Real Life Problems

What happens when math people get together for dinner?  We see dinner as a series of real-life problem solving!  First, I'll give you the problem--division of a fraction by a fraction.  It's often hard to think of real-life examples of this type of problem.  This problem is a good one to solve concretely (with manipulatives) or pictorially (with model drawing.)  An added bonus;;; This no-bake pie is a refreshing summer dessert!  

Lemonade Ice Cream Pie

Sharon wants to make a Lemonade Ice Cream Pie. The recipe calls for ½ gallon of ice cream, but when she gets to the store, she finds that ice cream containers now come in only 1.5 quart containers.  How many containers does she need to buy, and how much does she need to use, to make the pie?

Recipe for Lemonade Ice Cream Pie

2 Oreo-cookie pie crusts

1/2 gal. vanilla ice cream, softened 

1 container (12 oz.) frozen lemonade concentrate (either pink or regular), completely thawed

Chocolate sauce

Using a mixing spoon or a whisk, combine the ice cream and lemonade. Pour into the pie crusts. Freeze overnight. Drizzle with chocolate sauce before serving.

Notes: It seems to be fine to let the ice cream get almost liquid, which makes it a cinch to mix. And you can thaw the lemonade right in the can; just open it when you can squish the can.

Another Great Singapore Math Problem

Marilyn from NJ sent me this 4th grade problem.  First, I made a video using my smart recorder.  In my defense, I got in VERY late last night and woke up VERY early this morning, so thinking wasn't very high on my list.  This problem is a great platform for having students visualize the problem before they start to solve it.  Lots of ways to incorporate the CCS PRACTICE standards here!

Priscilla was making gift baskets. Each basket would contain three soaps and two bottles of lotion. Priscilla had 293 soaps and 167 bottles of lotion. How many gift baskets could Priscilla complete?

If I think about it, I realize I don't have to do all the division.  I can just estimate first.  I can make just under 30 baskets using the soaps and just over 80 baskets using the lotion.  Since I only want complete baskets, I need to figure out the exact number of baskets using lotion. Wish I'd thought of that before I did all this work.

This problem also highlights the issue of remainders in division.  Do I round up?  Do I discard?  Do I make it a fraction or decimal?  It makes this problem really interesting.  

All in all, a great problem.  Wish I'd thought about it before I solved it.   But isn't that what your students would do?  

A Great Problem for Mathspot.Net

I found this problem on Mathspot.net, a great blog by Lisa Englard and really liked it.  It was co-written by Lisa and first appeared in Teaching Children Mathematics, Math by the Month column, October 2013.  It is here with Lisa's permission.  

Jared’s mom works for a company that publishes books. When he visits her office, he likes to watch the machine that binds the books. Mr. Green, who runs the machine, told Jared that the machine can bind 12,000 books in 1 hour and 20 minutes and that the machine runs steadily for 10 hours every day. He also found out from Mr. Lee in marketing that last month, the company printed fiction and non-fiction books in the ratio of 4:1, with 540,000 more fiction books printed than non-fiction. Jared’s mom asked him if he could use all the information he learned to figure out how many days it took last month to bind all the fiction and non-fiction books that were printed. Does he have enough information? If so, how many days did it take? If not, what other information does he need? 

There's a Sale! What Percent are you Saving?

I was sitting at the airport, one of my favorite places to find math problems. I'm also an accomplished eavesdropped.  An commercial played on TV, touting a huge savings of $10 off every $25 spent.  The woman behind me turned to her friend and asked, "What percent savings is that?"  I thought it would make an interesting question to ask our students, since they might have lots of different ways to show their number sense as they solve it.

Thinking Blocks is an App!!

It's actually four apps, and they are wonderful!  For all you model drawing enthusiasts, get on board and download these apps NOW!  They are free until Aug. 15.  I love how they make the make the models proportional.  I'm not sure what they'll cot after Aug. 15, but I'm pretty sure I'd pay it!

Two Step Problem Solving with Second Grade

I love working with kids...and when I can't do it in person, I do it by email and sometimes, even, skype!  Theresa Trevino is an amazing second grade teacher in Houston, TX.  I saw a version of this problem at NCTM this week and wondered how her second graders would handle it.  Next week, I'm hoping to skype in and talk to them about it!

The problem reads
A zoo has 7 camels and some giraffes in a big corral.  There are 15 animals in the corral.  Then they got 4 more giraffes.  How many giraffes are there now?

You can see more solutions and some video clips by visiting Theresa's blog!

 http://trevinos2ndgrade.blogspot.com/2013/04/long-distance-problem-solving-with.html?showComment=1366425667754#c8757176304674489062   

Word Problems with Fractions

Part of the common core standards asks our children to contextualize numbers.  When faced with a problem like this, do your students know if it's a multiplication or division problem?

Model drawing will help them visualize what to do with the numbers!  

Fractions are tricky!  Adding and subtracting is conceptually easy, but the procedure is tough.  Multiplication and division are the opposite!  It's easy to teach kids to invert and multiply, but why does that work?  If children understand WHY, they'll be much more successful in the short and the long run!  

Adding Fractions the Singapore Way!

I'm getting lots of fraction questions lately...must be close to testing time!  There are so many important teaching points here.  I think this addresses that we can only add like things together.  If they aren't alike, we have to find a common term.  That's true in first grade.  When we add circles and triangles, first we have to find the common term, shapes.  In fractions, if our denominators aren't alike, we have to find the common term before we can add them!

How does this address the common core standards?  What extension questions are you asking?  Can you step back and bit and teach them to persevere? 

Singapore Math and Equivalent Fractions

Roxanne, a fourth grade teacher from Toledo, sent me this problem.  There is often more than one way to draw a solution to a problem.  I always just look for a solution that the students have labelled, can explain, and makes sense to them.

I could have also drawn a unit bar, divided into fifths, than divided each section into three parts.  That would have achieved the same thing.  I love having multiple, visual approaches--and of course, it aligns to the practice standards of the Common Core State Standards for Mathematical Practices!

Anchor Charts

Take an objective look at your room.  What percent of the space is taken up with each content area?  What is taken up with store-bought materials that just becomes wallpaper?  Does math have equal representation? Your walls should reflect your teaching style.  Our walls need to be dynamic and part of our instruction   I strongly believe in anchor charts.

This is an anchor chart used in my old school district

 I wish I could remember where I got this one!!

Anchor charts don't have to be cute.  As a matter of fact, I believe they should be made with your students and should be in the children's natural language.  You may continue to edit them as you continue instruction in that area or spiral back to it, increasing the depth and complexity.  They need to be referenced during instruction so they don't just become wall paper.  Studies show that students look towards these anchor charts, even though they are removed or covered during testing, as a memory trigger.

 This came from a classroom in Holland, MI

Thanks, Jana Hazekamp for sharing these!

You can see lots more on my pinterest anchor chart page.  Pinterest.com/Ricky_Mikelman

Fifth Grade Model Drawing

This problem came to me from some friends.  It's got a "hidden question" that you have to answer before you can answer the stated question.  I also show the array model of multiplication here instead of the traditional algorithm.

How Would You (or your class) Draw This?

David weighed 240 pounds on Earth and 40 pounds on the moon. How much would Steven weigh on the moon if he weighs 180 pounds on Earth?

This problem was presented to an 8th grade class.  I think model drawing makes it much more accessible to students in a lower grade.  Here's how I solved it!  

Elapsed Time

I just spent a wonderful week in Salt Lake City, Phoenix, and Albuquerque.  The #1 question was, "How do I help my students with elapsed time?"  Here are some suggestions.  I look forward to your comments on other ways to teach this difficult concept in a way that makes sense to students.

First, student should understand how to use number bonds to add time or to break minutes into hours and minutes.  This is stressing the concept that the hour is a unit.

From there, they can move to model drawing.  

The biggest challenge for students is deciding how to divide up the unit. It helps the kids to label the beginning and ending times.  Reading one piece at a time and plugging it into the model really helps!

 Remember, not all the models will look the same.  Some may divide it into 15 minute chunks and some will see the whole hour.  As long as its labeled and they can explain it, I take it!

This is a two-step, part-whole problem.  Reading one piece at a time is the key to success!

This problem is a little harder.  First, you'll need to discuss the answer statement with your students.  I decided to leave a place for "will" or "will not" in mine.  You'll notice my unit bar didn't end proportional.  Oops!  That's why we do math in pencil.

How do you teach elapsed time?  I'd love to hear your suggestions.

SDE's Singapore Math Website

I'm so excited about SDE's new Singapore Math website.  This is a great way to introduce Singapore Math to others, including your parents.  There are some great videos (with more to come!) and resources.  Please take some time to explore!

http://sde.com/singapore-math/