Subitizing, Number Sense & Fluency

I worked for several years as a numeracy teacher, meaning I spent a lot of time making sure that students can subitize numbers accurately and quickly.  I soon became know as the dot lady because counting dots quickly by grouping them is what we did a lot.  Since that time many website have lots of activities that help students improve their number sense.

The same is true for subitizing numbers when adding or subtracting.  There are not very many ways to make ten, yet students are still struggling with adding and subtracting past third grade.  Even the adding by nine's trick where you move one number over to make the nine a ten, therefore only having to add a ten to the other number making it easier is a struggle for students.  How many students do you know that have trouble adding ten to a number. Below is a nice video that explains the 9's trick.

From Walmart site,
 Students taught me this game.

From Rainbow Resource website
Kids of all ages love this game.

from Really Good Stuff website
This is a great game because it teachers number sense, vocabulary and kids love it.

From Target website
Old school, not too many kids are familiar with this game.

From Target Website
Competitive Kids stop counting on their figures after a few days playing this game.

There are a lot of board games that help students learn number sense that I have had great results using.  Below are just a few ideas I have used that students seem to enjoy and learn from.

•  Mexican Train Dominoes.  
• Yahtzee
• Make 7
• Card games with Ten Grids on them  Teachers Pay Teachers Ten Frame Card Game
• Build and Block board game
• What's my Number 

Image from Greg Tang Math Website

Here are some online sites.  Just click on to link to webpage.  Let me know what you think!

• Greg Tang Math
• Arcademics Jumping Chicks
• Speedy Numbers
• Learning Box
• Making Bonds
• ABCya Sum of Dice
• ICT Games Shark
• Illuminations NCTM

And just a fun, rewarding site kids love (it also makes them think!)

• Hooda Math

Why do I need to learn this..... I am never going to use it!

I am going to guess that many of you have either said or heard those words.  I remember saying them myself in school.  For years I would try to make sure that my math lessons were relevant to the students' lives and although I was often successful I still heard these words.  I have also heard students say they didn't need to learn what I was teaching because  their mom, their wife or they just planned on hiring someone to do their bills or another life skills or math lesson I was teaching. Since then I have one answer.  Don't you want to grow dendrites?  That answer seems to actually motivate them to learn and try harder.  When new students as why they have to learn something, the other students fill him or her in on dendrites for me.

Neuron

Dendrites grow in your brain, the more you use your brain the more dendrites and the stronger dendrites you will grow. Even though it has been argued that worksheets definitely aren't the best way to grow dendrites, when I see someone cheating, or copying another students answers instead of struggling a bit and figuring it out on his own.  I tell the student that the person he or she is copying from won't be around to solve his problems forever, I then ask them don't you want to grow your own dendrites so you can problem solve for yourself?

Who wants to play chess?

Even though you may not use the math you are specifically studying, don't you want your brain to have lots of these great problem solving dendrites?  Now as a parent you might think this is all school related.  You can do puzzles, play chess or even have your child figure out how to increase a recipe she is cooking are all ways that you can all help your child grow dendrites.  Don't worry about your child making a mistake or having to start over, this is part of the learning process.  Figuring out how to fix a mistake challenges the brain. Challenging the brain is what learning is all about. Let you students and own children know that making mistakes is all about learning, nothing to get upset about.  We know when a person is upset their brain actually has trouble connecting all the pieces due to being stressed out.  When students feel confident and don't worry about making a mistake it helps learning be at its best.

There has been talk about the brain having plasticity.  This basically means that your brain can grow and change all your life.  Carol Dweck has coined the term "growth mindset".  where a person can continue to learn, their brain will continue to get smarter.  In 2013 I took  Jo Boaler's online class at Stanford University, "How to Learn Math".  Jo Boaler recently co-founded  the website  www.youcubed.org  One of the things Jo talked about was students learning from their mistakes and not being afraid to make mistakes. Although I had already been doing this a bit, I took it a step further from what I learned in her class.  One way was when we worked out a difficult problem I would call on several students to tell me what answer they got and how they got it.  As I went from person to person I didn't say who was correct or who was incorrect.  Students listened to each other, figured out how they went wrong or why several people might be correct and how different students arrived at the same answer using a different technique.  Other times I would have students document words, pictures and symbols on paper and take turns going up to the Elmo and showing the class what they got for the answer and how they solved it.  Students loved the fact of self-discovery teaching them another way to do a problem, or figuring out where they missed a step.  

I recently found online that Jo Boaler has developed a reference card that gives you great ways to encourage mindset growth when you are teaching or with your child.  Mindset Cards

One of the lesson Jo Boaler showed a video on when I took her class was students telling how many squares around a numbers chart (like the picture frame on the outer number boxes).  So how many squares are around a 10x10 hundreds chart?  A 8 x 8 chart? This is a great activity.  How many of you said 40 squares? 38 squares? 36 squares?  I get all those answers, we then discuss and go on and do a few more squares.  When we do our final discussion, students have come up with different formulas to figure out how to be correct each time without having to count all the squares.

Competitive and Engaging Rote Learning

Okay, I know, rote is a four letter word in education.  I wrote my master's thesis on the benefits of rote learning.  My instructor told me her view on it but I still thought it was important.  My study group that I used was sixth grade math students who had an F or D in math.  After eight weeks of rote learning their math grades went up to either a B or a C without any tutoring in their daily lessons from their math teacher.  I basically had them memorize their multiplication tables in a variety of ways.  Any math teacher that has ever tried to teach a student to reduce a fraction, find a common denominator or factor an algebraic expressions can tell you that if the student does not know his or her basic multiplication facts it turns into a frustrating lesson for both the student and the teacher.

The same could be said for reading.  Sight words are usually not easy to decode, sound out or figure out in context (whole language).  By third grade students that do not know their sight words really start to struggle in school.  Think about how important reading is in every subject.  A student that has difficulty reading will have a challenging time in middle school, high school and college.


One of my favorite sites for rote learning is Arcademics.  It is a free site to use if you don't mind the ads and let your students know that is not part of the site, or you can pay to use it ad free along with the benefits taken directly from their website are show below.

On the free version up to four students can compete against each other,  I also have done something the kids really love.  My students often complain about having to not only do grade level work, but become efficient in their basic skills (memorize them!).  I tell them if they can beat me in a race I will consider their complaints.  (Thank goodness in all my years teaching I haven't had a student beat me yet!).  So they line up at the SmartBoard to take turns racing me while I play on my desk computer. It is a lot of fun.  I do the counting coins or multiplication one.  Once the students see how fast I am they actually want to improve.  I think up until that point they really didn't see a need to memorize their basic facts or think that they could recall them quickly by memorizing them.  I even allow several students at the SmartBoard to help each other and occasionally allow them to have a calculator.  

Screen shot from www.arcademic.com

Besides math the site also has a typing, language arts, spelling and geography section.  And if you homeschool or have only one or two students playing, they can either play against the computer or students from other schools. Students use either an assigned player123 screen name or you can have your student create an appropriate fake screen name.  There is no chatting or texting while playing against students from other schools, which is really a nice safety feature.  I have used this website for almost a decade, and they continually improve it.  The site has won numerous awards in the past few years, and I can see why.  Take the time to try this site out, I know you will love it!

Bell Ringers and Sponge Activity

I recently found a wonderful website that students can read about the news and then take a very short quiz.  Quiz results are even sent to the teacher so that he or she knows which articles their students are reading.  The site is maintained by the Smithsonian , which was founded in 1846 by using the funds left by James Smithsonian for the purpose of "the increase and diffusion of knowledge". More information can be found at  Smithsonian Institution .

The website is TweenTribune and has articles for teens on many different subjects.  Recent articles included why we vote on Tuesdays, the real Smokey the Bear, The Cubs win the World Series, and about pandas in the United States. Quizzes are short, around 3 questions and both the teacher and students can see their results.  Teachers need to register in order to utilize the website for quizzes but there is no cost at this time.  Articles can be read without logging into the website.  Each article is written in four different Lexile levels so you can differentiated the lesson for every student allowing them read the same subject material  and discuss it in class.  The articles are also written in Spanish so that students who are more fluent in Spanish  can read the article in their native language. If a student understands an article better their participation in the classroom discussion will be more enhanced.   According to their website there is also an iphone and ipad app for this TweenTribune. The teacher's login has many resources, lesson plans broken down by grade level taught, and a grade-book that keeps track of your students quiz scores.

I have also found that over the years many of my students dislike reading nonfiction and/or do not do well on standardize testing on nonfiction reading. These articles are short and appear to be somewhat interesting.  The students that I have shown the articles to have had some discussion about the content and what their own opinion is on the articles.  This would also be a great way to discuss option vs fact when the class is discussing one of the articles.

Bullying Questions Rise for Teachers and Parents

Whether you voted for Trump or not, we now know that on January 20, 2017 he will be sworn in as president.  The problem is that during the last year Trump has blurted things out that hopefully he didn't mean, he just didn't think before he spoke.  The problem is that teachers are now reporting an up-rise in bullying, with some news reports of parents keeping their kids home due to them being afraid.  They even have a name for it, "The Trump Effect".  I don't think this is the "Keep America Great Again" that Americans want.  I watched Trump's acceptance speech and really felt he tone down his negative comments and tried to sound like he really wants American's to be as one.  I think he stated several positive ideas and objectives in this speech that can be used to point out some ways that Donald Trump plans to improve the United States. This does not stop the many children in America from wanting to know why Trump has said some of the things he has said or emulating him.  My guess is that no one informed Trump that his T.V. audience involved everyone, including children.  While an adult might get upset, mad, angry or not even take what he said seriously, a child most likely will really have a hard time figuring out what is going on with this type of talk.  A lot of administrators today are going to have to meet with teachers and have a game plan that involves their school communities making sure that students feel safe and not feel bullied. Bad mouthing the future president will only portray the exact type of behavior that we want to eliminate and cause additional conflict.

Students  need to be reminded to think before they speak, text or post things online.  Something that may seem funny at the moment may actually hurt other people.  My guess is Trump thought he was being funny to one person in the elevator and didn't know he was being recorded. In today's world with so little privacy we all need to think before we say something.  Many people tell students if you would not say it in front of your priest, your grandmother or your principal, you probably should not say it.  Melanie Trump has said that as first lady she will fight against cyber-bulling and has even told Donald Trump that what he said 10 years ago is unacceptable.  One of my favorite websites that cover some of these concerns is Netsmartzkids for kids and nsteens for teenagers

The way I handled it with my own children was to discuss the history of how the treatment of woman has changed since I was young.   I was teased daily about being flat chested, wearing coke bottles on face and walking like I had a pole stuck up my ****. Back in those days it wasn't uncommon when walking down the street to get vulgar comments yelled at you and get whistled at as you were walking home.  Having to pick a route home to avoid rude comments was common.  In high school two very muscle smart girls that I was friends with wanted to play football.  I have no doubt they would have been great at it, but unfortunately they were locked out of the locker room and were not  allowed in the discussion or  voting process.  You probably guessed that the answer was no.  Ironically the state I went to high school in was also the first state to have a woman football player whose position was a placekicker. I will tell you that happened about 13 years ago, and I graduated from high school 36 years ago when my friends wanted to play football.   Fast forward to my job in college where I was sexually harassed on a regular basis. In fact the manager who was harassing me a one point went to my boyfriend and apologized (note he never apologized to me).  I never reported it, I am not even sure there was a way to report it. Several years later I found out that there were several other woman being harassed by the same person and apparently none of us knew how to report it.   My senior year in college where I was helping a young man who was a sophomore in college from my work do his taxes I found out that he was getting health insurance and I was told I could not get it. I went in again to request health insurance. I was again told even though I worked 40 hours a week, I was a students so I could not get it.  I pointed out that Pete* was also a student and he received health insurance.  I would have accepted no and probably had no idea how to peruse this in the earlier 80's but apparently my boss thought I would take it further and the next month I had health coverage.

Just recently I watch the movie Enigma (2001) fyi rated R with my family.  One of the main characters in the film was Joan Clarke, who was the only woman in the movie hired to work as a crypt-analyst.  When she showed up to take the test they didn't believe she had done the first test herself. She was never allowed to be awarded the actual degree she earned in college because woman were not allowed a full degree until after 1948.   One of the other main characters was Alan Turing, who I am embarrassed to say I had never heard of before this movie.  According to  http://www.biography.com/, Alan literally saved over 14 million lives in World War II with his invention of the enigma machine.  Haven't heard of the enigma machine?  It was the first computer even invented, before electricity! After saving this many people, would not Alan be a hero?  He was found to be gay and arrested and put on medications.  He was finally pardon from the Queen just a few years ago.  I think these are they types of movies that remind us not to repeat history.  Would the war have lasted longer if Joan would not have been hired or if Alan would have been arrested earlier?  Would the computer have been modernized as the basic model for making a computer was not designed by Alan, who spent hours working on it?

There are so many great people in history that show us that our differences can help us succeed.  People who were told they couldn't do things.  Helen Keller, Fred Astaire, and Michael Jordan, along with Katie the first woman football player who wasn't even born until I had graduated high school.  Knowledge is so empowering but so is kindness.  I encourage everyone to show love and compassion to everyone, pass on your smile!  Learning should be fun!  It doesn't matter if your public schooled, homeschooled, unschooled, private school or self-taught no one wants to worry about saying things that hurt other people or having people say things that hurt them.  Random acts of kindness, the Gold Rule, or say hi and give a genuine smile.  Peace and love to all!  I felt this was too important to not address and will return to more fun ideas later this week!

*name changed

100% Student Interaction

If you haven't played Kahoot with your students you are missing out on a lot of fun.  I haven't found anyone that does not enjoy this game.  It can be played from a laptop, tablet or cell phone.  Students go to kahoot.it to sign in with the pin number assigned to the teacher's game.  There are a bunch of premade games to choose from if you don't want to create your own game.  I usually play one of the premade logo games, students really love it and it is a great way to introduce students to Kahoot.  Adults even like it so you could use it for teacher's meetings.  If you really want to be original and insert your own photos along with test questions, I will warn you it takes quite a bit of time.  After I create a game I usually play the game myself with one of my kids to help me proof for mistakes.  Teachers can sign up for free at https://getkahoot.com/ and start creating their own game based on their lesson plans or using premade games.  I have used it to review books read, math concepts and rules or practice for an upcoming test in another subject.  Everyone gets to answer every questions and you can even get a read out of who missed which questions.  Students get to choose an appropriate game name, if they don't , one click from the teacher on the inappropriate name and the student gets bumped out of the game. Student especially love it shows who is in the top 5 contestants, which can change with a simple incorrect question or one that a students takes too long to answer. Below is a sample of a question page that you present on wall from a projector or a Smartboard and also what the students see on their device.

Sample Question Screen

Sample Student Answer Pad

Money

     Remember the 5 gallon jug filled with coins? I bet you could find a few people that cashed in on a rather big purchase once it was filled up.  You could find a penny laying on the sidewalk for good luck quite often in the good old days. Counting change used to be a pastime for many kids, yet very few people have a pocket full or purse full of coins anymore.  Debit cards and EBT cards are the way most items seem to be paid for these days.  There are even a few places that no longer take cash.  Identifying coins can be difficult for  kids, especially since in the late 1990's quarters started having different state backgrounds on them.  It is fun for kids to try and collect each state, but I find that students still seem to be confused with looking carefully at coins to be able to see the difference between a nickel and a quarter. Children also have trouble identifying a nickel, dime, or quarter and remembering which value to assign to each coin. This video featured on schooltube is fun to watch.  Coins in My Hands Video

     Counting by quarters, something that it seemed the majority of students could do in years past, is now starting to be difficult.  I am guessing that vending machines rarely have anything in them that cost 50 cents or 75 cents.  Add that to men no longer have pocket full of change to share with the kids or grandkids anymore and woman's purses are definitely lighter without their coin purse over flowing.  The problem is that for a student to have number sense and mental math these common place manipulatives are no longer readily available.  That means teaching a young kid to do mental math when paying for his item is much more difficult for him to tangible visualize when swiping his parents ATM card rather than counting out coins and dollars.  Even vending machines show when the correct amount of money has been put into the machine, doing the math for the child.  Here is a few activities you can do that don't take long. 1. Have your child identify a coin and tell you the value of the coin. 2.  Listen to your child count aloud by quarters.  3. Have the child start with a quarter and add dimes (25,35,45,55,65,75) .

If you teach life skills class or work with teens that need to know how to compute change without relying on the cash register to give them the answer I have published the book Making Change.  There are a few businesses out there that still test future employees by expecting the person to demonstrate the proper way to make change, the old fashion way, by counting up.       

Making Change 

Online sites I enjoy     Math Playground        Mr. Nussbaum's site

                                     Smarty Games            Sheppard Software
ABCya

Thanksgiving.....just around the corner

Here is a chance to teach your kids life skills and make memories.  Let you child make the list of what he or she wants to eat for Thanksgiving.  Chances are they have their favorites, recipes that busy parents don't have time to make very often.  Let your child make the list. This teaches them how to plan and practice their spelling!  If your child is very young he or she can draw pictures. In our house there is always a lot of compromising as to what type of pie we will have and they usually can narrow it down to two varieties.

     Then when you go grocery shopping let your child bring the holiday shopping list and keep his or her eyes peeled for the items you will need to buy to make the meal.  My kids love that they get to plan much of the menu, in which they often want children's wine (nonalcoholic wine) which is too expensive to buy anytime other than the holidays and they know it!  Plus if you kids help plan the meal they will be more willing to eat it. 

Yummy!

Painted Rock Hunts

More Rocks Found

Update:  With the weather changing from freezing to almost 80 degrees this past week we started rock hunting again.  Even if you aren't getting park weather where you live you can start painting rocks to hide when nicer weather gets here.

Many small communities have started up in the past year rock hunts.  Families with kids of all ages seem to love to participate in these rock hunts.  People have commented that their T.V. sets are turned off and their kids are getting more exercise and outdoor time.  You paint rocks and then hide them.  When you find other peoples rocks you can take photos and share what rocks you discovered.  Kids and adults usually try to re-hid most of the rocks that they find but they occasionally keep a rock they love too much to re-hid. Since kids of all ages love to participate it is important to treat preschool painted rocks just as important as the more artistically decorated ones.  If you paint a rock, please send it to us to post!  BTW the smile rock is a rock that I found and loved too much to re-hid.

Cute Model Homes

Lots of ideas here.