Tag Archives: 6th grade

Compare and Order Decimals Day 2

In a previous post, I spoke of my introduction to comparing and ordering decimals. In an even different post, I reviewed an amazing Kagan book called Discovering Decimals by Laura Candler. The two activities we played for our second day of comparing and ordering decimals were out of that book.

Decimal War:

In “Decimal War”, students are given a set of cards with different decimal numbers on each card. Students are grouped in pairs. They pass out the whole deck between the two of them face down. At the same time, the students flip over their first card. The person with the largest number wins that round and those cards. In case of a tie, they “declare war.” They each place three cards face down and turn the fourth one face up. The person with the highest fourth card wins all of those cards. Game continues until time is called.

I’m the Greatest:

For this activity, the students are still grouped in pairs. This game requires a deck of cards with all face cards removed. We used the 10′s card as a 0, and the ace card as a 1. The book has a black line master to record the numbers for this game. Students pass out all cards and then they each flip over six cards. On the black-line master, the decimal places are put in different places for each round. The students are to make the largest number with the cards they flip over. After making the number, they compare it to their partner’s number and the largest value wins that round making them “The Greatest”. To make it a little more stimulating, when I notice that all of the groups are finished I say “travel” and the students get up and find a new partner. I do this for each round, and there are four rounds.

“Discovering Decimals”

I can’t stress to you enough, that if you teach decimals this book is a “must have.” There are so many excellent activities and games. The directions are very clear and precise with many extensions and additional activities for each lesson. There are templates and black-line masters for everything you need. Pretty much every aspect of decimals is covered in this book, from grades 3-8.

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Circumference of a Circle

This is the second year that I have taught finding the circumference of a circle using the lessons out of the “Hands On Math!” book. Refer to my “Resources” section to find this book. Here is a picture of the book though……

Circumference:

The “Hands On Math!” book is set up by objectives. Each objective contains three different activities. The first activity is very concrete, the second lesson is pictorial (they are usually drawing or coloring something), and the third activity is a cooperative learning game. The lesson I used for teaching circumference of a circle starts on page 355. Before I started these activities, I gave them a colored sheet of paper and we drew a circle and labeled the diameter, radius, center, and we wrote along the margin that the circumference is the distance around the circle.

For these activities, I had the students grouped in pairs. The first activity is called “All Wrapped Up.” The actual activity calls for assorted plastic lids, but I didn’t think about saving up lids (maybe I’ll start saving now for next year’s group. I’ll make a note). Instead of actual lids, I drew three different sized circles on a piece of paper and made copies for each student. While they are in pairs, I still wanted each student to actually do this exercise themselves but still look at their partner for “security” making sure they are doing the activity correctly. This helps because as there are twenty-something students in the class, there is only one teacher.

I also gave them cotton twine (not stretchy) long enough to at least go around the largest circle.

 

The students were asked to, as accurately as they could, put the string around the medium sized circle and then mark with their fingers where the end of the string meets the rest of the string after it wraps around once. Basically they are measuring the circumference of the circle with the string.

Then ask them to see how many times that marked off string will go across the center of the circle (the diameter).

Go around the room asking the students how many diameters they were able to get out of the marked off string. Hopefully they will get “three plus a little more.” After several of the students saying three plus a little more, then you can explain that this “three plus a little more” actually has a name in math. That name is pi. I draw the symbol on the board and tell them that the actual number is 3.14………

Second Activity: Around and Across

With this activity, I give each pair a copy of the worksheet in the book, adding machine tape, centimeter rulers, and a calculator.

The students are to wrap the adding machine tape around the circle (a little easier since it already wraps).

They should mark the adding machine tape with a pencil at the place where the end meets the rest of the tape. They then need to measure the marked off piece of the tape to see the measurement of the circumference of the circle to the nearest cm. You may have to explain how to measure with a ruler. They then place that measurement in the appropriate place in the table on the back of the worksheet. Then they need to measure the diameter with the ruler and record that in the table. Using the calculator, they need to type in the circumference divided by the diameter. They need to do that will all of the circles. After everyone has completed, go around the room asking for what there circum/diam was. Hopefully most of them will say three point something. I always emphasize the “three plus a little bit more”. I then ask them if that sounds familiar, and they always yell out pi! This is where I go into the discussion and I question them until they start realizing that the distance around the circle (the circumference) is the same as three plus a little bit more diameters. Drawing pictures on the white board is always beneficial in my classes. I then tell them that the actual formula for the circumference of a circle is C=pi * d (sorry, I don’t know how to type the pi symbol on here). We also talk about how it takes two radius to make a diameter, so we also may need C= 2 * pi * r.

Activity Three: Circlespin

This is a pretty cool “game”. Still in pairs, I give each group a copy of the spinners, a large paper clip, and they need a pencil.

This is not the original spinner that came out of the book. I used white out and changed it to fit our sixth grade PASS. First of all, we don’t use decimals with circumference and area, and they won’t have to find the diameter or radius given the circumference. Because of this, I changed the “circumference” on the spinner to “both” and changed the numbers to all be whole, even numbers. The students then flick the paper clip once for each spinner. Both students must find the circumference based on the information they are given by the spinner. For instance, if the paper clip landed on “radius” on the top spinner and “6″ on the bottom spinner, both students would find the circumference of a circle with a radius of six. They are to then check each others answers to see if they are the same. In sixth grade, PASS only asks them to find the circumference to pi and not multiply it out. Because of that, this game should not take very long at all. I usually ask them to do ten problems all together. Each pair’s paper should look identical when they turn them in.

I have different worksheets that I give them if I feel they need a little practice. I usually give them at least one homework assignment for finding the circumference.

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Cut, Fold, Tape, and Repeat Revised

OK, I wanted to put pictures and stuff but I’ve been running around like a chicken with its head cut off. I finally got it done and am finally posting this!! Yay!!  Here is a picture of the 3D figures I bought to demonstrate with. They were completely awesome! From looking at the picture of them, I thought the inserts were paper and would fall apart quickly. They are actually acrylic frames with plyable plastic nets inside of them. They should last for years. They were an excellent purchase.

Monday we made the foldable graphic organizer that compared the different characteristics of pyramids and prisms as well as cylinders and cones. Tuesday I gave them nets of different three dimensional figures for them to cut out, fold, and tape. Unfortunately for myself, I didn’t read the “content limits” for this PASS which tells me that all they have to know are rectangular and triangular prisms and pyramids, cones, cylinders, and spheres. Because I failed to remember this, I had them do several different nets. Oh well, a little extra knowledge never killed anyone. My point is this, if you’re an Oklahoma sixth grade teacher I would only have them do the nets within our content limits. 

Here is a link to the net templates that I used.  www.senteacher.org

Here is a picture of some of the nets my kids made. It’s not an art class, so I don’t grade or make a big deal of how “pretty” the folded shapes are. The point of the activity is for them to take the net and make the 3D figure.

There were nine nets, so I put the students in groups of three and each student configured three different nets. Some of the nets were built to perfection and some look like they had been run through a ringer. This project took approximately one and a half days to complete. My wonderful mom and dad bought me a set of geometric shapes. They are clear plastic with one side opens as a lid. Inside of the shapes is a plastic net that opens up when you take it out. I used these to show them models of the nets and how they fold up to be the different shapes. I work extremely hard to include every style of learner. I am always verbally explaining things. I use lots of hands-on materials to help them learn, in this case was actually cutting out the net and folding it up into the three dimensional figure. I also try to incorporate visuals such as the geometric shape kit my parents bought for me. This was a very engaging activity that the students enjoyed.

I also found a great site that had a “matching” activity for three dimensional shapes. I gave each pair of students a copy of the matching papers and also a red colored paper. They were to cut out the cards and match the discription with the appropriate picture and glue them on the colored paper. This was just an added exercise to connect the nets in words with the pictures. Here is a link to the matching worksheets. 3D Shape Matching Activity  The following pictures are student examples.

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The 3D War….Pyramids vs Prisms and Cylinders vs Cones

Whew! Today was a big one. It started off a little crazy first hour (maybe because it’s Monday), but finally got it going. Here goes my lesson on three-dimensional shapes and their nets. I started off the lesson talking about two-dimensional figures. That they only have two dimensions: length and width. I drew a picture of a rectangle on the board and demonstrated this. I then told them that three-dimensions have the length and width like 2D have, but we add another dimension….height. I then handed out colored paper (Monroney blue for this project, Go T-Birds!) and explained my love for foldables (handy graphic organizers). I took pictures, so we’ll see how this tutorial turns out…….

First take a blank piece of colored paper……..

 Then fold the paper in “Hot Dog” style…….

Fold one side of the paper two-thirds of the way to the other side……

Then fold the other side to meet the opposite edge………

Open the shape up and cut down the creases on one side of the paper…….

We labeled the three flaps…..”2D Shapes, Pyramids vs Prisms, and Cylinders vs Cones”

On the inside of each flap, we listed the different names for the different sided polygons under “2D Shapes” flap. We listed the characteristics of pyramids and prisms under the flap for “Pyrmaids vs Prisms”. Finally we listed the different characteristics for cones and cylinders under the flap labeled “Cones vs Cylinders.”

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Venn Did You Go Back to School?

Annnnnddd we’re back! What an exciting first couple of days back to school!! Today, we constructed the water cup origami for the first part of the class. The link to this is www.wipapercouncil.org/origami.htm  I give them the instructions and then come around and pour water in their cup to see if they folded it correctly. It’s not hard origami, so it doesn’t take very long. After this exercise, we discussed Venn Diagrams. Venn Diagrams are a part of PASS for sixth grade math. The students were already in groups of two based on the seating for the day. I showed them an example using two of the kids and used funny items to compare and contrast them. I gave the students each a colored piece of paper had them each come up with five items (for a total of 10) and then place it on the Venn Diagram in the appropriate place. Most of the students knew Venn Diagrams already, so they were able to do it with ease. A couple of groups had a tougher time, but with further explanation I was able to get them on track. The best part was when there was an odd number of students, I had them make a triple Venn Diagram. After everyone was finished with the project, I asked different groups to go on the board and reproduce their diagrams. It was a great way for students to learn about each other as well as learn their names. I know this was probably one of the best “back to school” projects I’ve done in order to remember their names. Overall, a very successful day! So glad to be back, and I’m excited to get on with next week…….three dimensional shapes!!!

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Please Excuse My Dear Aunt Sally……

If you are a math person, you’ve probably heard about dear Aunt Sally. It is a mnemonic that helps students remember the order of operations (the order in which we work a series of numbers and operations). It is “Please Excuse My Dear Aunt Sally. Please is for parenthesis, Excuse for exponents, My for multiply, Dear for divide, Aunt for addition, and Sally for subtraction. Every math teacher I know uses it and if they don’t, then they probably should.  I taught the students the mnemonic, worked several examples, had them work several examples, gave them a short worksheet, and then today we played a game. The game was a set of 40 pieces of paper cut up into about 2″ by 4″ or 5″. I wrote a different numeric expression on each paper. The students were in groups of three or four. Each group got a set of the cards and a dice. The whole set of cards was placed upside down in the middle of the group. The first person rolled the dice and flipped over a card. They worked the problem on the card while (at least) a second person worked the problem as well, as a “checker”. If the person got it correct, they added the number on the dice. If they got it incorrect, they deducted the number of points on the dice. It was absolutely hilarious to listen to the students argue and correct each other the whole time they played. There was very little off-task conversations. They occassionally asked for my help, but not often. It was a very successful game and lesson! It sometimes got very loud in the room, but what was I going to say, “Quit talking so loud about math!”? Uuummm… NO! I’m goint to post pictures of the cards I made up, but honestly I just got them out of the book.

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