Thursday, December 13, 2018

The 2018 Cost of the 12 Days of Christmas

Partridge, Ave, Bird, Wild, NatureI grew up listening to the 12 days of Christmas, both the traditional version and the Hawaiian version.  I'll admit that for the longest time, I thought it was 3 French Horns because I'd never heard of a French Hen.

It was only after I started to read, I discovered how far off I was.  Around Christmas time, it is possible to find the current cost of giving the 12 days worth of gifts.

This year, I managed to find a wonderful article in Forbes which included the increase or decrease for each item. According to the article, published in November, it will cost $39,094.93 to buy all these gifts.  This is an increase of $450 over last year which comes out to a 1.2% increase.

The list, including increases is:
  •  1 Partridge in a Pear Tree: $220.13 (+.1%)
  • 2 Turtledoves: $375.00 (no change)
  • 3 French Hens: $181.50 (no change)
  • 4 Calling Birds: $599.96 (no change)
  • 5 Gold Rings: $750.00 (-9.1%)
  • 6 Geese-a-Laying: $390.00 (+8.3%)
  • 7 Swans-a-Swimming: $13,125.00 (no change)
  • 8 Maids-a-Milking: $58.00 (no change)
  • 9 Ladies Dancing: $7,552.84 (no change)
  • 10 Lords-a-Leaping: $10,000 (+3.0%)
  • 11 Pipers Piping: $2,808.40 (+3.5%)
  • 12 Drummers Drumming: $3,038.10 (+3.5%)
Much of this information comes from the PNC Christmas Price Index which for the past 35 years has calculated total cost complete with increases and decreases.  The method used to do the calculations is almost the same process as the government uses to calculate the Consumer Price Index.

Their list is done for each item with a infographic like graphic for each item along with the percent change.  Furthermore at the bottom of the webpage is a graph showing the increase of the cost, year by year, beginning in 1984.  This is a great graphic to read and interpret.

In addition, at the bottom of the page is a 12 page activity guide with everything needed  to teach lessons on this topic.  The activity includes reading data, estimating, graphing, and requires students to explain their rationale for certain things.

I know what I'll be doing next week on the last couple of days before holidays.  Let me know what you think, I'd love to hear.  Have a great day.

Wednesday, December 12, 2018

Why Use Exit Tickets?

Fax, White Male, 3D Model, Isolated, 3DWe see recommendations to use exit tickets regularly in class but one often wonders why use them in the math class.  Why even use them at all because its one more thing to use in class because its just one more thing to keep track of in class?

Exit tickets are like thermometers where the teacher checks overall student understanding.  They can be used to check for student understanding on a topic so the teacher knows if they need reteaching or if they are ready to move on.

In addition, the exit ticket provides information on if the whole concept needs reteaching or if a small point needs clarification such as if you multiply or divide by a negative, the sign changes.

Furthermore, exit tickets help students understand that the material is important and they are accountable for learning it.  It helps them synthesize the material, helps them move it from short term to long term memory because they are accessing it.

Another plus for using exit tickets is that students have to learn to communicate in writing.  If the teacher checks answers and has questions, they can clarify points to understand student thinking better.

If you do not currently use exit tickets, it is recommended you start slow.  Perhaps use it once a week and only on one or two topics.  It is suggested teachers do not grade exit tickets because its an assessment tool designed to provide data for instruction.  It lets the teacher focus on students who still don't quite have it with a bit extra instruction while provided more advanced problems for those who "have it".

To create an effective exit ticket does not take much.  Just follow a few simple rules:

1.  It is linked to the objective of the lesson.
2.  Focus on one skill or concept taught that day.
3.  Questions may be multiple choice, short answer, or require a couple of sentences.
4.  Exit tickets should have no more than 5 questions but fewer are usually better.
5.  Students should be able to finish the ticket in a few minutes.

The questions should not require a simple yes or no answer because that give no information.  Exit tickets should have questions that assess understanding, allow student to demonstrate the concept through work, or application of the concept.  You might create a problem based on the day's topic that could show up on a test redone, discuss how the topic could be used in real life, rate your understanding of the topic based on a 1 to 10 scale, or write a short paragraph on the day's lesson.

In addition, it is quite easy to set up digital exit tickets using google forms, or other app so you don't have tons of paper to keep track of.  More on this topic in a while.  Let me know what you think, I'd love to hear.  Have a great day.

Tuesday, December 11, 2018

Multiple Choice Questions - Other Uses.

Quiz, Test, Exam, Questionnaire When most of us hear the term "Multiple Choice" in connection to math, we automatically joke "Multiple Guess".  I remember taking a few where I just plugged the answers back into the problem to find the correct choice, or I used the elimination method to narrow the choices until I got it down to the most probable one.

Many multiple choice questions are set up so the most probable incorrect answers are included so if someone makes a mistake, they'll find it in the choices.  More often than not, you aren't sure if they know the material, got tired, or didn't care.

The other day, I read a blog on how to use multiple choice questions in ways that may be more effective in class. There are ways to use it other than as a major test.  I liked what the author said so I'll share it with you.

I'd like to thank Pear Deck for these suggestions  which are easily integrated into math.

1.  Use multiple choice questions to poll students on a topic or get feedback on something.  You might ask them if they'd prefer to play kahoot or jeopardy as a way of reviewing the material in preparation for a test.  You might also ask which step is next in a problem by listing several steps to  see if they understand the process. 

2.  Multiple choice can be used to check for misconceptions and understanding in topics such as
      GCF & LCM
      Equivalent Fractions
      Order of Operations
      Binomial Multiplication
      Combining like terms
      Solving problems
The use of whiteboards either virtual or real is great for this because you post the question, students write their answer on the board and with a quick glance, you see who understands it and who needs a bit more work.

3. Use multiple choice as an exit ticket.  Ask how they feel about the material studied that day using emoji's and multiple choice.  Faces can range from great to crying so students can choose one to show how they feel about their understanding.

These are just a few suggestions for using multiple choice to learn more about student understanding outside of a testing situation.  I think they are cool and add to my teaching toolbox.  Let me know what you think, I'd love to hear.  Have a great day.

Monday, December 10, 2018

Compare and Contrast in Math

Compare, Query, Contrast, Documents Compare and contrast is something often used in Social Studies, English, or other subject but it is not something used as often in math, not because its too hard but because most math teachers have not been trained to use it.

The closest thing we have is the Vann Diagram but its not exactly a compare and contrast exercise.  So with a bit of thinking and working, it can be used in the math class but not for every topic.

First its important to know that when compare and contrast is used, it can strengthen the student's memory, help develop higher order thinking skills, improve comprehension, precision and helps build good work habits.

Lets look at some ways to use compare and contrast in math.

1.  Compare and contrast inequality signs.  Many students have difficulty in distinguishing between less than, more than, greater than or equal and less than or equal.  Requiring them to fill out a chart comparing similarities and contrasting or finding differences can help them put into words their understanding.

2.  Compare and contrast place values such as tenths and tens, thousands and thousandths, so students learn to tell the difference between decimal values and whole number values.  They are very similar but with a small difference.  Some of my students arrive in 9th grade not knowing their place values which hurts them at times.

3. Long division and synthetic division in Algebra.  Although they appear different, the methods share quite a few similarities.  Using a compare and contrast will show students their similarities and differences.  In addition, they can see that it doesn't matter which method used, the answer is the same.

4. Compare and contrast distributive property with binomial multiplication.  It doesn't really matter what method you use to complete binomial multiplication but it still involves distributing terms, just like we teach when using distributive property.

5.  Compare and contrast Greatest Common Factor with Lowest Common Multiple. I can tell you, my students are having so many problems with this topic so completing a compare and contrast in the hopes they can learn to distinguish between the two.

6.  Compare and Contrasting congruent with similar triangles since both share similar methods of proof. 

7.  Compare and contrast bisectors with medians and altitudes because students often have trouble remembering the differences among them.

8. Compare and contrast area with surface area.  I realize one is 2 dimensional while the other is 3 dimensional but they do share similarities.

Any two math topics which have similarities and differences can be used in a compare and contrast exercise.  Let me know what you think, I'd love to hear.  Have a great day.

Friday, December 7, 2018

December 7, 1941

Pearl Harbor, Ship, Warship, DestroyedToday is the day to remember an event that happened 72 years ago.  Japan bombed Pearl Harbor, killing both military and civilians while trying to cripple the American fleet.

Its sometimes difficult to find activities designed specifically for the math classroom.  Most of the ones I've found are for history or English but that has not stopped me at all.

This particular day has lots of possible activities which you can provide the data for, or you can have them find the data for the project.

1.  Its easy to find the number of people killed in each branch and civilians on December 7, 1941.  This information can be turned into a chart to show the information visually or it could be turned into an infographic with the graph.

2.  Another graph could be done showing those from each branch and civilians who were wounded during the attack.  You can find the information from the Honolulu paper showing how many and the ages of civilians who were killed by bombs or bullets from the attack.  Again, its easy to create a graph showing age distribution.

3.  Number and types of ships that were damaged or sunk. The Japanese wanted to sink aircraft carriers but there were none in port that day.  Instead they got battleships, destroyers, etc. This exercise could also include the number of planes destroyed or it could be done seperately.

4.  Find out where the mini-subs departed from the mother subs, when they left and when they arrived at pearl harbor.  This is enough information to calculate their average speed or you might find the average speed to determine how long it took them to travel the distance.  Furthermore, its possible to calculate the volume of the two man mini-subs.

5.  Another activity dealing with distance is to find out where the Japanese planes took off from, find the distance, and how long they took to get to Pearl Harbor to determine the average rate of speed. 

6.  Find out how many total planes the Japanese sent to bomb Pearl Harbor and the number of each type of plane to create a graph.

7.  Students can also create an infographic containing all sorts of numerical information on the attack on Pearl Harbor. 

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