Math Teachers at Play 15?!

The new carnival is up at mathfuture. One of the most interesting things about it is the host site, which looks at Web 2.0 math applications. For example, their GameGroup, which I may be seeking to join.

Other than that the 2 posts that were most interesting to me are a description of a role-playing site for math-centric careers and 25 uses of Wolfram Alpha (which I love).

Denise has a good starter on Mental Math, but I don't see these as techniques you teach as much as ways of thinking that you demonstrate and can grow out of kids' number sense. I was saying to Xavier (my 4th grader) last night, knowing 6x9 is not as important as being able to find it efficiently, and knowing things like it's connected to 6x10 - 6 or 6x5+6x4 is much more important.

Perubahan Tampilan Blog

Blog in memang memiliki beberapa perubahan tata letak sejak kemarin, bukan karena perubahan itu disengaja tetapi lantaran karena terpaksa harus dirubah. Awalnya hanya ingin mencoba fitur baru yang ada di blogger ( fasilitas read more ), padahal sebelumnya blog ini sudah menambahkan beberapa kode agar tampilan read more berjalan. Saya sendiri tidak paham dengan yang terjadi, ketika setingan edit

Angles

What do you see as the big ideas with respect to teaching angles?

To me:

• filling around a point, no gaps or overlaps between two boundaries
  
• connection with a circle (filling all the way around a point) - important for units
• size of the angle corresponds to how open

So I love to begin teaching angle with pattern blocks. The activity I start with is adapted from one taught at GVSU by Jan Shroyer, don't know where she got it or whether she wrote it. The activity as a Word .doc is here. If printing from the web, try to size the pattern blocks so they are life size. (Doesn't affect the angles, of course, but makes it much more natural.)

A Very Special Blossom

A blossom is a special pattern in mathematics when copies of the same shape are arranged to fit together all the way around a point. Try to blossom the following shapes. Record how many fit around a point. Sketch either the shapes or the edges that meet at the point.

What do you notice?

Would the blue or red pattern blocks blossom?

Teaching notes: the white rhombus is chosen especially, since the wide angle doesn't blossom. The narrow angle will provoke a little discussion, 11 or 12 to blossom, because if they're tracing one block, the thickness of the drawn lines add up. The wide angle will draw responses of 1, 2, 3, 4, and 8. 4 will usually be two wide and two narrow angles (tessellating the rhombus) and the 8 is from filling the rest with the narrow angle. The red trapezoid and blue rhombus will sometimes have the students seeing blossoms with the narrow angle but not the wide.

After the connection of 360 degrees with filling all the way around, these blossoms can be used to deduce the measures of the pattern block angles. This is nice in conjunction with measuring practice with a protractor or angle ruler.



Filling Time

Use pattern blocks to measure the following clockwise angles. (Start at 12, and then measure in clockwise direction to the other edge.) Use all of the same unit for each angle. Measure each angle twice using different units, if possible.

Teaching Notes: You will see students make a lot of connections with congruent angles doing this. Also, there will probably develop an appreciation for the smaller angles as units. There is a natural tendency to measure the smallest direction, so that will bring up the clockwise/counter-clockwise thing, which is a nice connection with rotations, which will be a great way to teach angle to kinesthetic learners. The middle left angle brings up the idea of partial units, as it is not a whole number of pattern blocks for any of the shapes. The scientific standard is to measure to half of the smallest unit, so a good answer is 1 1/2 white rhombus (small angle) or 1/2 square. How many green triangles is a nice discussion.

The next activity I'm including the way I work it for preservice or inservice teachers. Easy to adapt for 5-12th grade students, though. The Word .doc version is here.

Telling Angles

Objective: TLW expand their understanding of angles, connect with the angles on a clock face, and use reasoning to find angle measures by comparison with known angles.

Schema Activation: What do you know about angles, measuring them and degrees? List your top 3 facts or bits of relevant knowledge.







Activity:
1) Forget the time, what angle is it? Record the angles made by the clock hands below. Add one sentence of justification for how you know.

2) Teacher question: why might I have sequenced the clocks the way I did?




3) Record the angles made by the clock hands below. Add one sentence of justification for how you know. Notice the hour hands are no longer pointing directly at a number.

4) 11:50, 1:10, 3:20, 7:40. For each time, draw in the hands precisely, and then determine the angle between the hands. Describe your process for each time. Start with the one you think would be easiest.

Reflection: What 3 ideas do you most want your students to understand about angles and angle measure?







Extensions: Challenge questions:
a. Is there a time for any angle?
b. Is the clock more likely to have an acute, right, or obtuse angle when you look at it?
c. How many degrees does the angle change in 1 minute? 5 minutes? 10 minutes? Does it depend on what time it is at the start?

Mohon Maaf

Mohon maaf atas ketidak nyamanannya,saat ini blog sedang dalam perbaikan, anda bisa kembali dalam 24 jam kedepan.

Different methods of starting a Math lesson

Well start is half done!

If a teacher is able to capture attention in the beginning of a lesson then half of the job is done. This means the first two classes of a Math lesson are very crucial. There are various methods of beginning a Math lesson in a creative manner.

#1 Making a connection- Everytime it is not essential that we are going to start a new concept. Students have some knowledge about it earlier. So, forming a connection by asking questions based on previously gained knowledge of students is a tried and tested strategy which helps in motivating students for further learning.

#2 Showing a picture - A picture says a thousand words. In a math class, one may begin a lesson by showing a picture from surroundings showing the use of some Math concept leading to introducing new concept.

#3 Story telling - This helps a lot in the beginning of a lesson. I believe we as teachers need to capture attention of students so that their focus is on the new topic. Story telling is indeed a good way to start a lesson.

#4 Realising the need to learn- Why we are learning this concept ? Why it is important ? This must be answered in the beginning.

#5 Involving students - Calling students names in between , taking their help ,taking their examples helps in capturing attention till the end of class.

#6 Showing real objects - Sometimes it is feasible to carry real objects in a classroom. Students may be asked to look around themselves to observe things also.

It is the way how a topic is introduced which matters a lot.

Soal Matematika SNMPTN

Awalnya saya mengetik kumpulan soal matematika yang ada di blog ini menggunakan word 2003, tetapi ketika mulai banyak yang menggunakan word 2007 akhirnya beralih juga untuk mengetik soal - soal dalam word 2007. Hanya masalahnya word 2007 ini kok belum bisa ya untuk upload di ziddu.com ( atau sayanya yang belum paham ), sehingga setiap file harus dirubah ke word 2003.

Masalahnya ketika file

Sorting and Math Teachers at Play 15

The new carnival is up.

Some of my favorite items: Kindergarten sequences (good for older kids, too) and the math skits idea.

I'm not crazy about the fractions or quadrilaterals activities, as I think both fall into some common pitfalls of the traditional thinking on these topics.

Sorting
As we started class this week, one activity we did in both my classes (geometry for K-8 and math student teacher assisting) is a Piece of Me. Students come up with one question about the class and one question about the teacher(s). They then get together in pairs/groups and decide on one of each to ask. They never ask the sort of thing you'd expect, or the sort of thing I used to share in my own introductions. It's an excellent quick pre-assessment of where they are with the class and what they care about. And, they get to discuss with other students what makes a good question. I got this activity from Dave Coffey, but I can't remember from where he got it.

The first activity I had the geometry students do was a game, that I've played with many levels of students.

In or Out
Materials: rope or chalk circle (For 20ish students a 40-50 ft rope will suffice. Of course, divide by 6 to estimate the diameter of the circle formed.)

Students stand outside of the circle. To demonstrate how a circle sorts, have a few different rules, and students who fit the rule step in. I usually use the old riddle: how many sides does a circle have? (Highlight for the answer: Two - inside and outside)

The game is a guess the rule game. Someone has a rule for the circle and people guess whether they are in or out. If they are correct, they can guess at the rule. If you guess the rule, you can make up the next rule.

I usually demonstrate the first three rules. One that is obvious, one a bit more subtle, and then a hard rule. The hardest rules are ones that change: in or out depends on body position, or on what the person before says. (Almost a guaranteed rule stumper is - you're out or in based on what the person before you guessed.) This can also be used to demonstrate the concept of function. (That's when I'm using the game in a college algebra class.)

Mostly the point is to get students thinking about characteristics. With upper elementary students or middle school students you could ask the questions I asked this time, after playing the game for awhile:

Activity: Work your way through some of the following questions.
1) What were some of the rules used?
2) Was there a rule that was easy to guess? Why?
3) Was there a rule that was difficult to guess? Why?
4) What is a rule that would divide our class into two groups of roughly the same size?
5) What are two rules that would divide our class into 4 groups of roughly the same size?
6) Why do two rules divide a population into 4 groups? Give an example.
Extension: Into how many groups would 5 rules divide a population? N Rules?

Reflection:
• Whole class: Share some of the ideas from (5). Try them out.
• Analysis: What are you doing when you’re sorting?
• Inference: What does this lesson have to do with geometry?

13 Learning Times Tables Links

Multiplication tables plays an important role in learning Mathematics. Children move away from learning them. Technology has helped teachers by offering interesting tools/games/software for helping children to learn concepts and practise.

Here are some interesting links
#1

1. Times tables generator You will get times table generated in click of mouse. Just type in the number and click...

#2 (Free and Downloadable )

Here is an interesting downloadable Math game which may be used for practising tables. I find it different and challenging too.Try it!

Valgetal Falling Numbers 3.23

#3 (Free and downloadable)

Another one is Multiplication Master...Free multiplication tables practice software.Fast, simple and easy to use for budding multiplication masters of all ages!Keeps your score so you can see how well you're doing.Single table mode lets you focus on one multiplication table at a time - the fastest way to improveRandom feature tests you against all the multiplication tablesIncludes reference tables to help you learn multiplication tables fastUnlimited use. Practice as many multiplications as you want, as often as you want.Completely free. No charge for this software - ever.Here is the link to download.

#4 (Free Junior edition)

This one is learn MathMatic JuniorMathmatic is a program for learning and drilling multiplication tables 1 through 12. It is dedicated to that unique task and it does it thoroughly. MathMatic generates and PRINTS DRILL SHEETS. The user can choose between Mental and Written learning modes and use the timer to measure performance. MathMatic's sounds and colors are fully user definable. The Junior Edition is Freeware and is directed towards young students (multipliers bound to low values).

#5
A free multiplication program for kids... MULTIPLICATION FACTS lets you learn and practice the basic times tables using the numbers zero through twelve. And it's FREE! MULTIPLICATION FACTS lets you work with any digit(s) you choose. Review times tables, see graphic representations of problems, or take speed drills. The program grades your performance and provides feedback. Print worksheets for practice away from the computer.

#6
Checkout Times tables activities,games and worksheets ...quite interesting!!
#7

Tables tree-an interesting game to practice multiplication tables.

#8

A complete website on multiplication for teaching learning multiplication facts.

#9

Visualising Multiplication tables using this applet.

Visual Multiplication

#10

Answer 10 multiplication questions. How much time did you take?

Tables times

#11

Multiplication flash cards on Quizlet.

#12

Interactive practice of times tables. Click on a box. Drag the right answer from the numbers given on RHS.

#13
Explore Multiplication tables in an interactive manner.

15 Places to find Teaching Resources and Math teaching strategies

Trying to get a classroom of 20 to 30 individual thinkers to understand difficult math concepts can sometimes be challenging. Fortunately, there are many websites that offer lesson plans, activities, teaching strategies, and other resources to help you out. Here is a list of 15 sites that math teachers will find especially useful:

National Council of Teachers of Mathematics - The NCTM, a public voice in mathematics education, provides professional development strategies, lessons, journals, books, and other resources that can be used in a K-12 math classroom.

The Math Forum - This free online math warehouse offers lesson plans, activities, educational materials, teaching strategies, career development resources, and much more. The Math Forum also provides links to other resources that are useful for math education.

TeAchnology - TeAchnology, a huge database of lesson plans and classroom resources, is loaded with lesson plans specifically for math teachers. The lesson plans cover all grades, areas, and concepts.

Math.com - Even though this site was created to help students with math, Math.com features a variety of resources teachers can use as well. Under the teachers section of this site, you can find lesson plans, classroom resources, career information, standards, and other free resources.

Math-Videos-Online - This free online math site features math videos that teachers can use with their lessons to demonstrate important concepts. The site also offers interactive games, quizzes, and printable worksheets to be used in conjunction with the videos.

Rader's Numbernut - Rader's Numbernut is a site that contains interactive math games and activities for beginning and advance math. Teachers can use these activities within their lessons to illustrate important concepts.

Illuminations - The Illuminations site features a library of 103 activities that teachers can use with their K-12 students. In addition to the activities, this site also features over 500 lessons specifically for math.

TheTeachersCorner - Teachers looking for a wide range of online teaching resources will enjoy the lesson plans, worksheets, and activities offered on TheTeachersCorner. This site also features a message board, printables, bulletin board, and other general resources that teachers will find useful.

AAA Math - AAA Math provides a comprehensive set of lessons for K-8 students. The lessons come with unlimited practice to help students master concepts.

FREE - The Federal Resources for Education Excellence (FREE) features a huge list of teaching resources for algebra, data analysis, geometry, measurement, numbers and operations, and other math concepts. The teaching resources cover lesson plans, tools, learning activities, and more.

Discovery Education - Discovery Education offers free math lesson plans for elementary to high school students. The lesson plans are broken up into three sections for elementary, middle school, and high school children.

Mathematics Learning - This blog, created by an educator with over a decade of experience, provides math teachers with a place to find and share new strategies in the teaching of math. Throughout the pages of this blog, teachers will find resources, activities, and strategies that have been successful in other math classrooms.

Terri Husted - The Terri Husted site is designed specifically to give math teachers information and ideas on how to improve their teaching strategies. Throughout this site, you will find information on classroom management, new teacher resources, math activities, homework assessments, and much more.

National Library of Virtual Manipulatives - The National Library of Virtual Manipulatives is a free online activities site that teachers can use with their K-12 classrooms to visually demonstrate numbers and operations, algebra, geometry, measurement, and data analysis.

Math Drills - Math Drills provides thousands of free printable math worksheets that are great for assessing student's abilities, giving extra practice, and teaching new strategies.

Guest post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes for OnlineCollege.org, an online college resource.

Soal Latihan Integral

Kalau pada postingan sebelumnya saya menyajikan tentang materi integral seputar pengertian dan beberapa contoh soal integral tak tentu, integral tentu dan beberapa integral trigonometri, maka postingan berikut ini saya ingin berbagi beberapa soal integral yang saya comot dari beberapa tempat.

Seperti file saya yang lainnya soal latihan integral kali ini pun saya sajikan dalam bentuk microsoft

Motivation

Good thing to be thinking about as school starts. I'm a bit skeptical about Dan Pink, but several people I know and respect have a high opinion of him. It feels sometimes like he's selling creativity.

But on his recent TED talk, he reports (link to his talk) some social psychology experiments that help me understand a big divide in teaching: incentives in classroom management. A simplification of his point would be that incentives work best on simple, direct tasks. On more challenging problems rewards don't work and, in fact, impede. What does work? Choice! Autonomy! (Conditions of Learning chalk up another point.)

Plus he's pretty entertaining.

Picture click leads to a Florida reading teacher site.

Riddles and Reasoning and Math Teachers at Play 14

When is a carnival full of problems? Besides like every circus movie ever?

The new carnival is up, hosted this week by Susan Van Hattum at Math Mama Writes.

My favorites include the Math Recreation post on origami and a clever lesson using statistics to catch cheaters which also uses bad jokes.

The bad jokes thing reminded me of a lesson I use with riddles about reasoning.

Reasoning and Riddles
The framework David Coffey and I use for reasoning, based on the NCTM process standards of course, is:
Mathematicians are engaged in reasoning when they:
-Make sense of something (sorting, understanding a problem, interpreting a representation)
-Make a conjecture about something (initial answer, plan of attack, possible relationship)
-Make an argument for something (justification, verification, proof)

I then give the students a list of riddles and ask them to figure out the answers. As we look at their answers, and more importantly, how they got their answers, they generate lots of examples of making sense, making conjectures, and arguing for why their answer fits.
(General riddles and Halloween riddles are posted at my faculty page. Click the links for the pdfs.)

We then explore a more math-centric riddle (it's usually a geometry class):

Four Sided Riddle

1) Taking the clues for a mystery shape in order, put a checkmark next to the last clue you need to know exactly the type of shape that the mystery shape is. Then explain your answer.

1. It is a closed figure with four straight sides.
2. It has two long sides and two short sides.
3. The two long sides are the same length.
4. The two short sides are the same length.
5. One of the angles is larger than one of the other angles.
6. Two of the angles are the same size.
7. The other two angles are the same size.
8. The two long sides are parallel.
9. The two short sides are parallel.

2) Using one less clue than your answer to number (1), draw a shape that satisfies all those clues BUT is different than the mystery shape, or explain why this cannot be done.

There is also a nice Van Hiele connection here as students at different levels approach this task very differently.

Dinosaur Comics are perfectly qwantzian. Click the cartoon to see it full size, click the link to get to the web comic's home. (T-Rex does not always subscribe to human norms of taste and good form, obviously, so, at your own risk.)

Eventually I'll work all my favorite webcomics in here.

Running Out of Options

This game was a favorite for Paul Rettinger, a brilliant grad school room-mate I had at Penn State. He went from a Master's of Fisheries and Wildlife to a law degree. Amazing guy. I was lucky to ever win.

Last Letter Loses

Players take turns adding a letter to a word. The first player to be forced to spell a word (at least three letters) loses. A player can challenge the previous turn if they think there is no such word. If there is such a word, the challenger is out. If there is not, the challenged player is out.

Example:
1- A
2- A-M (doesn't lose because less than 3 letters)
1- A-M-E (P would lose, even if you're thinking of 'amplify', since amp is already a word.)
2- A-M-E-R (thinking of america)
1- (thinking they're in trouble) A-M-E-R-I
2- (happily) A-M-E-R-I-C
1- (inspiration strikes) A-M-E-R-I-C-I
2-(thinking what? that's not a word!) Challenge
1-Americium! I still would have lost but thought you might not remember that word. (It's an element.)

In that example Paul would have been player 1, snatching victory from the jaws of defeat.

(From a repository of free educational clipart, click the image.)

That inspired the following game, which I use to introduce prime number decomposition.


Last One Loses

Players take turns breaking down a number by multiplication. The first player starts with a whole number. The next player makes a string of two numbers that multiply to give the first. The next player then can break down one of the two numbers, making a three number string. The last player who can break it down is the loser of the game. Numbers chosen must be able to be broken down more than twice. A player may challenge if they disagree with a breakdown, or if they say it's the end but it's not. Players may not reuse starting numbers. 1 may not be used in the breakdown. You can't use a number that's been used this session.

Example 1:
A- 24
B- 3x8
A- 3x4x2
B- 3x2x2x2 - augh! (loses)

Example 2:
A- 112
B- 2x56
A- 2x2x28
B- 2x2x4x7
A- 2x2x2x2x7 - curses! (loses)

Instructional uses:
Have students keep track of which numbers make first player lose, and which numbers made second player lose. When the data is collected, students will see that the same number almost always has the same effect. (Although there's usually a number that was mis-factored.)

Pose the questions: what if you break the number down in a different way? Is it always the same number of steps? Is the end result always the same?

Several important ideas about the prime decomposition will come out immediately, including the idea of prime numbers! Also why 1 is not a prime. (And 1 is NOT a prime.)

I allow calculators for numbers bigger than 144. Follow up investigations can be things like: find a number that takes 6 steps and is between 500 and 1000, or trying the Sieve of Eratosthenes.

Materi Integral

Mengajarkan integral kepada siswa memang agak sedikit sulit, apalagi kalau dasar - dasar dari turunannya tidak kuat. Yup, turunan menjadi sangat penting untuk memahami materi integral karena sebenarnya integral adalah kebalikan dari proses turunan. Ketika materi baru sampai pada dasar - dasar integral mungkin siswa tidak terlalu kesulitan, tetapi ketika materi sudah mulai merambah ke integral

More Math Correlates to Higher Income

The blog where I saw the study referenced: Free Exchange at the Economist.

The study the blog is citing: Joshua Goodman

The cartoon that teaches correlation:


(XKCD is occasionally profane, almost always funny, and frequently geeky. Clicking the cartoon leads to the site.)