Love Learning

Teaching Math Facts Using a Visual Approach

A customer recently shared: "Thank you for the coupon (607INTRO). I have ordered the Snapword cards and they are unbelievable. My first grader learned his words after going through them one time by himself. We've done through "C" Snapwords and will be starting the "D" set soon. I only wish you had cards like those for his math addition and subtraction facts. We're struggling in this area. I think if he embeds the picture and story with the number it will help him. We'll see. Can't wait to get started. Thanks for all your wonderful products."

Our reply was...

We're so happy that your first grader is doing so well with the sight word cards! As far as math goes, we have three math books that teach math facts using a visual approach. One is Addition & Subtraction, another is Place Value, and a third is Right-Brained Multiplication & Division. These provide the same strong foundation for math that the SnapWords cards do for reading... all with a visual approach!

How to Make Learning Numbers Easy and Fun for Young Children

Any concept that is based on symbols will present a problem for some children. Especially for the very young who don’t have a burning desire to learn numbers, letters or words, enticing them into learning these concepts works so much better than the plain ole’ way we have always taught them.

In addition, when we teach these important foundational concepts, the more we target multiple regions in the brain at one time, the bigger the chance that learning will occur and that learning will be permanent.

So, what we’ve done with our numbers 1-20 is pretty exciting! We designed a poster that you can display at home or in the classroom. The numbers are stylized like our SnapWords™ are; each number has a line of text that helps to tie the image to the name of the number… well, instead of going on and on using words, let me just SHOW you!

Here is the full poster:

Notice that the numbers are arrayed in lines of 5 numbers, so that the patterns emerge as you go down each column. There is the column of 1, 6, 1, 6, of 2, 7, 2, 7, etc. This design makes it easy to teach skip counting by 5’s and 10’s. Later you can show the children that if you add 5 to any number, the answer will be directly below the first number. Ex: 8 + 5 = 13, which is found directly beneath the 8. If you add 10 to any number, you will find the answer 2 rows below. See 8 + 10 = 18, which is 2 rows below the 8. You can also show, rather than tell that when adding 10 to any number, you just put a 1 in front of the original number. SO many cool learning experiences will present themselves!

Now for some close-ups:

Here is the image for 4. 

 Here are the images for 8, 13 and 16.

When you are enjoying the numbers together, have your child(ren) sky-write the numbers as they stand up and involve their whole bodies in the activity. Something like this:

It works really well to have the child(ren) first sky write the number, involving their whole bodies, and then run to the table to write what their body did on paper or whiteboard with marker.

The numbers 1-10 are found in our new book I Can Sing from 1-10 and in our first Kid Friendly Math book: Addition & Subtraction. If you utilize these tools for teaching, I promise, your children will love learning!

Help Your Children Have a Ball with Multiplication and Division

We have a new resource out that makes learning multiplication and division facts fun and easy. It is called Right-Brained Multiplication & Division: a Forget Memorization Book. For children who memorize and don’t seem to retain the facts in the long term, or who struggle to memorize and retain the facts even for a few minutes, why not abandon this frustration and go to a method that makes learning stick? It is common knowledge that images and stories act like glue to carry otherwise dull facts into a child’s brain. Using images and stories and body movement also reaches out to several regions in the brain at one time, making the likelihood of learning and recall very high.

Consider this: You can attack the x7 table with your child or your students and struggle through the dry facts, hoping that the facts will somehow stick to their brains OR you can take those facts and embed them in images and then attach a storyline that explains why those particular numbers are used. The story behind the images below is that the Seven Brothers decided to sell balloons. The day was very windy, so turnout was not great and they sold nothing at all. The next day, however, a couple came back (Mr. 5 and Mrs. 6). The wind had died down and Mrs. 6 saw a beautiful pink and orange balloon she felt she simply had to have! In fact she liked the balloon so much she bought two. One she carried in her hand, and the other she tucked into her purse for another time.

Oh, and by the way...

The next day, Mrs. 6 decided to go for a sail and for the occasion, she dressed up with her yellow shoes, pink purse and scarf and off she went with her two balloons! Our final chapter in the book has only one single fact the children have not learned to date (the other facts for this table have been learned with other times tables). Here is the fact that remains: 8x8=64.

 

See inside Right-Brained Multiplication & Division.

Snag a copy for yourself!

 

Hands-on activities and practice problems complete with answer key make teaching easy for the adult! 123 full-color pages.

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Parent review:

MARVELOUS!!!!! We just started using this book last week, and we have had wonderful success so far! My 2nd and 3rd graders actually look forward to math now...which is totally amazing because they have always "hated" math! This is definitely money well spent...especially for kids who are right-brained and/or don't enjoy memorizing math facts! :D

At Last! Math for Visual & Other Right-Brained Learners

We are at last expanding our focus to include math resources especially designed for visual, active, right-brained learners. We’ve carried three books in the Kid Friendly series for five years now, and while our intent for some time has been to publish up-to-date versions of these books as well as add supplemental products, we felt it was critical to focus on reading as a first priority.

Because, after all, let's face it: while math is a critically important subject, if children cannot read, they won’t be able to read math problems or science texts, or decipher social studies lessons…you catch my drift. While we are not slacking off in our continued development of reading resources, we are so happy and proud to announce that we’re also beginning to focus on math in a more concentrated way.

WHY MATH?

During my early years (meaning all the years before age 22), math and I were not particularly friends. I often said “I’m not good at math,” which meant specifically that I did poorly and also did not like it. It is really hard to like something you do poorly in. In grade school I usually failed every math quiz; as a high school student I could cram for a quiz enough to make an A or a B, but I did not retain what I had learned after the quiz was over and I left the classroom. It was as though someone took a big soapy sponge and wiped my brain clean of anything that contained numbers or equations. I blamed my brain and its shortcomings.

What I did not understand is that I—as a right-brained learner—have a superior memory for visuals or any information, actually, that I am able to make links to memory for. These links could be a jingle, a discovered pattern, a body motion that had become automatic, and so forth. After college it took me a very long time to voluntarily sign up for a math class and when I did, it was because I had to. I had to either take the teaching of math courses or not complete a graduate degree in teaching. I cannot recall dreading anything more.

WHAT I LEARNED

What I came to realize during those classes was so eye-opening. I learned that math and numbers are fascinating. Oh, not the way I’d been taught math, but once I started noticing them, the patterns I found in numbers were so engaging. I already knew that I could not memorize, but I came to understand this in a much deeper way. Beyond that, I realized that just memorizing facts or equations would not help me know how to apply what I had “learned” in various situations. It was far too abstract. I suppose that other people might think in numbers like I think in pictures.

During graduate school I began to explore how to teach little kids with brains like mine to learn to read and to love math. Over time an approach has evolved that makes so much sense to right-brained learners. It is the practice of taking left-brained facts (such as I before E, or 1+1=2, or that 3x3x3 is written as 3³) and embedding them in right-brained elements such as visuals and so forth. The research I have done with these approaches has demonstrated just how highly effective this practice is with those who naturally learn best through right-brained teaching methods.

NEW RESOURCES

So, back to Child1st beginning to create more math materials for visual and other right- brained learners...We’ve started with a book called Right-Brained Multiplication & Division: a Forget Memorization Book because learning these facts is onerous for so many children. The book is packed with color, fact families are embedded in images, stories explain the visuals, and explanations of procedures use color-coding to make it easy to see at a glance the relationships between numbers and what happens to those numbers when you multiply or divide them.

Rather than memorizing, children are able to store the visuals and the stories and recall them intact when they need them. The hands-on activities deepen the action in math and the processes that are taking place. The right-brained elements act as the glue that cements these facts in memory and as hooks that pull those facts out when the child needs them. If you have a child who glazes over when it is time to learn a new multiplication table, I'd encourage you to grab a copy of Right-Brained Multiplication & Division. You will see a big difference in your child’s engagement and long-term knowledge of the facts!

Tips for Helping Active and Spatial Children Remember Numbers and Other Abstract Concepts

The reason I so clearly identify with our visual/spatial and active learners is because I am one of them myself…albeit a middle-aged version. How these children learn and remember are not just things I have studied; I live them, so they're very real to me.

There is a particular four-digit number that factors into a lot of our paperwork at home. Because I tend to do much of our paperwork, it is incumbent upon me to learn and remember this number. It is a number my husband came up with, has no trouble remembering, and has patiently reminded me of more times than I can count. Something really interesting having to do with this number happened the other day. I needed it in order to unlock a keypad, so once again I asked him for the four digit number.

That time, because I keyed it in on a number pad, I was able to remember it. If you were to ask me what the number is, however, I would first have to visualize the keypad and then because of the shape of the movement as I keyed in the four digits, I would be able to tell you that number. The significance of this to our understanding of how visual/spatial and kinesthetic children learn and remember is huge.

I still cannot memorize a random string of numbers, but I can remember a number forever if I have seen its shape on a keypad. I remember the layout visually, and I can see the shape the sequence of numbers makes. I have visualized a body motion that mirrors that shape.

Here is the keypad:

Say the number I need to remember is 2139. The shape that number makes on this keypad is a backwards L.

And this is the hand motion I attach to that number:

The knuckle on the thumb represents the starting point or the 2. I then go to the tip of my thumb, then to the base of my thumb and finally to the tip of my pointer finger. Voila. Never to be forgotten.

If you happen to bump into me in the airport, just ask me for the number and I will now be able to tell you!

So what does all this have to do with children and learning and remembering? Simply that it's easy as parents and teachers to spend a lot of time beating our heads against a brick wall telling and reminding, and drilling, and flashing cards…to no avail. What often happens when trying to teach an active children through drill and verbal instruction is that we become frustrated and the child winds up feeling a bit dim and very discouraged.

So, taking this to the practical level, what are some ways to utilize the visual/spatial and kinesthetic learner’s strengths in learning? Here are some ideas:

1.    Relate the concept to the child’s body whenever possible. For instance, when teaching a child how to correctly form letters of the alphabet, ground the various letters to her body. The capital E is her upright form, with the top bar being a table coming out of the top of her head, the middle bar being a table that comes from her belly button, and the lowest bar being a table that comes out of her feet. Capital K is her upright body, her arm and leg extended to make the slanting lines. (See Writing the Visual, Kinesthetic, and Auditory Alphabet for more alphabet ideas.)

2.    Use the child’s hands to mimic the ideas they are learning. A powerful tool in learning sums to 10 is the child’s own pair of hands. Sums to 5 of course can be done on one hand.

The illustration above is taken from Kid Friendly Computation: Addition & Subtraction. When a child maps out the sums to 5 on his own hand, he is seeing the sums as tangible objects (his own fingers). He is feeling the pull of his fingers as he makes the sums, and his mind will tie those facts to what he felt and saw on his own body.

3.    Use a visual as often as possible. Oh I say this every day, don’t I? But visuals are so powerful, and for children who are visual/spatial, supplying them with a visual that is directly embedded in their learning is magical.

4.    Basically for anything a child would simply need to memorize, find another way to link learning to memory. It is what we do at Child1st; what we are here for. If you need ideas for teaching difficult concepts, feel free to comment below or email me at info@child-1st.com. I'd love to chat with you!

New Math Materials in Progress....and the Rationale Behind Everything We Do

We're currently working on expanding our line of math materials, starting with a new book about Multiplication and Division. I wanted to share the introduction to the book with you as it tells both about this upcoming product as well as the rationale behind all the materials we make. So here it is!

ABOUT THIS BOOK

The purpose for writing this book is to appeal to children who are strongly visual, who need hooks for remembering math facts, and who need to understand the process behind each math problem they solve. Child1st teaching and learning resources all follow the pattern of conveying learning pieces using a variety of right-brain-friendly elements. We take learning tidbits that utilize symbols and abstractions, which are left brained, and embed them in right brained elements that beautifully integrate the left and right hemispheres in the brain.

Right brained elements:

1- We embed symbols in VISUALS so that the child can take a quick look and absorb the learning piece which will be stored as a visual to be retrieved intact later.
 
2- We use PERSONIFICATION which is a powerful element in teaching and learning. The use of personification makes for rapid learning because the very look and personality of the character conveys the substance of the learning. For example, Mr. Zero with his circular body, bouffant hair style, his leer, and his magic wand will be an unforgettable visual reminder that when a child multiplies or divides by Zero, the magic wand will slash the air and the number will be transformed into a zero. POOSH! Instant learning!

3- We rely on PATTERN DISCOVERY as a way of making numbers come alive and as a means of conveying the amazing relationships between numbers. What results is number sense. I was rendered nearly comatose when I was a child and had to “do arithmetic.” Math was dryer than sawdust to me. It was not until I was preparing for teaching math in the classroom (ME? Teach math? You are joking, right?) that I began to play with arrays of numbers and became fascinated by them - because the brain is a pattern seeking organ. It is my desire that through this teaching resource, many children who are overwhelmed or daunted by math might come to truly be fascinated by it instead.

4- We use STORY to contain the meaning of what we are teaching in math. Stories, like visuals, make learning unforgettable. They explain the “why” behind math concepts, and tie everything together making a vehicle for meaning and for recall.

5- We use BODY MOTION - both gesture and whole body movement. Some of the movement includes clapping and chanting, some is acting out the story of the individual table. Again, body movement is a powerful agent for learning and remembering. For many people, body motion makes recall effortless if the learning piece is directly tied to a unique motion.

Read more about the philosophy behind Child1st materials.

Teaching with Body Movement Results in Enriched Learning Experiences

I can still remember when educators were beginning to talk about using movement in lessons as a way of enhancing learning for active children. The first night of a graduate class, the instructor invited us all out into the hallway. Our introduction to each other was an activity that was also meant to show us the value of using movement when learning new material. The theory was that if we did a body movement during the process of learning each others’ names, we would more easily acquire the names of our classmates. We stood in a circle and one by one we introduced ourselves. Once we’d been around the circle once and everyone had said their name, the instructor produced a ball and gave it to a lady. She was supposed to bounce the ball to another class member and say their name at the same time. The bouncee was to then become the bouncer, bouncing the ball to another member of the class while saying his name. This went on for a while. Finally, our instructor stopped the exercise and had several members of the circle see if they could accurately name every class member. Everyone was very pleased with the exercise.

Another activity was aimed at showing us how movement can help active learners learn high frequency words. A student laboriously cut out a stack of footprints from construction paper and wrote a sight word on each paper foot. Then she arranged the feet into a long path down the corridor. The game was played by asking a child to hop on each paper foot and simultaneously say each word as he hopped on it.

In many classrooms, active children are encouraged to bounce quietly on big balls while studying, or are allowed to swing their feet while doing their seatwork. We do understand that movement is helpful to many children, but is it just moving that helps? Or is it most helpful when movement is specific to the material being learned?

What the activities I described above have in common is that the body movement for each part of the lesson is exactly the same. When we bounced the ball during our learning-each-others’-names activity, the bounces were identical. In hopping-on-paper-feet, each word received a similar hop.

What I would like to explore is whether or not our students would gain far more if they were encouraged to mimic their learning with body movement. When learning the word JUMP, for instance, if the child sees the word and jumps as she reads it, she is reinforcing the meaning of the word with her whole body. Later, when she sees the word JUMP, she will likely make a little hop in place, and most certainly she will remember not only what the word says, but what it means. She will have absorbed the meaning of the word in her body in multiple regions: eyes, ears, and whole body. Gesture or body movement that reflects the concept being learned will deepen the meaning for the child, show that he understands the concept, and become a means of recalling that concept later.

Let’s look at some other examples. When teaching the meaning of addition, you could print the following equation on paper in a large size:

                        4 + 3 =

Have the child point with her left pointer finger to the 4 and to the 3 with her right hand pointer finger. When you say “Four PLUS three,” have the child move her pointer fingers towards each other, signifying the numbers will come together and combine to make a new, bigger number.

                        7 - 3 =

In the subtraction equation above, again have the child point to each number with pointer fingers of each hand. Say, “Seven minus three” and when you do, have the child move his right pointer finger decidedly to the right to signify that the 3 is going away from the seven, leaving a new, smaller number.

The ÷ sign can be acted out in a way that helps the child understand the action of division. Put 10 round plastic math counters on the table. Look at the problem 10 ÷ 2 = and push the counters into two groups. You can then have the child draw an imaginary line on the table in between the two groups, using their hand palm open, with the edge of their hand running along the table to mimic the line in the “divided by” symbol.

Finally, a whole body motion that shows the action for + is simply to bring both arms up and cross them tightly against your chest. You can make the action more to the point if you pick up some objects in each hand before crossing your arms over your chest to mimic the plus sign. This is the action of taking two groups and pulling them together to make a new total.

Use body motions for the math functions as you teach word problems. Teach your child to listen to specific words and do the related body motion when your child reads a word problem; this will help him understand which function to use for each problem. Example: “Jane had two apples. She picked five more. How many does she have now?” Have your child act out the problem. 1. Jane has two apples: The child will pick up two plastic math counters. 2. She picked 5 more: The child will pick up 5 more math chips and then with chips in both hands, he will cross his arms in the plus sign when he hears the word “more.”

Your students can become their own best helpers as they learn to create and use body movements that reflect the concepts they are learning. Let’s try it today!

Using Body Movement as a Backdrop for Learning to Write Symbols

I’m not a big fan of putting really young children at a desk with a paper and pencil… unless of course they are happily drawing a picture out of their own imagination and because they want to. At some point, however, these tots are going to be in school, and depending on the classroom, they might be placed at a hard desk with a pencil and paper and the task of learning how to write symbols (letters and numbers). Ugh.

What can you do to prepare your child for the experience of writing numbers and letters with pencil on paper? Something fun! Show your child a number symbol (let’s use the number 6),   and then using the fullest range of motion you can (really stretching out those arms and legs), sky-write the number in the air. You should model this sky writing, standing to the side and just a little in front so your child can get a good look at what you are doing. Then write the number using your pointer finger to lead the way and stretching your arm to make the hugest number you can make…stretch way up and when the number goes down, go WAY down, just brushing the floor. (The great by-product of this game is the aerobic benefit to the parent!)

When you have played this “game” a few times and have given your child a chance to store the movement in his brain and body, consider transferring that motion to paper. Please don’t use a pencil, though! Let your child choose a crayon or big fat marker in the color she feels matches the number. Once you have given your child the chance to sky-write the number in the air one last time, say, “Now can you draw on paper what your body just did?”

Just try it! You’re going to be amazed at what your child can do!

A beneficial ending to this exercise is to ask your child if he would like to draw 6 dots in a grouping that seems nice to him by way of illustrating his magnificently written number. Another great activity to establish number sense for hands-on learners is to make math dot cards. 

Building Visual Memory for Number Relationships

Global children will benefit greatly from building a visual base to understand where each number falls in relation to other numbers. We’ve spent some time using dot cards to build a visual memory bank of how many each number is, of which combinations of numbers equal each target number, and now we will move on. For these games let’s use a different kind of number card.

Use a Five-Frame

I personally prefer the Five-Frame Dot Cards because when you make an array of numbers in rows of five instead of ten, the result is quite a few benefits. One benefit is that the five frame reveals wonderful patterns in numbers. Another is that we use fives for so many things in life. We have five fingers, five toes, we read an analog clock (do they still make those?) in increments of five minutes, etc. Another less obvious benefit of placing numbers in Five-Frames is that it provides another great opportunity for visual imprinting for computation.

Note the patterns that exist in the columns. 1 and 6 alternate rows, as do 2 and 7, 3 and 8, 4 and 9 and finally 5 and 0. To add five to a number you just pick the number just below it (ie:  3+5=8, which is found just under the 3). To add 10 to a number, just jump down two rows. 4+10=14, which is just below the 9 on the Five-Frame.

Seeing the numbers arrayed in this fashion is going to help your child in thinking about numbers.

But for now, let’s go back to dots instead of numbers and play some games!

Five-Frame Dot Cards

If you make some Five-Frame dot cards, you may play the same games you played with the other dot cards. Numbers are anchored to 5 and to 10 in this two-row dot card. Study this first dot card that shows 7. Notice that the dots on the top row are blacked in, plus two more dots on the next row. Children can learn rather quickly that the top row is like the five fingers on their left hand, while the second row is like the five fingers on their right hand. So, the 7 in the Five-Frame is like one hand and two more fingers. The visual background the child will gain is that 7 is 2 more than five and 3 less than 10. You will be letting your child gain a visual background for how each number relates to the numbers around it.

In the next dot card, 4 is shown. You can see 4 anchored to both 5 and 10. 4 is one less than 5, and you need six more to get to 10. Relate this dot card to your child’s hands by having him show you four fingers up on his left hand, but not his thumb, nor any fingers on his right hand.

Playing with the Five-Frame Dot Cards

1. Begin with number-recognition games. Show a card and ask, “How many is this?” Remember as always that the child is going to guess at how many, not count dots!
2. Next make the connection to the child’s own hands. Hold up  a dot card and have the child show you on her hands how many as she tells you orally how many the dot card shows. For example, if you hold up the 7 dot card, the child will hold up all five fingers on her left hand, two fingers on her right hand, and will say “seven.”
3. Next, ask, “How many more than 5?” She will answer “two.”
4. Finally ask, “How many more to 10?” She will compare the three fingers she’s NOT holding up to the three white dots on the Five-Frame and will answer “three.”
5. If the child is still engaged and having fun, ask questions like, “How many would it be if I took off one dot?” or “How many would it be if I colored in one more dot?”

Play Other Games with the Five-Frame Dot Cards

Turn the child loose to play memory or war or go fish with another child, or play with him. Try to limit the teaching moments and just let the child have a lot of experience focusing on playing the games because as he’s playing, he will be storing up a wealth of visual information about numbers! Visuals and play are great ways to help your child love learning!

More Dot Card Games

Visual Imprinting for Computation

The goal of these activities is for children to develop such a rich visual background for computation that they will “see” the answers in their heads in the form of visuals when confronted with abstract problems on a page. When playing the games, however, the process of laying a visual background is passive. The focus will be on the game, and during the game, visual images will be building in the child’s memory.

Introductory Game

Give the children blank squares of paper and a crayon or marker. Tell them you are going to play a different sort of memory game. You will show them a dot card, they will give it a good look, then you will hide the card and they will draw on a blank card what they remember seeing on your dot card.

Procedure

• Show the children a card.

• Let them take a good look at it, then put the card back into your stack.

• Ask the children to shut their eyes and “see” the card in their imagination. Can they see the pattern of dots? Great!

• Now ask them to open their eyes and draw the same pattern on a blank card.

• When they have completed this task, show them your card and compare yours to theirs.

Computation Imprinting

For these games it will be best to have two identical sets of cards – two copies of each dot pattern. 

Explore the dot patterns before you begin. Pay particular attention to how many different combinations of numbers that each number has. You can only make a three from 2+1. (We are ignoring 0 + the number for now). Four is made of two combinations of numbers, as is five. Six and seven have three possible number combinations, while 8 and 9 have four. Over time, the children will learn that if  you divide a number in half, it will have that same number of possible combinations. Odd numbers can be divided in half but will always have one extra “odd” number that cannot be paired up. I think  there is value in creating dot cards that have two colors like the ones in the illustrations. The color will help the children as they form visual memories. It is likely the children will forever more associate pink and blue with five, and orange and blue with four, however!

Go Fish

The first several times you play Go Fish, play it like you did before, using the total number of dots on the card when asking for a card. When the child has played this way a few times, switch. This time when you play Go Fish, instead of saying “Do you have a  5?” you will say, “Do you have a 1+4=5?” or “Do you have a 5+1=6.”

Memory

Similarly, when playing Memory, at first when you make pairs,  say the total number of dots on the  cards. After a few times playing that way, switch. Rather than calling out the total number, you will say, “6+1=7,” or “2+3=5.”

Next, we will explore ways to build visual memory for number relationships, so watch for that post next Tuesday! And by all means, have fun playing!