Math Brain Teasers

 

For warm-ups we tend to use problems students have already done, new problems to provide review, begin a 3 act task, or even use "What do you notice? What do you wander?" but what about using a brain teaser?  

Math brain teasers by definition encourage students to look at math in a different way. If the brain teaser is associated with the topic being taught, it provides a natural hook otherwise, it makes a great change of pace for the warmup.  

The nice thing about brain teasers is they require students to  use critical thinking skills, logic, and develop problem solving skills.  Furthermore, it helps improve reading and comprehension ability because they have to read brain teasers carefully and understand what information is needed.

In addition, brain teasers can help students feel a sense of accomplishment when they find the answer, improve memory and additional cognitive skills including the speed of processing done by the brain. Furthermore, brain teasers stimulate students to think quickly and critically while helping to increase student participation and engagement.  They also help students develop reasoning ability.

Brain teasers can be done as part of the warm-up, between activities to give students a break from instruction, a break for stimulating thinking, an exit ticket, or use it as a once a week thing.  

Brain teasers can be used to further math skills especially if it is presented as a riddle, puzzle or game.  You might couch a problem like "If 6 transforms into 13 and 14 transforms into 29, what does 15 transform into?"  This problem asks students to find the rule of 2x +1 where x is the original number.  2(6) + 1 = 13, 2(14) + 1 = 29 and 2(15) +1 = 31.

Another way is to create a trick question which has a play on words or a bit of a pun but requires extra attention.  One question might be "I am odd and if you remove one letter I am even. What number am I?"  The answer is a play on words so the number is 7 because seven is odd but when you remove the s you are left with the word "even".

The hard thing sometimes is finding brain teasers or riddles one can use in class so I've assembled a list of sites with ready to go material.

1. Steve Miller's Math Riddles is a website filled with a variety of riddles ranging from easy to hard and classified by topic. Some of the topics include combinatorics, geometry, algebra, probability, logic, even game theory.

2. Learn with math games has links to several different sets of brain teasers. Some of the brain teasers are visual while others are word problems and the few I did, I really enjoyed because the answers were not obvious but required a bit of thought.  They have one logic puzzle which asks "What month has 28 days?" A person's first instinct is to answer February but the actual answer is "All the months because they all have at least 28 days."

3. Prodigy Game has a list of at least 45 brain teasers made for kids but some are such they could be done by high schoolers because the reader is trying to follow a pattern rather than reading and understanding the problem.  I found myself jumping to the wrong answer.

4. Math Warehouse has a lovely set of brain teasers for students in the upper grades to high school. I found one riddle quite fun. "Two fathers and two sons sat down to eat eggs for breakfast.  They ate exactly three eggs, each person had an egg.  The riddle is for you to explain how?"  You can check the link for the answer if you aren't sure about the answer. 

If you want more, just type in "Math brain teasers for high school students" or the grade level you are interested in.  Let me know what you think, I'd love to hear.  Have a great day.  

Warm-up

What do you notice?  What do you wonder?

Warm-up

What do you notice?  What do you wonder?

What is feedback in Math?

 

When I first started teaching, no one spoke about feedback in math.  It was pretty much assumed that correcting the assignment, was valid feedback but in reality it really wasn't because very few students actually looked at their work again.

Since then, research has shown how important proper feedback is for students but it's only recently I've found better ways of providing it and having students pay attention to suggestions.

Feedback is a way for students to know how well they are progressing towards a goal.  It lets them know what they've learned and what they still have to learn.  It is a way to move from teacher oriented to student oriented.  

It is important to connect feedback to learning targets and success criteria.  Remember learning topics cover what the student is expected to learn while the success criteria is what they use to see if they've met the learning target.  If a student can look at the learning target, the success criteria, their work and are able to judge where they are in the process, they are providing their own feedback.

Furthermore, teachers need to make sure that any feedback provided is based on evidence.  All assignments need to be aligned with the learning target and the feed back should be very specific, based on the work done rather than relying on inferences.  This means feedback should be based on the quality of work, not the student.  In addition, the teacher should use student work to note which areas need improvement and how to make those improvements.

Because the feedback is specific and meaningful, students are able to take the information and to make changes.  It is best if the feedback identifies one thing to change which leads to immediate improvement.  It lets the student know how close to meeting the criteria of the learning target they are and offers them direction to make it.

In addition, feedback needs to written in such a way as to both engage and motivate them. It should also be useable and not overwhelm them.  It is suggested that the teacher meet with students to make sure they know what makes quality work and understand the feedback given.  It is also suggested that students repeat back what they heard.

All feedback needs to be given in a timely and ongoing manner so students have time to make changes.  As soon as students are given feedback, they should be given a chance to act upon it.  If the feedback is given while they are working, they can connect it to the learning target and success criteria.  This also helps students listen and retain their mathematical learning.  Furthermore feedback should include information on content, skills, and Standards of Mathematical Practice.  

Feedback does not have to be given only by the teacher.  Give students an opportunity to talk to each other  so students get feedback from their peers.  The conversation should include questions beginning with "Why" or "What" or "Can you explain?"  Questions that require explanations and justification. Let me know what you think, I'd love to hear.  Have a great day.

Turning Textbook Questions Into Open Ended Questions.

Textbooks are so nice but most of the time, the questions found in each section are closed ended because they have just one answer which is either correct or not.  It is important to learn to take the questions out of the textbook to rewrite them into open ended questions so as to inspire mathematical thinking and conversation. 

Furthermore, students get used to the idea that all questions have one answer when in reality that might not be true.  For instance, if you are buying new cabinets for your kitchen, the cost is often dependent of the type of wood used, the type of cabinets, and size.  

So to change textbook questions into open ended questions, there are a couple of different ways to do it but there are some things to keep in mind.  One needs to identify a mathematical topic or concept to address.  Think about how to express the question so that it has several possible answers rather than just one.

One way to accomplish this is to take look at the question such as "What is the perimeter of a rectangle that is 13 inches long and 8 inches wide" and find the answer - 42 inches.  Rephrase the question " Construct two rectangles with a perimeter of 42 inches.  This question has more than one answer which makes it a better question.  

Other strategies one can use to convert open problems or questions into open questions include turning the question around by asking the student to suggest ways to get the answer instead of finding the answer.  Ask the student to identify similarities and differences such as in "How are 85 and 90 similar?" "How are they different?"  This question might lead to a student saying they are similar because they are multiples of 5 but they are different because one is a multiple of 10 while the other is not.

Ask students to explain something such as "6 is a factor of two different numbers.  What else might be true about two numbers?" This could lead to something like "If 6 is a factor of two different numbers, the two numbers are also divisible by 2 and 3."  Have students create a sentence such as "Create a sentence that includes the numbers 5 and 8 with the words "more" and "and"?".  You might end up with a response of " The product of three and four is more than 10."  Include soft words such as almost or nearly such as "You multiply two numbers together and the product is almost 600.  What might those two numbers be?"

If you are want to rewrite word problems to make them more open ended, there are six different things one can do to make it open ended.  The original problem from the book read " How many nickels are in 55 cents.  The first thing is to remove all restrictions so it reads "How many coins does it take to make 55 cents?  Students have a choice of which coins they will use to answer the question.  Second is to remove the known so you might say "I have a closed handful of nickels, how many do I have?"  This requires students to estimate a reasonable number of coins.  

Third way is to swap the known with the unknown and remove the restriction so instead of saying nickels, write the question so it is more general "I have 5 coins, 3 are the same, how much do I have?".  Again students have a variety of choices from pennies to nickels to dimes, to quarters or even half dollars and dollar coins.  Fourth, one needs to remove the known and the restriction and change the unknown such as I have 5 coins, how much money do I have?"  Finally change the known, unknown, and restriction such as "What is the shortest or longest line that could be made with 5 coins?" or "I have some coins in my hand, how much money might I have?"

It doesn't take much to change the closed question into an open ended question. Let me know what you think, I'd love to hear.  Have a great day.

The Answer Is.....What Is The Question?

There is a joke I often heard my father crack when I asked him for help.  He always replied "The answer is 42" which it never was.  At least for the problems I was doing. When I stumbled across a image with "The answer is..... What is the question?", I realized I had another open ended question exercise I could use in class.

This activity  involves giving students the answer and letting them come up with the problem or question associated with it. The teacher provides the answer such as 42 while asking students to create a problem whose answer is 42.

One student might come up with 41 +1 or 43 - 1 while another might use 7 x 6 or 168/4.  There are as many possibilities as there are students.  This problem requires students to think about what problem yields this answer.  Someone might even come up with 4 x 10 + 2.

This type of activity is not restricted to only numbers, it could involve measurements such as the answer is 42 cubic feet.  The cubic feet immediately indicates a cube or rectangular prism with a volume of 42 cubic feet.  This means there are fewer possibilities but still quite a few ranging from 42 x 1 x 1 to 2 x 3 x 7.  This type of problems uses the measurement to provide context which students do not always pay attention to.  

Another type of problem could have an answer of x = 3 indicating the problem might be a one or two step equation or even one that has variables on both sides of the equation.  The context indicates it has to be an equation with at least one variable - x and when solved has a value of three such as x - 2 = 1 or 2x + 3 = 9 or 3x - 2 = 2x + 1.  

Then there is the answer of 1/2 pizza which might require the student to create a word problem to have this answer.  The problem might be that three boys purchased two pizzas which they ate 3/4th of the total pieces, how much is left?  or they might write, Dad brought home a pizza for dinner.  Out of 12 slices, we ate 6, how much was left?   Both problems can be answered with 1/2 a pizza.

The answer is..... what is the question? activity has students go beyond the usual procedural methods to using higher level thoughts to determine how they get to the answer.  Furthermore, the activity helps students to make mathematical decisions, while applying mathematics to new situations.  In addition, using this activity can help create a culture where students feel free to try different paths to get to the requested answer.  

It also provide automatic scaffolding because students use the type of math they are most comfortable with to come up with the question.  It also encourages students to feel successful because their question, as long as it gives the answer is correct and as they feel more confident they are likely to try and be willing to make mistakes.

Let me know what you think, I'd love to hear.  Have a great day.

 

Warm-up

The largest faceted Topaz weighs 6.2 pounds.  When it was faceted, it lost 83% of it's weight.  How much did the stone originally weigh before it was faceted?

Warm-up

The largest emerald in the world weighs 841 pounds and worth $400 million.  How much per pound are you paying?

"Which Would You Rather?" Open Ended Questions.

It is important to incorporate open ended questions in math that encourage math-based conversations and helps students learn to justify their thinking used to support their thinking.  The best thing about an open ended question is that there is no one answer.  These types of questions encourages higher level thinking to solve problems.  In addition, open ended questions allow students to see that it is possible to use different ways to solve the problems and can produce more than one answer.

By having students open ended questions, they gain confidence in themselves because struggling students can use basic skills to find an answer while more advanced abilities can use different skills to find an answer and both are correct.  If the problems are written well, they easily become engaged. Furthermore, open ended questions encourage students to utilize creativity to solve the chosen problems.

In addition, student responses to the problems can be used by the teacher to assess their level of understanding and ability.  Open ended problems provide informal assessment but the teacher can see the thinking used to solve it, the methods used to solve it, and their understanding of the situation overall.  

The last thing about using open ended math problems is they can be used as warm-up or bell ringer problems, independent, small groups, or even whole class.  When introducing the use of open ended problems, it is important to model the process which can be done as a whole class activity.  Another time, students can work in pairs or small groups to find an answer to the problem and share the answer with the teacher via a video or google classroom.  

I read about the “Which would you rather” activity in one of Matt Miller’s blogs.  I wondered how I could use it in my math class because math is a bit different.  I found a site which provides  “Which would you rather?” Activities to help get started.  There are quite a few already created to start you off.

The selection offered at this site has quite a few ready to use questions for grades K to 12, enough for several months if you do one a week.  Each “Which would you rather” possibility are very open ended. The answer may depend on what you prefer, while others make the person think about the differences based on the situation.

One has students decide which possibility would you rather?  The situation is that you and two friends want pizza for lunch.  If you buy one pie and get a 10% discount, buy two pizzas and get 20 % off, and buy three pizzas to get 30% off.  Would you prefer Option A where each of you buys an individual pizza or option B where one of you buys three pizza on one check and you split the cost with the others.  

It is nice to have a separate worksheet for students to fill out as they work through the question.  The worksheet should have a way for them to say they prefer option ? Rather than option ? because.  There should also be a place for them to show their work and what things did they consider as they began the problem.

There are other types of open ended questions that I’ll cover another time.  This is something I could easily send home for students to work on because there are no correct answers they can find on the internet and they can’t do it via some app like photo math.  Let me know what you think, I’d love to hear.  Have a great day.

What To Think About When Creating Any Assignment.

Yesterday, I discussed some general points to think about when creating an assignment but today I’ll be exploring parts of the assignment in more detail. When looking at creating an assignment, it is important to think about what the assignment being anything that is assigned to students from the warm-up to the exit ticket and everything in between including the actual assignment focused on learning the content.

  

First one needs to look at the type of assignment being given.  Is it a short task of under 15 minutes such as bell ringer, journal entry, or the exit ticket or is it a task spread out over two days or is it a project that takes longer than two days such as a performance task.  Does the assignment focus on content standards associated with the grade level or does it use standards from other grades.  Does the assignment include any mathematical practices.  Are the directions clear and easily interpreted by the student.  

Next, does the assignment require high levels of cognitive thinking of the students.   If the assignment does not require higher levels of cognitive thinking, look at how you can change  or adjust it so it demands more.  This includes warm-ups, journal entries, and exit tickets.

Think about the rigor involved in the assignment.  Does it allow students to develop mathematical understanding of the skills and processes as well as concepts.  Does it provide opportunities for developing an authentic understanding of math via the use of multiple representations. It is important to use multiple representations of the material because that makes it better for students to learn the material.

Does the assignment help students learn to discuss topics mathematically?  Does it ask students to provide a response to an argument, justify a response, or explain their thinking to others while using the language of mathematics.  Did the assignment include opportunities for whole class discussion, small group conversations, or talking between peers. It is important for students to develop the ability to converse mathematically.

Does the assignment help students bridge their understanding from unknown to known and does it make the math feel relevant to students even if the material feels foreign.  Does the assignment provide choices for students so as to support their autonomy.  In math the choices could be in which problems they can do or the method of doing the problems such as flipgrid, or a video.  

Finally, is there scaffolding included in the assignment and what type is it.  Is there scaffolding written in for a part of the assignment or for the whole assignment?  If only a part of the assignment, what is the scaffolding and why is it used only for that part.  Is the scaffolding done via a graphic organizer? Is the material broken down into small chunks?  Does the student have a list of steps to follow?  

So when you are thinking about creating assignments, especially now after students having been out of school since the beginning of the fourth quarter, it is important to include scaffolding and to look at all of these items to create assignments so they are the best for students.

Creating Effective Assignments

 

I suspect the books you use in math are similar to the ones I have in that the teachers edition has recommended problems for basic, normal, or advanced.  The assignments are a bunch of different problems students are expected to complete and turn in.  The problems are always in order and coincide with all the examples.

Unfortunately, that is not the best way to assign problems especially if you want students to learn.  Today, I'm touching on a few changes to make the assignment better.

1.  Figure out what the objectives are that you want students to meet and decide how they will show they've met that objective.  To do that, begin with rewriting the learning objective as "I want my students to be able to: ____________".  In addition, use active verbs when writing the objective such as compare similarities or discuss differences, or explain the steps necessary to solve this type of problem.

2.  Try to make the assignment more interactive and interesting than just straight problems.  See if there is a way of designing the assignment to make it creative and challenging while motivating students at the same time.  Think about how you can change the assignment up so it is no longer the "do every third problem".  Perhaps you can change it to "Write a letter to a friend explaining how to do the problem because they were sick that day" or "Create a video showing how to check your work for this type of problem."

3. If the assignment does include problems from the book, make sure the problems are not in the same order as in the book.  Instead of assigning "Every third problem", maybe do 2, 10, 22, 4, 12, 24 so the problems are mixed up.  This helps students learn the math better.

4.Once you've created the assignment, go back and make sure the assignment still meets the learning objectives.  If the learning objective requires students to compare and contrast two things and you only have the comparison in the assignment, you'll need to go back to include the contrast part. 

5.  Think about how to order assignments so skills are built in the proper order. You want students to build the necessary skills incrementally and make sure students see the connection between what they already know and what they are learning. If you plan to end the semester with some sort of project, make sure the smaller assignments build all the skills they need to complete the project.  

6.  Determine the frequency of assignments and how often they need to be turned in. Will students complete an assignment for each section or for two or three sections with a few problems from each section.  Normally, I'd recommend  having a calendar of assignments and due dates completed prior to the beginning of the semester but with the coronavirus, that might not be as easy to do.

7.  Think about the ability of students to get the assignments done.  Will they have enough time or so they struggle and need additional time?  This is important when creating assignments because more is not always best.  Do students really need to complete 20 problems for every section or will 10 be enough especially if you ask them to discuss how to do it or talk about issues they had working the assignment.

This is just an overall look at creating good assignments but on Wednesday, I'll be looking at questions one needs to answer in more detail when creating an effective assignment.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

One of the largest cakes ever made in the world has a diameter of five feet across and weighs 50 stone.  If one stone equals 14 pounds, how many pounds did the cake weigh?

Warm-up

The World's largest pizza is 122 feet 8 inches in diameter and weighed 26,883 pounds.  How many pounds is that per inch?

Using Multiple Choice Questions In Class

 

Personally, I don't like using multiple choice questions in class but many standardized tests such as ACT or SAT use them and most of my students struggle with this type of question.  On many of the standardized tests given by the state have the right answer, two wrong answers that students will come up with if they don't take the problem to it's natural conclusion or only get half done and one that is totally wrong. 

Even though I don't like giving this type of test, it is important that students learn to take them and not just guess.  In my textbook, the pre-tests for each chapter are multiple choice along with certain questions in the problems for each section.  Many students need to be taught how to take multiple choice tests effectively.

There are strategies to help students when taking multiple choice questions.  First, students should cover up the potential answers without even looking at them before they read the problem because they need to know exactly what the problem is asking.  If they cover the answers, they do not get distracted and they can reread the question multiple times to understand it. 

In fact, it is recommended that students rephrase the question to themselves, before trying to answer it in their mind first. If the problem requires calculations or simplification, students should try to answer the question before they look at the answers otherwise, many students tend to guess rather than trying to do the problem.  If the problem requires them to find an equivalent equation or find a fraction closest to a number, they should still cover the answers to they are focused only on the question before going through each answer slowly to see if the answer goes with the question.

Secondly, have students highlight key words, especially words like always, never, sometimes, not and others that place limits on the situation.  The question might ask you to find the probability of not drawing a red or green ball, rather than asking for the probability of drawing a certain colored ball.  Many students miss the qualifiers if they don't highlight certain key words.

Next, after reading the question and highlighting key information, students should read through the answers to eliminate any that are obviously wrong.  If a student does not see any that are obviously wrong, then there is another technique to use.  If the answer required is an actual number, one can substitute the answers back into the original equation to see which one makes the whole problem correct.  I've used this last one myself on multiple choice questions.

One person analyzed over 2400 questions from 100 different tests to determine the four strategies to help increase a person's chances of getting multiple choice questions correct when they don't know an answer.  First, if you have see "None of the above" or "All of the above",  one of these is likely to be the correct answer over half the time.  Secondly, two questions in a row seldom have the same answer.  For instance if you don't know the answer to question 2 but know the answer to question 1 is a and the answer to question 3 is d, then chances are question 2 will not be either a or d.  Next, the correct answer is more often than not the longest answer because the people who write the test want to make sure the correct answer is definitely correct.  They are not going to take as much care with an answer that is wrong.  Finally, eliminate any questions that are out there.  Often, on math tests, people can eliminate answers that are too small or too large just by using estimation.  

I also tell students to keep an eye on the time if the test is timed.  Always do the questions you know how to do first, followed by those you sort of know, and leave the ones for last that you have no idea how to do.  You can do this for some computer tests but not for all and it works well for paper based tests.  I advise students to spend no more than two minutes if they get stuck on a question otherwise they'll get frustrated and not be able to complete the test.  I also include some practice questions with their homework.  Let me know what you think, I'd love to hear.  Have a great day.

Always, Sometimes, Never?

I've occasionally seen and used always, sometimes, and never statements but I've never made a practice of it because I've not been sure what they accomplish.  As stated earlier, for the first few weeks of school, I have to send work home for part or all of the week and after reading up on these, I think they will be a good addition to the packet. 

If you've never seen or done one of these activities, they are fairly simple.  Students are giving between two and five statements to look at.  They have to decide if the statement is always true, sometimes true or never true.

When teaching mathematics, statements are made which are only true in certain contexts and usually the context is what is being taught.  This activity allows students to think critically about math to determine when things apply or don't apply.  Furthermore, it promotes mathematical reasoning and introduces the idea of counter examples to prove something isn't always true.  

It is important to have students provide counter examples for sometimes statements because it helps students see the context of when it is true or false and requires deeper delving into the statement as they think about it. Determining if the statement is always true, sometimes true, or never true requires higher level critical thinking skills rather.  In addition, this activity helps  identify misconceptions in student understanding.  

The always, sometimes, never activity also promotes dialog and communications because students are required to explain why the statement is always true, sometimes true, or never true.  It is a good activity to help students learn to "Justify their answer" which is often seen on tests.

Overall, always, sometimes and never activities are considered low floor with a high ceiling because students who have low mathematical reasoning skills can still participate by substituting numbers to see if it seems to always be true or find a counterexample.  It is high ceiling because students have to justify their conclusions. Furthermore, always, sometimes, and never is also a way to introduce logic statements to students without using straight mathematical language and theorems.  

Always, sometimes, and never also helps students develop perseverance as they look for examples or counter examples.  They build arguments while evaluating their logic and the logic of their peers arguments. It also has students engaging in authentic mathematical thinking.

When doing this with students, they often will try one number to see if it works but they will need to be guided into trying several possibilities such as zero, fractions, or negative numbers and not to just accept the first possibility.  Take the statement "Any number added to five gives a number larger than five" which on the surface seems to be true because people automatically assume one or above which makes this true but if you add a negative number to it, the answer will be less thus making the statement, sometimes true.

So if you want a way to help student develop mathematical thinking, this is a good way to do it.  Let me know what you think, I'd love to hear.  Have a great day.

Taking Notes From The Textbook.

Many schools are starting this virtually this fall complete with distance lectures and reading assignments.  Some students have the idea that one does not need to take notes because the material is all there but that is not quite true.  When students take notes, it can improve their reading comprehension, and helps them retain information.  

Currently, research indicates when students use pen and paper to take notes, they are better able to retain information when compared to using digital apps such as Evernote.  

Furthermore, when taking notes by hand, it means a person does not have to toggle back and forth between the class and pages or other note taking app.  One can also watch videos or streaming lectures while jotting notes down.  When students first learn to take notes, they try to take down everything they can. I know in college, I'd try to write everything down but I'd go over notes later to make them neater and to make more sense.

One should not try to write down everything because it can lead to information overload, which limits the amount of material a student is able to recall later.  Since most classes require reading, it is important to jot down notes while reading and don't be afraid to draw pictures or diagrams.

I want to focus on teaching students to take notes from their textbooks during the time they work at home since I won't have as much time available during class.  In math, taking notes is a bit different than for English or History and most of my students do not have those skills yet.  In addition, reading and taking notes from a math textbook should be done when the student is alert. 

It is recommended students write down definitions, key concepts, and theorems in their own words rather than copying them down verbatim.  If they find terms they don't understand, they should look it up and make notes.  When writing down definitions, they need to include examples of things that meet the definition and those that don't. As for theorems, students need to read those carefully and determine why they apply in various situations.  

When the student comes to the example or application of the theorem, they need to look carefully at them, working on understanding each step in the process, and once they've finished, they should try working the example or application of theorem without using the book or notes. In addition, as students work through examples, check the end of the chapter to which ones are like the ones just done and try those.  If there is something students don'e understand, they should ask the teacher.

Furthermore, students need to read the text slowly because mathematical texts are extremely information dense and they need to pay attention to understand everything.  Students need to be prepared to read and reread the material sentence by sentence, paragraph by paragraph to comprehend the written word.  Take time to analyze all the diagrams and pictures.  When looking at a picture, students need to identify how it relates the the topic.  

This is important to help students learn to take notes from the textbook.  For the first couple weeks, I have to send work home, I am going to include a partially started set of notes students can copy into their composition books and finish on their own.  This is the only way, I'm going to teach them to take notes when reading.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

Miki Sudo ate 48.5 hot dogs in just 10 minutes setting a new record.  How many hot dogs did she eat per minute?

Warm-up

Joey Chestnut holds the world record for eating hot dogs.  He consumed 75 in just 10 minutes.  How many did he eat per second?

Notice, Wonder, and Notes.

I've been wondering how to set up things like "What do you notice?"  "What do you wonder?", Three Act Tasks and other activities so my students can do part of the activity at home and finish it off in class.

  I decided that for most things I might use the notice and wonder for, it is possible to send a photo in the packet with a chart for students to write their observations on.  The results can be turned in when students arrive for school.  

The photo might be of a real life application of the math topic we'll be covering in class or perhaps its one they've done before but need to review.  

This is a great way to introduce students to warm-ups for instance by sharing the picture from Estimation 180 with the notice and wonder questions and then have students make their guesses during class.  If I included a hint, students could include their estimation with their finished work.  

I can do the same type of thing with the three act tasks by providing a photo of the situation, any information needed and ask a few questions in preparation for the second and third act.  If the first act is a video, I can let the students see the question before I show the video and then show the video just before class ends.  Then I'll include the picture and the questions as part of the take home packet so students can record their answers.  There are lots of three act tasks one can find on the internet, it just takes a quick search for the answers.  

Then there is the activity called "Which one does not belong?".  This is where a picture with four things or terms is put up and students have to decide which one does not belong and then explain why they chose what they chose.  The sets usually have at least two answers to this question or more depending on how a student works.  The site WODB has so many possibilities a teacher can use.

On the other hand, it might be possible to set up certain situations and rather than using the mathematical language associated with the task, make the language simpler so students are more engaged.  For instance, I might include a picture like the one to the left and ask students something like "Wow how do  you describe the pattern used by the artist to create the print?"  or  "How many ways could fold this so it folds exactly in half?  It would also work as a notice and wonder.

All of the above can include some sort of notice and wonder activity in preparation for finishing it in class.  This allows students a chance to think about things before they do it and one can use so many different resources for this. 

A second area of activities one can include in the take home packet is to include those algebraic logic picture puzzles.  The ones where you might have heart + heart + heart = 27.  The second line might be a heart + heart + a square = 22 and the third line would be a heart + square + circle = 20.  So using the first one students figure out the heart has a value of 9,  the square has a value of 4 and the circle is worth 7.  This type of worksheet requires students to think about how the pictures relate to numbers and find the values.  

The next topic I'll be exploring is how to teach students to take notes from the book and use examples in the book to learn to do problems on their own. Let me know what you think, I'd love to hear.  Have a great day.

Unique Version Of A Hybrid Model.

We just received word that the first couple weeks of school will be distance and then around mid September we are switching to a hybrid model.  In our model, the kids will be divided into two groups so group A will attend on Monday and Tuesday while group B is in school on Wednesday and Thursday.  Then for the other days of the week, I am expected to send work home to complete and be turned in when they come back for the next class meeting.  It is possible this will change before I have to set foot in class.

The sending work home part makes our hybrid model a bit different than the usual because the normal method has some face to face mixed with an online component. The district chose to do take home because many of our students do not have enough internet to watch multiple videos or complete online activities.  Since this schools model is a bit different, I'm having to make a few adjustments to standard model.

The in person section will require me to focus on key ideas and concepts so I make sure the students have at least been exposed to the material while designing the take home assignments to be completed independently or with little help.  Consequently, I'm having to  rethink the course structure so I meet the needs of all my students while covering all the course concepts.  I also have to look at how I'm going to assess their work to meet district requirements.  

One recommendation I've seen is to allow time for collaboration in a hybrid class via discussion boards, etc but that won't work for take home.  Instead, I can divide students into pairs so they can call each other with questions or work together to complete the assignments.  In addition, I can make small adjustments to the take home part of the assignment to encourage collaboration.  For instance, I can create pairs assignment where each student has different problems but the answers are the same.  If their answers do not agree, they can work together to see where the mistakes occurred.  This type of collaboration also allows students to participate in discussions because they have to communicate the steps and where they or the other person goofed.

 

Unfortunately, my students will not get the same amount of practice in class with only two days of in person meetings so I am going to provide practice with the take home.  I am taking two different activities and modifying them for students.  The first is to write out all the steps to solve a problem but leave the numbers out so they write in the numbers and the answer.  I only put in the operations and lines between steps.  The other is to write down all the steps except the last one for a few problems, then take away one step for so I've done all but the last two, then take away one more line, and continue until they are doing the problem all by themselves.  

As far as assessment goes, I will be including some actual problems for students to do totally on their own and without my guidance via the worksheets.  It would be more like a quiz and I do not plan to record a grade unless it is done well.  If there are mistakes, I plan to return it to the student to make corrections so the grade is higher.  Those three days at home will give time for students to make corrections and turn it in.  I am thinking of asking them to identify the mistake they made in the original problem. To help with error analysis, I plan to send home problems that have been done incorrectly for students to practice on but we will do some in class at the beginning of the year so students learn how it works.  I am still working on how to give tests so I do not have to give up the limited face to face time so I might be giving take home tests or including test questions as part of the homework assignment.

I don't know how this will work but I am starting to read up on ideas of things that could easily be sent home in paper form for my students.  I am also thinking about how to have videos available for students so they have them at home.  That is one of my next things to figure out.  I'd love to hear from everyone. Let me know what you think, I'd love to hear.  Have a great day.

Sites To Help With Distance Learning.

I just heard the school year at the moment will be by distance for the first few weeks of school and then it switches to dividing the students into two groups.  One group will attend on Monday and Tuesday while the other group is coming on Wednesday and Thursday with no students on Friday.  That could possibly change because our town just reported it's first case of the coronavirus.  We'll have to see if the person who is a non resident infected anyone else. 

There are several sites I fully recommend using for distance learning. These sites are in no particular order, I  have used them and like them a lot because they make learning more active.

1.  Edupuzzle - This site is great because it has lots of videos that have been curated and those that you can curate.  By curate, I mean you can take a video, shorten it if you want, add questions that are open-ended, multiple choice or even add in notes.  When ever you add in questions or notes, the video will stop and require students to answer the question or read the note before it moves on.  If you don't feel like doing it all yourself, you can use an already curated video.  Another nice thing is that if you use multiple choice questions, Edupuzzles will automatically correct and assign a grade to the watched video but you have to grade the open-ended ones.

Furthermore, the site allows you to access videos from YouTube, Khan academy, National Geographic, TED talks, Veritasium, Numberphile, and Crash Course.  In addition, it allows you to cut, do a voice over, or add questions for any video on the site.  These voice overs, notes, and questions turn the video experience from passive to active so they are more involved with their learning.  The last thing this site has going for it is that you can log in using a google ID and you can export scores to google classroom.

2. Thinglink - This site allows links to be embedded into a picture or a video for students to follow as part of their learning.  This site has a free version, a paid version for up to 60 students, or the version for school districts that have everything.  This allows you to login with a google ID and it connects to google classroom.   What you end up with is an interactive picture or video containing everything you want students to learn associated with the top.

There are many completed Thinglinks you can go through or you can create one for yourself. Creating one is not that hard as the site has some wonderful tutorials and help.  I did a picture based ThingLink in a very short time. I just needed to select an image from my computer, start adding tags which are where you place the link, text, image, or video for the student to experience.  Then it can be assigned and students work their way through it. 

3. Hyperdocs - This is a site where you can learn to create one document that is set up with engage, explore, apply, share, reflect, and extend.  It is interactive google document designed for students to work their way through the document rather than giving them a ton of worksheets.  The authors of this site wrote a book on HyperDocs, offer some free training, along with samples, and templates. 

Hyperdocs is like providing a map of the instruction for students to work independently through a topic. It has it broken down into the first thing to do, then what comes next, and next, until the student has worked totally though the lesson.  Each section allows the teacher to create a link to all the resources needed by the student for everything from start to finish.  This is a wonderful thing to use for distance learning because it puts everything in one place and the whole document is around one to two pages long.  So it is short and manageable.

These are the sites, I recommend to begin with if you have to look at starting the year using distance learning.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If a humpback whale weighs about 66,000 pounds as an adult, how many tons does it weigh?

Warmpup

If a whale can swim 19 mph, how long will it take the whale to travel 9800 km?