Singapore Math Source - a blog from a national trainer

Cassy Turner is a trainer in Singapore Math that has a blog I have found very helpful in the past week. The last two posts I have added have come from this site. I have been in contact with her and she is a great source of information on Singapore Math. If you use Twitter, you can follow her: @Cassyt.

Bar Model Structure

Help in determining whether one bar or two is needed to solve problems. Three clear examples.
"Content from http://SingaporeMathSource.com (c) Cassandra Turner reproduced courtesy of the Author."

Old School: Traditional Standards New Methods - register for free to access Singapore math problems for guided practice, formative assessments, quizzes, tests, etc.

You can search for problems based on grade, topic, and question type.

Here is an example:

 

Test Papers

Search	Topic Addition and Subtraction Combination Questions Fractions General Graphs, Tables and Piecharts Lines, Curves and Surfaces Measurements Multiplication and Division Notation and Place values Shapes and Patterns
Question Type Free-response Multiple Choice

---

21.

At a soccer match, Team A had 300 supporters. Team B had 80 fewer supporters than Team A. How many supporters were there in Team B?

Ans:_________

---

22.

10 groups of children went camping. There were 3 boys and 2 girls in each group. How many children went camping?

Ans:_________

---

23.

Mrs Tan gives 30 stamps to her pupils.
Each pupils recieves 3 stamps.
How many pupils are there?

Ans:_________

---

24.

473 is ____________________ more than 463.

---

25.

______________________ is 100 less than 390.

---

26.

Do the following sums.

    6 5 2
 + 1 3 7
_______

_______

Ans:___________________________ .

---

27.

    5 4 6
 + 1 2 9
_______

_______

Ans:___________________________ .

---

28.

    7 4 5
 -  3 0 8
_______

_______

Ans:___________________________ .

---

29.

    4 0 0
 -  1 5 7
_______

_______

Ans:___________________________ .

---

30.

There were 275 books in Box A.
There were 87 more books in Box B than in Box A.
How many books were there in Box B?

Ans:_____.

Would you like to sponsor Old School? Contact Us!

Singapore Math Blog from Math in Focus trainer

Kelli Trainer has a Singapore Math Blog. She was a trainer for us in late July and in October. You can subscribe, so you will get notification when a new post has been added. Look at her post dated November 28 to learn about the free online math interactives at MathFrames. Great visuals and explanations to see what is available. There are games for number bonds, multiples, patterns, missing digits when multipliying, etc.
Tobe Joffe recommened MathFrames to me this week. Now you can get an overview on one page before you try it. http://www.mathsframe.co.uk/free_resources.asp

Polar Express Math

An elf that wishes to remain anonymous shared this with me today. There are 10 word problems that relate to the Polar Express book. Most could be solved with Model Drawing. The teacher changes out the names used in the problems with students' names. This teacher will do one a day the last two weeks before Christmas break. Ten engaging and relevant problems that would be most appropriate for 2nd - 3rd grade. Here are Problem 1 and Problem 9 as a sample:

1) When Kelly got on board the Polar Express, there were 31 seats available. The train has a total of 159 seats. How many seats were already filled?

9) As Santa and his reindeer took off into the sky, they were traveling at 431 miles per hour. The farther away they got the faster they would go. The Sky Officer measured Santa traveling at the speed of 900 miles per hour. How much faster was Santa traveling than when he first took off into the air?

Thank you so much for passing this on!

Winter Model Drawing Problems for 2nd and 3rd grade

Read it, draw it, solve it!

1.     A cup of hot chocolate had 19 mini-marshmallows. 14 of them are gone.

How many are left?

2.     A group of friends has four sleds. A friend brings 2 more sleds. How many sleds do they have?

3.     During November and December students collect hats to give to others. If 33 hats were collected over two months and 24 of them were collected in December, how many were collected in November?

4.     A box has 36 candy canes. Another box has 12 more. How many candy canes are in this box?

5.     There are 40 pears in a box of fruit. There are 8 less apples than pears in the box.

a.     How many apples are in the box?

          b.     How many pieces of fruit are in the box?

6.     There are 38 icicles hanging from a home’s roof. If the neighbor’s house

has 56 more icicles, how many icicles are hanging from its roof?

Thanksgiving Model Drawing

                                                                                    

Read, draw, and solve the following Thanksgiving math puzzles.

1.      At my Thanksgiving meal there are 5 pumpkin pies and 2 chocolate pies.

a.      How many pies are there altogether?

b.      How many more pumpkin pies than chocolate pies are there?

2.      Aunt Betsy brings 3 dozen deviled eggs to Thanksgiving. Great Aunt Linda brings 2 more dozen deviled eggs than Aunt Betsy.

a.      How many dozen deviled eggs does Great Aunt Linda bring? How many deviled eggs is that?

b.       How many dozen deviled eggs are there altogether?   How many deviled eggs are there altogether?

3.      At the end of the 3^rd quarter of the football game, the Detroit Lions are beating the            

New England Patriots 24 to 17.

a.      How many total points have been scored in the game?

     

b.      How many less points has New England scored than Detroit?

4.      The 2010 Macy’s Thanksgiving Day Parade will feature 25 large floats and 15 giant balloons. How many more large floats than giant balloons are there?

5.      A farm has 730 turkeys and ducks. 426 of the birds are turkeys.

a.      How many ducks are there?

b.   How many fewer ducks than turkeys are there?

Conrad Wolfram: Teaching kids real math with computers | Video on TED.com

Conrad Wolfram: Teaching kids real math with computers | Video on TED.com

Wes Fryer on Digital Storytelling in the Math Classroom

Kids Playing Math - Differentiating Instruction

Here are some pictures of my kids today playing math! We divided the kids up into 4 ability groups. Our stations were: fact practice (on paper and on computers), independent work on past skills from previous chapter, teacher directed doing practice pages in our current chapter (model drawing), and a game that was in our book. The game ended up going over really well with the kids. They had to pick cards from different tubs. The cards had a "Who" a "What" and a "Number." They had to pick one who & what, and two numbers. They created their own real life story problems on their own.
I'm sorry that some of the pics are sideways....not sure why:(

Kids Playing Math!

Real World Math - Movies with Math Activities

The Futures Channel presents a plethora of movies highlighting math in the real world.  From kitchens to computers, your students will quickly understand that math matters because math is hands-on - everywhere.

November Number Bonds

Dear Teachers,

I should have given you an alliteration alert. As we begin November it is a perfect month to add a daily focus on Number Bonds no matter what grade level you teach. A first grade classroom I was in recently was able to give me all the number bonds for the number 4 They told me that 3 and 1 bonded to make 4 just like 1 and 3 because of the Commutative Property of Addition. Wow! Then, theyextended their thinking to let me know that since 2 “ones” and 2 “ones” bonded to make 4 “ones”, 2 “hundreds” and 2 “hundreds” would bond to make 4 “hundreds”. Let me again say, “Wow”!

Tomorrow is November 3^rd.  If you have younger students, it would be wonderful to review the bonds for one, two and three. There aren’t a lot of bonds for these small numbers to work on. Just 5 minutes to visually revisit the part, part, whole concept, could pay big dividends. A number bond is simply a graphic organizer and is “stickier” for the brain than 2+1=3 which is the abstract concept. It is also a different approach because it helps to start with the “whole” and ask how many different ways can we make 3? Do we “own” all of them for life?

Thursday will be November 4^th. Number Bonds for 4.( Kindergarten might want to start by focusing on recognizing a set of, for example, 3 items without having to count 1, 2, 3. Our 1^st -5^th Math in Focus trainer taught us that this skill is called “subitizing”. Recognize 4 items, 5 items. Play “I Spy”. I spy 3 items. I spy 4 items, etc., perhaps even try a few very small number bonds.) First grade, you have been working on mastery of the number bonds up to 10. This is a great time to reemphasize these bonds. You will be working on number bonds to 20 in Ch. 7 and addition facts in Ch. 8, so having more and more of the bonds to 10 mastered will

be worth any extra time you can find.

2^nd -5^th grade teachers: any extra help your students are given on mastery of these number bonds would greatly benefit them. Whether it is mental math or paper and pencil calculations, we can help our students by making these bonds with numbers, bonds for life. The 2^nd grade teachers were all sent some 1^st grade reteach materials to use as a supplement during warm up time or during a time when you want to differentiate to each learner’s needs, etc.  I know the 3^rd -5^th grade teachers are working with students who do not have bonded that 5 and 3 make 8. Next Monday is the 8^th.

It would be an opportune time to help students make these connections. What are all the ways to make 8? Working on 5 through 10 on Monday,

Tuesday and Wednesday, you could then proceed to 11-20 the next two weeks.

If you feel your own background knowledge on number bonds could use some help, that is understandable. This is a link from a Blog

that explains the concept well:

http://www.google.com/imgres?imgurl=http://letsplaymath.files.wordpress.com/2007/01/number-bonds.PNG&imgrefurl=http://letsplaymath.net/2007/01/13/number-bonds-better-understanding/&usg=__O9YhE73j0dZ1liImOJoAXT8EN9E=&h=250&w=243&sz=8&hl=en&start=4&zoom=1&um=1&itbs=1&tbnid=NyDE9jBJttB0TM:&tbnh=111&tbnw=108&prev=/images%3Fq%3Dwhat%2Bare%2Bnumber%2Bbonds%253F%26um%3D1%26hl%3Den%26sa%3DN%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7SUNA_en%26tbs%3Disch:1

If you would like an interactive online number bond game that is free, check out the following:

http://www.amblesideprimary.com/ambleweb/mentalmaths/numberbond.html

In this game students can work on bonds to 5, bonds to 10, and even bonds to 100. You can set the game to work on the bonds for the

number you choose. You could use this game with your students on the Mimio to work on this together.

Number bonds for five minutes a day, try it! See if you can find the time during the transitions. Lining up to go to recess?

Work on the number bonds for 5. Coming in from lunch? Have the game on the overhead as students enter to set the tone for academics after lunch. Use individual white boards for students to write the number bonds and show you. I am sure you have even more ideas that would allow you to find those teachable moments to creatively sneak number bonds into November.

As always, please let me know if I can help in any way.

Respectfully,

Lorinda

My Hero, Zero!

Teachers,

I've seen some amazing seasonal themed lessons this week:  predicting the number of pumpkin seeds, using pumpkin seeds for number bond manipulatives, estimating pumpkin weight, etc. If you are looking for a mathematical theme for tomorrow consider, Zero.  Why Zero? Did you know that zero has a scary past? Zero is so unusual and interesting it has its own "biography", Zero: The Biography of a Dangerous Idea, by Charles Seife. Seife states, "as natural as zero seems to us today, for ancient peoples zero was a foreign - and frightening - idea." The Greeks banned it!

Zero doesn’t' behave like other numbers. Add a number to itself and it changes. Not with zero,

0 + 0 = 0, no change. Zero is neither positive or negative. It is the only number separating these two number realms on the number line. In our decimal system zero is the only number that can act as a placeholder and not as a number. In fact look at your computer keyboard, your phone - where is zero? It isn't before the one; it's after the nine. This is a remnant of viewing zero as a placeholder only and not as a number itself. Does zero matter? Start counting. 1, 2, 3, looks like we don't need it, but wait, 8,9, 10. There it is as a placeholder. We can approach infinity with 0 as a placeholder. Place value is all about the power of zero to allow us to only use 10 digits to represent numbers as large as we need. But, sometimes zero as a number acts as if it doesn't matter at all. Add 0 to 7,

still 7,  The Identity Property of Addition. But multiply 7 by 0. Ahh! Zero is suddenly very powerful as a number. Poof! Zero is all that is left, The Multiplicative Property of Zero. Zero can by scary - we wouldn't want to multiply any student by zero because we like them, right? :) When zero becomes a multiplier it destroys everything in its path - Wow! Wait, there's more, what about division? 7/0, what is that? Well, we can check division by multiplication, correct? Let's see, what if 7/0 =0,  0 times 0 would have to equal 7. But, 0 times 0 = 0 and the last time I checked 0 was not equal to 7, so we have a huge problem. Dividing any number by 0 throws our mathematical system out of whack. ERROR - is what your calculator tells you. But, divide by a number that approaches but is not quite equal to zero and we approach infinity. Crazy, isn't it?

Dress zero up in a hero costume and you have a 3 minute classic on Zero as a place holder from Schoolhouse Rocks, "Zero, my Hero, how wonderful you are": http://www.youtube.com/watch?v=Nvc2PPTlW7k

So, zero ... hero or ...?

Happy last weekend in October,

Lorinda

We Play Math!: Welcome!

Check out this new blog by our Math Coach, Lorinda Kline. Share this link with parents an others who are interested in understanding our adoption of Singapore Math - Math in Focus.

We Play Math!: Welcome!: "Dear parents and community members, This is the newest development in an ongoing effort to improve communication and collaboration in our p..."

Extra Guided Practice Fraction Word Problems for 5th Grade Model Drawing

Fraction Word Problems 1. Muriel read 5/8 of a book on Monday and 1/4 of the remainder on Tuesday. If she read 60 pages on Monday, how many more pages did she read on Monday than on Tuesday?

2. Henry has 70 balloons. 1/10 of them are green, and 3/5 of them are orange. What is the difference between the number of orange and green balloons Henry has?

3. Kim has 45 picture books. 1/9 of them are mysteries. 3/9 of them are animal
stories. The rest of them are nonfiction. How many more nonfiction books does Kim have than the total of mysteries and animal stories?

The American Math Challenge starts today!

 The American Math Challenge is held on these days. It is not too late to get your students involved. It's free!

Harrison 4th grade students test their math skills in the American Math Challenge. 

Lorinda Kline works with a 4th grade student during the American Math Challenge.

Edutopia News / October 20, 2010

There are some great math tips in this edition of Edutopia Magazine.
Check it out!

Edutopia News / October 20, 2010

24 Model Drawing Problems

Here is a copy of an email you should have received from Lorinda.  It is a PDF file so you should be able to save it to a resource folder of your choice.  

Teachers,

I wanted to pass on to you a handout from the 2009 North Carolina Council of Teachers of Mathematics conference has 24 word problems that increase in complexity from #1 to #24. They would make very good extra guided practice problems for Model Drawing as you go through the year. Take a look at which problems would work with your grade level and begin a bit easier to learn the structure if you haven’t already.

Sixth grade teachers have been included in order to see an overview of the principals behind Singapore mathematics and the Model Drawing problem solving approach. These 24 problems would be a wonderful supplement to your resources, too.

First, learn the structure with the easier problems and then progress to solving quite difficult word problems using the structure as a tool.

Have a great fall break,

Lorinda Kline

My favorite interactive sites

A few have asked about my favorite interactive sites.  Here they are.  Some sites have great activities in other content areas.  Please add your favorites to the list.

Cool Math I (ages 3-12)

Cool Math II (ages 13-100)

Sheppard Software (all ages & abilities)  Mimio friendly!

Internet4Classrooms (multi-age skill-builders)

That Quiz  (adaptable skill practice)

Interactive Math Library

Math Buddies - Bridging the Gap

A Harrison 4th grader coaches a 2nd grade student in using digital base 10 blocks to represent a number.

A Harrison fourth grader uses linking blocks to help a second grader learn counting-on.

Deb McClintock closes the 2nd/4th grade Math Buddies lesson with a 

picture book story illustrating odd and even numbers.

A Reading Buddies program is being effectively used at Harrison, so Deb McClintock and Rick Glass came up with the idea of starting Math Buddies.   They are combining their 2nd and 4th grade classes for weekly joint lessons.  The students are using their time together to share what they are studying in Math. They are solving Math problems as they work one to one and in small groups.  The students also use maniplulatives and the interactive white board to demonstrate what they are learning.  The teachers believe that this time together is well-spent.  The second graders are learning from their peers as well as their teacher and the fourth graders are reinforcing their skills by teaching them to others.

Playing to learn math

"Playing to Learn Math," is a Prezi presentation by Maria Anderson.  When you visit this site, be sure to check out the other presentations she has created.  There is "Play to Learn Math v2," as well as one titled "Playing to Learn" and one to "Future-Proof Your Education."

Math is not linear

"Math is Not Linear" is a Prezi presentation by Alison Blank.  Her presentation is a thoughtful follow-up to our earlier post on "Rediscovering the Beauty of a Triangle in a Square," and the embedded article, "Lockhart's Lament."  Prezi is a non-linear presentation tool that is free for teachers.

"That was the best Math lesson ever." Phillip C.

At the risk of sounding hokey, I need to share a bit about today's Math lesson.  But first, I need to back up a bit.  In the middle of the day, we took the Acuity Mathematics assessment.  Most of my kids finished the hour-long test in about 20 minutes.  My discouragement was somewhat tempered by the fact that some of them took time to review their original answers.  Then, I looked at their scores.  Discouragement came rushing back.

We left the computer lab and returned to the classroom.  I wanted to deride them for not using the test-taking strategies I had laboriously presented.  I wanted to berate them for the poor scores I was noting from the Acuity report as they relaxed with a library book.  Unable to choose a course of action, I sent them out to recess.

While they were outside, I glanced through my earlier post, Rediscovering the Beauty of a Triangle in a Square.  I wondered what purpose a rant on my students would effectively serve.  I wondered if I could rediscover the beauty of numbers and their patterns I enjoyed when I was a fourth grader.

My students returned from their recess.  They sensed that I was either upset or otherwise distracted.  I stood for several long minutes.  The silence intensified everyone's expectations.  I finally handed a marker to a student and instructed him to write "72" on the board.  I stared at it.  The room fell silent once more.  I called on another student to apply a number bond.  He properly added an eight and a nine.
We added more.  Some came up with the idea of using a multiplication table to help.  Still others decided that just because they couldn't fine part of a number bond on the table, it didn't mean their ideas were incorrect.

While questioning the reasoning of their choices, we found ourselves in an animated discussion of even and odd numbers.  They began writing rules for working with them after they discovered even numbers plus even numbers equaled even numbered answers.  They followed that by realizing with a bit of amazement that odd numbers plus odd numbers equaled even numbers, too.  Imagine their astonishment when they proved to themselves that odd numbers plus even numbers would result in odd numbered answers.  Each student scribbled furiously to prove ideas and present them to classmates.

I "suggested" the relationship between addition and multiplication.  More brain synapses began to fire as a few began to realize their theories about odd and even numbers might apply there as well.  It was nearly time for busses to be called when I said that I would love to see an encore performance tomorrow.  A student asked what "encore" was and one of my ESL girls began to clap as I tried to answer.  More kids started clapping.  They stood.  They cheered.  They wanted to know if we could do Math first tomorrow.

I sent them home still laughing and applauding.  One of them turned and came back to me.  It was the boy who wrote "72" on the board an hour earlier.  He hugged me and looked up and into my eyes.  He said, " Mr. Glass, I never liked Math until today.  That was the best Math lesson ever.  Thanks."

I'm still trying to sort out what happened.  For that one precious hour, my students and I were completely in synch with each other.  I did very little talking.  When I did, it was to pose scenarios, to speculate about possibilities.  I hope I can recapture the experience, push the buttons that get them thinking and wondering.  I hope for an encore.

Rediscovering the Beauty of a Triangle in a Square

Do you have an "intellectual relationship" with your students? Read this blog post by Miguel Guhlin.

Rediscovering the Beauty of a Triangle in a Square

New puzzles from KenKen

KenKen, "The puzzle that makes you smarter." has shared some free puzzles for you to play with and share with your students.  Enjoy them here.

The American Math Challenge

Fun way for students to work on their mathematical fluency!
Practice begins on Oct. 18. The competition is from Oct. 26 at 8 A.M. until
Oct. 27 at 11 P.M. Students will compete with others from all over the USA in
real time. To learn more and register your class go to the link.

Get on the Mathtrain

Eric Marcos has a nice learning site going using podcasts to deliver his lessons.  I appreciate his use of technology to share his teaching.  Go to the iTunes store for a free subscription to the podcasts, subscribe via RSS, or simply bookmark the Mathtrain site.  He also has a site called Mathtrain TV.  Much more is available there.  You can follow him on Twitter as well.  The podcasts are short, sweet, and to the point.  They make great supplements to your lessons.

10-Frame online activity

During our Math in Focus conferences at Claypool, we learned about using 10-Frame as a teaching tool.  Illuminations has a great interactive 10-Frame activity tool you can use with your students.

NCTM president says it is time to stamp out the phrase, "I'm bad at math."

Collaborating toward Excellence

Teachers:

It has been a joy to become a part of your classrooms these last few weeks. Please continue to invite me in for math chats,visits, and/or to model a lesson. Don't expect me to sit back and just observe when I visit, I will dive right in with you to help students in whatever capacity necessary.

Last week, twenty of your colleagues came together in grades two through five to determine the best course of action in mathematics for this year. We are ahead of the state with Math in Focus because we are already addressing the Common Core Standards. However, the 2000 Indiana Standards are still the focus of ISTEP+ this year, so we felt it necessary to look for any gaps and give teachers a guide to how to proceed. The twenty teachers below worked diligently to find all target areas in the quarterly mappings from the state. Each grade has a longer document that will be emailed soon that shows where each target area is in Math in Focus or if it is missing. Although the document has excellent information, it is a bit cumbersome to be used as a guide. The teachers came back the second  day (unbelievably) and put together a compact plan to give direction for us all in this year of transition.  A tremendous thank you to the team that represented you so well:

2nd Grade:  
Tiffany Cooksey
Pam Brail
Deb DeMuth
Emily Hornaday
Neena Kishan

3rd Grade:
Julie Bishopp
Becky Brodhead
Paula Hunter
Barb Bean
Julie Martin

4th Grade:
Henry Zehr
Michelle Little
Rick Glass
Stacy Huffer
Marc Andrews

5th Grade:
Dennis Allison
David Wayne
Tori Reneker
Ann Sibray
Sarah Ashton

At this point these documents have most likely been given to you by your building team member. We wanted you to have electronic copies as well, so they are attached.

These teachers also benefitted from discussing math with their fellow professionals across buildings. Next week, we will all have this opportunity during the grade level trainings at Claypool Elementary. Monday: 1st grade, Tuesday: 2nd grade, Wednesday: 3rd grade, Thursday: Kindergarten and 5th grade, and Friday: 4th grade. Please bring your teacher editions if at all possible. We will start at 8:30 and end at 3:30 and break for lunch from 11:30 to 12:30. 

Lunch is a great chance to learn and laugh with each other. The Homestead Restaurant nearby is opening their doors to us for the week and offering 3 special buffet style options. The menu is found in the attached image. We hope you are able to join us for lunch and another hour of growing together as a grade level mathematics team. 

We truly are better together and with that spirit Rick Glass has started a Math in Focus math blog. You can access it at school at http://wcsmath.blogspot.com/ . We are continually adding information at this one site from videos of lessons to links on how to use your ebook and sometimes pure inspiration to remind you that what you do every day matters mightily. This is a medium in which we can consult with each other continually to improve our craft. 

Join us for a day of learning at Claypool, a country lunch and fellowship time, and high tech interaction all year long.

I look forward to spending time with you next week! 

Lorinda