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.
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.
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.
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.
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,