baggie.  I also copy the answer key onto cardstock and make multiple copies of the record sheet.  Now when I want to use this, it is always ready to go.    
Want to try this out?  It is available at my TPT store!

Looking for more information on QR code scavenger hunts?  Check out my other posts about using them with my own students.
Fraction Operations
Decimal Operations

If you work with middle school students I also have QR code scavenger hunts for solving 2 step equations and inequalities!  You can check out the entire collection of QR code scavenger hunts here!

Wednesday, November 27, 2013

Using Technology to Practice Combinations of 10

Anyone who teaches a primary grade will tell you how important it is for kids to know their combinations of 10.  It leads to much more efficient strategies for addition and subtraction and will help a kid be more fluent with math.  Let's see where combinations of 10 shows up in the Common Core

It first shows up in Kindergarten!
CCSS.Math.Content.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

 In first grade it talks about kids using making 10 to help with addition and subtraction within 10
CCSS.Math.Content.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

In second grade it is not mentioned by name but the little 2 has a comment on the bottom that says see the first grade standard above for a list of strategies 
CCSS.Math.Content.2.OA.B.2 Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.

Because of its importance, combinations of 10 is something you will see me working on in grades K-2.  I spend a lot of my intervention time with second graders (and sometimes older students!) who do not have strategies for addition facts working on combinations of 10.  I have written about how I use double flap cards, a simple double sided chip game, and how I use 10 frames to work on this very important skill.  I even wrote about how I extend this idea and work on combinations of 100.  Today I want to share with you a few of my favorite computer games that can be used on any PC or on a smart board that work on this idea of combinations of 10.

Math Lines

This is a student favorite and for a very good reason.  It is so much fun!  It also has multiple levels and is a race against time to complete a level before the balls all drop off.
Here is as look at level 1.  You shoot the ball in the center at one of the balls on the outside that  pairs with it to make 10. That makes both balls disappear.  The object is to get rid of all the balls before they make it around to the hole and all disappear.  If you do that successfully (and it takes a few times to get there when kids are first starting out) you get to move to level 2!
Level 2 gets more challenging in the sense that there are some balls you can not reach.  By the time kids make it to level 2, they are getting fairly fluent with their combinations of 10 and the game gets to be really fun and helps give them that extra push to fluency that kids really need.
Level 3 builds a great deal of excitement over the 2 holes that the balls may disappear into.  This is the level that is very tricky for kids to beat!

Missing Number

I often use this game for combinations of 10 but it can also be changed to use for combinations of other numbers as well.  I LOVE that this game represents equations and uses a missing addend.

You will see my target number at the top middle is set to 10.  I can choose to set this number anywhere from 1-20 which makes it a VERY versatile game.  Kids click and drag the correct answer into the box.  I love the format of the equations.  

Number Bond Machine

This one is less game like but still fun for kids and very effective at getting at the concept.  I have posted about this before but I do use it all the time for combinations of 10.  (it also has an option for combinations of 5 and 20 so it gets a lot of use in various grades)
Simple but effective

Save the Whale

This is another student favorite.  It is from ict games which is just a great resource in general.  The object of the game is to get a long enough pipe (10 units) to bring water to the whale who is a bit land locked and help him escape to the ocean.  I love that it has the units displayed for kids who still need to count.  I often use this game for kids who still need some support with combinations of 10 although kids who are more fluent still benefit from playing as well.  

The pipe at the top says 8 and is 8 units long.  I can see that I need 2 more units to get to 10.  See how this supports kids who are new to this concept?
I successfully put a 7 pipe with the 3 pipe to make 10.  Now the pond fills with water and the whale escapes to the ocean.  

Ten Frame Fill

I have previously written about an iPad app that is very similar to this but this is the one I go to when I am on the smart board or a PC.  This game actually does several things, so to work on combinations of 10, you need to click on fill along the left hand side.  Then it simply asks you how many more counters you need to fill the frame (get 10).  It is a very supported way for young learners to begin their work on combinations of 10.  

How do you use combinations of 10 in your own classroom?

Tuesday, November 26, 2013

Estimating and Counting Routines Part 4

New to my estimating and counting routines series?  Check out part 1, part 2 and part 3!

This week, I knew I wanted to work with a group of first grade students on their counting and estimating skills.  We have been working on counting by 10's in class (going over 100!) and these kids still needed help with that as well as needing a great deal of help with estimating quantities.

I decided to pull my Teddy Bear Counters for this group.

I place my tub of counters on the table and asked kids to think about how many bears might be in here.  I asked them if they thought there were more than 10? (everyone said yes)  More than 20? (everyone said yes)  More than 100? (only one kid said yes)
Then I dumped the bears on the table and spread them out a bit.  I again asked them if they still thought there was more than 20.  (all said yes) Is there more than 100?  (all said no!!!)
I then pulled 10 off to the side to give them an idea about what 10 looked like and asked them to think about how many teddy bears in all.  
A student recorded everyone's estimates in the middle column of this white board.  You can see that the estimates ranged from 25 up to 65.  I asked, is there enough so that we can all take 10?  They all said YES- even the kid whose estimate was 25.  Once we each had 10, one of the kids suggested we arrange them like they were sitting on a 10 frame so that we could "tell just by looking" that everyone had 10.  I then had kids think about the fact that 50 bears had already been removed and there was still quite a pile if they wanted to make another estimate
The new estimates are recorded in the third column.  You can see some kids got the idea that they needed to increase their estimate and some really still need a great deal of practice.  Notice one child chose 53 even though 50 had been removed and a large pile still remained.
We each took 10 more bears.  You can see here that the students continued to arrange them as if they were sitting on 10 frames.  They really bought into this idea and it really helped them keep their counting organized.  We counted each group by 10's and found we had 100 bears and STILL MORE in the pile.  The students got SO EXCITED that we were going to go over 100!  After we each had 20, I again asked them if there was enough for us each to take 10.  Most kids agreed there was, so I let each of them take 10 but waited to take my turn.  When they each had 10, there was only 3 remaining bears so my last group was a group of 3.  
We counted by 10's a few more times to confirm that we had 140 bears with some left over.  I wanted to make sure kids got repeated exposure to counting by 10's over 100.  Then we decided to count on by 1's to figure out how much 3 more would be.  We had 143 total and the kids had a great time.  I learned that this group of kids needs a lot more experiences with counting and estimating.  
If you want to read more about the importance of counting in the classroom, there is a great article called Counting Collections that was published March 2007 in Teaching Children Mathematics.  A Google search should lead you to a copy of it!

Click here to head to part 5!

Monday, November 25, 2013

Monday Math Literature Volume 20

If you missed last week's post about literature around the 100th day of school, click here to check it out!

This week I want to show you some of my favorite early counting and rhyming books.  I use these mostly with K-2nd grade students.

This is a fun book with lots of great animals in it.  There are tons of rhyming words and I have  seen primary teachers use this when teaching rhyming and spelling as well as for the math content.
Another fun animal based book, this one looks at all the combinations of 7.  It is a great story to read during your addition unit in Kindergarten or first grade!

An amazing book to use when looking at the concept of zero!
This book convinced me that the Pete the Cat craze is here to stay!  I love this story about Pete the Cat and just purchased it and used it with great success to introduce the idea of subtraction to my kindergartners.  If Pete the Cat isn't the most popular new series in your school, it will be soon.  On a side note, I just ordered several copies of Pete the Cat Saves Christmas to give as gifts and I am hoping they arrive today!
Head over to Volume 21 where I have shared a very unique math literature book!