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?  

Singapore Math--Model Drawing vs. Algebra

I was lucky enough to watch Kim Bell present at NCCTM a bit ago.  Kim is another wonderful SDE presenter.  She showed this wonderful comparison of model drawing to algebra.  I'm using this here with her permission.

Mrs. Grant made 300 cookies. She sold  3/4  of them and gave  1/3  of the remainder to her neighbor. How many cookies were left?

¾ * (y )+ 1/3 (1/4 * y) + x= y
Let y=300 (total cookies)

¾ * 300 + 1/3 (1/4 * 300) + x=300

225 + 1/3 (1/4*300) + x=300

225 + 1/3 (75) + x=300

225 + 25 + x=300

250+x=300

250-250 + x=300 – 250

x=50

Watch to video to see how much easier it is with model drawing!!

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? 

Building Number Sense with the Open Number Line

I've been playing a lot with the open number line lately.  It's a great way to add or subtract and works with all grades.  Each student can approach it at their level (which makes a great assessment!)  I love to have students do it by themselves and explain their thinking.  This is a great way to have students see more efficient ways of solving the problem.  It's also wonderful for children who have trouble with subtraction...they now see that it's just a relationship between two numbers.  The video shows examples of two digit and three digit numbers and numbers with decimals.  If your students understand the concept, they can take it to fractions, elapsed time, and measurement!

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!