How to Teach Math Facts (Subtraction) Image

This Post is a Long Overdue Follow-on

to the post I wrote on Teaching Addition. The addition facts are the first to be memorized, and they’re arguably the most painful and time consuming to learn.  That’s why they get a post of their own.  If you’re teaching your student addition for the first time, start there.

If your child has memorized the addition facts once, and you’re hoping to move on to subtraction, hang around.  That’s where I’m going with this post.

Still here?  Great!

We’re going to cover addition review, memorizing subtraction, multiplication and division.  We’re going to do them one after another, because this is all “connected learning.”  The new skills will all be connected together like train cars.  Addition is the engine, subtraction is the coal car, multiplication is the passenger car and division is the caboose.  (Yes, I do like trains.  Who doesn’t?)

Please do not feel shocked and hurt if your child forgets nearly every addition fact you taught him the previous year.  Almost EVERYBODY does this.  These facts need to be memorized several times before they truly stick, so yes – back to the drawing board.

Check to see which of the addition facts your child remembers.  If your kid is a rare genius and remembers them all, then congratulations (I hate you).  If your kid is like most of humanity, a refresher course will be in order.  This can seem like a giant step backwards to both you and your child.  How you react to the necessity of a review will greatly affect your child’s morale and self-esteem – so be cheerful about it!

Addition Review (To be Skipped by the Lucky Few)

Whenever possible, always have a second (or third) teaching method available for every skill.  This is particularly important for mathematics.  This addition review is your change to teach addition from a new perspective, helping the skill and memories stick even more firmly in your child’s brain.

Check out this addition table.  (Festive, huh?  I love color.)  Anyway, in this review of addition facts I encourage you to find twenty-four items to use as counting manipulatives.  M&M’s, Counting Bears, Counting Blocks, Pennies, it doesn’t matter.  Twenty-four identical objects to demonstrate addition – diagonally.

Would you like to print out this Addition Table?  No problem. Here it is in a PDF.  You may prefer to have your child color diagonal rows into their own addition table. (‘Cause you understand how kids learn – you crafty parent you!)  Here’s a Plain Addition table, just for your kinesthetic learners.

Display three objects in a row, and demonstrate 0 + 3 = 3, 1 + 2 = 3, 2 + 1 = 3, 3 + 0 = 3, simply by separating the objects as follows:

In doing thusly, you have just demonstrated the green diagonal row of pairs of addends equal to three in the chart above.  Keep going, demonstrate each diagonal row, until you’ve done twenty-two.  Make sure your child mirrors the words and movements of the objects back to you.

Did you save your triangular flash cards from the earlier addition lesson?  (I did tell you they would come in handy later!)  We’re going to use them for subtraction, so it’s NOT a waste of time to make these handy manipulatives.  If you missed that, or you need to replace them, here they are again:

Triangular Flash Cards

Cut your triangular flash cards out on card stock or from paste-board cereal and cracker boxes.   Triangular flash cards feature the two numbers being added in the bottom two corners and the sum in the top corner.  You will use them again very soon for subtraction.  Triangular flash cards are great for helping kids memorize a sum “backwards and forwards.”  They also help children easily grasp the connection between subtraction and addition.

Another Flashback

Like I said previously – USE YOUR WORDS!  When you speak while performing memory tasks, saying the entire number sentence and expecting your child to do the same, you “light up” a far greater percentage of your child’s grey matter.  The auditory, visual and kinesthetic processing work in a synergy to increase the rate at which your child acquires new memories and weaves the new memories more permanently into your child’s developing schema.  Model it and demand it!  In doing so you are not just teaching addition; you are teaching the child how to efficiently memorize new material.

Drill, Drill, Drill!

Go at it for twenty minutes at a time, drilling your child on the facts she or he has forgotten.  If possible, let an older child help.  This enforces your older child’s memory of addition facts.  Always be positive, and keep an addition chart with the facts already mastered colored in.  Add to it every time a fact is mastered, making encouraging remarks every time.  When the chart’s filled in, it’s time to celebrate in whatever manner your child most enjoys.

Subtraction time!

For a printable copy of this chart, please go here.

Let’s Start With What We Know. 

This can and should be fun, but it can also be intensely challenging for your child.  Keep in mind that you should only be working on this new material for twenty to thirty minutes at a time, no more than twice a day.  You know your kid.  You know for how long and how often your child can endure an intensive instruction session before becoming mentally fatigued.  Stop BEFORE your kid is too frazzled to learn.

Sort out all of your triangular flash cards where 1 is among the addends.  (In addition, addend + addend = sum.)  Hold up the flash card featuring 2=1+1.  Cover one of the ones with your hand, and ask, “Two equals one plus what number?”  Chances are your child will easily sort out that you’re covering a one, and state that the answer is one.  If not, be patient.  Simply reveal the one you’re covering, cover it, and ask again.  Do this for 3=2+1, 4=3+1,…12=11+1 and 13=12+1.  Is it easy and a bit dumb – sure.  Do it any way.  You want your child to build up lots of confidence.

Take out your counting objects and place two of them together. State “Two,” separate the objects and touch one, “equals one plus,” and touch the other object while looking up expectantly at your child.  chances are you child will chime in with a one.  If not, wait a full five seconds before providing the “One!” yourself.  Then repeat the process until your child responds correctly.  Once your child responds correctly, go through the same motions with your fingers and the objects while saying, “Two,” separate the objects and touch one, “take away one,” touch the other object, “is…” and wait expectantly for your child to provide the answer.  Again, WAIT for a full five seconds before providing the answer, and repeat as often as needed.

Repeat this process for all twelve facts.  To drive the point home, Write “2 = 1 + 1” and prompt your child to write beneath, “2 – 1 = 1.”  Repeat this for each fact.

Now it’s time to drill, drill and drill with the triangular flash cards.  Keep these sessions down to less than ten minutes and no more than three times a day.   At this stage, cover the one, making it the difference.  (In subtraction, minuend – subtrahend = difference)

When you think your child is ready, let one be the subtrahend.  Again, this will probably go pretty quickly.  If it doesn’t, go back to the counting objects and demonstrate with them.  Talk, talk, talk.  Use your words.  Expect your child to mirror the words you use.  The more your child hears, speaks, sees and manipulates the objects, the faster this will go.  Don’t discount writing either.  Having your child repeat the writing exercise with one as the subtrahend rather than the difference can work wonders.

As soon as you’re done with the “minus one” facts, ask your child to highlight them on the chart.  Remember that finishing the “minus one” facts also means finishing all the facts in which one is the difference.  Bring out the highlighters and celebrate every fact mastered.

I suggest you tackle the “minus ten” facts next, then the “minus 11,” “minus two,” “minus twelve,” “minus nine” and the lavender “take away half” facts.  Always highlight your victories.  I like to use lots of color.  Colored pencils work well for this.  If your child has particular difficulty with memorization, color in a block with each individual fact that is mastered, rather than waiting until an entire fact family is complete.  After you’ve done with the “take away half” facts, your kid’s chart should look like this:  Notice that by tackling the easiest facts first, we’ve shrunk down the more challenging fact families to a very manageable size.

Yeah Team!

Use your manipulatives, encourage lots of writing, and consider a few manipulatives and games – but only if they comfortably fit into your budget.  I’ve suggested a few below.  Remember that even when you’ve finished you’re going to need to review these facts again and again.  You’ll probably have to review the addition facts a few times too.  Keeping triangular flash cards in the car probably isn’t a bad call.


What’s next?

For you?  A year or so of  respite before you have to worry about helping your child memorize math facts again.  Just keep the flash cards handy, because kids do tend to forget their addition and subtraction facts a few times before these memories come permanent.

As for me, I will be describing how to help your child master their multiplication and division facts next week.  This week I will be writing about homeschooling “tweens” and how to add some low cost art projects to your curriculum – even if you don’t have an artistic bone in your body.  (Trust me – I don’t!)

Please write any suggestions and questions you have in the comment section.  I Love hearing from you, and I read and answer comments every 12 hours, so you can count on a prompt response.

All the Best,

Elizabeth

 

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Comments

Jennifer

I really like the triangular flashcards. They are much more engaging than the ones I remember as a kid … “5 – 2 =” on front and the answer on the back. I look forward to your articles on homeschooling tweens and if there are any different approaches to take!

Apr 04.2017 | 04:15 pm

    Elizabeth

    I love triangular flash cards too. One such flash card “connects” 2 + 3 = 5, 3 + 2 = 5, 5 – 2 = 3 & 5 – 3 = 2. One card – not four, as with traditional cards. How cool is that? As you can readily see, once multiplication and division memorization roll around, those triangular flash cards come into use again, because 3 * 4 = 12, 4 * 3 = 12, 12 / 3 = 4 and 12 / 4 = 3 can all be connected by a single flash card, illustrating an important point that makes memorization of all four facts easier. Triangular flash cards rock!
    Tweens are cool. I enjoyed homeschooling through the middle school years. Tweens naturally make the leap from memorization to abstract though, and they’re capable of greater independence. Their sense of humor is more sophisticated, so they make much more entertaining companions. They seek increased independence, and naturally take on greater responsibility, both academically and domestically. It’s a golden time to be a parent/educator.

    All the best,

    Elizabeth

    Apr 05.2017 | 01:55 am

Yvonne

As the earlier reader commented, I love the triangular flashcards too! They show how addition and subtraction are connected. I wish I had used this method to teach my girls when they were younger. And yes, I believe that a child (and even some adults) can easily forget what they’ve learnt in Math so constant practice is crucial. A strong foundation in basic Math will help children to cope with more challenging questions when they’re older.

Apr 05.2017 | 01:42 am

Maun

Hi Elizabeth,
This is the most simple and effective article I come across. I am very good at math and science, but never ever can put these thing together and be able to explain them.
Love the explanation so much here.
Perhaps, I am accustomed to using the scientific calculator for solving math problem.
Mathematics very important for everyday life, but my son is not good at it. I would like to know the step by step how to help him with these basic calculation. Please suggest.

Apr 05.2017 | 02:34 am

    Elizabeth

    It depends on your son’s age. If he is using calculators at school and he is not yet on the Algebra level, check to see if those calculators are scientific calculators or not. As you know, a scientific calculator understands the order of operations, while a consumer math calculator does not! I suggest that you NOT introduce a scientific calculator until your child is at least in pre-algebra. He needs to be of an age to analyze and understand the difference between the two types of calculators. At that point I’d do some research to find out what calculators your school is using. Even with scientific calculators, brand matters. There are significant differences in the algorithms of different brands of scientific calculators. You don’t want your kid to have to spend too much time learning how to use a particular brand, or unlearning how to use that brand in order to use another brand properly. If you’re lucky your child will be able to stick to the same brand of scientific calculator from middle school to graduate school! I suggest that Texas Instruments has the biggest market share – but check with your kid’s teacher! While you’re at it, I want to recommend the Desmos graphing calculator for every teacher and student who is working at or beyond the pre-algebra stage. This thing is really powerful, and increases student understanding exponentially! https://www.desmos.com/calculator It is also great for displaying and sharing – helping students and teachers communicate their ideas.

    All the best,

    Elizabeth

    Apr 05.2017 | 04:21 am

Ian Johnson

I love this post. When I was in school math was my favorite subject so I really relate to this and you have great technique’s. I like all of the repetition because that was the way that I learned and the colors real set it off. I can tell that you are passionate about your work and that is wonderful. We need more teachers like yourself. I would definitely recommend your site. Keep up the great work.

Apr 05.2017 | 06:48 am

Helen Vella

Love this post especially about alternative methods and more than one way to teach. I am always telling my clients that we have different learning styles and when you get a teacher who understands that it is amazing, Great post

Apr 05.2017 | 11:24 am

James Kelly

A very interesting and comprehensive article on that very important subject of mathematics which I first started learning at school some 60+ years ago! No calculators used in those days! Teaching methods have certainly changed a lot over this period as I can see from reading this article. A very informative article!

Apr 09.2017 | 12:47 pm

    Elizabeth

    My Dad used to carry a slide rule. Now I can’t find one. I think it would be fun for modern students to play with one – at least once. What do you think? I love mathematics more and more with each passing year. It’s the connection to everything.

    All the Best,

    Elizabeth

    Apr 09.2017 | 01:41 pm

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Wow, that’s what I was looking for, what a data! present here at this website, thanks admin of this website.

May 24.2017 | 09:13 am

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