Winter Themed Equality

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I have been hard at work this week creating some new things for my first grade students.  I know it is a little early to be thinking about winter but we had snow last Friday morning and I wanted to see how my first graders are doing with ideas of equality.  Can they use the equals sign to balance two equations or do they think it just means the answer is coming?  I expose first graders to lots of ways to write equations during whole group instruction but our math program like many others has little to no practice in this area.  Here are some of the types of equations I am talking about

7 = 4 + 3

8 = 8

4 + 5 = 5 + 4

7 + 3 = 8 + 2

If students have not seen equations written like this, and I ask them if these equations are true, they will often say no.  I was thinking my first graders were getting these big ideas quite well.  I decided to seize the moment and take advantage of their excitement over seeing snow and gave them a quick formative assessment on equality that happens to have a fun penguin theme.

Students read the equations and circle T if they think the equation is true and F if they think the equation is false.  If you want to try this with your own students it is a freebie at my TPT store.  Click here to head over and download it!

Anyways.... The students did not do nearly as well as I had hoped.  There were several students who got most or all of the answers right but many other students demonstrated that they are still not sure about how to use the equals sign.  I tried some of these activities but still felt like they needed more.  It is all well and good to provide whole group and small group instruction around these ideas, but I wanted another way for students to use these ideas during our math stations.

So I created a set of equations on cards that can be physically sorted into true and false piles.  We worked on this as a whole class and I will be using the cards as part of math stations and partner/individual work time during the month of December.  I will give another formative assessment after a few weeks and we will go from there.

Here is a peak at us trying it out as a whole group

I used a pocket chart to hold the cards so everyone sitting in the discussion area could see.  We only got through 8 of the 18 cards on our first attempt at this because we had so many great math discussions along the way.  I pulled out the math balance during this whole group lesson and students loved using it to prove their thinking

Later last week, I pulled a small group who I felt needed more practice either due to the formative assessment or what they were saying (or weren't saying) during the whole group lesson.  We worked on sorting some other cards.  (I made the cards at 2 different levels to meet the needs of ALL my students).  Level 1 is addition facts to 10 and level 2 is addition facts to 20.  I held off on subtraction for now but will be addressing equality around subtraction in January.  I want my students to be solid here first. 

This was small group work so we put the cards on the carpet. 

Starting Monday, these sets of cards and the record sheet that goes with them will be added to my math stations for the next few weeks.  If you want to grab these for your own students, they are available here!

Here is a look at the record sheet for use during math station time

How do your make sure your students have a good understanding of equality?  Please respond in the comments below.

Great Computer Activity: Speedy Pictures

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If your students K-3 are working on subitizing or addition, you will love this computer activity.  It is similar to the Subitize Tree app for iPad that I have written about in the past.  It is a great way to work on subitizing and addition and is easy to differentiate to meet the current needs of your learners.

The best part?  Its free!

I selected the rekenreks to 20 for this round.  I also adjusted the flash time to about 2.5 seconds.  It simply flashes the given picture for the length of time requested and then removes it and lets you click on the number you saw.  The green vertical bar to the far right keeps track of how many you have got correct.  

This time I selected fingers and put the flash time to just over 1 second.  Think about how changing the flash time or the model used would change the challenge level for your students.

This time I chose dice and love how this version gets kids thinking about addition!  

Ready to check it out?  Here is the website!

Monday Math Literature Volume 19

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Missed last week's post?  Check it out here!

I know it seems way to early in the school year to be talking about this, but the 100th day of school will be here before you know it.  I was planning with a brand new teacher the other day and she was looking for fun and creative ways to celebrate the 100th day and to add some more math into the day.  I shared some of my favorite books for the 100th day with her and now I want to share them with you as well.

First, here is the book that many of my ideas have come from on how to celebrate the 100th day.  I do teach math 6 times per day to 6 different grade levels so I need a lot of ideas.

100 Ways to Celebrate 100 Days

This is a great way to get more ideas about celebrating 100 days no matter which grade you teach.  You might find so many ideas that you need to spend a week celebrating the 100th day.  Remember how much kids love learning with themes?  Here is your chance for a very fun, very math based theme.

100th Day Worries

This is a great book to use during read aloud time around the 100th day.  It tells a story of Jessica who is asked to bring in 100 objects to celebrate the 100th day.  It is a very sweet story and a lot of fun to read.

100 Days Of School

This is a rhyming book about different ways to make 100.  This can be read during read aloud time or as part as math class.  It is also a fun book for kids to put in the book boxes to read to themselves.

100 School Days

This is a story of a class that collects a penny per day.  It focuses a lot on the groups of 10 that can be found in 100.  It makes a great read aloud for K and 1.

Fancy Nancy: The 100th Day of School

For your Fancy Nancy loving kids, here is a great level 1 book that kids can read themselves

The Night Before the 100th Day of School

This story is modeled on the Night Before Christmas  poem which makes it a lot of fun for kids and adults alike.  This is probably my favorite book to read aloud and I often read it to several grades each year.  

The 100th Day of School 

This is a level 2 hello reader and another great one for kids to read to themselves.  The focus this time is on the different ways you can count to 100.  

Happy 100th Day

This is another great read aloud for a wide range of grades.  This is a story about Graham, a boy who is not excited about the 100th day until he realizes his birthday will fall on the same day.  It always happens that someones birthday is on the 100th day and this book is a great way to celebrate that.  

Head over to Volume 20 where I have reviewed some of my favorite counting books.  

Making Subitizing Cards and Double Flap Cards with First Graders

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Here is a peak inside one of my favorite boxes

It is simply a pencil box, blank index cards,dot stickers and binder rings.  I use these to create subitizing cards and other projects with K-2 kids.

Today I want to show you 2 of the things I have been working on with these materials with a group of first graders.

Subitizing Cards

Subitizing is the ability to recognize a quantity without counting.  It is further broken into perceptual subitizing and conceptual subitizing.  Need more information on these words?  Check this out!

I use the dot stickers and cards to work with students to create different arrangements and combinations of a given number.  You can see on this day we were working on combinations of 6.  See how the different arrangements and color patterns lead you to see 6 in different ways?  This is a great example of conceptual subitizing and is a great way to work on combinations of numbers.  The hole punch in the top lets me put these on a binder ring and then we use them in class and small groups.  We flash a card at a group of kids and they tell how many they saw and how they figured it out.  

Double Flap Cards

I actually made these this week in first grade and with some intervention second graders.  These are a great way to work on combinations of numbers and fact families.  The particular kids I had that day were really needing more work on combinations of 10 so we made double flap cards for 10.  I used the same stickers and a few sheets of card stock.

This is what is written on the back of each double-flap card

Here is the 3+7 card with both flaps open.  We can use this card to generate all the facts in the fact family for 3+7=10

I might open one flap and ask kids how many they see.  I then might ask them how many are under the other flap.  

I vary my language a bit and ask other questions such as, "how many do we need to add to 6 to get to 10?"  I also might open both flaps and ask what will be left if I cover up the 10 (or take the 6 away etc)

Using the Area Model to Teach Mixed Number Multiplication

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Have you started using the area model to teach multi-digit multiplication?  How about using it to teach fraction or mixed number multiplication?

Here is an example of using the area model to teach double digit multiplication.  I do this in fourth grade with students and it really helps them develop their conceptual understanding.  It really helps students see why you can't just multiply the tens with the tens and the ones with the ones.   If students are exposed to this model in grade 4, it is a natural extension to use the area model to teach fraction multiplication

Here is the area model for mixed numbers.  Again it really helps kids see why you can't just multiply the whole numbers together and the fractions together.  It is also very efficient and involves less computation (and therefore room for error) than the traditional algorithm for fraction multiplication.  As you can see, students must be comfortable multiplying two fractions less than 1 and a fraction by a whole number. 

Here is the same problem done with a standard algorithm.  See how little fraction understanding goes into this way and how much computation takes place?  I find once my students know both methods, they pick and choose which to use based on efficiency which is always a great thing!

If you are looking for further evidence that the area model can be a great conceptual tool for students learning multiplication, check out how well it works in an algebra classroom.  Instead of teaching kids to just FOIL, you can connect their new learning to the knowledge they already have about multiplication.

How do you use the area model when teaching multiplication?  Respond in the comments below!

Have you Heard of Digiblocks?

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Have you heard of digiblocks?

I was talking with a friend about base 10 representations and found out there is an entire base 10 model which has apparently been around for over 10 years that I had never heard of.  I borrowed a few of these blocks from a friend and started exploring with them as well as looking more at the Digiblock website.  Here are some things I have discovered already that I could do with my students using digiblocks

Digiblock trains

The digiblock website and lesson ideas (and even a few fun videos) show them using the digiblocks as trains with very young children  (pre-K and K).  The blocks can be left open so that kids can actually count each individual block if they need to.

You can put several digiblock trains side by side and compare lengths as well as think about adding and subtracting trains.

Expanded Form/ Breaking numbers apart many ways

I have been working with my second graders on different ways to represent numbers.  We have been working on reading and writing numbers up to 1000 as well as writing numbers in expanded form and thinking about different forms of the number that are the same.  We have been using base 10 pieces for this but I kind of like the idea of using the digiblocks as well.

132 represented with digiblocks.  This was a great way to show second graders that 132 can be written as 100+30+2

When we opened up a ten block and moved it over we could see that 132 is also equal to 100+20+12

Opening another ten block let us see that we could also represent 132 as 100 + 10 + 22

Do you use digiblocks in your classroom?  Do you find they are more useful than base 10 pieces?  Respond in the comments below.  If you have a post about digiblocks that you want to link to, feel free to do that in the comments as well!