Happy Birthday!

We hope this joyful student has a fun birthday on Sunday!

Subtraction: "Take Away" or "Take It Away!!!"

During a recent conversation with our students, I shared a few secrets.  At the beginning of the year, when we learning how to solve "complicated problems" (multi-step word problems), I told them that when I was in school, I thought math was OK, but it was never my favorite subject (though now I appreciate and understand math much more and *enjoy* the challenge of solving *elementary* math problems).  I also confessed that as a second and third grader, subtraction with regrouping was confusing and difficult for me, especially having to regroup numbers with zeros.  To this day, as an adult, when I need to subtract numbers quickly (Let's be honest...First, I look everywhere around me for things to write with or a calculator!), I often count up from the lower number to find the difference.  Say what?!

Most students are familiar with removal subtraction (take away) situations,

but struggle with comparison subtraction (How many more?  How many less?  Find the difference...).  Over the next couple weeks, we will focus on comparison subtraction problems during Math Workshop.  We will use both "counting up" and "subtracting back" strategies to compare numbers, or tell how far apart they are (their distance from each other/difference).

 Since last month, I have been sneaking these strategies into Calendar Math when we compare the number of days we've been in school to other numbers (How many days since day 9?  How many days until day 50?  100?):

and into an activity we did comparing football scores last week:

and then into other elements of Calendar Math such as when we look at the pictograph we've been making of the weather this month in Jacksonville, FL and Jacksonville, IL: How many more sunny days than partly cloudy days?  Even today, I was talking about how we're approaching the end of the month and will be taking our October Calendar Math assessment and picking new leaders soon: Today is October 23.  How many more days until our test on the 31st?  Comparison problems are everywhere!

Using both of these strategies together also nicely ties in how addition and subtraction are related (they are inverse, or opposite), as we're starting to see while practicing our basic fact families.

First Day of Second Quarter

Just a reminder from our Teachers of Tomorrow (TOTs):

Keep listening, following directions, respecting others, working hard, being responsible, earning good grades, and making good choices every day if applying to be a TOT at the end of the year is a goal you have set for yourself!

Red Ribbon Week

Coincidentally (I love it when that happens!)  our Second Step lesson this morning was Dealing with Peer Pressure.  We had some great discussion about when peer pressure is good (encouraging someone to try harder, make better choices, or do the right thing) and when it is bad (when someone tries to get you to say or do something you know is unsafe, unfair, or hurtful).  We came up with a plan for dealing with peer pressure:

To tie this lesson into Red Ribbon Week, we discussed how most likely, our peers (not strangers) will be the people who try to get us to use drugs or bully others and how difficult it can be to have courage and say no to our friends.  We practiced using assertive "I" statements to let people know what we think or want in a polite, strong way.  This often stops things from getting worse.  For example: "I'm sorry to hear that.  You're my friend, but my answer is still no."

We had a great turnout for Wear Red Day:

Our amazing PTA provided students with red wristbands today so we can express our commitment to stay drug and bully-free.  Students--make sure you wear your bracelet every day this week!

For homework tonight, your student will be creating a red (construction paper) ribbon listing the reasons s/he has for staying drug-free.  I gave a few examples in class today:

I stay drug-free so I can love my family and show my friends I care about them.

I stay drug-free so I can do things I enjoy like running.

I stay drug-free so I can think clearly and do my job.

I stay drug-free so I can feel and look my best.

A Belated Birthday!

I forgot to post this before the weekend, but we hope this great student had a fun birthday on Saturday!

Uno, Dos, Tres Bailamos!

During our study of Hispanic culture, we learned that many people in Spanish-speaking countries enjoy dancing and music.  We were so excited to have Ms. Ashley (Briana's mom) and Mr. Adam teach us several Latin dance steps and Hispanic folk dances this afternoon:

As you can see, even the boys had a good time (they especially liked the "cockroach" step!).  A few curious teachers even popped in the Multipurpose Room when they heard the Spanish music, wishing they could join us!

What Is Addition?

Today we spent some time reflecting in our Math Journals about what we've been learning.  We had some great discussion about the meaning of addition and what happens to numbers when we add them.

Amarius:

(I like how he remembered we can combine more than two numbers!)

Briana:

(Great example of adding greater numbers with regrouping and use of math vocabulary!)

Lauren W:

(Yes, addition is putting numbers together!)

Shawn:

(Wow, what a great observation about the digits changing, sometimes "getting lower" when regrouping happens!)

Lauren K:

(This girl understands how to use the algorithm!  I like how she was so specific about starting in the ones place, finding the sum, and working to the left!)

Sydnee:

 (I was very impressed that she remembered our discussion about the Identity Property of Addition!)

We are really growing in our ability to explain our thinking.  Keep it up!  :-)

The Great Fact Debate

Over the years, there has been much debate about memorization of basic facts among teachers and parents. To sum it up, it pretty much goes like this:

(Old School Teachers) Break out the flash cards! Set the timer! Students MUST have the basics memorized!

(Do these pictures make anyone else's heart start racing as they recall that jittery nervous feeling before, during, and after such timed tests?!)

(New School Teachers) Have you seen the reading comprehension needed to solve math problems these days?! We don't have time for memorizing basic facts in class! or As long as the student knows a strategy, s/he can use that to figure it out.

(Or are you nervous now???) 

 

I can honestly say I've been both of these teachers at various points in my career. I agree with the Old School teachers that the basic facts need to become automatic at some point. It is developmentally appropriate (and a Florida second grade math standard) for students to know the basic facts (sums to 20) automatically. However, traditional flash cards are too abstract for most students at this age, who are still developing number sense. Coming up as a teacher in the New School, I can totally relate to this perspective as well. The majority of math "situations" (word problems as we called them in the Old School days) are no longer straight computation (numbers only), but require moderate to high levels of thinking (reading comprehension) in addition to performing the actual math skill assessed!

So, what is a teacher to do? Each day this week, your student should be bringing home a red booklet s/he made of Doubles and Near Doubles. We used a visual strategy (ten grids) to help the students "picture" or "see" the combinations. In class, we practiced how to use the booklets to become fluent Doubles and Near Doubles combinations/fact families. Your student needs to practice the fact families shown on the pages of the booklet for 10 minutes each night. This will help students save precious mental energy for thinking about the math situation s/he is solving instead of using it to figure out basic facts, which are often part of the process. To ensure that the booklet does not get damaged or lost, please keep it in the front pocket of the planner/have the student return it to school each day.

Next week, your student will receive a Math Facts Practice Log to keep track of minutes spent practicing basic facts. Please sign it each night to verify your student is practicing. Our first timed test (with a New School twist: fact families as opposed to isolated facts, flexible presentation to introduce variables and reinforce the relationship between addition and subtraction) will be next Friday (October 12). Your student will receive a practice sheet on Monday that is similar to the test. We will test on Doubles and Near Doubles again the following Friday (October 19), and I will include the better of the two scores in your student's quarterly math grade.

Number Sense and Representing Numbers Flexibly

The most important factor in a student's ability to become a successful mathematician is number sense, which is the ability to understand how numbers are built in our base ten number system and how they interact with each other when performing operations such as addition, subtraction, multiplication, and division.

Over the course of the next several weeks, I will feature several number sense routines on here that are part of our Math Workshop, including Everyday Counts Calendar Math. Check out this video for an example of a typical Calendar Math session. (We did not do the graph featured in the video for September because as of 2010, Florida's third grade math standards no longer address probability.)  Our sessions are starting to have student leaders take a more active role in updating elements daily and facilitating discussion at the beginning, middle, and end of the month.  Most months have additional elements such as Coin Counter, Clock, and Measurement, so stay tuned as I post about these later this month!

A question that several parents have asked me recently is What is flexible form?  

Flexible form of numbers is the idea that a number's value can be shown in different ways. For example, 947 can be thought of as 9 hundreds, 4 tens, and 7 ones. Using regrouping, you could also trade in one of the hundreds for 10 tens, showing that 8 hundreds, 14 tens, and 7 ones also has a value of 947.

One way we practice this is with the number of days we have been in school during Calendar Math. For example, today we have been in school 33 days. We can show 33 flexibly using 3 tens and 3 ones, 2 tens and 13 ones, 1 ten and 23 ones, and 33 ones.

At least once during every school year, the students will be taking a test, and a student will raise her/his hand to let me know, "I found the answer, but my answer isn't one of the choices! Ieven checked my work!" This is a perfect example of the higher-level mathematical thinking and number sense expected of today's young mathematicians.