Fraction Games

I love learning about fractions.  We play these wonderful games that give kids an excellent conceptual understanding of what fractions are and how they relate to each other.  By playing these games, our kids naturally learn how to compare fractions and how to find equivalency.  I remember at the end of last year, my students and I were discussing a problem related to fractions.  Several of my students told me that they instantly began visualizing our fraction kits and the games we played earlier in the year.  These fraction games stick with the kids (and they have blast playing them, too!). 

Fraction games

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Making Arrays

In order to gain a better understanding of the relationship between multiplication and division, we began studying arrays.  We looked at them in different ways and learned to see the multiplication and division facts they could represent.  In this activity, each team of students created an array with objects in the classroom.  Then they visited other teams' arrays and discussed the fact family they saw.  Students took along their white boards and wrote down the facts they discussed. 

Making arrays

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Multiplying Large Numbers

We learned several different algorithms for multiplying multi-digit numbers - partial products, lattice, and the traditional approach.  But I want my students to go beyond learning the algorithm.  I want them to really understand what is happening when we multiply these large numbers.  When our study of multiplication began, we spent a lot of time exploring repeated addition and arrays.  So I built on this knowledge and asked our kids to build BIG arrays - like 23 x 34 - using base ten blocks.  We then were able to connect the array to the 4 partial products we made when using the partial products algorithm.  Our kids were actually able to see what happens when we multiply large numbers together. 

In the video below, you'll see kids solving problems using the partial products algorithm and "building" the array using base-ten blocks.  But the important step comes after creating the array.  You'll see kids making a connection between the numbers on their white boards and the actual base ten blocks. 

Multiplication Baseball

One of our goals in 4th grade is to increase each student's "fact power."  I want students to have an instant recall of all the multiplication facts.  This ability will help them become faster and more efficient mathematicians.  Fractions, division, number stories, life - they all involve multiplication.  To increase our fact power, we've been playing lots of games in class.  One of the kids' favorites was Multiplication Baseball.  If you would like your own copy this game board, I'll be glad to send one home.  All you have to do is leave a comment below, and I'll send one home with you (or if you're a parent - your child).  Here are some pictures of our kids hitting the ball out of the park.

Multiplication Baseball

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Subtracting with Base Ten Blocks

In too many cases, subtraction with regrouping is learned as a step-by-step procedure.  It's true for me.  When I learned to subtract with regrouping, my elementary school teacher taught me the steps - not actually what was happening with the numbers. Because I just learned a process, I sometimes became confused with the steps and made mistakes.  Because I just learned a process, I struggled with number sense and estimation.  I didn't really understand how numbers worked together.  I didn't want this to happen to our kids.  So - to learn a conceptual understanding of regrouping, we used base ten blocks to demonstrate what was actually happening when we "cross out" a number and change it into another one.  We started by using this incredible website to actually see the base ten blocks in action, then we moved to using base ten blocks on our own.  Students had to use the base ten blocks to explain exactly what was happening in each step.  I was really proud of our kids for the understanding they gained this week.

Subtracting with base ten blocks

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Adding with Base Ten Blocks

After spending our first week of math workshop playing games and figuring out puzzles, I wanted to spend this week using base ten blocks.  Yesterday in class, we used base ten blocks to demonstrate our understanding of regrouping in addition.  Most kids know to start by adding the ones place, and sometimes you have to "carry the one."  But it's not really a "one," is it?  It's really a ten.  And when kids add the tens place, they often times have to "carry the one" over to the hundreds place.  But it's not really a "one" - it's really a hundred.  The base ten blocks gave us a concrete understanding of this concept.  I'm always pushing for kids to understand the WHY behind math.  I want us to go beyond the procedures and steps and really develop a conceptual understanding of how numbers work.  Below are some pictures of our kids at work. 

Adding with base ten blocks

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Flips, Turns, and Slides

We began this study by using pentominoes.  We flipped them, turned then, and slid them around.  We explored different methods of translation, and we recorded our observations on graph paper.  On the next day, we began using reflection mirrors to better understand the "flip."  We played games of billiards and darts (ask your child about it) to better understand this concept of reflection.  We noticed that points on the pre-image and image are always an equal distance away from the point of reflection.  Our final exploration was with pattern blocks (I saw Mrs. Stucky doing this with her students, and I thought it was a great idea).  Students created an image using pattern blocks, and then created the reflection.  Students used their reflection mirrors to check their work.  Here are a few pictures of the reflections they created.

Reflections (Flips)

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Building Geometric Solids

To better understand 3-D shapes, pairs of students spent time building geometric solids with straws and twist-ties.  This activity gave us a better understanding of faces, bases, edges, and vertices.  We were able to describe solids and compare them more accurately.  Here are a few pictures of our mathematicians at work...

Building 3 D Shapes

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Building Polygons

In math workshop, our new unit of study is on geometry.  Yesterday's lesson explored polygons.  We began by exploring what a polygon actually is.  By studying examples and non-examples, we found out that polygons have straight sides, at least three vertices, one interior, and is a closed shape.  We then set out to build as many different polygons as we could.  After each team was given straws and twist-ties, they quickly began building.  After 10 minutes of creating shapes, we decided to classify our polygons by their number of sides.  We built everything from triangles to decagons!  Here are a few pictures of our students building their shapes. 

Building Polygons

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Multiplication Tricks

During our last unit of study in math, we looked at different "tricks" that could help us memorize our multiplication facts. We decided to record these tricks on video. I edited into two parts (since the length was a little long). Do you know any more tricks for multiplication? Do you have any other methods you use to memorize your facts? Leave a comment below with your own ideas!

Beat the Calculator

In my weekly newsletter, I know I've mentioned the math games we play in class. These games are a great way to practice our multiplication facts in a fun way. We learned a new game last week that quickly became a class favorite - it's called Beat the Calculator. One person is the caller, one person is the Brain, and one person is the Calculator. The caller draws two cards and calls out a fact, and the Brain and Calculator try to be the first person to get the correct answer. Whoever calls out the correct answer first gets the cards. The person with the most cards at the end of the round is the winner. This game is high energy, so there is a LOT of noise in our room while small groups of kids play this game. But I hope this short video gives you a feel of our class "game time"...

Adding with Base Ten Blocks

Too often, kids know the "how" of mathematics instead of the "why." Today we got out the base ten blocks to find out exactly what happens when we add multi-digit numbers. Many of our kids were surprised to find out that you don't really "carry the one." You're actually regrouping ten ones together, and then moving the ten over with the other tens. They were really surprised to find out that you don't "carry a one" over to the hundreds. You're actually regrouping ten tens into a one hundred! I demonstrated this lesson with a really cool website you and your child can visit. Students then had the opportunity to use base ten blocks to connect what they know on paper (the traditional addition algorithm) to what was really happening with base ten blocks. I hope activities such as this one build solid conceptual understandings of math for our kids. I want our kids to know the "why" of math!

Math Games

One of the best ways to learn math is by playing games. So far this year, we've learned several math games: Poison, NIM, Addition Top-It, Subtraction Top-It, Name That Number, Number Top-It, Around the World, and High Number Toss. Ask your child about these games. Which ones were their favorite? What did they learn by playing these games? Here are a few photos of our students playing hard...

Tangrams

In all my years of teaching, I have never explored tangrams. I found a nice bucket of these unique shapes in my supply closet (a teacher had given them to me long ago), and I decided it would be fun to teach the kids how to use them. A tangram is an old Chinese puzzle that is made by taking a square and cutting it into seven shapes. These shapes are then used to create the shapes of animals, people, and objects.

We began our exploration by sharing a picture book titled Grandfather Tang's Story. Grandfather Tang tells the story of two fairy foxes who play a shape-shifting game of tag. As each fox turns into a different animal, Grandfather Tang would create the animal with his tangrams. The kids were hooked. I gave each student his or her own set of tangrams and challenged them to put them into a square. Our kids quickly mastered this challenge, and we began creating all kinds of shapes (a running man, seal, bear, duck, boat). Tangrams are a great mathematical tool - they force us to think spatially, look for patterns, and try new strategies to solve problems. I was so proud of our kids. If you'd like to learn more about tangrams, I've included some links on the blog's sidebar. You can make your own tangrams and begin creating! Take a look at the pictures below to get an idea of what tangrams are all about...

Tangrams

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Investigating Weight

Last week, I set out several different scales and let the kids explore with weight. On this particular day, we were exploring the US Customary system (ounces and pounds). Kids were finding the weight of various classroom items; they really enjoyed using the balance. Here are a few kids describing their investigations...

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How Much Snow?

We were lucky to get some snow this school year - it's been a long time since we've had some March snow. With two snow days and a two hour delay, I was WAY behind on my lesson plans. When we came back to school that Wednesday, I was ready to jump back in the curriculum. But...as the kids walked in and greeted each other, there was so much talk about snow. We shared our experiences about the snow and gave descriptions of what it was like at each of our houses. There was a lot of talk about how much snow we received. So, I asked each child to make an estimate about the amount of snow fall at their house (we got out our rulers and reviewed inches), and everyone recorded their data on a post-it note. We put all our data on a line plot and analyzed it. We noticed lots of interesting trends (which we charted)! In order to show our results in different ways, teams of students create bar graphs, pie graphs, and pictographs. Below are some pictures of our work...

How Much Snow?

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Exploring Area

We had a fun time exploring area last week. We used one inch and three inch squares to find the area of two dimensional shapes around our classroom. Our kids quickly found out that you don't have to cover the entire shape to find the area. Rebekah figured out that you could lay out your squares on one row, and then find out how many squares would go into each row. Lots of our students began using multiplication to help them find their answers. Here are some pictures of the kids at work.

Alex and Rebekah had to work together to find the area of a cinder block face.

You can see how Coco has recorded her findings in her math notebook.

Jo'nae, Clayton, and Alaina are trying to find the area of a writer's notebook.

Fraction Games

For the past two weeks, we have been learning about fractions by playing Fraction Games. Each student built a fraction kit and we used special fraction dice to play games like Cover Up and Uncover. The kids had a blast and naturally learned how fractions relate to each other. At the end of each math workshop, I asked students to fill out a reflection sheet to share what they learned and noticed. Cameron and Allison's reflections are below. I've also posted some pictures of the kids playing the games.

Fraction Games

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Estimating and Measuring

One of the best was to understanding measuring systems is to find personal references for certain lengths. Each student found common examples for millimeter, centimeter, decimeter, and meter. We then used these personal references to make estimates for objects in the classroom. To check our estimates, partners worked together to make an exact measurement. Tape measures, rulers, and meter sticks were all over our classroom - it was great! The kids found out that they were very good at making estimates when using their personal references! I was proud of them.

Jo'nae and Ben estimated the length of the classroom. They're using their meter stick to see how close they came.

Alex and Andrea are discussing strategies for using their measuring tape.

Learning Our Multiplication Facts

I remember when I was in 2nd or 3rd grade, my teacher gave me a piece of paper with all the multiplication facts on them. She then told me to memorize them. I remember sitting on the back porch with my dad, going over and over and over the facts. It took lots of time, practice, and determination for me to memorize the multiplication tables. Those three criteria still apply to our kids today. Fortunately, we've developed some more "fun" ways to memorize the facts. In class, we used flash cards to determine what facts we know and what facts we still need to practice. We've played Name That Number, Multiplication Top-It, Beat the Calculator, and Multiplication Baseball. All of these games help kids memorize their multiplication tables. But parents - I encourage you talk to your child and identify those facts that he or she does not know. Practice them in the car, make flash cards, play games - do what it takes. Remember- time, practice, and determination. Here are some pictures of the kids playing math games in our classroom...

Coco and Mia are playing Name That Number (one of my favorites).

Austin and Porter think over their facts as they play Multiplication Baseball.