INTEGER CHIPS

Teaching adding/subtracting integers is sometimes a difficult lesson for students to grasp. I have used the integer chips(red/yellow chips) to give the students a pictorial view of the concept for the last few years and the seem to understand better when I demonstrated adding and subtracting using the chips.

I have an overhead set of the red/yellow chips which makes it very easy to demonstrate. Having the pictorial view is very beneficial for students who are visual learners. They are able to see the red chips represent negative and yellow represent positive. This is also great when explaining zero pairs to add or subtract integers. Subtracting integers appears to be harder than adding integers and when using the integer chips it is easier for the students to see that we're actually adding the opposite by showing them how we're doing it and not just telling them this is what is done!

The only down fall in using the chips is when problems consist of large numbers. Who wants to count out 25+ chips? Plus that can be very time consuming! So, just stick with smaller numbers when demonstrating with the integer chips.

If anyone has any other ideas about teaching integers please let me know!

Unifix for Pythagorean Theorem Proof

I had a student come in for tutoring this week because he was having trouble applying the Pythagorean Theorem. In an "aha" moment I pulled out the cubes to walk through the proof again with him (in class the students used the Pythagorean Theorem Model from the state's website). I could see the lights getting brighter as we created Pythagorean triples with the cubes and walked through solving for a missing side with the manipulatives. He had a break-through and did very well on his quiz the next day.

AngLegs

I've made lots of use of the AngLegs lately teaching SOL 7.7 . The are great to show the students how perimeter is like a distance and by pulling the sides apart we merely get a straight line. It helps them to understand keeping the units straight for perimeter vs. area. Also, I made a parallelogram with them, layed it flat on a table, and poured some beans inside....making sure they were flat and not piled. As I adjusted the shape of the parallelogram the students could see how the side lengths stayed the same but the area changed as the beans started to overflow the borders of the AngLegs.

Also used one of the Sir Cumference books and it went well with some students however, others were bored.

Tarsia

Tarsia is a simple computer program that allows you to create puzzles that students solve by matching. I used this during SOL 7.1. The student had to match fractions, decimals, and percents. One of the finished puzzles looks something like the image to the right. There are a number of different options and shapes.

Suffolk Schools will install the program with a tech request. I requested it one afternoon and had it the following morning. It's also available for free to download from the Tarsia website.

Most of the time I had the kids work in pairs and they loved it. They've been bugging me to make one for area & perimeter.

Real World Shocker

As part of an incentive program in my clasroom, my students earn "Pittman Bucks." I have made a money template with my picture on it and I have denominations of $1, $5, $10, and $50. At the beginning of the year I explain to the students that coming to school is their job and therefore they should be paid for it! I give them a weekly "pay check" of $50 and they earn money for various other activities as well. They can also lose the money for breaking rules or not doing all of their assigned work for the week. I have also thrown in a monthly "bill" of rent in the amount of $60. Boy do they love that! At the end of the nine weeks they have the opportunity to buy things in an auction. Well, today I broke the bad news to them. I informed them that as good American citizens it is their duty to pay taxes. As you can imagine, they were not to pleased! (Don't feel too badly for them though, it's only a 10% tax.) They then had to calculate and pay me their tax money. Each student has a money envelope and on the outside they have a basic check registry that they have to use to keep track of what they earn, lose and spend. Shockingly enough, most of them have great difficulty maintaining an accurate balance. All of this falls into SOL 6.8, consumer applications, not to mention the basic life skill of balancing a checkbook.

Quadrilaterals with Anglegs

I taught a lesson to a 4th grade class on quadrilaterals, using the anglegs. The students were in groups of 3-4. At first, each student had four anglegs of the same color, but each person in the group had a different color. We talked about the shapes they could make and what those shapes were called (square and rhombus). The students formulated rules for their squares and rhombi. We also discussed congruent and noncongruent. Then I had each student take their shape apart and pass two of their anglegs clockwise to the next person. Some students constructed parallelograms and some constructed kites. We discussed the similarities and differences. Next, I had the students who had created the kites change theirs to parallelograms. We compared rectangles and parallelograms and the students again formulated their set of rules. The students loved using these manipulatives!

Math Ticket

Hello everyone,

I recently did a math ticket with my students as a review for their nine weeks test. The students really enjoyed it. The were given a 3 by 3 like bingo card with nine topics of choice on it. They were to choose one square from each row and work on each topic. They were given several days to work on it in class. The students really enjoyed it because they had a choice on what to do. It covered topics such as percent, fractions, and decimal conversions, tips, tax, discounts and simple interest, order of operations, interger models, and math properties. The only thing I see myself doing differently the next time it only allowing them to complete it in class. All of the students worked on it, but when it came time to turn it in some were misplaced or lost because they were also allowed to work on it at home.

We recently just finished teaching conversion of decimals to fractions and fractions to decimals. The students really liked the activity which required them to match cards together that showed the equivalency of the two. Repetition of the most common conversions helps it stick to memory as well as having them think decimals and fracitons in relative terms to money ie. one fourth of a dollar is $.25.

Order of Operations Monarchy

This year I took a different approach then the typical PEMDAS or Please Excuse My Dear Aunt Sally to teach order of operations. Teaching it last year, many students still struggled with questions that had both multiplication and division or addition and subtraction. You may have seen it as well with yours. For the problem 7 - 5 + 3, students run down their list and do addition first because A comes before S in PEMDAS.

To combat this I used a monarchy to teach Order of Operations. Each part of the order had a title according to their position in the kingdom.

King G (grouping symbols)

Queen E (exponents)

Princes M & D (multiplication and division)

Princesses A & S (addition and subtraction)

This may seem a little silly, but worked great with students prior knowledge about a monarchy. The concept is simple, who assumes the throne next? The King is always first. If the King is not present, the Queen is on the throne. This continues down the line.

The problem with multiplication/division and addition/subtraction was solved by drawing upon the students knowledge of a monarchy. I posed the question: "If more than one Prince is present, who assumes the throne?" Students shouted out: "The oldest" and "Whoever's first in line." They got it!!!!! There is our left to right. The same question was posed about multiple Princesses; and the same answered received.

I have had much success with SOL 7.2 using the monarchy. If you have students who are struggling with the left to right for multiplication/division and addition/subtraction and are looking for another way to teach it, give this a try. I also created a foldable with pictures of a King, Queen, Princes, and Princesses, notes, and sample problems that the students worked in to reinforce it.

I'll take a picture of a student's foldable and post it. What do you think?

DaVinci Man- Measurement and Multiplying Fractions

One activity I use to help students understand how math is part of nature is the Proportions of a Man activity. It brings art and math together. Students can measure each other, which involves cooperative learning. First start by measuring height and base proportions on this. Students then measure arm span to see that height and arm span match. I open the activity with the measurement of each other to grab their interest.
Then I give them a model of a circle with a 8 inch diameter and have them work the proportions based on this height. They draw an 8 inch circle and draw the Vitruvian Man with the proportions illustrated below (taken from Wikipedia):

• the length of a man's outspread arms (arm span) is equal to his height
• the distance from the hairline to the bottom of the chin is one-tenth of a man's height
• the distance from the top of the head to the bottom of the chin is one-eighth of a man's height
• the distance from the bottom of the neck to the hairline is one-sixth of a man's height
• the maximum width of the shoulders is a quarter of a man's height
• the distance from the middle of the chest to the top of the head is a quarter of a man's height
• the distance from the elbow to the tip of the hand is a quarter of a man's height
• the distance from the elbow to the armpit is one-eighth of a man's height
• the length of the hand is one-tenth of a man's height
• the distance from the bottom of the chin to the nose is one-third of the length of the head
• the distance from the hairline to the eyebrows is one-third of the length of the face
• the length of the ear is one-third of the length of the face
• the length of a man's foot is one-sixth of his height

The activity can be tailored to just the proportions of the face, or the whole human body. Conversion to percentages is also an option. The finished products are quite beautiful, targets the visual/artistic learning style, and is a way to show how math really is used in nature.

Getting the students to talk

A huge goal for me is to get the students talking to each other about math. We all know that with middle schoolers this can be a HUGE challenge. The Kagan Cooperative Learning books have been a huge help in creating activities that get kids to talk. One of my favorites is called Showdown and involves using dry erase boards. Every kid get a board and a marker. In groups of three to five, give students a set of problems to work. It works best if they have the problems on cards in a ziplock bag. One person draws out the card. Each student works the problem on their own board and turns the board face down when they are finished. The "Showdown Master" calls out "SHOWDOWN!" when everyone has their boards flipped over. The students then show their boards to each other and work together to correct any mistakes. This activity really gets the students talk about the math.

If anyone has other activities, I'm always looking for something new. THANKS!

Fractions in Action

I used the fraction transparency squares to help introduce the concept of multiplying fractions. The kids really liked them and it made the concept easier for them to understand. However, I wish I had a class set of them so that the students could see the multiplication process at their desks easily and they could work their problems out faster. I had the kids fold paper to represent the fractions and the multiplying process. However, this took alot of time to model and for the students to complete their problems. Does anyone know where I can get a class set of them cheap?

Fraction Dilemmas

We are getting ready to start our first unit on fractions. I absolutely love the colored transparencies for multiplying fractions. I am running into a problem because of the limited amount of these. I am looking for ideas because extra kits cost $14. The AIMS books have a non color version, but the color is more "impressive."

I have created a SMARTboard activity that includes this and trying to get the colors just right so we can show the colors as a whole group. This will enhance their learning in whole group, but I'm afraid that group work will not workout so well.

I am looking for any help with these ideas. Also, any other ideas to getting the students engaged and REMEMBERING the fractions would be appreciated as well. :)

Promethean Activevotes

I have a Promethean "Smart" board in my room. I have been using it for everything. I was not that familiar with it so I just began using it as an extension of my computer, e.g. flipcharts and powerpoints. Then I found the ActiveVotes - wow! I have a changed class atmosphere - the students everyday come in and ask if we are using the "eggs" as we call them, and that encourages class participation as well as giving me a plethora of ways I can assess their progress, know what their weaknesses are, teach, and just let them learn. Further I do not have to be concerned about a messy chalkboard!

The thing that has been the most useful is when I use it for the daily warm-up. Our daily warm-ups are given to us by the district but I like to remind them of the things we have done in the past - especially topics in which they struggled but pacing has required us to move on. So we do a daily warm-up consisting of 5 to 10 items that address the current topic, their areas of weaknesses, and just review of topics they understand. They are very competitive and love it when they get it right, but when they get it wrong - they immediately know (instant feedback) and if a lot of them get it wrong it is a chance to review. Otherwise a student gets to go up to the board and show how they got their answer and the whole class gets a chance to see where they made their error.

My measure of success is on Friday, mid-class, how many students are still with me and wanting to learn and so far I have been amazed that they will work up to the bell! It is a fantastic tool!

Promethean ActivExpression

I do not have a Promethean ActivBoard in my classroom. However, I have recently incorporated the ActivExpression, one of the many Promethean’s products, into my lesson. This interactive tool is amazing. It definitely increased the participation of all my students during class.

The ActivExpression hardware is like a mobile phone device. It has a keyboard that allows students to vote for multiple-choice format questions, enter yes or no responses, and convey their thoughts by entering full sentences and character texts.

I was creating a lesson to help my students to review for their upcoming benchmark test. I was going to ask my students to complete a review worksheet. However, I understand that it can be boring to students. Students were still required to complete all the review questions individually using the ActivExpression, but all students got to share their answers with the rest of the class by voting or texting. All of my students agreed that it was a much more fun way to review.

To use the ActivExpression devices, all you need is to install the “ActivExpression” software in your computer. You don’t need to have the Promethean ActivBoard in your classroom to use the ActivExpression!

Blog in the Classroom

My Class Blog

This year I began using a blog with my Math 7 Class. I have found much success with using the blog in the room. Students have used it as one of four stations, as extra credit, also as a whole class assignment. I find it is very helpful so I do not have to have the students type in lengthy websites or frequently ask for directions when we transition into the computer lab. Even if used infrequently, when used in class, the students are more engaged and on task. I have not taught them yet how to post comments, so they are mostly disabled. On the downside, some of my students do not have Internet access at home and most parents have yet to check out the blog. I posted this both to share all the links I have found but also to look for comments that might dialogue about best practices when it comes to blogging in the classroom.

Percent and Consumer Applications

Last week we worked on Percent of a Number and introduced Singapore Math in which you use modeling and illustrations. For example: What is 20% of 80. Make 100% 80 and encourage students to use knowledge of benchmarks (50%, 25%, 10%, 5%, and 1%) to get to 20% (10% x 2, 5% x 4, 1% x 20, etc.). You can also use this when you start with proportions.

Currently I am teaching the consumer apps unit involving discount and sales price, tax, tip, mark up and mark down. The most important piece I believe is vocabulary. I was amazed that the students had no idea that discounts save us money and tax adds to our total. We use the same concept of benchmarking and the Singapore math to find discount, etc. Also it helps if students understand that if there is a 30% discount I am only paying 70%. So if they know 10% they can multiply by 7 and get the 70% and still figure out how much they will pay.