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Multiplication

Multiplication Stairs for the Kinesthetic Learner

I found these stairs in a school in which I had a professional development meeting.  You have probably seen a similar idea on Pinterest of a staircase with brightly colored multiplication cards that exactly fit the stairs.  I have checked into the prices to have custom cards made like those on Pinterest and the prices were well over $500.  Ouch!  The great thing about these stairs (pictured below) is that they look like they were made on a much cheaper budget.

All you would need is someone who has access to a Silhouette die cutter and a selection of the sticky vinyl to print the numbers on.  (In this blog post, they explain that they were able to get sticky vinyl scraps from a print shop.)  Well, you would need a ruler to mark off the placement of each number also-and lots of time!  When I saw this, I thought the idea was fabulous, but I didn’t think that the colors were dark enough to stand out on the  concrete.

If your school has used the spaces on their stairs for math facts, leave a link and/or share your experience.

Have You Heard About this Great New Math Practice Site?

Screen Shot 2016-08-25 at 8.41.54 PMTell everyone you know about this great new free animated website iknowit.com that helps elementary kids practice math skills by playing games.  This site will remain FREE for at least the next year while improvements and more lessons are added.  Iknowit was built by the makers of Super Teacher Worksheets and Modern Chalkboard, a SMART board lesson site.

The lessons give children immediate feedback so that they know if they have answered each question correctly or incorrectly.  There are drill lessons for basic math facts–addition, subtraction, multiplication, and division.  These lessons are timed.   Then there are lessons based on progress in which students answer a certain amount of questions.  Right now the lesson topics include addition, multiplication, division, time, money, fractions, and there are many more to come!

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In the future as a teacher, you can log in and set up a class roster.  You will be able to assign lessons, monitor student scores, and track their progress.  You will also be able to adjust the number of hints children are allowed to have on each problem.  Teachers will be able to set the amount of time students practice drills and set the number of questions a student must answer for a lesson.

Because this small business was set up by teachers, they value teacher’s and student’s constructive feedback as they venture forward with improvements to this site.  You can follow them on Facebook, Instagram, or Twitter to give your input.  Just imagine a website built with your feedback in mind

Use This Strategy to Easily Multiply Large Numbers and Fractions

You know the guys who easily multiply in their head who leave you picking your jaw up off of the floor?  Well, these folks have special strategies.  I am going to teach you one of these so that you can teach your students!

FirstSlide1, let’s look at this example with fractions.  If you double ½ you get one.  Instead of going through all of the steps it takes to multiply fractions, why not simply double the fraction and multiply?  In the case of one half or any other fraction with an even denominator, this process is simple.  ½ becomes 1.  Then multiplying by 1 is super simple.

In the case of a denominator such as ¼,  in the second example, you can double the number twice and halve the other number until you find a factor that is easy to multiply.  ¼ doubled becomes ½ and ½ doubled becomes 1.  As long as the other factor is easy to halve, this works great!

This may be done with mixed numbers as well.  As long as one of the numbers is even, you can double the other.

Now let’s look at examples with whole numbers.  Again, double one factor and halve the other.  Hmmmm 6 x 24. I don’t know that in my head, but I do know that I can easily double 6 to 12 and halve 24 to 12.  Wow!  I do know 12 x 12! 144!

I will skip the next two examples (12 x15 and 25 x 16) because these are self-explanatory.

Let’s look at 6 x 32.  If we double 6 and halve 32, we get 12 x 16.  Still not an easy fact.  Ok, I will try to double and halve again, and I get 24 x 8.  Hmm, again I don’t know that one.  Let’s try another time.  We get 48 x 4.  Whew!  Still difficult.  One more time.   Ok, 96 x 2.  To solve this problem, I will use a combination of strategies.  First I know that 96 is 4 away from 100.  If I have two groups of 4 away from 100, then I know that I will be 8 away from 200 because 96 is almost 100.  If I take 8 away from 200, this gives me 192.  Teach children through number talks etc. to think flexibly about numbers and ways to solve problems.  By teaching children these strategies, you will become stronger at solving math problems in your head as well!

Know Your 5s Facts by Doing This…

So recently I discovered that the 6s multiplication facts multiplied by an even factor have a repeating pattern in the tens place.  This made me rethink the 5s multiplication facts.  Could there be patterns there, too?   Here are the 5s multiplied by even numbers.  Well, tell me what you think. Slide1

 

I see that the facts all end in zeros and the tens place is half of one of the factors.  Is there anything else?

Here are the 5s multiplied by odd factors.

Now for students who count on their fingers for their 5s this is another tool that could help them arrive at the answer faster than counting by 5s on their fingers.

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I notice that the 5s multiplied by odd factors always have a 5 in the ones place.  Now is there a way you could describe the pattern in the tens place? Hmmmmm….I don’t know.  What do you think?  Do you have any strategies for making 5s easier for kids to learn?

And finally, here is a question you could pose to children.  How can knowing your tens facts help you learn your 5s facts?

 

Don’t Take This for Granted When Teaching 5’s Facts Multiplication

Most people assume the 5’s are easy for students to learn because they can count easily by 5’s.  That may be true, but that still requires counting to occur.  That is still not the best method for them to become fluent because the methodSlide1 isn’t efficient.  Now, if your students can tell time, then they can easily become fluent with their facts by looking at the clock and thinking of the middle of the clock as having a “x5” literally taped in the middle.  Then they can visualize the numbers around the edges as the other factor.  The product or answer will be the number of minutes that each number  on the clock represents.  Look at the picture for further clarification.  I must say that you may think that students will naturally draw the correlation between the clock and their 5 multiplication facts.  However, this is not always the case and may need to be pointed out especially to your lower performing students.

Nifty Tricks for the Number 6!

The other day I came across this and never realized that 6 multiplication facts repeated in this way or had this pattern!  Imagine, I have been looking for patterns in the 6’s for years and never realized this.  Did you?!

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I mean I knew you could double your 3’s facts to find your 6 facts, but I never realized this happened with the even numbers.  I am sure you can tell by the image above that the factor multiplied by 6 repeats in the ones place of the product!  Hmmm, I wonder if this happens with more digits?  Well, does it? 🙂  What a great problem to pose to your students.  Then ask them to show other examples of this working or not working with larger numbers.  I wonder about odd numbers….does this idea work with odd numbers?  Hmmmm?  What fun!!!  Do you know any more tricks that work with 6?

Best Results Ever with Kids Learning Math Facts!

I am going to share with you what I did this year to be successful in helping our school be more fluent in math facts than ever before!  We have had Reflex Math for about 2 and a half years now.  The first year everyone didn’t know much about what to expect.  The second year some classes were making progress with it.  Now this year being in a new school with new people (we consolidated with another school), we had a slow start but by the end students’ fluency took off.  Albeit some of the increase has been due to the increase of available technology and the new Reflex Math app on the iPad, but students this year were more motivated to achieve than ever before.  I believe that is due to a few things I added to encourage friendly competition!

1.  I added the 70% and up club.  What child doesn’t want to be a part of a club?!  When children reach the 70% mark, I post their certificate on the wall with their pictures in a central location.   I try to take their pictures close to window light so they look nice.  If students’ certificates are up too long without their picture they make sure they let me know about this.  I print the certificates off weekly.  These are available to easily print off from the home dashboard screen underneath the unprinted milestones link.  I also have these students names called on the announcements with “Welcome to the 70% and up club…” and then I have their names called out.

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2.  To encourage students along the way to reach the 70% and up club, I send home their certificates if they are below 70%.  Students get certificates for answering facts and they get certificates for answering a certain amount of facts.  One of these certificates may say something like Joe Bob solved 2,000 facts.  If the certificate is one that is fluency related then I attach a little prize such as a pencil or fake tattoo.  These certificates may say something such as Mary Sue learned 25 new fluent facts.  All certificates that are 70% and up go on the wall.  I replace the 70% with an 80% or 90% certificate so that others walking by can see their achievement.

3.  I have a special place to hang students who achieved 100% fluency during the year.  These students have their picture retaken again for this spot on the wall.  Also, I had a special ceremony for these students at the end of the year in which I invited the principal and guidance counselor to shake the students’ hands and pin them with a special pin I ordered from Jones Awards.  I had wanted to order them all trophies, but I didn’t think I would be able to afford enough trophies with the school budget for those kids who had achieved 100%.  I also have the 100% fluent students’ names called out on the announcements when they achieve fluency.

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4.  Each quarter I have parties for all the students who achieved at least 70% fluency.  Once students achieve 100% fluency, they are able to go to all parties for each quarter.  Most students who achieve 70% fluency go ahead and work towards the 100% fluency spot on the wall even though there isn’t much more reward to achieve 100%.

5.  In addition, I have parties for a class winner in 1st-2nd grade and a class winner in 3rd-5th grade.  I didn’t do a party for the 1st quarter.  In the 2nd quarter we did a hot chocolate party with toppings, in the 3rd quarter we did an Easter egg hunt, and in the 4th quarter we did a water play party outside with sprinklers and water squirters.  The kids anticipate these parties with great excitement!

6. Within each grade level I hand out 1st, 2nd, and 3rd place ribbons for the highest percentages of fluency achievement.  These students pictures are also displayed in a central location for everyone to see.  Some students are very competitive about this.

Because of all of these things, more students achieved 100% fluency than ever before.  The excitement built around the achievement of math fact fluency built a positive momentum with the children for something to earn.  When parents visit the building, they can often be found near the wall looking at all of the children’s pictures on display.

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Some teachers became very competitive about their classes beating another class.  These teachers built a competition within their own class.  Towards the end of school, some teachers were sneaking their children who were still below 70% to the computer lab just so they could reach 70% fluency to attend the party outside. (I know the paper colors don’t exactly match, but I was just working with what I had :/.  I will make it look better next year :))

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I hope this sparks some ideas within your own building!

Do You Need Some More Math Activities for Math Night?

Take a look at these exciting photos of our recent Family Math Night.  Originally we had scheduled Family Math Night on the 100th Day of school to build more momentum for the event, but we had to reschedule Math Night due to weather.  I’m mainly including activities that we hadn’t done before, and I will include links to former math nights so you can get even MORE ideas!

To start, tables with parent information were set up in the hallway.  The more inviting and fun student tables were set up inside the cafeteria.

Since many parents are unfamiliar with ten frames (I had never heard of them until I had started teaching), we had a table informing them of how ten frames work.

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Then we had an information table showing the parents of 2nd and 3rd graders addition and subtraction strategies.  Parents even had an opportunity to see how base ten blocks were used to do regrouping.

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Here is a station explaining to parents how Reflex Math works.  We had a laptop set up to show parents Reflex Math from a kid’s perspective.MathNight2014Blog-43

One teacher put together game packets for parents to play math games with their children at home.

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Now it’s time for the fun stuff!

Below you will see beach balls with math facts written all over them using Sharpie permanent markers.  When someone catches the ball, the right thumb’s landing spot determines the math fact that must be answered.   We had large beach balls for the kids to play with and small ones for them to take home.  We ordered the beach balls from Oriental Trading Company.

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How many books will it take for YOU to weigh 100 pounds?  That is the question that students had to answer when they stopped at this station.  Students estimated how many heavy encyclopedias it would take for them to weigh 100 pounds.  Having experiences with measurement is the best way for students to make reasonable estimates with measurement.

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Uh-oh!  Looks like he picked up too many books, but he’s close!

Fractions beckoned to students’ interests under the guise of a messy pudding party.  Students had to measure out two cups of milk without using a 1 cup measuring cup.  They had to use ½, ⅓, or ¼  measuring cup .  Doing so made them repeat these measurements until they had milk equivalent to 2 cups.MathNight2014Blog-4

What is Math Night without estimation stations?

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I have done estimation stations every year we have had Math Night, but I wanted to do a little something different this year.

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Instead of just having the estimation jar, ziploc baggies were placed in front of the jars with 10 of the candy item inside.  This helped students make more precise estimates.  I also had a wild idea about gluing base ten blocks together to see who could come the closest to estimating the total of the blocks in a base ten tower.

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How many are in this base ten structure?  Can you guess?

(above) I know the tower looks more like the leaning tower of Pisa than anything of mathematical value–it looks like a hot mess–a hot glue gun mess ;).   What can I say…I think I should pose like one of Charlie’s Angels with my hot glue gun!

(below) Making 10 groups of 10 was a kid favorite last year and remained a kid favorite this year.  Kids took small food items and grouped them on a mat.  They got to eat their 10 groups of 10/100 items when they had filled up their mat! Yummy!

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(below) Where did Freddy the Frog land on the hundred’s chart?  These kids played Toss and Guess, a game with a giant hundreds chart grid and a beanbag–in this case a bean bag frog.  The idea for the grid and the Toss and Guess game came from The Learning Carpet.  Kids received prizes when they guessed where the frog landed correctly.

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Below is my absolute favorite booth of all booths!  How many hulas can you hoop?  Students hula hooped until they could hula no more.  Then they counted their hulas and wrote the total of their hulas on a piece of paper.   They stuck this paper to the wall so other students could compete with the highest total.  The two hula hoopers with the greatest number of hulas won a hula hoop!

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The following made the evening worth while.  This parent solved math problems with her Pre-K student.  She helped him count on her fingers!  This embodied the goal of the whole evening–helping parents connect to their children through mathematical thinking!

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 If you liked this post about Math Night, you might also like Math Night from 2012 and 2013…

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 I hope these posts inspire you to make your math night fun!

How Can You Motivate Your Class to Learn Math Facts?

This year, I have had the most competitive success when I have given attention to students progress on Reflex (an online math fact video game-like program for learning math facts–Read more about Reflex here).  Each Friday, I pass out the reward certificates and recognize students who get a certificate at our morning meeting.  Students who get a certificate also win a little prize with each certificate.  What has helped the classes become most competitive is the bar graph I have hung in the hallway.  Each class name is at the bottom of a bar.  I update this graph nearly daily.  Every time students go down the main hallway, they look to see if their class has grown on the graph.  I have placed the graph below…

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As you can see the taller bars are the 3rd-5th graders which have gotten VERY competitive.  On our last contest 1st, 2nd, and 3rd place were only 1 point away from each other!  I took a picture of the classes who won on the last contest to place beside the graph.  I personally reward the 1st place classes with a party.  This time I was so proud of the special ed class who won 1st place!

In addition to the above graph, one of our teachers has developed a class thermometer for her individual class competition out in the hallway.  She moves each student’s name on a clothespin closer up the thermometer to 100% fluency each week.

I am not paid a dime to say this, but I must say Reflex math is the most effective tool I have ever used to teach math facts!

I must be honest.  I hope the wall isn’t red underneath the paper at the end of the year.  I think that every time I color on the paper to fill in the bars…the paper is kind of thin.

Try This to Promote Fact Fluency at Your School!

Reflex Math…I LOVE IT!  Kids LOVE it!  In case you aren’t familiar with Reflex, it is a computer program that web based and helps students learn their math facts.  The computer program is like a video game so it is very engaging to kids.  I wrote more about Reflex math here.  I am always trying to think of ways to encourage students to be a little more competitive about learning their facts, so I  host a contest every quarter.  We just finished our first Reflex contest a few weeks ago.  While the contest was going on, I created a bulletin board with the students who were in 1st, 2nd, and 3rd place weekly.  I also announced these students every week.  When the contest was over, I posted the students photographs on the bulletin board with their names.

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I also posted the students’ fluency certificates on the wall beside the bulletin board.

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When students earn a certificate, they get to pick out a prize.  A teacher at my school met one of the representatives from Reflex at a conference this summer and the representative gave her lots of free prizes.  The kids especially love the fake tattoos.

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In case you don’t have Reflex at your school and you would like to try it out, they offer grants to teachers to try it out for free for 12 months.

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