Hundred Chart Heaven




Hello! This is Kelly from Little Green, writing to you once again from Sydney, Australia. Well, four hours south of Sydney, to be precise! It is summer in Australia and we are on our long summer school holiday break. I am writing this post from the beautiful beach-side suburb of Kioloa, on the south coast of New South Wales, where I am holidaying with my family. The sun is shining, and the sounds of waves crashing and cicadas chirping are almost deafening! To my left, tree-covered hills and ridges fill the landscape beyond the few rows of houses in this tiny town. To my right is the ocean, with the sun rising splendidly over the blue water. There is nowhere I would rather be right now!

But we’re not here to get jealous about my beautiful, warm, sunny location; we’re here for mathematical inspiration! And today I want to use one of my favourite math manipulatives as the starting point for that inspiration: the Hundred Chart. This versatile tool has been instrumental in the development of mathematical understanding in countless students. In fact, I would hazard a guess that pretty much every teacher reading this post used one when he or she was a student and has used one at least once with their own students.

Why has this particular tool stayed with us for so long when so many other great tools have come and gone? In my opinion, it is because it is both versatile and simple. Sure, you can buy a super-expensive, whizz-bang, high-tech Hundred Chart, but equally effective is a dodgy black-and-white blurry photocopy of a Hundred Chart, or even a hand-drawn Hundred-Chart on the back of a fast food store napkin! It is often the simple things that stand the test of time and become our constant companions in the classroom.

So, I’m dedicating this post to the Hundred Chart. May it continue to be our mathematical friend for many years to come.

Here are a few ways I use a Hundred Chart:

Counting Aid

Using a Hundred Chart as a counting aid in the early years will help familiarise students with its use and provide them with an effective aid to help them ‘follow along’ with counting. I would introduce this tool with five-year-olds as soon as they have a firm grasp on the idea that numerals represent numbers and are beginning to count to numbers larger than ten. If you are working with numbers up to twenty or thirty, shield the lower numbers on the chart (with a piece of paper, for example) to allow your students to focus on the numbers they are working with.

Skip Counting Aid

Skip counting is a terrific precursor to multiplication. A Hundred Chart can be used as an aid to the skip counter. Begin by modelling this skill to students then have them ‘have a go’ on their own. Simply point to the numbers as you count and be sure to ‘notice’ out loud any obvious patterns (e.g. when counting by twos, you skip one number each time).

Looking for Patterns in the Times Tables

For me, Mathematics is all about locating patterns, looking for logic and making order. If our students can see the patterns in the times tables, they will have a much richer understanding of them than if they simply commit them to memory. Of course, knowing your tables off by heart is important too, but we want our students to be able to do more than rattle off a few numbers! A great way to see the patterns is to colour in the multiples of a particular set on a Hundred Chart.

To extend this further, have them choose a different colour to colour in the multiples of a different set on the same Hundred Chart. In this way, they can see where the sets overlap and can draw conclusions based on this visual evidence.



Showing One More, One Less, Ten More and Ten Less

With a simple modification, a Hundred Chart can be used to help students easily see one more, one less, ten more and ten less than any number. Using cardstock or sturdy paper, create a shield with a cut-out in a cross shape that will reveal the desired numbers (see picture below). Students can move this shield around the chart to discover one more, one less, ten more and ten less of any number (except numbers on the edge of the chart – some explicit teaching is required to help students find the answers for the numbers on the edge).





Calculation Aid

Once your students are familiar with the use of the Hundred Chart, it can be used to help students calculate the answers to addition and subtraction problems to 100. For example, the problem 83-54 might look a little daunting to a student, but it can be easily solved using a Hundred Chart. Begin by putting your finger on the 83 square. To subtract fifty, move your finger up five spaces to the 33 square. To subtract four, move your finger to the left (then up to the end of the row above) four spaces to the 29 square. Easy! Allowing students to use the Hundred Chart in this way will build a strong foundation for mental strategies, such as the ‘jump’, ‘split’ and ‘compensation’ strategies (search for these terms in a Math glossary if you are unfamiliar with them).





Demonstrating Working Out

When students are able to use mental strategies to solve addition and subtraction problems, a Hundred Chart can be used to allow them to demonstrate their working to you or to the rest of the class. It is always fascinating to see the different ways other people solve the same problem. Using the above example of 83-54, some students may use a completely different strategy. They may, for example, make the 83 into 80 by subtracting 3, subtract 50, subtract 4, and then add on the 3 they took away at the beginning. Or, they might start by subtracting the tens (80-50), add on 3, and then subtract 4. Using a Hundred Chart to assist in demonstrating thinking will help the abstract thought of an individual become visual for others.

This is certainly not an exhaustive list of ways to use a Hundred Chart – there are certainly many other terrific uses for this versatile tool. How do you use a Hundred Chart in your classroom? Feel free to share any brilliant ideas you have come up with in the comment section below.

And before you go, I’ve created a Hundred Chart resource pack, which is available for free in the Little Green TpT store. Click here to get your copy. 

And one quick plug: a huge giveaway is about to happen on the Little Green blog! Make sure you keep an eye out for it - you won't want to miss it!

Right, back to the beach for me! See you next month!

The Chocolate Chip Cookie Challenge

Hi everyone! I'm so excited to share a math project we did recently...all about chocolate chips!

We are smack-dab in the middle of a unit on addition and subtraction. And of course that means there's a little estimating and problem solving thrown in there as well. And maybe some data collection? Maybe.

My teaching partner (who is a-maz-ing) came up with the great idea of this fun project that includes estimating, rounding, adding and collecting data to create a scaled pictograph. We used this book's Chocolate Chip Hunt as an inspiration!

Math Wise! Over 100 Hands-On Activities that Promote Real Math Understanding, Grades K-8
Click the picture to get your copy!

 We were *trying* to hit these CC Standards:


First, my friends got one cookie. Just one. It was torture. Because I wouldn't let them eat it. Or touch it. Or sniff it. I couldn't take a picture here because I had to give everyone the evil eye so they wouldn't eat/touch/sniff their cookie.

Their job was to estimate how many chocolate chips were in their cookie. No cheating by counting of course! So they looked at their cookies and finally a few turned them over to see what was on the bottom and they came up with some estimates. We had LOTS of ideas..."10!" "No, 25!" "No, 50!" (Whoa.) Then they recorded them in their Chocolate Chip Cookie Packet.


After they estimated, they were allowed to count the actual amount of chips in their cookies. My evil eye worked almost too well, as some of them didn't want to touch the cookie to turn it over. But we got past it and started counting chocolate chips and recording the actual number in our packets.


Once we estimated and counted Cookie #1, we estimated Cookie #2 and Cookie #3. I tried to emphasize using the previous actual number of chips to improve the estimates...some people saw the value in this, and some did not. We are still working on it...

Everyone estimated and then actually counted the chips in all three of their cookies. They recorded all their data in their packets. They also wrote about how they estimated.

In the packet they also estimated the total number of chips in all three cookies by rounding and then added to find the total amount. No pictures here because I was helping people remember adding strategies... :-/

Once everyone was done remembering how to add three numbers, we collected some data. They wrote their estimates of the total number of chocolate chips on a sticky and put it on the board. We organized it and then they made a line plot to show our estimates.


Then they wrote about how the data looked on the line plot. We tried to make a line plot of the data of everyone's actual number of chocolate chips, but that didn't really work out since EVERYONE had a different actual number. That would have been one gigantic line plot...so we just talked about it and moved on.

Last, but not least, we learned about scaled pictographs and used our chocolate chip cookie data to create one with a key!



They used their scaled pictograph to answer a few questions, and it was interesting! We still need some work on this, but I thought they did a pretty good job for their first try. :-)

Overall, I felt like this project was a success! They practiced estimating, rounding, adding, and collecting and organizing data! It took us a few days to get through it all, but they loved every minute of it.

ESPECIALLY when they got to eat their cookies...no evil eye necessary!

What fun math projects have you done with your kiddos?

Thanks for stopping by!

Nichole

The Craft of Teaching

What's The Angle?


I am writing this post from Sydney, Australia and it is late spring. The garden is full of life, I'm spending a lot of time in my hammock and the weather is beautiful! Well, it is today. It rained for a week before today! I'm not quite sure what inspired me to write about angles. Perhaps it is the view out my home office window - the carport, with its angular support structure. Or perhaps it really is because angles are all around us, so they creep into our subconscious and occasionally leap out into conscious thought! Either way, I have been thinking about angles a lot lately. 

In Australia, we don't start teaching about angles until 3rd or 4th Grade. By this time, students have a fair bit of life experience with angles in the real world. One of the best ways to help students get their head around the different types of angles is to tap into this real world understanding. Take your students for an angle-spotting walk around the school. Here are some angles to look out for:

Acute Angles
Look for slightly opened doors, gaps between a building and an eave, a slice of pizza in someone's lunch box, and triangles in architecture (at least two angles of a triangle will be acute).

Right Angles
Look for the corners of squares and rectangles in architecture, handball squares painted on the playground, windows, doors and bricks.

Obtuse Angles
Look for triangles in architecture (at least one angle of a triangle is likely to be obtuse) and the inner angle of triangular roof-tops.

Straight Angles
Look for straight lines - any kind - I think this one is pretty self-explanatory!

Reflex Angles
Look for open rubbish bin lids (we call them wheelie bins in Australia - the kind of bin with a hinged lid) and the outer angle of triangular roof-tops.

Revolutions
Look for a closed book, and 12 noon on an analogue clock.

Another fun idea is to have students make angles with their bodies. Divide students into pairs and have them lie on the ground with their feet touching. Call out an angle and have the pairs make the kind of angle you have called out with their bodies (the two students are the lines of the angle). 

I came across a terrific Pinterest board devoted to angles, which has lots of great ideas for teaching about angles. You can find it here.

In order to help students remember the different kinds of angles, repetition is the key. Once they are familiar with the terms, the more they hear them and use them in context, the more likely they are to remember which is which! 

In the Little Green TpT store, I have just posted a new resource to help your students review angles. It is a Scoot Review Game. I've made it a little bit Christmas to suit the season, but the theme is subtle enough that the set can be used at any time of year.



And I've also created a freebie for you: an Angle Identification Poster.



How do you teach angles? Can you think of any other good real-life examples of angles around the school? Please share your ideas in the comments. 

Kelly at Little Green

Fantastic Fractions!

Hey all! Guess what we are learning about in third grade??

You guessed it...fractions!

Ok, ok. I know I sound way more excited that any one person should be about fractions. In fact, fractions are frustrating (for me and the kiddos) and they often lead me to feel like I should find an empty space on the brick wall and bang my head on it a few times.

However, I have found a few things that help make fractions a little more fun tolerable.

First off, have you seen this adorable book?

http://www.amazon.com/Whole-y-Cow-Fractions-Are-Fun/dp/1585364606

It does a great job of introducing fractional ideas, and I think it was fun to use at the beginning of our unit. The kids liked it and it's so cute! You can click the picture to snag a copy on Amazon.

We are using a Math Workshop model for the first time this year, so I've been looking for activities to help the kids practice fractions independently.

I found this amazing freebie by Michelle Walker that they can use in a small group to practice matching the fraction, the word and the picture. It is fun and cute! And FREE!

Spring fraction matching cards FREEBIE!

They have been using them to practice matching and using them as a memory-style game. They love it!

Last, but not least, I found a few online games that groups can use on laptops or the Smartboard.

http://www.abcya.com/fraction_fling.htm

This is a fun Angry Birds style game. It shows the kids a representation of a fraction and they have to line up the rock and fling it at the correct fraction! It's a big fave right now.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/fractions/index.htm

Fraction Booster has a few different levels. They have everything from splitting pizza into equal pieces to identifying fractions to putting fractions on a number line!

http://www.bbc.co.uk/skillswise/game/ma17frac-game-dolphin-racing-fractions

Dolphin Racing lets the kids race their dolphin by choosing the fraction with the highest value. You should hear the shouts when their dolphin is winning!

That's just a few of the games I found by Googling that my kiddos love! If you want a few more ideas, click {here}!

What great ideas do you have for teaching fractions??

Have a great week all!

Nichole
The Craft of Teaching

The Craft of Teaching



Free Stuff?? How about 37 free products?



Who doesn’t love free stuff?  Especially free stuff for your classroom!  Tara at 180 Days and Counting is celebrating her 37th birthday by hosting a big giveaway this week.  This giveaway includes 37 items perfect for a first or second grade classroom.  Included in the giveaway are 10 winner’s choice, 7 ELA items, 16 math items and 4 other products.  The activities are at varying levels so they could be used for grade level activities, interventions and acceleration/extention activities. 

I am one of the donors of a winner’s choice item, so if you win this awesome giveaway, you get to pick an item from my store.  The giveaway goes from the 26th until the 2nd (Tara’s birthday) when a winner will be chosen. 

If you would like a chance to win this giveaway and add to your bag of teacher tricks, use the rafflecopter below or head over to Tara’s facebook page for more information:
www.facebook.com/180DaysAndCounting 

You might also want to hop over to Tara’s TpT store.  She has some awesome stuff especially for second grade.  It makes me miss being in my second grade classroom but I loved looking through the items she has created.  She has a lot of great math activities that would be perfect for centers.  Everything is Common Core aligned, user friendly and visually appealing.  I’m definitely her newest follower.  I love how the TpT community helps you to find other teachers with awesome ideas.    
www.teacherspayteachers.com/Store/180-Days-And-Counting


Hopefully one of our readers will be the big winner!  Good luck!

Happy Teaching,

Sara
a Rafflecopter giveaway

I Heart Task Cards - An ode to my latest obsession


 
Since finding TeachersPayTeachers, I’ve become obsessed with task cards.  I saw them all over the site and had to do some research to figure out just what a task card was and how you use them.  A few blogs I used to help with my research were http://www.teachingwithtaskcards.com/ and http://task-cards.com/ and once I read these, I was sold.  Where were task cards when I was in the classroom?  These would have been awesome to use during math workshop.  We created different activities that were similar, but I had never heard the term task cards.

A task card is basically an individual card (sizes vary) that has one problem on it.  Task cards can be used for any subject but thinking about math task cards, it would have one problem related to the subject being taught.  They can be used in a variety of ways.  Here are just a few ideas:

-Replace Worksheets - Task cards could replace worksheets in your classroom.  Instead of completing a lengthy worksheet, students work on one card at a time to show their understanding.  This makes it less overwhelming and cuts down on paper.

-Math Centers – You could put a stack of task cards at a center and students work to complete as many as possible in the given amount of time.

-Whole Class Activity – Task cards could be used by the whole class at the same time.  Usually the games or ideas for this have to do with getting the class up and moving around the room.  One idea is to place cards all around the room.  Students need to wander the room and solve the problems on the cards.  Another game is called Scoot.  In this game, there is a card on each student’s desk.  Each student solves their card and then after a given amount of time, they all move to the next seat and solve that problem.  They continue this until they have solved all the problems. 

-Preassessment – Use in a whole group or small group setting to see what students know before you have taught the concept.  This data would be helpful to group students with common needs for small group work during the rest of the unit.

-Assessment – Again, this could be done as a center or as a whole class activity but use the task cards to determine what the students learned during the unit you just finished teaching.

-Review – A great way to review before the end of a unit or an assessment is to use task cards to review the concepts covered.

-Problem of the day – Hand out a task card as students enter the classroom.  Have them glue them into a math notebook and solve.  Discuss as a class strategies used to solve the problems.

-Early Finishers – Keep early finishers on task (haha) by having them work on task cards while other students are still working.

-Partner activity – Give each student a card.  Have them pair up and solve their partner’s card.  Once they finish, have them find a different partner and solve that card.  Continue pairing up until all cards have been solved.

The great part about task cards is that it is easy to differentiate for each student.  For example, have a high student solve the entire stack of task cards.  A struggling student can have the goal to solve five cards.  Making it just one problem at a time makes it less overwhelming for those struggling students. 

I’ve been busy making task cards for my TpT store ever since I fell in love with the concept.  When I head back into the classroom, I plan on using these in all subject areas but especially in math.  So far I’ve created place value task cards for second grade, telling time task cards for first and second grade and Halloween math and literacy cards.  These can all be found in my store.  I also have a freebie for you.  A set of place value task cards for second graders.  Enjoy!
 

Do you use task cards in your classroom?  What ideas do you have for using them in the classroom?

Happy Teaching,
Sara

Delicious Data and Great Graphs!

Hello again from sunny Sydney, Australia! It's Kelly from Little Green here, and today I want to talk delicious data and great graphs with you! When I teach data and graphing, I find that there are a couple of areas in which students consistently struggle: asking questions that can be answered by the data in a graph and graphing conventions.

Asking Questions

There are two different points at which we have students ask questions with graphing. Firstly, our students ask questions in order to collect data that they can then turn into a graph. While it may seem obvious to us that only some questions will lead to valid data for a graph, it isn't so obvious to our students. While we certainly don't want to crush their natural curiosity, students need to know that when it comes to graphs, only some questions are useful.

Common mistakes at this point of the graphing journey include:

  • Asking too many questions
  • Asking open-ended questions
  • Asking questions that are too complex
  • Giving too many options
  • Not giving enough options
  • Not giving the right options


Secondly, our students ask questions about graphs at the other end of the graphing journey, in order to analyse the information they contain. The kinds of questions they might ask could include:

  • What is most popular?
  • What is least popular?
  • Combining questions (e.g. Which two options have the same value?)
  • Pattern questions (e.g. looking for trends)
  • Comparison questions (e.g. How many more people chose 'x' than 'y'?)


Let's look at a simple graph about pet ownership.


Where do our students go wrong in analysing a graph like this?

  • They ask questions to find information that cannot be known for sure (e.g. The question 'How many students are in the class?' cannot be answered by this graph. We would be making an assumption that each student has only one pet if we said 32. We also don't know whether everyone in the class has a pet - were the non-pet owners excluded from this graph?)
  • They ask philosophical questions (e.g. Why are there more rats and mice than any other pet? Although we could make an educated guess that people usually have more than one of these pets at a time or that they reproduce at a fast rate, we cannot honestly say that this information is stated in the graph itself.)
  • They forget about what has been excluded from the graph (e.g. Looking at this graph, one might say that rats and mice are the most owned pet in the class, but if 12 people have horses, horses would be the most owned pet. They just weren't included as an option.)


We need our students to understand that graphs are limited in their scope. This is an important critical literacy skill to develop, as graphs are part of our everyday experience. Advertisers use graphs and data to sell us things, and if we don't have the critical literacy skills to not only read the information in a graph, but also to consider its source and what has been excluded, the proverbial wool may be pulled over our eyes. Giving our students real examples of graphs (including poorly-constructed and biased graphs) from different sources will help them to develop this vital skill.

Graphing Conventions

The other aspect of graphing that can cause some trouble is in graphing conventions. I must admit, I'm a bit of a stickler for neat, ordered work in Math, as I find that sloppy work often leads to errors. When it comes to graphs in particular, there are some non-negotiable inclusions that add to our understanding of the graphs we read. These are:


  • a title (How can we know what the graph is about without a title?)
  • labels on each axis (Labels let us know what is being measured in a graph.)
  • a key (A key lets us know what is being graphed and, in the case of some graphs, lets us know the value of each segment.)


If any of these elements are missing, it is impossible to determine exactly what has been graphed. And, let's face it, precision is important in Math!

A Freebie!

Help is at hand if your students are struggling with their graphing conventions (or if you wish to reinforce their understanding of these conventions). I have designed a little poster to remind students of what they need to do when they create their own graphs. You can get it here.


You might also be interested in my 'Roll, Tally Graph' game, which allows students to collect data in a fun way, then graph up a storm! I'll be marking the price of this resource down for the next few days, so be sure to check it out!


That's it from me for now. I'll be back next month to talk Math with you once more. In the meantime, drop by the Little Green blog for more ideas and resources.