Pancake Proportions

Personal Reflection:
I'm looking down the road a few weeks to when my 7th grade class begins a long haul with Ratios and Proportions.  (Stretching and Shrinking, Comparing and Scaling for those using the CMP books!)  It makes sense that we will spend a lot of time on this unit because it's what the CCSS emphasize as the fundamental skills in 7th grade, and what we should build all 7th grade learning around.  For that reason, I suspect many of my posts in the next few weeks will be around proportional thinking.  (And I'll be going back to some of my others, such as the FitBit post, the Treadmill post, etc.)

We participate in the BIC program, Breakfast in the Classroom, so I can't make this one a hands-on activity, but I would sure LOVE to.  I'm finding that BIC (while I support it in theory) is going to force me to change my style of "bribing" kids to get engaged because of all the food I like to incorporate.  :)  Anyway, here we go!

Grade Level: 6-8

Course: Math, Pre-Algebra

Standards:   6.RP.1, 6.RP.2, 6.RP.3, 7.RP.1, 7.RP.2,

SMP: MP1, MP2, MP3, MP4, MP6
Skills:Writing ratios, analyzing ratios, analyzing proportional relationships, solving proportions, using proportions in the real world, solving for missing values using proportions


How to use this as a mad minute:
I've taken to noting that each of these not only depends on the amount of time you are willing to commit to a given activity, but also to note the proficiency level of your students.  I say this because I'm working with a population of students that is causing me to shift my thinking about what a "warm up" might look like, due to lower levels of proficiency, language challenges, etc.  For a quick check in, 60 seconds or so, I would ask:

• What is the unit rate for mix, milk and eggs for 1 pancake?

How to use this as a warm up:
The above question would also work well for a warm up, if that is the skill you've been working on.  However, I might ask the students to find the ingredients needed for a simple number of pancakes in order to highlight proportional reasoning and multiplicative relationships:

• How much mix would I need for 28 pancakes?
• How many pancakes would 6 eggs make?  What about 7 eggs?

How to use this as a mini-lesson?
As you may have discovered reading other posts, I usually find images that catch my eye because I am skeptical.  So my first thought was, does it make sense for this box of pancakes to make that many pancakes?  Is this truly in "scale" or proportion?  I would ask my students, is this in proportion? If so, how many cups does the entire box hold?

• Note, I don't think it is!  If we use the eggs as a guide, the recipe is scaled by a factor of 9, but 9 times 1 cup is 9 cups, which is not 3Q.  (A great way to work on unit conversions!  Have you seen the "big G" conversion chart?  I love it!)  (Here's one place I found the image.)
• If we also use the factor of 9, the box would contain 18 cups of mix, which I would assume is more of a "Costco" size box, not what we see here.
• Finally, a scale factor of 9 would make only 126 pancakes, not 155. 
• If we use the milk as our guide, the SF is 12.  That would mean we need 24 eggs and 24 cups of "mix".  That should also make 336 pancakes.    Hmmm.....

How to use this as a full lesson?
I don't think this could be used as a full lesson, but it depends on your students.  If you choose to use it, I would extend the warm up and mini-lesson into a full discussion AS WELL as setting aside time for students to present rebuttals and/or corrections to the "recipe."  A great interdisciplinary connection would be having the students write the company (can we tell which company this is based on the colors?  I think so.) with their discoveries.  I suspect that the company might respond with some coupons or other "swag"!!

How to use this as an assessment?
Any one of the questions listed above would be perfect to use as an exit slip, a mini-quiz or an assessment question!


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

But it's a dry heat...

Personal Reflection:

I love "math fails" but I think these are really just "editing" fails!  We all make typos, some are just MUCH BIGGER than others!  I found two temperature fails in a short period of time and decided to go with them!  I encourage my kids to "wonder mathematically" a lot, and my own mathematical wondering led to this exploration.

Grade Level: 4-9

Course: Math, Pre-Algebra, Algebra

Standards:  5.NF.3, 5.NF.4, 5.NF.6, 6.EE.2, 6.EE.3, 6.EE.9
SMP: MP2, MP3, MP4, MP5, MP7
Skills: Research, Conversion, Science, Temperature scales


How to use this as a mad minute:
You have 60 seconds.  Name 3 different temperature scales.  Would these temperatures be appropriate in any of those scales?


How to use this as a warm up:
You could ask the students to consider one of the following:
1.  Do you think the temperatures listed are in Farenheit or Celsius?  Why? 

2. Given the chart at the right, convert one of the "high" temperatures from Kelvin to Celsius and Farenheit.  (Assume the temperature is in Kelvin.)
3. Why do you think there are multiple systems of temperature measurement? 
4. Can you think of a place that might actually be 519 degrees?  Where?  Why?
5. The weatherman is pointing at a temperature of 519 degrees, but immediately below, it says the high temperature is 52 degrees.  Based on this, can you guess what error might have occurred?  Explain.  Do you think the 789 degree temperature was the same mistake?  Why or why not?

How to use this as a mini-lesson:
I would start with a conversation, asking students what they know about temperature, different temperature scales, etc.  You might want to ask what body temperature, room temperature, and freezing and boiling points are on different scales.   They really need a way to frame this number!
Feel free to use the Dan Meyer technique of saying, "Choose a number you are SURE is TOO BIG" for room temperature in Celsius," or a number that is TOO SMALL for body temperature in Farenheit.  This helps the students work on both estimation, number sense, and confidence in math.

Introduce the Kelvin scale and why it is used.  Offer major numbers such as freezing and boiling, room temperature or body temperature on the scale.  Talk about why we have a scale like this.

If kids have access to technology, set them free to answer these questions themselves and be prepared to come back and share their findings!  You could challenge them:  "Is there a place in the US that could reach these temperatures?"  "Is there a place on Earth that could reach these temperatures?"  "Is there a place in our Solar System?"  Ask them to use their knowledge to make informed decisions, not random searches.

Gentle guidance could help:

• What planets might be more likely to be warmer?  Why?  
• What kinds of environments are warmer? 

Depending on the level of your students, ask them to explore the temperatures of different planets.  What traits do they possess when they are hotter?  How do scientists record temperatures on other planets?  If it's a mini-lesson, it's probably not a major lesson or life goal, but a chance to spark interest, address a cool concept and move on.  Don't let the details stop you from letting the kids explore!


How to use this as a full lesson?

Use the EQUATE thinking routine.  Give them the photos with NO guidance.  Let them Explore, Wonder, and Question.

Record their questions and clarify!  Develop depth to the questions by extending them, drawing out detail and asking how they might go further.

For example, a student might ask, "Is that even possible?"  This is a great "wonder" but not enough to explore mathematically.  What are they going to investigate?  How can they extend this question?  As you draw out these ideas, make sure to ask them to list what information they need to answer their questions.  Feel free to share answers or to encourage them to FIND THEIR OWN answers.  This is a great time to use technology to your advantage.  Students can research on phones and iPods, or you can nominate a class researcher who will research the answers to these questions while you continue to work with the rest of the class.  Narrow down your questions to your top two or three questions.  Tell them they can choose from "These" deep understanding questions.

Establish expectations for products, time frames, behaviors, and jobs.

Set them free!  Help them question and explore and apply their mathematical knowledge to solve their problems and answer their questions. 

How to use this as an assessment?
You know your students best! I would not use this as a formal assessment.  You could, however, find a similar graphic and ask it as a constructed response item on an assessment of your own!  You could take any of the lesson options above and extend it with provided rubrics, more structured questions, etc.

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

That's Some Inflation!

Personal Reflection:


I've heard recently about the collapse of Zimbabwe's currency and how they just keep printing larger and larger notes and that something like this probably wouldn't buy a cup of coffee.  (Apparently not true!) What causes inflation?  How does this connect to our own currency?  I know I wanted to investigate, so I hope students will too!

Grade Level: 4-9

Course: Math, Pre-Algebra, Algebra

Standards:  6.RP.1, 6.RP.2, 6.RP.3, 7.RP.1, 7.RP.2

SMP: MP1, MP2, MP3, MP4, MP5, MP6, MP7
Skills: Research, Conversion, Scientific Notation


How to use this as a mad minute:
You have 60 seconds.  What is this worth in US Dollars?


How to use this as a warm up:
You could ask the students to consider one of the following:
1.  Write one hundred trillion in scientific notation.
2.  As of May 21, 2013, 1 dollar in Zimbabwe is worth 0.00276 US Dollars.  How much is this note worth?
3.  What would 100 trillion US dollars be worth in Zimbabwe currency?
4.  If the US had 100 trillion dollars and divided it evenly among the citizens, how much would you get?
5.  Can you name the largest US bank note?  Why is that the largest one?
6.  Why can't poor countries just create these kinds of bills to pay off debts?


How to use this as a mini-lesson:
I would start with a conversation, asking students for their immediate thoughts and ideas.  PLEASE explore those and go with the flow!  They will ask amazing questions and take your class in directions you can't imagine!  If conversation stalls, try the warm up questions to get them talking and thinking.  They really need a way to frame this number!

Ask them to think about why the US doesn't create bills this large.  Is this even a real bill?  If so, could you cash it in at a bank?  Why or why not?

Why don't poor countries just make money like this and bring it to the US to cash it in? 

How to use this as a full lesson?
I would start with the warm up and mini lesson outlined above and then I would set the kids loose with a challenge.

CHOOSE ONE:
a.  Research inflation.  What causes it?  How is it controlled?  What happens when it isn't controlled?  How will inflation affect YOU in 20 years? 
OR
b.  Consider the IMP activity about the price of eggs.  (This is best for an Algebra 1 level class.)  It helps students to understand inflation and how prices grow and to predict the price of eggs in the future!  Link
OR
c.  Research the reasons for the collapse of the Euro and the financial crisis in Europe.  Create a 1 page poster that explains the BIG issues.  WHO?  WHAT? WHERE? WHEN?  WHY?
OR
d.  Choose a common item.  (Such as a pair of jeans.)  Find out the cost of that item in 5 different countries and convert it from the original currency to US Dollars.  (Use proportions to convert!)  Consider why prices vary so greatly in other countries.  Discuss why a pair of jeans would be more or less expensive elsewhere.

I'd ask students to be prepared to share their findings (perhaps in a jigsaw) with other students with about 15 minutes left in class.  This isn't intended to be a long term activity!

How to use this as an assessment?
You know your students best! I would not use this as a formal assessment.  You could, however, find a similar graphic and ask it as a constructed response item on an assessment of your own!  You could take any of the lesson options above and extend it with provided rubrics, more structured questions, etc.

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

Swimming Pools of Saliva

Personal Reflection:

Let's start off with being honest.  I do my share of internet surfing.  Two sites I visit regularly for their awesome "kid" content are uberhumor.com and 9gag.com.  You'll see their watermarks at the bottom of most of my photos.

This one stood out to me right away because I thought, "NO WAY!"   (And I bet your students will think that too!)  So, I thought, "Let's find out."
  

Grade Level: 3-8

Course: Math, Pre-Algebra

Standards:  6.EE.2, 6.EE.3, 6.EE.9, 6.G.2, 7.RP.1, 7.RP.2, 7.G.1, 7.G.6

SMP: MP1, MP2, MP3, MP4, MP5, MP7
Skills: Estimation, Volume, Unit conversion, Scientific Notation


How to use this as a mad minute:
Get out those smart phones, those electronic devices, iPods, laptops, iPads, etc.  Is this true?  Can you find an answer in 60 seconds or less?  GO!


How to use this as a warm up:
You could ask the students to consider one of the following:
1. List the information would you need to gather to determine this is true.
2.  Estimate how much saliva you produce in 1 hour.  1 day.  1 week.  1 year.
3.  How big is a swimming pool?  How much water do you think it holds?
4.  Calculate the volume of a swimming pool that is 50m x 25m x 2m.  (Olympic average.)
5.  How much saliva do you think is in a single cubic meter of water?
6.  If the volume of an Olympic Pool is 2,500,000 L, how much saliva does one person produce each day?

How to use this as a mini-lesson?
You have to decide how much freedom to give your students and how structured you want this to be.  It could be a great inspiration for how to find the volume of a rectangular prism (true swimming pools that are more like trapezoidal prisms), or how to convert between metric and English measurements, or how to convert between large and small numbers, or even how to use scientific notation appropriately.


Mini Lesson 1:  Volume
Let's find the volume of different pools!  (Olympic, neighborhood, backyard pools)
Olympic:  50m x 25m x 2m  (Note: Olympic pools are not rectangular prisms, but this is an average.)
Neighborhood:  25m x 10m x 1.5m  (Kids could find out their own measurements!)
Backyard:  Radius=2m, Depth= 1.5m (Cylinder volume!)

Mini Lesson 2:  Unit Conversion
Saliva is measured in ounces.  How much is 2,500,000 Liters  in ounces?  How do you convert?  What proportions do you use?

Mini Lesson 3:  Scientific Notation
An Olympic Swimming pool has a volume of about 2,500,000 Liters.  Write this in scientific notation.  If the average person creates 1 liter of saliva every day for 79 years, how much saliva will they create in a lifetime?  Write your answer in scientific notation.  Which number is larger?

Mini Lesson 4:  Is this reasonable?
If you are trying to do this as a mini lesson, kids will need as MUCH information as possible.  You will need to tell them how much an average pool holds.  (Olympic=2.5 million liters)  You'll need to tell them how much saliva a person produces each day.  (Approximately 1 liter)  How long does the average person live?  (In the US it is approximately 79 years)  Can you use this information to determine if the average person would fill a swimming pool with saliva?


How to use this as a full lesson?
Expand any of the mini lessons above to include practice problems, a homework worksheet, or a continued exploration.  For example:  How long would it take to fill a bathtub with saliva?  How much saliva does the city of Denver create each day?  Each year?  Is the amount of saliva created each year by the population of China MORE or less than the amount of water in The Great Lakes?

How to use this as an assessment?
You know your students best!  If I were doing this with a GOOD group of middle school students who had mastered volume, this is the assessment I'd give them.

Look at this meme!  Is it true?  Use your technology to research both saliva production and the size of swimming pools.  Then use your knowledge of volume to answer whether or not this is reasonable.   Justify your answers with clear mathematical knowledge and computation.  Use the rubric to get full credit!

My rubric would require showing formulas for volume and how it was computed, how they got their numbers for the dimensions of the pool and the amount of saliva and the life span, including documenting sources.  I'd want them to explain answers in complete sentences with correct mathematical vocabulary.

If your kids aren't ready for this freedom, structure it for them!  (But, please, give them a chance and build the opportunities.  They'll get there, I promise!)


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