Monday, December 30, 2013

Monday Math Literature Volume 24

Missed the last post?  Check it out here!

If you are a regular reader of my blog,  you know how important I feel estimating and counting routines are in the K-6 classrooms.  The books I will be featuring today are must reads in K-6 classrooms.

Great Estimations


This is a GREAT book!  I use this book with students in grades K-4.  It does a great job explaining how thinking about tens, hundreds and thousands can help with estimating.  It starts off by showing a lot of different types of items in groups of 10 and then moves to 100 and 1000.  Then it gives students a referent of a group of 10 and/or a group of 100 next to a random group and has them estimate how many are in the random group based on what they already know.  The end of the book gets into more sophisticated estimation strategies like box and count, clump counting and counting a fraction of the total amount and multiplying.  Using this book with kids has helped many of them make connections they previously lacked and I myself find I am now better at estimating. 

Greater Estimations

After being a fan of Great Estimations, I was excited when I saw a similar title available and it hasn't let me down.  This book is laid out in a similar format to the original but goes into larger numbers like showing what 10,000 looks like.  I still use this book with young children because they LOVE seeing what big numbers really are.  I have used this book from grades K-6 with great success.  This book also gets into bigger questions like how many hairs on a cat or how many blades of grass on a football field.  If you have ever wondered how people make really big estimates, this is a great book even for adults to learn a few new things from!

These are currently the only 2 books around estimation in my collection.  Know any others I should be checking out?  Please leave your recommendations in the comments below.

Head over to volume 25 to learn more about some great literature connections to use when teaching odd and even numbers.  

Wednesday, December 18, 2013

Double Digit Addition QR Code Scavenger Hunt

Are your students working on two digit addition?  I have been working on this concept in both second and third grade the last few weeks and decided to create a QR code scavenger hunt to give them the extra practice they need.  Because we have been having quite a bit of winter weather, I decided to make it snowman themed.  There is nothing like cute clip art to make kids think they are doing something special!  With vacation just days away, I knew I needed something fun and engaging to help kids get through this week and still have the opportunity to practice math.  Looking for more ideas on helping kids with double digit addition?  Check out this post about quick easy and free games you can use with your students.

The perfect thing for a wiggly day!  I did this with my third graders and will be doing it with second graders later this winter!
When not in use, I like to keep my QR code scavenger hunts organized in a folder.  Multiple copies of record sheets, the answer key and the cards ready to go when I need them.  

Students scan the start card using a QR code reader (there are many free ones available in the app store)  They need a digital device with a camera such as a tablet, iPad, smart phone, iPod etc.  
A student works on her scavenger hunt.  
Ready to try this with your students?  Head over to TPT!

Tuesday, December 17, 2013

A Quick FREE Common Core Reindeer Game for Combinations of 5

Last week, I wrote about the reindeer themed subtracting from 10 game I made for my first and second graders.  It is free and available here!

Anyways, I had just played this reindeer game with some first and second graders and went to grab a group of Kindergarten kids.  When we got to my room, they immediately noticed the reindeer counters out on the table and they were VERY INTERESTED.

My goal for the day had been to work on combinations of 5 and this Common Core standard
CCSS.Math.Content.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

I was going to play a game similar to this one but quickly made a few changes to we could play it with reindeer.

The reindeer counters from this game have a picture of a reindeer on one side and are blank on the other so we used them like 2 sided counters.

Students put 5 reindeer counters into a paper cup, gave it a shake and dumped it out.  They sorted into reindeer up and reindeer hiding.  They then wrote an equation to show how many reindeer they could see and how many were hiding. 
A student writes an equation to match how her counters landed.  We just made our own record sheets on white boards.  I already had the reindeer counters prepared from another game so this game required no prep work.  My favorite kind!
At this point the student noticed that 1 + 4 = 4 + 1.  Gotta love when a simple game brings out the big ideas of mathematics.  
This game would also work for combinations of 10 and 20.  Want to try it with your students.  Head over here and print out the reindeer counters.  FREE!

Monday, December 16, 2013

Monday Math Literature Volume 23

Last week, I wrote about several of my favorite measurement books and this week I want to tell you about a few more.

This is a Hello Math Reader level 4.  It is an engaging story about a third grade class that decided they will plant a class garden and each grow a sunflower.  They are trying to see whose sunflower will be the tallest by the end.  There are some great ideas around planting and measuring in inches, spacing plants in garden and ways to keep track of height.  It also touches on perimeter when they measure the garden for a fence.  In the back of the book, there are 6 pages of activities related to the book and the math concepts contained within that are written by Marilyn Burns who has some impressive math credentials to her name.

This story is from the Math Matters series and focuses heavily on perimeter and area.  Grandpa gets his grandchildren some chickens and they have to construct a chicken coop for them.  They have 24 feet of fencing.  They use it to build a 9 foot by 3 foot coop next to the house.  They realize that the location doesn't work when the chickens wake them up early the next morning.  They move the coop and try other rectangles in other locations always using the same 24 feet of fencing.  They realize that the area changes even though the fencing stays the same.  It is a nice, gentle introduction in a real world context to get kids exposed to the idea of constant perimeter and changing area.

This book is from the Math Start series.  It is all about the US customary system for measuring capacity.  It includes gallons, half-gallons, quarts, pints and cups.  The story is about a boy named Carlos who wants to get a fish.  His sister helps him set up a fish tank and he slowly adds water.  There are many pages that use visual images to show how cups, quarts, pints and gallons are related.  I think this is a concept kids (and adults!) don't always understand.  Adding this book to your literature collection gives kids one more exposure to this big measurement idea!

What measurement books are your favorites?

Head over to volume 24 to read more about some great books about estimation!

Friday, December 13, 2013

Counting and Ordering Numbers under 1000

A skill I notice many of my second graders (and some of my third graders!) struggling with is counting forward and backward and ordering numbers within 1000.  I want to share with you a quick and easy to manage activity I do with kids in the second half of second grade or anytime after that if they still need work on the concept.

Here are the Common Core Standards addressed by this activity

CCSS.Math.Content.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.

CCSS.Math.Content.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

The hardest part with the counting and writing of numerals is when kids have to pull through a century.  I do this same activity with other numbers under 1000 but today will be showing you how I really focus work on pulling through the century.

I pulled 4 kids out who were having a difficult time to do this activity.  The cards we made as a result of the activity will be used with the whole class.  All you need is a box of 2'' x 3'' flashcards or some cardstock or index cards cut to be around 2 inches.

After some counting as a warm-up focusing on pulling through a century, I assign each kid a set of cards I want them to make and give them a starting number and an ending number.

Here are the 4 kids I worked with today and the numbers I wanted  them to record on their cards.  This lets them practice writing some of the trickier numbers like 808 and 401.  
 They put the cards in counting order from least to greatest.  When they have all the cards made, I have them read them from least to greatest (counting forward within 1000) and then from greatest to least (counting backward within 1000). I have them write them in pencil and once they get approval that they are all correct, they go over the pencil with a marker.

This student counts from 594 to 603.
This student works on their card set.

As kids finish, I have them read their neighbors cards and check with folks to see if they are correct.  Once these cards are made and we have agreed that they are correct, they mix them up and paper clip them together.  They are now ready to be used by other kids as a quick warm up, exit ticket or math station.  

I love quick, focused activities that give you a lot of learning with little prep or directions needed.

Wednesday, December 11, 2013

Reindeer 10 Take Away: A Common Core Game for Subtracting From 10

It is so important for primary students to be fluent with combinations of 10.  I have been hard at work with my first graders working on this concept and trying to get them to fluency with this idea.  My favorite way to do this is a lot of little games that work on this big idea.

With the holidays coming up, I find themed games to be much more engaging for kids.  Because I have been working on subtracting from 10 with my first graders and I have a few kiddos who still don't have the understanding and fluency that I would like to see, I made a quick, easy and cute game to give them the extra practice they need.  You can grab it for free!

This game uses a 10 frame and reindeer counters to support developing understanding of subtracting from 10 and support the idea of combinations of 10
A pair of students playing and recording.  I also have had many students who want to play themselves and fill in the entire record sheet on their own. 
This student is playing using a 10 sided dice.  You can also use 10 frame cards or regular playing cards or the included reindeer cards.  I find these dice to be my go to choice because there is no prep work involved and they get used over and over again throughout the year.  

If your kids need more work on subtraction and combinations of 10, head over to TPT and and grab this freebie!

Fluency with Double Digit Addition

I spend so much time in grade 2 working with kids on thinking strategies for double digit addition. First, I make sure they are comfortable adding and subtracting 10 from any 2 digit number we do many problem strings and spend time sharing strategies and ideas.  By the end of grade 2, I expect that kids will fluently be able any two double digit numbers in their heads.  I NEVER introduce the standard algorithm for addition of 2 digit numbers because it makes kids stop thinking about the math and just do it and because I really don't believe anyone should need the traditional algorithm to add two double digit numbers.  Everyone should develop the skill of doing it in their head.

Why is it so important that kids are fluent with this by the end of grade 2?


In grade 3 we get into strategies for multiplication facts and MANY of these strategies only work if students can quickly and easily add double digit numbers.

Example 1: 4x9= ?

The student decides to double the 9 to get 18.  They then have to do 18+18.  If this is easy and effortless and does not require paper it helps kids learn multiplication facts much quicker.  If they have to write 18+18 down and do the traditional algorithm or if they do not have an efficient and reliable method to figure out the answer, they are stuck.  They don't learn their multiplication facts as quickly as their peers and that will hurt them for years to come.

Example 2: 6x8=?

The student sees six groups of 8.  They know 2 groups of 8 is 16.  16+16 will give them 4 groups of 8.  32+16 will give them six groups of 8.  They just had to do 2 double digit addition problems.  See why fluency with this is important?

So how do I get them there?  Here are a few quick, easy and low to no prep ways I have kids practice this skill at the end of grade 2.  I do these after a lot of whole group instruction around strategies for adding two double digit number.  I also pull these out just as we are about to head into our multiplication fact unit in grade 3 and add them to math stations to make sure ALL KIDS are fluent with this.  If I have to, I do a small group intervention with third graders to get them solid on this skill.  Since I started assuring kids could fluently add double digit numbers before introducing multiplication facts, kids have learned their multiplication facts faster and with less frustration.

Flip and Add

This is one of the first ways I have kids practice independently or with a partner.  They just flip 2 cards from my place value to 120 deck.  The visual image of the  base 10 pieces supports kids who still need it.  I sometimes have them flip and add alone and sometimes with a partner.  I also sometimes have them make a simple record sheet like the one shown below.  I also use these cards as exit tickets.  I pass out 2 to each kid and they can line up when they know the answer.  I stand by the line and each kid tells me the answer as they line up.  

Rolling Dice

20 Sided Dice (level 1)

I have a huge bucket of 20 sided dice and I like to use them for a quick, easy and no prep addition fluency game.  Students simply roll 2 dice and add the numbers.  They can do this alone or with partners.

This student is adding 12 and 6.  See how having this skill will help support them when they learn 3X6?

These students rolled 17 + 19.  They have to think about regrouping.  These kids ended up doing 17 + 20 = 37 and then subtracted 1 since they were only supposed to add 19.  37 - 1 = 36.  

The Infamous 7 dice (level 2) 

Earlier this week, I posted about how I use the same set of  7 dice in classrooms from grades K-6.  I like to get 2 of these dice out once kids are fluent with adding the 20 sided dice and do the same thing.  The numbers are mostly in the 20's and many require thinking about regrouping. I often don't use record sheets for these games but occasionally do, especially if I have a large class or am unsure about how accurate they are.  
With this roll, kids can just add the 10's and add the 1's.  Straightforward but important to make sure kids have fluency at this level.
This pair brings up a lot of good ideas about thinking strategies and what parts to add first.  

Bringing out the big dice (level 3)

Once kids have shown me fluency using the last set of dice, I like to give them even larger double digit numbers to work with.  These will include some where the sum is over 100.  I have a set that I made out of card stock that I like to use to introduce this part to the whole group because they are REALLY BIG.  I also make my own double digit number cubes with higher numbers using blank dice.

I made an origami cubes following these directions.  I have also made these cubes with students.  I find some second graders are successful but third grade and up is the best choice if you are making these with students.

Students love rolling and adding with these big dice and it gives them the extra practice they need to achieve fluency.  
What do you do to make sure your kids are fluent with double digit addition?  Please respond in the comments below!

Tuesday, December 10, 2013

A Quick Review of Common Core Fraction Second Grade Concepts

Earlier this week, I posted about how I pulled out a small group of kids from a third grade classroom to do a quick mini lesson on odd and even.  I got another chance this week to pull a different small group from the same classroom that is getting ready to do their fraction unit and has a small group of kids struggling with basic fraction concepts.

Here is a quick review we did to remind them of the big ideas around fractions.  The cards I used for this are from my Fourths or Not Fourths game I use with first and second graders.  It is a freebie and available in this post if you want to try it out with your students.

Here is the common core standard for fractions in grade 2.  These were the concepts I wanted to review and reinforce with my students
CCSS.Math.Content.2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have  the same shape.

There were 4 kids in this booster group and we all sat around a table. I told them I wanted to talk with them about fourths and gave them each a card.  I asked them to think about if their card showed fourths or not and how they knew they were right.

As we went around the table, each kid placed their card in the fourths or the not fourths areas and explained to the group why they thought it went there.  Through this, I got at the big ideas of equal pieces and fourths meaning four pieces.  After each kid had placed their cards, I gave them another one and we continued around the circle in this fashion.

I saved the ones I consider the most challenging for last.  I wanted to make sure the big ideas were out there first before I brought up the idea that the equal sized pieces do not have to be the same shape.

I saved this card for last.  I showed it to the entire group and had them give me a ready signal when they thought they knew where it belonged.  I had them turn and talk with a partner and then we shared with the entire group.  I was pleasantly surprised to see how well kids did with this card! 
A student explains to the group how he knows the pieces are equal
We had a few minutes left so we read one of my favorite fraction books to wrap up our review session.  I hope this will help these kids be successful during their fraction unit!