Literacy With Flipgrid or Google.

 I love the idea of having students explain their thinking but so many of them can do a selfie but won't speak in front of the class.  That is where Flipgrid or Google comes in as they allows students to share but allows them a chance to do it without being watched by everyone else.

Fortunately, there are ways to encourage literacy while allowing every student the chance to do something.

1.  One way to encourage literacy is to have students present work on the board, explaining how they solved it and answering  other student questions.  For students who have problems speaking in front of the class, they can record their explanation on Flip Grid and share it that way.

2. Give students a problem to solve.  They work their problem on a google slide and then take time to explain how they reached their solution but first you have to teach them what constitutes a good explanation.  Students should use steps, explain how the step applies to the line they just did, and why they chose to use that particular step.

3.  Have each student rework a problem they missed.  They need to explain what they did incorrectly and how they should have done the problem to get the right answer.  This can be done via Google slides or Flipgrid.

4. Ask students to produce quizzes with answers for each other using google quiz forms.  The teacher needs to set the rules for the construction of the quiz.  Once everyone has written their quiz, the teacher can share links with other students so each students takes the quiz of at least one other student.

5. Have students write a letter to their friend using Google Docs to explain how to do a certain problem or explain the lesson they missed when absent.  This requires them to provide a written explanation of the concept or lesson.

6. Set up a class discussion site where the teacher posts a question and requires students to place their answer on the site.  The teacher will be the moderator and it is up to the teacher to decide the rules for student commenting on other's entries.

7.  Use exit tickets via Google or Flip grid.  Exit tickets can be a question on how to solve something, or requires students to reflect on their understanding of something, or even a question as simple as "What do you need to work on for the upcoming test.

8.  Divide student up into pairs and assign two problems to each duo.  Then on Flipgrid, one student explains how to do their problem to the other and then they switch but before they switch, the listening student must be given a chance to ask questions.

These are just a few ways to help increase literacy in the math classroom because it gives students the opportunity to develop their ability to communicate their thinking which is essential. Let me know what you think, I'd love to know.  Have a great day.

Warm-up

The bamboo is 3 feet tall and growing at a rate of 31 inches per year.  How long will it take for the bamboo to reach 80 feet tall?

Warm-up

If bamboo spreads at a rate of 3.5 square feet per year, how long will it take to cover 128 square feet?

Active Listening

 Most of us listen but do we actively listen? Do our students actively listen?  Do they even know how?  None of us naturally practice actively listening, we have to be taught and that includes our students.

In math, it is especially important for students to listen to the ideas of others so they can make meaning of everything they hear.  Listening does not mean just being quiet, it means making a conscientious effort.

Although many think that hearing and listening is not the same, they are not.  Hearing refers to receiving sound while listening is receiving ideas and thoughts and comprehending them.  So we need to teach them to be participatory learners so they can interpret and make meaning from others verbal ideas.

There are certain steps we can take to help students learn active learning.

1.  Take time to teach students the difference between hearing and listening.  This means students stop to examine the difference between hearing and listening and helps them be more aware of which one they use during conversations and discussions.

2. Model Active learning for your students.  Ask another teacher to come in and help you demonstrate what active learning looks like.  Include "Think Alouds" so students know what your thinking is during the process.  Things to think about include "what did you actually hear?", "What might you be wondering about?" in terms of what was just said, "What new ideas pop into your head as you listen?" so students see what type of thinking goes on during active learning.

3. Schedule some time for students to practice active listening by sharing a mathematical thought with them and afterwards ask them what they heard, what they understood from listening, and did anything pop into their minds from the thought.

4. Set things up so they can actively listen better by minimizing distractions, change the seating so it is better for both speaking and listening, and go over their responsibilities as listeners before beginning the discussion.

5. Encourage students to practice active learning in all their classes.  In addition, speak with other teachers so students are offered the chance to practice active learning across the curriculum.

6.  Another way to practice active listening is to share three things with your students.  After each item, pause so students can discuss what they heard with one other person (pairs work).  At the end, have one student read a paragraph from the textbook while the other would say what they heard as they listened.  Then they switch.  Both of these activities give students a reason for actively listening.

7.  As students are learning active listening, provide a two column paper so one side is labeled thoughtful questions, while the other side is labeled thoughtful comments.  This way students can write down questions and comments that pop into their heads as they are learning.  This also helps students focus on what is being said so their minds are less likely to wander.

Basically, active learning boils down to paraphrasing what the speaker said  so you show you are listening and to show your understanding, summarize what the speaker said into one or two sentences  including key words, ask questions to clarify what is heard and to encourage the speaker to expand on certain things, make connections between what the speaker said and the listeners base of knowledge, and reflect on what is said by sharing a comment.

These are some ways to help students become active listeners and when they practice active learning, they learn more.  Let me know what you think, I'd love to hear.  Have a great day.

Suggested Reading For Older Students

 A few days ago, I wrote about certain reading techniques to help students accomplish deeper reading but most of the time, we tend to think about applying them to textbooks but what about fiction.  I am aware that it is easy to find picture books and books made for elementary kids but many high schoolers wouldn't want to read those.  Today, I'm providing a list of books for middle school and high school that are math oriented but real books.

1.  The Math Inspector 5 book series by Daniel Kenny and Emily Boever, and good for students aged 9 and above or 3rd grade and above.  I'm starting here because I usually have a couple of students in class who do read that low and struggle to read the textbook.  The books are between 150 and 200 pages long and every book in the series has received between 4 and 5 stars on Amazon.  The book involves several young friends who banded together to start their own detective agency where they investigate a jewelry store heist, serial vandalism, a toy store mess-up, trying to save a roller coaster, and a mine.  These detectives use their math skills to ultimately solve the crime.  The books can be found in hard back and e-book form.

2.  The 3 volume Math kids series rated for upper elementary is another one to look at for students who read well below grade level.  The stories revolve round three students who make up the advanced math group in their class and they form a math club where they solve mysteries. They solve a case on neighborhood burglaries, a kidnapping, and a theft.  This series also received between 4 and 5 stars on Amazon.

3. Do the Math Series is a two book series for older students. The first is Do the Math: Secrets, Lies, and Algebra  and the second is Do the Math: The Writing on the Wall  both by Wendy Lichtman. In the first book, an eight grader begins Algebra and faces one missing test, three cheaters, and a math whiz make Tess's live interesting as she learns about life and variables.  The second one shows Tess that life is filled with patterns including the patterns of graffiti found on the walls.  These books are recommended for middle school to high school. These books are rated between 4 and 5 stars according to Amazon.

4. The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger contains 12 dreams telling of how a math hating young man meets the number devil and learns more about math.  He learns about prime numbers, infinite numbers, Fibonacci numbers, and so many other numbers.  This book is geared for middle school but would work for high school students and has between 4 and 5 stars according to Amazon.

5. The Man Who Counted , written by Brazilian mathematician Malba Tahan.  The main character, Bermiz Sahir show the reader how math can be used to settle disputes, give advice, and in the process learn about historical mathematicians.  These short stories are considered to be similar to Arabian tales and each one shares something with the reader.  This book is rated between 4 and 5 stars on Amazon.

6. Humble Pi: A Comedy of Math Errors by Matt Parker for students who read at a higher level.  In this book, the author examines situations where the incorrectly done math cause issues.  He shows how no one notices the math until it is done incorrectly such as when a misplaced decimal caused problems with the stock market, or when someone converted measurements incorrectly so a plane crashed or someone divided by zero causing a ship to stop in the middle of the ocean.

Think about having a few of these in the classroom for those days that your period is shortened due to a last minute assembly, or you have a regularly scheduled short period you can't use for much else.  These would be good for practicing the skills they learn in English but in Math.  Let me know what you think, I'd love to hear.

Dolores Richards Spikes

 Just the other day, I was talking with someone about mathematicians and I realized I could name more male ones than female ones modern or ancient.    I think it might have to do with more males are listed in textbooks for most of the standard theorems.  So I decided that every so often, I'd highlight a female African American mathematician who was not one who worked for NASA but had a career that changed things.

Dolores was born on August 24, 1936 to Margaret and Lawerence Richards in Baton Rouge, Louisiana.  She attended both parish and public schools through elementary and high school to get her high school degree but she grew up in a household that encouraged her to attend college because neither parent graduated from high school.   In 1954, she began attending Southern University and in order to pay for it, her father worked a lot of overtime.   Three years later, she obtained her B.S. in mathematics and joined the Alpha Kappa Alpha sorority.

Upon graduation, she attended University of Illinois at Urbana - Champaign working towards her Masters degree of mathematics.  When she graduated, she returned to Louisiana and took a job teaching at Mossville High School in Calcasien Parish in 1958, the same year she married Herman Spikes.  She improved the ratings of the school by implementing independent study courses before returning to Southern University in 1961 to teach mathematics as an assistant professor.

She applied for and received a National Science Foundation to attend LSU in 1966, to work on her Phd but she was only able to go there for one year but in 1968, she received a three year Ford Foundation Fellowship that allowed her to attend college to continue her education.  In 1971, she earned the distinction of becoming the first African American to receive a PhD from Louisiana State University and was immediately promoted to associate professor of mathematics at Southern University.  She earned a PhD in pure mathematics specifically focused on commutative ring theory with. her thesis on "Semi-Values and Groups of Divisibility". Then in 1975, Southern made her a full professor and six years later she was appointed to as a part-time assistant to the Chancellor of Southern and coordinator of the mathematics program.

One year later, she became full time assistant to the Chancellor and remained in the position for three years when she was appointed as executive vice-chancellor in 1985 and later vice-chancellor for Southern University Baton Rouge.  Later in the 1980's she became the first female chancellor of two different Southern University campuses and later on, she became the first woman president of both the Southern University system and the  A & M college system.  In 1996, she became the president of  the University of Maryland Eastern Shore for five years.

Before her death, June 1, 2015, she received numerous awards such as the Thurgood Marshall Educational Achievement Award, the Thurgood Marshall Scholarship Education Fund Leadership Award,  and was named as one of the most influential black women in America by Ebony magazine.

and served as an adviser to historically black colleges.  She outlived her husband who died in 2008 and her only daughter who passed in 2010. Dolores managed to set several firsts in her career. I plan to touch on minority mathematicians every so often so we can tell our students about them.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If the White Cedar is only 4 inches tall after 155 years, what is it's average yearly rate of growth?

Warm-up

If a Empress Tree can grow 6.5 feet per year on average, how long will it take the tree to reach it's full height of 40 feet?

Helping Students Deeper Read Digital Material

 This past Wednesday, I spoke about the differences between reading hard copy and digital materials.  Today, I thought I'd look at some of the ways to help students learn to deeply read digital materials since there seems to be a shift that way.  Even many adults are reading using digital devices.  I do because it is easier to haul a reader with me than to haul several boxes of books.

Many of the strategies developed for use with digital books have been adapted from ones used with regular books.  Students need these digitally applied reading strategies because digital books are so new, the research is just catching up with the use of books and students need the skills to learn best.

1.  Heading and Highlighting Strategy - using Google Docs, post an excerpt of the digital article you want them to read.  It could even be a part of the textbook.  Ask students to open the document and read it to themselves.  They should highlight the words they do not understand.  Next divide students up into groups of two and have them read one paragraph or section highlighting the key topics.  After they've spent a few minutes on this, ask them to come up with a four word heading based on the key ideas they identified and write it on their copy of the document using a document outline tool.

As students to type the four word heading into a google document set up for this activity.  Have students compare headings to see how their differs before discussing why theirs is better than the others but they do not act on anything yet.  This means they have to dig deeply into the text to come up with a four word summery.  Then  combine pairs into groups of four who decide which groups heading is the best for the selection.  At this point, have the groups share their choice and write them on the board.  Let the students vote on the best four word heading after they've had a chance to discuss all the headings.  Although this can be done with pen and paper, it is a good way to have students achieve deeper reading of the digital material.

2. Highlighting strategy - is a strategy that takes highlighting a step farther than just coloring an idea. When students open the document and then get the highlighter add-on that allows students to assign various colors to various ideas and then the information can be exported to create a table with all the ideas.  Rather than just highlighting, students are getting a chance to organize the materials into something that helps them read the material better.  Once they have the table, they need to add another column and they can summarize the ideas for each color in the new column.  This asks them to reflect on what they've highlighted and they learn to consolidate the information.  This site helps explain how to use the tool.

Furthermore, this same highlighting can be used for new vocabulary words where they can define the words in the chart.  It can also be used for examples for students to identify steps that are the same across several different examples so students see how things work.

3 GSSW: Gather, Sort, Shrink, and Wrap is a method that could easily be used on digital material to help students with deep reading.  For the gather stage, students break up into pairs where they will read the material out loud while looking for ideas that seem to stand out or lead to other ideas.  The other way to do this is for the teacher to read the material out loud stopping on a regular basis so students can discuss the material and take a few notes.

Sort is where the class groups ideas to help students retain and understand the material better.  Students can work in groups and list the themes together digitally such as on a google slide or a padlet or similar app.  This often leads to discussion on what the theme is or what the steps are.

In shrink, students distill the list of themes into essential thoughts that are expressed in their own words via several sentences.  Each sentence represents a depth of knowledge and real understanding and are at a place where they should be able to explain the material to someone else.

The final stage is wrap in which students summarize the material and share it out in a mind map, graphic organizer, presentation, or other form.  As the student follows the process from gather to wrap, they find, distill, and organize the main ideas so they've accomplished deep reading and better understanding of the material.

Just a few ways to teach students so they can develop deep reading when using digital material so they spend more time on the actual material rather than skimming over it. Students need these strategies to develop deeper understanding of what they are learning.  Let me know what you think, I'd love to hear.  Have a great day.

Reading - Hard Copy vs Digital.

  So many companies are now offering digital versions of their textbook and other materials.  I linked to digital copies of the textbook and student journal for students who wanted to work on the actual work but I began wondering if the brain operated any differently between reading hard copy and digital.

Reading is a skill that has only been around for about 5000 years, give or take a few.  When a student is first taught to read, they have to retrain certain neural pathways to carry out reading.  Even before students learn to read, their brain areas associated with language, understanding, and vision are all engaged.  This happens when students listen to a story being read, they visualize the events throughout the story and the area that allows the visualization to happen is the same area students use when reading at a later age.

One study discovered that the more screen time a student has, the more decreased connectivity the brain undergoes in regard to the part of the brain associated with reading.  In other words, the brain is less able to coordinate areas of the brain associated with reading and those responsible for language, vision, attention, and concentration.  On the other hand, the more a student actually reads, the better their brain is able to coordinate areas associated with reading, language, vision, attention, and concentration.

Furthermore, neurologists have discovered that your brain uses different parts of the brain when reading an actual book vs reading the same material on a digital device.  They have found that the more time you spend reading on a digital device, the more likely your brain will engage in "non-linear" reading.  This practice is where your eyes skim a page or dart around a web page.  You no longer read line by line.

Unfortunately this leads to a loss of deep reading where we no longer immerse ourselves in our reading because we are concentrating on the material.  It is also the process you want to do when you read dense text such as a legal document or a contract.  When we read on a screen, we are not as focused on reading and are more likely to skim through everything.  In addition, it leads to increased stimulation due to all the available reading material.  One way to counter this is to have students spend a certain amount of time every day, reading a physical copy of a book or magazine.

Another study indicates that when students have digital copies of textbooks, they are more likely to be distracted by the device itself because it is easier to multitask on the device. Furthermore, students tend to multitask and it takes them longer to read the material.  It also appears that more students enjoy reading when using books than those who read the same book on a device.  In addition, when parents read a story to children using a device, children seem to recall fewer details than if the parents read the same story from a book.

It also appears that students who read from a physical book tend to have higher comprehension scores than those using a digital device unless the digital book was carefully constructed so it supports reading, then the comprehension scores are about the same.  One interesting result coming out of one study is that students who use digital devices seem to better at answering concrete questions but do not have good note taking skills while students who read books are better at answering abstract questions requiring inferential reasoning.

The bottom line when reading a physical book is that it allows us to slow down so we are better able to practice deep reading, practice critical analysis and thinking, develop empathy and so much more.  Since digital device is here to stay there are strategies we can teach students to help them develop more linear reading habits and I'll cover some of those on Friday.  Let me know what you think, I'd love to hear.  Have a great day.

You Have A Word Wall. What Now?

  I keep a word wall going in my room.  Every time, we start a new section, I add the words but I seldom do much more than post them.  This means, I am not using my word wall effectively.

Most students never pay attention to the words you post on the wall unless you have them do something with them. So I took time to find things I can do with the word wall to make it's presence more effective.  I've found some activities I hope to include with my class this coming year so students take a more active part in learning the words.

1. Give the students clues about the word and have them choose the word from the wall.  The clue could be something like "I have four 90 degrees and four equal sides."  The students would answer "Square".

2.  Assign each student or pair of students one of the words.  They can look through magazines to find pictures that represent the term and use the pictures to create a collage.  This activity could also be done with an app and picture sites such as pixabay.com.

3. Create cloze sentences in which students find the proper word to fill in the blank.  The sentence might be something like "The car stops at the three sided sign which is shaped like a __________".

4.  Assign each student a different vocabulary word.  Let them create word webs that remind them of the vocabulary word.  If they don't want to use words, they could use pictures but all the words need to relate to the vocabulary word.  If a student is given cube, they might use words like six faces, equal sides, boxes, and others.

5. Organize a Pictionary game with groups of four.  Divide the group of four into pairs of students.  One student will draw a picture to illustrate the word while the other pair tries to guess the word.  When they guess the word, they sides switch and repeat.  if you'd rather get more movement, have the students act out the word.

6. Divide the students up into pairs and let each student select a word.  The students have to figure out how the words are related.  Some relations might be the terms might have similar or opposite definitions, or perhaps they describe each other.  Then have the pairs share their answers with the rest of the class because it gives students a chance to see the relationships others find.

7. For this type of activity, I'd let students take pictures of the word wall before beginning the activity.   When you are ready to begin, name a math topic such as "types of three dimensional shapes", students look at the words on the word wall and find words that match the topic.  Other uses might be to have students find words that mean the opposite of each other such as parallel and perpendicular.

8.  Have students create a Freyer model for each word.  To make them more effective, you might change the headings to  "Definition/Description" with more than just a minimal definition.  Use "Good Stuff to Remember" where students might record all the possibilities.  Include several examples under examples and not examples.  In addition, when students put the word in the middle, they might also include other names that mean the same thing.  For instance, if the student is defining scatterplot, they might also write scatter gram, correlation graph, or scatter diagram because they are all names for the same thing.

9. Give students a chance to be artistic with doodle links.  The teacher reads one vocabulary word off the wall and waits for about 30 seconds while students create a doodle, sketch, or picture of the word, then they draw a line to the next place they draw another word.  This continues so all sketches, doodles, or pictures are connected with a single line and at the end, have students go back through and label all the drawings without looking at the word wall. Finally, have the students call out the words in unison at the end.  It is recommended that they do between seven and fifteen numbers for this activity.

10. Remove the words from the word wall, mix them up, and let students place the words back up on the wall in an organized manner.  This means students have to think about the words and the way they are related.

11. Instead of just putting words up on the word wall, add pictures or visuals and have students connect the word with the visual using yarn or string.  To add more depth to the wall, include examples for students to connect to the word and drawing.

11a.  If you want students to learn more about all the meanings of a word, include the non math definitions and illustrations for students to connect to the math word.  Since math vocabulary often has several layers of meanings, include those on the board.

Another way is for the teacher to place the word on the wall and have the students create examples, and pictures for each word or the different definitions, math and non math to place on the board.  When students create the rest of the word wall, they are more likely to understand the words.

12. Play the "Flyswatter game" where the class is divided up into teams.  The teacher has two students (one from each of two teams) go up to the wall carrying only a flyswatter.  The teacher gives a clue and the first student to swat the correct word, earns their team a point.

Have fun trying some of these things out in your class next year.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

Could you  figure out how far it is from where you are standing to the top of the stairs just from the photo?  Are there any basic assumptions you could make based on the picture? Explain your answers to the two questions using explicit reasoning to support them.

Warm-up

Look at the picture.  Figure out at least two ways to determine how long the ladder is.  Explain in detail how you would obtain the information to calculate the length of the ladder.

Vocabulary Activities For Math

 Vocabulary is such an important part of teaching math because many of the words used have several meanings, some of which may not deal with math.  If a student has a good mathematical vocabulary, they will also be more proficient because the vocabulary offers them the ability to access concepts.

If students develop a good mathematical vocabulary it helps them understand exactly what the question is asking.  As mentioned before, many mathematical terms have both a general meaning and a specialized meaning and it is important for the student to know both.  Many times, there are students in the class who are English Language Learners who may not yet have acquired all the vocabulary needed to do well in mathematics. When students have a good vocabulary, they are able to participate in mathematical discussions with more ease because they can express their ideas properly.

When teaching vocabulary in class, it is important to begin with the vocabulary they already know before introducing the mathematical vocabulary.  The vocabulary they have may be informal in that they describe a rhombus as a diamond due to the shape.  The teacher would then affirm it did look like a diamond and was called a rhombus.  In other words, repeat back the language used by the student to include the correct mathematical terms because it acknowledges the student has some base knowledge.  It is important to use the mathematical language even if it is paired with a regular description such as area or the inside part of the shape so they build an association between the word and a definition.

Second, the words must be taught explicitly to the student and they must be given a chance to use the new vocabulary so they learn it.  The words can be introduced in a pre-teaching session, taught during the actual session by using definitions, pictures, drawings, and examples.  Post the vocabulary on a word wall or have students write them into their personal dictionaries they are making.  Afterwards, review the words by having students define each new word and provide both an example and non example of the word.  Always teach and use the words in context.

Next, have a classroom word wall to post the new words along with pictures and definitions of each word if the picture is not enough.  For instance, if the chapter has the word line, you might draw a straight line all the way across the page.  Most high school students know what a line looks like so you may not need a definition but you might need to include a definition for the word "betweenness". 

Another possibile activity is have students fill out vocabulary cards using the Freyer Model.  If you haven't used them, they are great because they have students have students create definitions, list characteristics of the new world, provide examples and non-examples to show what it is and what it isn't.  The word always goes in the middle.  If you do a quick search, you can find templates that have several on each page.  

Finally, use math journals to help reinforce the use of mathematical vocabulary.  At the end of class have students use a writing prompt to think about the lesson itself.  One such prompt could have students begin "Two ways to solve this problem are........." or "One problem I solved was........".  These types of prompts have students reflecting on what they learned and on the concept taught in class.  It encourages self reflection.  

Sometime in the near future, I'll talk about ways to use word walls and writing prompts in class to help them develop a better mathematical vocabulary. Let me know what you think, I'd love to hear. Have a great day.

Poetry in Math

Poetry is not one of the first things you associate with math. In fact, poetry is usually only thought of as something taught in English or language arts classes. With the move to create cross curricular materials, why not try out poetry in math.

Believe it or not, poetry and math have quite a lot in common.  Both require a preciseness of thought to express ideas exactly as wanted.

There is at least one website, called "Intersections - Poetry With Mathematics"  that collects mathematically based poetry into one place.  Some of the topics covered by the poetry include primes, geometry, circles and so much more.  JoAnne Growney is responsible for creating this blog and finding all the poetry that is either on the subject of math or based on mathematical rules.  So far, she has managed to find over 900 entries so you'll have a lot to choose from.

If you would rather have students try writing poetry, there are so many different possibilities to use in class.  Haiku is a good one to start with as it has a very specific form and isn't very long.  It consists of three lines with 17 syllables total.  The first line has 5 syllables, the second line has 7 syllables, and the third line has 5 syllables.  If your students would like a few samples, this site has several written by several calculus students.  This site with a few Haiku examples written by a retired math teacher and they could be used to introduce the topic of Haiku so students can see the actual structure.

Another possibility is using sonnets in class since sonnets also have a specific form.  I admit, I only took the minimum number of English classes to graduate from college but fortunately, I found a nice site with great information on sonnet writing.  It gives you the exact structure and steps to use to write one.  Furthermore, it even explains how the sonnet tells a story, breaking down a poem showing how each group of lines contributes to the story.  To introduce mathematical sonnets, look at this site or this site.  On the other hand, let the English teacher introduce sonnets in that class so you can have students write them in yours.

There is a type of poetry based on the Fibonacci sequence call "Fib".  The numbers represent the number of syllables in each line so if you look at the sequence of 1, 1, 2, 3, 5, 8....... you poem would have one syllable in the first line, one syllable in the second line, two syllables in the third line, three syllables in the fourth line, etc.  This site has a nice example of this type of poem.  This type of poetry has been around only since 2006 or so when Gregory K. Pincus created it.  It is know a recognized form of poetry.

Then there is the "Snowball form" of poetry which can be found in two forms. The first is where you start with one word or syllable in the first line, two words or syllables in the second line, and it continues adding one word or syllable to each following line until the poem is finished.  The other form follows the same pattern until the fifth line and then begins decreasing a word or syllable for the next few lines until you are down to one word or syllable.

Finally is the "N + 7" form in which you take a poem, any poem, but it is recommended it be a relatively short poem.  You also need a large physical dictionary because you replace each noun with the next noun that is seven words away in the dictionary.  This site explains the process in more detail while this site has examples of the snowball, fib, and N + 7 forms.

Think about getting together with the English teacher to work together during a poetry unit.  It is easy to spend 10 or 15 minutes over several days and then share the poems at the end of a week or so.  Some schools have poetry events to share student written poetry.  Let me know what you think, I'd love to hear.  Have a great day.

Math Centers part 2

 This past Friday, I talked about what is needed to think about when using centers in middle or high school math classes.  Your centers might not be physical centers as one would do in elementary.  Instead they might use technology to complete centers.

One thing to remember about math centers when dealing with older students is that you can have the groups do one center each day.  So it might take the whole week to rotate through so the students had a chance to visit every center.

1.  Matching activities are excellent for math centers as they can be done with lot's of different topics such as order of operations, simplifying expressions, connecting equations with graphs, or connecting transformations with the equation.  There are so many ways this center can be done.

You can have students match the equation with the graph for so many different types of equations from simple one step, to natural logs, to trig.  Then they can practice simplifying expressions by matching all the correct steps from the choices on the table.  Or practice matching distributive property with the beginning and ending equations or expressions.  You could even have a matching exercise that matches reasons with steps in an equation.

2. Ordering activities can be used to order integers, fractions, or decimals.  The ordering activity could also have students take the steps and order them correctly so the problem shows every step from start to finish.  You could even use an ordering activity to review the steps involved in graphing something.

3.  Assign some sort of game, either via pen and paper or via an online site.  One game I like to use has two pair of dice in two different colors.  One color represents positive numbers while the other color represents negative numbers.  Students roll two positive dice to get the two numbers to fill in the blanks ( x +  )(x +  ) before they practice multiplication of binomials.  They repeat with two negative numbers and then one of each.  This could also be done with cards.

4.  Ask students to create a visual representation of the concept using manipulatives.  Once they have the representation, they can take a picture and post it to Flip grid or similar program. Research indicates that students when they create a visual representation on their own, have bridged between concrete and abstract.

5.  Have a vocabulary center focusing on the vocabulary associated with the current unit.  They can do a Freyer model for each word or perhaps create a video to illustrate the word.  In addition, make sure something at this center allows students to discuss the different meanings of each math word. For instance, product is the result of a multiplication problem but it also means something that is made by a company and sold.

6.  Every so often, put in mathematically based art so students see that math can easily be found in art.

7.  Have students create a short video showing pictures with short explanations of where math is used in real life such as in carpentry, they use the 3-4-5 triangle to make sure corners are square, measurements using standard or metric, fractions for screw sizes, etc.

What is in each center is limited only by your imagination.  If you don't have time to set things up, you can find some ideas already prepared at pay for use sites but if you do a look at the internet, you'll find ideas.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

The pie pan is 9 inches across at the top.  What is the circumference of the pie pan at the top?

Warm-up

The cake is 8 inches across and 3 inches tall, what is the volume of the cake?

Ideas for Preparing to Use Math Centers

  I often wonder why we do not usually use centers in middle or high school.  It seems that by the time students arrive in the upper grades, they are used to a more lecture based type lesson.  There are some activities that could easily be done in centers.

First of all, centers allow students to take a more active role in their learning.  Centers can be used at any stage in the learning process from introduction of the material to review and assessment.

Secondly, centers offer students the opportunity to choose which activity they want to do in what order.  Usually teachers have a specific order they deliver a lesson to students but with centers they can choose the activity they want to start with.  Furthermore, the use of centers helps foster the ability for students to work independently.  It also helps with classroom management because as students finish their current activity, they can move on to another.  In addition, centers can make it easier for teachers to differentiate so both students who struggle and who are advanced will have their needs met.

To successfully use centers, you have to plan everything ahead of time otherwise their use may not be as effective as they could be.  One of the first things to determine is how much time are you able to have students work at centers.  Will it be every day or three times a week.  Once the time issue is decided, you need to set up all the rules and procedures on how the centers should be done.  You have to decide if students will be working individually, in pairs, or in small groups.  What should they do if they finish early?  How will cleanup be handled? How are students expected to transition into center time and then how will they move from center to center?

Once you've got your procedures down, the next step is to plan for the centers themselves.  The planning covered everything from what concept is being addressed, to what is the activities will be used for that concept, to materials, and the number of centers total that are planned.  It is suggested the teacher keep a binder with daily and weekly planning sheets so you know the concept and materials for each center.  One should also have a binder where the master sheets and instructions are stored for every center.  It also helps to have materials organized according to concept and center so you spend less time having to prepare.

When you start using centers in class, it is important to go over both expectations and procedures with your students.  It will take several times before students get the hang of using centers.  When looking at designing activities, remember to vary the type of question and the way questions are designed so students do not get used to questions only being asked one way.  Questions can be written in several different forms such as true or false, correct or incorrect, multiple choice, short answer,  matching, or fill in the blank.

In addition, if you ask other types of questions make sure they are open ended rather than closed.  Instead of asking how many sides a square has, you might ask how a square and a rectangle are similar and different.  If you are asking question, do not ask simple questions such as "Round 12,438 to the nearest hundreds".  As them a more complex question such as "You have a number that rounds to 700 when rounded to the nearest hundreds, but rounds to 750 if you round it to the nearest tens, what are three possible numbers that match the criteria?". Do not forget to provide visual, models or manipulatives for each concept because this is the intermediate step between concrete and abstract.

Finally, be prepared to troubleshoot problems during the use of centers in class.  For instance, how do you handle students who are off task, finish early, students who do not engage in math talk, students did not get through all the stations, or cleanup can take longer than expected.  Think about these situations and decide how to handle them before beginning the use of centers in class.

On Monday, I'll address the question of activities one can do in middle school and high school math classes.  Let me know what you think, I'd love to hear.  Have a great day.

Teaching Error Analysis in Math.

 Many math teachers do not take time to have students analyze errors to learn more.  I know most of my students would rather not look at any problems to see what they've done incorrectly.

Learning to look at errors and analyze them is an important skill. There are several reasons to teach students to perform error analysis.  First, this promotes higher level thinking skills because it requires students to create, analyze, and proving hypothesis, thoughts, and ideas.

Secondly, it helps students connect the conceptual with the steps needed to solve a problem.  When students focus on the process, they often loose sight of the concept associated with the problem.  When they are able to find the mistake in the process and explain the error, they are showing they understand the concept.  Finally, it helps students prepare to take tests with multiple choice questions.  If they find an answer that is not one of the choices, they can review their math to find the errors.

There are some activities one can include in class to help students learn to analyze to find errors.  It is important to use these activities to help students learn to analyze their work for mistakes because most do not know how to do it.  I know from personal experience most of my student's analysis before they learn to do it usually consist of "I didn't know how to do the problem" or "I have no idea".    In addition, learning to analyze mistakes helps students develop their ability to communicate their thinking.

No matter what the error is in the problem, students need to rework the problem correctly so they get the expected answer.  It is not enough just to identify the error but they still need to do the problem correctly.  Both parts are needed for students to complete the error analysis.

One way is to assign a problem to students to work.  Then collect the solutions and check them quickly to find the ones that were done incorrectly.  Choose on of those to have students look and see if they can figure out what was done incorrectly and what needs to be done to do it correctly.  The other choice is to do a problem incorrectly and have students identify the error and how to correct it.  Some textbooks now have problems in each section in which allow students to practice their error analysis.

Create a gallery walk with several problems done incorrectly on them, spaced around the the classroom.  Divide the students up into groups of two or three and have them go through and find the error on each sheet.  You can have them write down their solutions on the sheets or on a separate sheet of paper.  By putting students into small groups, they need to discuss the error and it improves their communication skills.

It is suggested that students stop erasing mistakes as they do the problem.  Instead, have them circle the mistake and explain what it was before continuing to the end of the problem.  This teaches students to avoid making the same mistake in the future and it shows students that making mistakes is a part of the process.  It helps students accept that making mistakes is fine but you need to use those mistakes to learn to do the problems correctly.  Furthermore, students have a way of helping themselves assess their understanding.

My next entry will be about using centers in middle school or high school math because one center can be on analyzing errors.  Let me know what you think, I'd love to hear.  Have a great day.

2 Math Tricks To Impress Your Students With!

 If you look at various books and workshops, there is a move out there to create a hook to capture your student's interest.  Many of the suggest hooks are harder to implement in math but there are things you can do to capture their attention.

This is one popular trick from the 1990's that could be used in the class.  It is one magician David Copperfield has used as part of his magic act.

On 12 index cards, write the numbers one to twelve on them.  Arrange the cards in a circle so it resembles a clock face.

Have the students choose one number from the face of the clock. They then spell out the number beginning at 12 and moving clockwise.  For instance if they choose six, they would start at 12 and spell out s-i-x so they move through one to two and end at three.  Now you should be on the number 3.  You would spell out three so you'd move 5 spaces to the number 8.  Now you spell the eight beginning at the number 8 so you should end on the one because you keep going.

At this point you tell students that you do not know what number they are one but you know they are not on the 2, 4, 8, or 12.  Once those numbers are removed, have the students spell out the letters of the number they'd last landed on which in the case of the example is one.  They simply skip the spaces of the missing numbers.  So I spell out one and end up on the number 6.  At this point, you tell they they can't be on the 10, 3, 9, , 1 or any other number but the six.

No matter what number you select, if you follow this sequence, you will always end up on the 6 because it is based on the Kruskal count, named for mathematician Martin Kruskal.  The Kruskal count which is a special case of the absorbing Markov chain and is based on the idea of when the probabilities line up, people end up with the same number.  This site has a youtube video which shows the trick and then explains the math behind it.

Here is another math trick based on cards.  Make sure you have a full deck of 52 cards.  You can shuffle them or have someone else shuffle them.  Count out any 9 cards from throughout the deck.  You might want to count three groups of three out from the different parts of the deck.  Have the student select one of the 9 cards.  Place the card the student chose on the top of the 9 cards and you put the remaining cards on top of the students cards.  If you want you can get fancy with a couple of small fake cuts or you can move on to the next part.

Now you are going to make four piles but before you begin counting down from 10, you have to know that all jacks, queens, and kings are worth 10 while the ace is one.  So begin by turning the top card over and say 10, then the next card and say 9.  You continue doing this until the number of the card matches the number you just said.  When that happens, you stop and begin a second pile.  If you get all the way to one and none of the card values match the count down number, you place a card face down and go to the next pile.

When you get finished with the fourth pile, add the face values of top cards for all four stacks and that tells you what position the card the student chose is in.  If you have cards covering all four stacks so no values show, that last card on the 4th pile is the chosen card.  If you have trouble following my directions, check the video that explains it here.  So now you have at least two tricks you can use to start your class and grab student attention.  I hope to cover a few more later in the summer.  Have a great day and let me know what you think.