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Multiplication

Multiplication Hand Tricks–Multiplying by 4s

Again by popular request, here is a video showing how students can use their fingers to multiply by four.  This is my second video ever!  I think I’m getting better at it! 🙂

This video was made in response to an earlier blog post here.  Watch this for professional development, or allow your students to watch it for a brand new strategy for their math “tool box”.  Enjoy!

You may also like to watch this video about multiplying by 3s.

Multiplication Hand Tricks–Multiplying by 3s

Congratulations!  You get to watch my very first video ever!  This video is a result of my most viewed blog post ever  You can see this post here. It is the post with my multiplication hands, which show how to multiply by three on your fingers.

One of the comments suggested I make a video for this post to explain it further. At the time I wasn’t comfortable with video nor did I have the equipment to video.  So, just recently I decided to take this advice.  After about 10 takes, I finally decided to settle on this video.  I may come back and redo it later to make it better, but I’m at the point where I feel it is better to have something up than nothing at all.  I really hope you learn something while watching to help your students! 🙂

Have You Been Using Flashcards Wrong?

I sat in on a parent conference this past year with a student and her teacher.  The child was having difficulty learning multiplication facts.  The teacher told the parent several things one of which was to use flashcards and put the ones she knew in one stack and the ones she didn’t in another stack.  In other words she was prompting the child to memorize the facts.

Of course you know I interjected how the child might learn better with the flashcards by layering the ones she knew with the ones she didn’t know.  For example, if she had learned all of her 2s, she could then place all of the corresponding 4s facts behind the 2s facts.  Then she could learn how to double her 2s facts to get her 4s facts.

When studying multiplication, it lends itself so well to student led discussion about patterns they notice among the facts.  For students to see these patterns it is essential for us to line the facts up in such a way that they can see the patterns. Normally, we hand students a HUGE multiplication chart and children see this and feel overwhelmed.

SEE OVERWHELMING CHART BELOW


Why not break this chart down so that students can see the patterns more readily.

If students only see part of the chart, then the patterns are more readily recognized and students are less overwhelmed.  Students may also benefit from seeing patterns on a table like the following in which the patterns are more explicitly explained at the top.  Could this be the reason students struggle with learning their facts?  They don’t see the patterns.  Doing something this simple could allow students to make sense of multiplication and find patterns in the numbers…especially those students who need extra support.

I have put together a packet that can help teachers (and possibly parents) use flashcards more efficiently with their students.  In this packet, patterns in multiplication are unveiled and explicitly explained so that teachers can teach their students with patterns–not just by memorization.

Ways to use patterns for all multiplication facts are explained in this packet.  There are teacher notes, flashcards, charts, and tables all organized by helping strategy.  One could even use the teacher notes as a guide to plan lessons when beginning to teach multiplication.  This pack would also be great for intervention with those students who just aren’t picking up the strategies to learn multiplication facts.

Take a moment to check out this product and consider teaching multiplication with patterns! 🙂

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.

You would need someone who has access to a Silhouette die cutter and a selection of the sticky vinyl to print the numbers on.   In addition, you would need a ruler to mark off the placement of each number 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!

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