Developing Multiplilcation and Division Fact Fluency

Developing Fact Fluency can be quite a challenge. 

In fact it can be overwhelming for students!

Why? Well, to start with, there are 100 multiplication facts, and 100 division facts!

That's a whole lot of facts to learn! Take a look at this:

There they are, all 100 multiplication facts.

And the 100 division facts.

It just doesn't work to just hand these lists to the kiddos and tell them to learn them all! 

Here are some ideas to help ease this heavy load!

Before the children start to work on memorizing facts, it's essential they understand what multiplication and division are! I like to spend plenty of time with manipulatives, as well as making and drawing arrays. I make sure they understand that 6 x 5 means 6 sets of 5. They use manipulatives to show six groups of 5 (as in the picture: 6 rows of cups, with 5 cups in each row), and draw an array with 6 sets of 5. When they have done a whole lot of this, and have a deep understanding of what it all means, then they can move on to fact fluency.

As you can see from the list of all the facts, it's just too much to assign them all at once! It's best to break them down into smaller groups, and best to create those groups by patterns. I recommend starting with the "x1 facts," which would be anything with 1 as a factor, and the related division fact. 

Research on learning has taught us that this is how the brain learn best. 

Each family has a total of 4 facts that can be created with the same combination of manipulatives. (Doubles only have 2 per family.)

This can be seen in the visual below:

The upper left shows 5 sets of 6. (5 x 6 = 30) The upper right shows 6 sets of 5 (6 x 5 = 30) The lower left shows 30 sorted into 5 equal sets (30 ÷ 5 = 6) and the lower right shows 30 items sorted into 6 equal sets (30 ÷ 6 = 5).

Studying the fact families really makes the whole thing easier! If they learn one combination, they've got 4 facts!

Just for fun, here's how the doubles work. 

No matter how you turn the sets, it's still 5 sets of 5, so there's really only 2 possible combinations!

Research tells us that repeating the complete information orally helps the memory. They don't necessarily like to do this, but they'll admit it really helps them remember the facts!

If you've ever had to learn a new skill, I'm sure you've seen the value of practicing a little bit every day. Five minutes a day for 5 days will have more value than 30 minutes of practice once a week! Less time, more value! I work my fact practice into my math rotations in a variety ways: games, practice alone, practice with a partner, or practice with an adult.

Children develop their own tricks to help remember basic facts, and when they talk, they share those tricks! That makes everyone smarter!

Here's a trick I learned from my students! They've got plenty of ideas like this, that are worthy of conversation!

Most of the children will have a good deal of success with the above 6 strategies, but if they don't, don't let them fall through the cracks. I suggest doing some sort of assessment once a week, and keeping a record of how they do. Even when they don't show mastery, they should be showing growth each week. If they don't, something needs to be done. 

Here are some suggestions:

1. Limit the amount of fact families. One or two fact families is enough for some children.

2. Work one on one with that student: 5 minutes a day.

3. Assign an adult to work one on one with that student.

4. Send home a set of facts to be practiced with a parent.

The above would be in addition to your regular routine. 

Here's a freebie set of practice and assessments for the x1 Fact Families:

Fact Fluency System Level One: x1 Fact Families

 

It contains practice cards (with the answers to be printed on the back) 2 assessments, and access to Boom Learning Digital Task cards, which the children absolutely LOVE! And it's free!

If you're interested in just the Boom Learning format,that's a freebie, too!

If your students have success with this freebie, here's a link to the whole bundle: Fact Fluency System for Multiplication and Division: The Bundle

Here's a link to a similar bundle for addition and subtraction facts: Fact Fluency System for Addition and Subtraction: The Bundle

Plus, a chance to try out this system with this freebie: Fact Fluency System for Addition and Subtraction: Freebie

Want to read more about fact fluency and the brain? 

Here are a couple more blog posts with more information!

Making Addition and Subtraction Facts Stick

Ten Brain Tricks for Learning Math Facts

An Educational Winter Art Project

I love a craft that ties into something educational.  

I also love a craft that allows room for individual creativity. 

This time of year, we have to pull all the stops out to get them enthusiastic about learning, so we did this art project.

The kiddos made snow people with snowballs for each of the letters in their names. They made a math equation to represent their names, then decorated the snow people. 

 

Sorry, I had to cover the last names. Middle names were optional, but several wanted to include them. 

Look closely at this one: the third snow person is sad because the wind blew away his hat! Don't you love their imaginations?

Here's another, aren't these adorable?

One thing I really like about these: I can hang them in the hallway now, and I can keep them up until January!

Bullwinkle

I love when I get something from a workshop that I can bring back to my classroom the next day!

Today we had a Staff Development Day about Math. It had some good stuff about subitizing, Rekenreks (we used to call them abacuses) and different activities we can do with the kiddos  to help build that all important Number Sense.  

 

One fun activity was called "Bullwinkle".  (Do others remember the Rocky and Bullwinkle cartoon?)  Well, it's called that because you need to put your hands on your head so you look sort of like a moose.  (One could say you look like a reindeer this time of year!)

The teacher tells the kids to hold up a number of fingers. 

There are several variations:  making the number alone, making the number differently from a partner, making the number by working with your partner, making the number with your partner without actually talking.  

I'll bet you can think of even more variations, maybe even for practicing multiplication!

I really wanted to take a picture of a whole room of teachers (and administrators) playing Bullwinkle, but my hands were 

busy making the number 15.

Making Addition and Subtraction Facts Stick

I've been wracking my brain for years, trying to think of a way to get those basic facts to stick! 

 

There is way too much math that depends on knowing the basic facts, so we want the little ones to go beyond the "counting on fingers" or "counting on in your head" stage!

We've been using this sequence for learning facts at my school, and I must say, the kids are getting it! We all know it's not a good idea to introduce all the facts at once. There are 200 facts to be learned, and learning them in some systematic way is necessary. My knowledge of brain based learning tells me we need to help the children make connections, use visuals like color and pictures, practice frequently, add a social component, and make it fun. This will all help those facts stick!

 

I've taken 8 basic patterns and made 8 color coded sets of cards to be practiced based on these concepts:  plus one families, plus 10 families, plus 9 families, sums of 10, doubles, doubles plus 1, plus 2 families, and the remaining facts.  The "families" include 2 addition and 2 subtraction facts for each fact.  (For example, 1+8=9, 8+1=9, 9-1=8, and 9-8=1 are all connected.) These connections help children remember! I've even included a game that's connected to the cute little pictures on each card.

Practicing the facts is only half the challenge.  The other challenge is showing mastery.  

I've included assessments with each set. There are 2 basic assessments with each family. The 2 assessments are both similar. I just thought you'd like a second option so they aren't taking the exact same assessment each time. Each assessment has 5 columns of 10 facts. I give the children one minute to complete as many facts as they can. (The timing helps distinguish between the kids who know the facts, and the kids who still need to figure them out.) I have found that kids that get 20 - 25 facts in a minute are definitely ready to move on to the next level. (This, of course, is up to you.) Some kids really need a one on one assessment with the cards, as their writing skills just can't keep up with their thinking skills.

Want to check it out? See the image below for the freebie version of the first set along with the assessments. Addition and Subtraction Fact Fluency Freebie!

 

See here for the full system: Fact Fluency System for Addition and Subtraction

How do you help the facts stick?

Five Ways to Practice Counting By Fives

I've got some kids that totally need practice counting by 5s!  

This is a pretty important math concept, as it is needed to count money as well as tell time.  As they get older, it will help with multiplication.  

 

Plus, it's in the Common Core State Standards for second grade:  CCSS.Math.Content 2 NBT.A.2: Count within 1000; skip count by 5s, 10s, and 100s.

Yes, that does say within 1,000!  That means they should be able to start at 825 and keep going by 5s through 1,000!

That's why I brainstormed this list of 

Five Ways to Practice Counting by Fives!

1.  Here is a YouTube Video that's great!  It combines music, rhythm, visuals, and fun!  That's a brain-based recipe for learning!

Counting by Fives Song  by Have Fun Learning

I'll bet if you googled "counting by 5s" on YouTube, you'd find plenty more!

2.  Learning Games!  I posted about this game just the other day. It's great for learning any sequence that needs to be memorized. To download the directions, explore the image for the link, or go here: How to Play Countdown.

3.  Let them see the pattern!  I like to have loads of laminated copies of number grids around the room for the kids to look at, talk about, and mark up with their wipe-off markers.  They can call out the numbers by 5s as they circle them.  It really helps those visual kids to see the patterns. (Brain research tells us ALL students benefit from visuals! You can download a color-coded number grid here: Color Coded Number Grid.(or see  the image.) Plus you can download your color-coded grid to 1,000 grid here: Numbers 0 - 1,000.

4.  Get physical - and funny!  Kids need to move, and we know that movement and exercise help bring oxygen to the brain, therefore helping the memory!  We do loads of movement while counting, such as follow the leader, brain gym exercises, jumping jacks, push-ups, and just about anything we can think of to get the counting to be automatic.  Since laughter also brings oxygen to the brain, it's fun to do the counting with a funny voice. For some reason, I often break into a southern accent while counting by 5s, and the kids giggle like crazy and join right in!  (Waving y'all to all my southern friends... feel free to break into my Boston accent with your kids!)

5.  Don't stop at 100, and leave out the "and"!  I know, this isn't actually a 5th idea, but it's a pet peeve of mine.  My second graders are learning that counting by 5s keeps going after 100!  Those first 2 rows after 100 on the hundred grid are the toughest for the kids to learn, so it's important to go at least past 120!  Did you realize the proper way to say 105 is "one hundred five" without the word and. Technically, the word "and" stands for the decimal point, so "one hundred and five" really means 100.5.  (OK, you'd really say "one hundred and five-tenths", but let's get the kids in the right habit now so the kids won't get confused when they learn decimals!) 

 How do you practice counting by 5s with your students?

We're in the Money!

We started working on money this week in second grade! 

 Money is all about skip counting, so if the kids don't know how to skip count, it's going to be tough. Counting by 5s and by 10s is pretty easy for the kids, but I use a little trick from my past to count by 25s.

Brain research tells us that adding movement, as well as repetition helps the memory.

Did I mention that I was once a cheerleader?

This one dates back to the early 70s, but I think I remember my mother saying this one, so I'm guessing it dates back to about the 40s. Some of my girls volunteered to pose for the photographs. I usually call it a chant, not a cheer, so it doesn't scare away my little guys! These movements can be done in quite a manly manner, despite the daintiness you see in these lovely ladies.

A Chant for Quarters!

Twenty five! (punch arms up and left.)

Fifty! (punch arms down and left.)

Seventy-five! (punch arms up and right.)

A dollar! (Punch arms down and right.)

Everyone for money, (Arms out to sides.)

Stand up, (bend forward, roll arms)

and holler!  (Put arms up high.)

The kids absolutely love it! (Yes, even the boys!) It makes a nice brain break, or just a warm up for math class. The kids get to move around and practice their skip counting by 25s as well.

Instead of saying "Everyone for money", we usually insert the name of our school.

With my musical theatre background, every time we get ready for math when we're working with money, I break out into the song We're in the Money from the musical 42nd Street. I have a couple of kids in my class that are musically inclined, so last Friday at snack time, I showed them this video:

Every single kid was absolutely mesmerized! They even asked to see it again. (A couple of kids watched it a third time, while waiting for buses!) Then, when it was time to get ready for science, they all started tap dancing. Of course I let them tap dance their way to get their science materials. You can't discourage a desire for musical theatre!

Once they understand counting money, here's a fun game to practice the skill: Coin Trading Game