Preventing Summer Slide

Summer is here...Yippeee!  Today I listened to a news story discussing how much time our students have off due to summer break.  From kindergarten to 5th grade, they have 15 months of summer!  That's a ton!  Summer is an important break from "book" learning, but there's no need for students to slide.

Turn this into the Summer of Measurement.  Have students cook, doubling recipes or cutting them in half.  Give them only a 1/4 and 1/3 cup measuring cup so they have to multiply fractions.  Have them weigh ingredients.  Try a measurement scavenger hunt, looking for metric and customary measurements.

Taking a vacation?  Let them track mileage, figure out miles per gallon, and use maps.  Have them use an analog watch to keep track of time and estimate arrival times or elapsed time.  If you need to arrive at 2:30, and it takes 4 hours, what time do you need to leave?  If you have children of different ages, you can differentiate the problems.  An older child can get the same problem, but be told you need to arrive at 2:30 and have to drive 240 miles, at about 60 mph.


Your phone most likely has a great app to help them with walking, biking, or driving (you, not them!)  They will learn how far a mile is only when they have multiple experiences.

Don't forget to practice your math facts!  Also an important step in preventing summer slide.  Enjoy the summer and make math an everyday part of your break.

Just saw this on YouTube...worth watching, although it's about the differences based on socioeconomics.

Summer Learning Loss

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.

Is it Enough?

I've been so busy that I haven't sat down to blog more about my trip to Singapore.  It's coming, I promise.  Another experience that had quite an impact on me was teacher response to student work.  In every class, we watched students work in happy, noisy groups.  It was rare we saw a student off-task.  (Honestly, I can't think of a time we saw someone goofing off, but there must have been one!!)

When students thought they completed their work and approached the teacher, we never heard them ask if the answer was correct.  Instead, the more common question was, "Is this enough?"  In one class, we watched a group of boys given a very challenging problem.  Three times they approached the teacher to ask, "Is this enough?"

Each time, the teacher looked at them and responded, "It it enough?"

After the third time, one of the boys looked at his partners and said, "If the teacher asks 'is it enough,' it isn't enough."

How can we get our students to focus on the process, not the product?  Isn't that what the NCTM Math Practices and CCSS are asking us to do?   Enjoy these examples of journals from Primary 2 (second grade) journals.  I think they show enough!

School Visits in Singapore Day 1

We visited the Tao Nan School at its temporary site on Wed., hosted by Mrs. Fiona Soh.  I'd met her son at a UCLA party in Houston.  The school is 108 years old and the original building  http://tinyurl.com/m7tsc7j is being updated to meet the Ministry of Education's requirement that all schools run on a single schedule within a few years.  The old school is quite beautiful. The school's enrollment is nearly 2400 students, with grades 4-6 coming from 8-1 and grades 1-3 coming from 1:30-6:30.   We were greeted so warmly by Dr. Chin Kim Woon, who talked about the joys and challenges of being a principal in Singapore.


This building is used as rotating temporary housing as schools are being updated.  This is one section out of 4!!

We were privileged to see three lessons taught to two groups of students.  The first was a science lesson taught to sixth graders b Mrs, Fiona Soh, a master teacher.  As we entered the room with the teacher, the students stood up. The prefect said, "Bow."  The students bowed in unison and said, "Good morning Mrs. Soh."  After she introduced us, we got a bow and a choral welcome also.  It showed such respect!!
 The content of the lesson was interesting and engaging.  More important was how it was taught,  Mrs, Soh gave some very brief instructions on data that was to be collected.  Eliza Thomas and I were so impressed at how the students worked together on how they would organize their data  Each group had different ideas and charts, but all were very neat and clear.  All students had journals, pencil boxes, and white out!

The mood was very relaxed and light as the students got to work.  This class is the gifted class, so it is quite small by Singapore standards--only 18 students. but they were all on task and engaged.

Then the teachers moved to save instructional time and we saw a math lesson with the same students by Mrs Ngoh Poh Sze Wei. First, they were asked to explore the relationship between two angles within a circle on a computer.  Then, using only a piece of paper and a ruler, they were asked to find the exact center of a circle.

Students got right to work and would excitedly approach the teacher if they thought they had the answer.  Usually, her response was, "Are you sure?" or "Is that enough?"  Eliza and I had to cover our mouths when one boy said to another, "If she asks if it's enough, it isn't."

We were so impressed with how the students persevere and work together.  Students would share their answers with the group so others could learn from them.  It really exemplifies what we're trying to get to with the CCSS Practice Standards.      

The third lesson, taught by Mr. Clifton Lim,  was a fill the bucket lesson using a computer program, with gifted 4th graders.  I must admit we were happy to go the air conditioned computer lab!!  This lesson was very challenging to the students but they worked together and were gently guided by the teacher.  The lesson was not completed but they agreed to continue and discuss it again later in the week, after they'd had more time to explore the concept.   as we left the class, they bowed and said, "Thank you for teaching us."          
                                                                                   We ended the day with a discussion with one of the Vice Principals, Ms. Cheryl Chee about the challenges in the Singapore Schools.  She talked about how hard they are working to move away from summative  testing and its pressures and develop portfolios.  We also talked about teacher evaluation, professional development, and improvement plans.  It was a packed morning and we learned so much.  We are so thankful to the staff at Tao Nan School!

Fascinated by the Iditarod!

I've always been fascinated by the Iditarod.  So are your students.  And there's so much great math involved.  The dogs eat 200,000 calories a day.  How many calories will they need over the course of the race?  How many per dog?  How many miles do the mushers have to cover?  How many miles do they need to cover per day to finish in 9 days?  10 days?  Compare highs and lows and find the difference.  Compare to your city.  Follow the Iditarod and ask your students to write their own math stories.  Iditarod.com

Iditarod.com

Don't Be So Helpful!

I had the joy of spending a day learning from Dr. Yeap Ban Har, from Singapore, again last week.  I've seen him many times and always learn something new.  This time he talked about the importance of social learning for our students--how they can learn from each other with less help from us.

I use these strips for lots of activities, including vocabulary, divisibility rules, rounding and estimating, ordering, etc.  But this was a task for teachers.

  

Students have built the number 3,246. 

 You've asked them to find the number that is 300 less than this number, but they're struggling.  What questions can you ask the group to help move them?  And can you sequence your questions from the least helpful to the most helpful?  We tend to jump in and tell students what to do and rescue them.  As we work to build more perseverance, we need to be a lot less helpful.

These are the questions a group in TX came up with.  How would you sequence them from least helpful to most helpful?  What other questions would you add?  It's interesting to take the time to think through our questions.  To help our students more, we need to be a lot less helpful!

I've been working with place value strips for a long time. ( I'm very excited about Crystal Spring Book's new student-sized strips.  They come in sets of 10 or 30.  http://www.crystalspringsbooks.com/student-size-4-digit-place-value-strips-small-group-set.html .)

What is Number Sense?

We throw the term around but rarely define it.  I had two experiences this week that help bring the concept into sharper focus.

I was fortunate enough to work with second graders on Oahu, in a Hawai’ian language school.   I had beansticks and bundles and leftovers with me.  After the keiki (children) became familiar with beansticks, I posed this question to them; “Build the number that is 1 beanstick and 15 beans.” 

All children were able to figure out it equaled 25.   But some children built it with two beansticks and 5 loose beans and some did exactly what I’d asked.  Then we had to discuss if both answers were correct and equal.  It led to a lively discussion and some very strong opinions!

It was developmentally interesting to see the children struggle when we moved to bundles and leftovers.  Since they couldn’t see the 10s as clearly, building one bundle with 20 ones was much more problematic.  The children spent a great deal of time taking the bundles apart, counting 10s, and putting them back together.  Obviously, they didn't trust my bundling skills!!

My second experience was sitting in a workshop with Dr. Yeap Ban Har, our favorite expert from Singapore.   He talked about number sense as a complete understanding of number bonds.  Our children need to understand 25 is 20 + 5, but also 10 + 15.  Without this understanding, they won’t be prepared for regrouping.  As they get older, that understanding needs to generalize.  3/5 is 2/5 + 1/5.  If one dividing 351 by 3, it doesn’t help much to break the number into 300 + 50 + 1.  Number sense means the child understands that 300 + 30 + 21 is a much more logical way to decompose the number.  Ban Har will be joining us at our National Conference for Singapore Math on July 9-10. http://sde.com/nationals/2014/

Try posing some number sense questions to your students and then give them some time to struggle with the concepts.  Don’t jump in and help too soon!

Come See Me!

I have an exciting Spring planned.  Besides all my regular fun things, March 15 will be my first time presenting at ASCD in Los Angeles.  March 22-29 is my trip to Singapore!  I'm beyond excited.  I promise to post everyday about what I see and what I learn.  I already have two days scheduled in classrooms, thanks to Char Forsten.  Eliza Thomas, another fabulous SDE presenter will be joining me.

Shortly after my return,  I'll be presenting a session on Fraction Games at NCTM in New Orleans in April.  NCTM is always an exciting time to learn, shop, and see what's coming.  I know Kristin Hilty is also presenting there this year.

July is the National Conference on Singapore Math.  I'm so excited about this year's conference.  Dr. Yeap Ban Har is doing a full day on whole numbers this year.  Marcy Cook is presenting sessions on critical thinking and reasoning (all aligned to CCSS!), and Jasmine Kho is coming from Singapore to teach us about lesson planning and algebraic thinking.  For more information about the conference, visit the SDE website

http://sde.com/singapore-math2014/Presenters.asp 

Singapore Math and Flipped Learning

Theresa and Stacye approached me and asked how I felt about flipped learning.  I love the idea in principle but wasn't sure about how it would work with second graders.  Especially since they're also adopting Math in Focus this year.  It seems like a lot to tackle all at once.  But if they were game, so was I, and I agreed to help them on their journey.  Now, we're four months into the experiment and things seem to be going really well.  I've talked to parents, other teachers, the principal and everyone is enthusiastic.  I've even heard from other schools that they're using the videos in class for their students and to train teachers.

What really blew me away was when I went to do some model drawing in another second grade class, who are also part of the journey.  We'd drawn a model and were ready to subtract 179 from 603.  Buck raised his hand and asked if they should use compensation subtraction, open number line, or traditional algorithm.  Whoa!  Turns out an unexpected side benefit is children learn more vocabulary from watching the videos repeated times.  I asked Buck which method made more sense to him.  He said, "I like traditional, but compensation makes more sense because there's a zero."

Theresa and Stacye will be presenting a session on Flipped Learning at our National Conference on Singapore Math this summer.  Registration is now open.  http://sde.com/singapore-math2014/  I can't wait to see what they have to say.

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!

Singapore Math Method for Compensation Subtraction

After years of doing intervention work with subtraction across a zero, I was so excited when I learned about compensation subtraction.  It's also called constant difference.  It helped so many kids and it wasn't just a trick.  They understood why they were doing it!

When I taught larger numbers, I generally reverted to the traditional method, or used many steps.  After spending a really fun week in Cleveland, MS, Lon Hayes sent me an email describing this method of compensation subtraction with larger numbers.  Thanks so much Lon!!

Try this with your class and let me know how it goes!