Odometer

Personal Reflection:
Like many math teachers, I have a slight obsession with really cool number patterns.  "Palindrome" numbers are some of my favorites (along with series, repetition, etc.)  I took the opportunity to take a photo (stopped, you'll notice) of my odometer when it reached 77,477 miles.  (On a side note, my new job has me doing a LOT of commuting, and I'm over 90k now, which shows how much I'm driving and how much I procrastinated on this post!)

Grade Level: 4-5

Course: 4th or 5th Grade Mathematics

Standards: 4.OA.5,  4.NBT.4, 5.OA.3, 5.NBT.5
SMP: MP2, MP5, MP6, MP8
Skills: Patterns, numeric relationships, addition, subtraction


How to use this as a mad minute:
You have 60 seconds. 
List as many palindromic numbers as you can.

How to use this as a warm up:
Tell the students what this shows, review what an odometer measures, and what a palindrome is.
1.  Why is this a palindrome?
2.  What would be the next 10 times I'd have a palindrome on my odometer?
3.  Do you see any patterns in the palindromes?

How to use this as a mini-lesson:
I would repeat the warm up above, but exclude the third question.  I would ask the students to work in groups to try to figure out how many times my odometer had "hit" a palindrome from the time I bought it (7 miles!) to the time that is shown above.  I would use the third question as a way to help kids who ares struggling trying to list ALL of the possible answers.  If they can identify patterns, they will shorten their process.

Push students to make observations about the patterns, to look for ways to generalize, and identify the final answer.  (In my own calculations, I THINK the answer is 674 times.  I am not positive, and will recheck my work.  My thinking is posted in a photo here.)


How to use this as a full lesson?
Expanding on the mini-lesson above, the focus REALLY has to be on number properties and patterns.  Students are NOT going to quickly answer the question of "How many times."  In fact, if they are not developing effective strategies and using patterns, they could easily get stuck in the listing routine for an entire period.

With a focus on selecting students who have a variety of strategies, definitely ask students to prepare to share their thinking (either on a poster, a dry erase board, on to put under a document camera).  Select a variety of approaches and sequence them in a way that will help students who are stuck make more efficient progress.

Other extensions you might offer could include:

• If this person drives 3,000 miles a month, how often can she expect to see a palindrome?
• How long until her next palindrome?
• What other "special" numbers might this person look forward to?  (I like repeated numbers "33333" and "sequences" of numbers "12345")
• How many of these such numbers would she encounter between 0 and 1,000 miles?
• How many prime number has she hit between 0 and 77,477 miles?

Car Talk, one of my favorite radio shows, had a number puzzle dealing with palindromes and odometers.  Click here.  (A very advanced explanation and solution can be found here.)

Another great challenge that deals with palindromes, as well as merging speed, is included at this site.

How to use this as an assessment?

This is not directly tied to assessed standards.  I do not feel it is appropriate as an assessment item, only as a critical thinking, perseverance, and practice problem.


Please feel free to use any of these ideas and modify them to meet your needs.  However, please acknowledge the original source of the items and my own lesson outlines.  ©NatalieRSprigg 2014  

Giant's Causeway

Personal Reflection:

One of my most favorite places in the whole world (that I've never actually been to) is The Giant's Causeway in northern Ireland.

The summer after college I was a nanny for my cousins in a small town outside of Dublin called Dunboyne.  I was too young to get my Irish driver's license and ended up taking the kids to the city on the bus.  We did get to take weekend trips with the family to southern Ireland, but while I was there there was just too much unrest to visit up North.

Thus, this is the most amazing place in the world that I've always wanted to go to, but never have.  :)

The Giant's Causeway is a natural formation of rocks on the northern coast between Ireland and Scotland.  As you can see from the photos, these spires of rock form beautiful polygons, often hexagons, but reports are anything from quadrilaterals to nonagons. 

This, to me, is full of opportunities for great instruction.  I can see anything from estimation and basic polygon identification (3rd Grade) to tessellations and transformations. 

For this reason, I feel the EQUATE model is a perfect opportunity to explore these photos and this location.  Rather than focusing on a single grade, I encourage you to use the EQUATE thinking routine to apply appropriate standards at your grade level.

Grade Level: 3-HS

Course: Math, Pre-Alg, Algebra, Geometry

Standards:  3.MD.8, 3.G.1, 3.G.2, 4.MD.5, 4.G.1, 4.G.2, 4.G.3, 5.MD.5, 5.G.3, 5.G.4, 6.G.1, 6.G.2, 6.G.3, 6.G.4, 7.EE.3, 7.EE.4, 7.G.1, 7.G.6, 8.G.1, 8.G.2, 8.G.3, 8.G.4, G-CO.1, G-CO.2, G-CO.5, G-CO.6, G-CO.7, G-GPE.7, G-GMD.2, G-GMD.3, G-MD.1, G-MD.3
SMP: MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7, MP.8
Skills: Estimation, Number sense, reasoning, modeling, geometry, geometric shapes, properties of shapes, area, perimeter, volume.


How to use this as a mad minute:
You have 60 seconds. Name all of the shapes you can see.

How to use this as a warm up:
You could ask the students to consider one of the following:
1.  Name the shapes you see.
2.  Does this fit the definition of a tessellation? Why or why not?
3.  Are these "regular" polygons?  Why or why not?

How to use this as a mini-lesson:
If I only had 20 minutes, I would use technology to explore this VERY COOL region.  This website has an awesome interactive map, some history, and the legend of the Giant's Causeway.

http://www.voicesfromthedawn.com/the-giants-causeway/

How to use this as a full lesson?
As I mentioned before, I feel that this is an ideal EQUATE lesson.  Although there is a ton of math that is obvious to an instructor, this captivates my interest because of the combination of legend, scientific history, and visual appeal.  I feel your students will also be drawn to these elements.  If you are comfortable, let the students dictate the direction of the lesson and exploration (within reason).

I would show these photos, let the students explore, discuss, etc.
Then I would list all of their questions, encouraging them to "wonder mathematically" about them.
Focused on grade-level appropriate standards, I would ask students to narrow down the questions to make sure they are relevant to things you have already explored or discussed in your class.
I would let the students ask YOU questions and you can provide the answers you feel are appropriate.  (How are they formed?  How big is the region?  How many are there?  You can provide as much or as little information as you wish.)
I would settle on a question (or two or three) for your students to apply their knowledge and continue to try to solve.  Encourage them to TRY something!  Draw on the photo, measure it, get online and do research, look up formulas that might be useful, gather information, start playing with the numbers, rules, formulas, photos, etc.
Finally, ask the students to Explain what they did, what they found, and how they approached the problem.

 How to use this as an assessment?
It is up to you if you think your students can use this as an assessment appropriately.

It could be something as simple as providing the first photo and asking students to outline as many different shapes as they can see and explain why they are different and what they are (Elementary School).

It could be more advanced, offering the size of the region, the size of an individual "step" and asking the students to estimate how many are in the entire region.  (Upper Elementary to Middle School.)

You could ask the students to find two similar "steps" and justify why they are similar (Middle/High).

You could ask the students to find the volume of two or three different "steps" and justify their solution methods.  (Middle/High).

You could ask the students to PROVE that two items are congruent or similar based on transformations such as rotations, reflections, etc.

Works Cited:
Photo 1
Description: Giant's Causeway and Causeway Coast
Copyright: © Philippe Croo
Author: Philippe Croo
Image Source: Philippe Croo  (Link)

Photo 2
http://farm3.staticflickr.com/2755/4427445338_7869405855_z.jpg?zz=1

Photo 3
https://garystravel.wordpress.com/page/107/


Please feel free to use any of these ideas and modify them to meet your needs.  However, please acknowledge the original source of the items and my own lesson outlines.  ©NatalieRSprigg 2013 

"Friends" Gym Membership

Personal Reflection:

Not all of my inspiration comes from lame humor sites.  :)  Just the other day I was watching a rerun of "Friends" (probably while working on a blog post) and saw this intro.  I can't embed the video (but a link is included here), but did include screen shots.  Basically, Chandler has a Gym Membership that he doesn't use and can't get out of.

Here's the thing:  I think that in order to create TRUE mathematicians, kids need to "wonder mathematically" much more often.  Sure, they might laugh at the joke, but do they ever "wonder" what those numbers actually mean?  Do they have any number intuition?  Can we GET kids to wonder mathematically?  My EQUATE thinking model asks kids to do just that.  Unfortunately, I'm not sure that this is cut out to be an EQUATE type of problem.

Grade Level: 4 & 5 (Though, a fun, quick warm up at nearly any grade!)

Course: 4th &5th Grade Math

Standards:  4.NBT.1, 4.NBT.5, 4.NBT.6, 5.NBT.6
SMP: MP1, MP3, MP4  
Skills: Multiplication and Division, Unit Conversion


How to use this as a mad minute:
You have 60 seconds.  Estimate how long it has been since Chandler went to the gym.  Estimate how much money he has wasted. 

How to use this as a warm up:
You could ask the students to consider one of the following:
1.  How long has it been since Chandler went to the gym?  Write your answer in weeks and months.  Should your answer be written in years?  Why or why not?
2.  How much money has Chandler wasted by not going to the gym?
3.  List 3 things that Chandler could have purchased with that money.
4.  Explain how you could have estimated the answers to problems 1 & 2 using mental math.

How to use this as a mini-lesson:
Let's be honest.  This isn't going to be a major lesson at any grade level.  It's going to be a silly, fun, and quick activity to focus kids on thinking mathematically and to be aware of the math around them every day.

Usually I offer 20 minute mini-lessons.  I feel that if you want to use it as a mini-lesson, expand on the questions outlined in the warm up.  Give them time to reflect with partners, work with groups, explain their thinking and show their work.  REALLY focus on number sense, estimation, and mental math.  Consider giving a small prize (pencil?  Sticker?) to the student who estimates the length of time and expense most accurately. 

How to use this as a full lesson?
See above.

However, here are several other math "fails" in TV and movies that might spark discussion in classes for basic math.

I don't know the name of this movie/show, but it is Ma and Pa Kettle.

Abbott and Costello (Selling vacuum cleaners)

Abott and Costello (Donuts)  Note: The math logic is the same as the vacuums!

Abbott and Costello (Two Tens for a Five)

Abbott and Costello (It's Payday!)

How to use this as an assessment?
I wouldn't!  If you want to, choose one of the videos above and ask the students to explain the flaws in their thinking!


Please feel free to use any of these ideas and modify them to meet your needs.  However, please acknowledge the original source of the items and my own lesson outlines.  ©NatalieRSprigg 2013