Strategies for basic addition and subtraction facts

In this video I show several strategies for learning the basic addition and subtraction facts:

• finding all the possible sums for a certain number; e.g. for 6, these would be 0 + 6, 1 + 5, 2 + 4, and 3 + 3;
• writing out all the fact families where the sum is a certain number;
• the 9 "trick"; 9 + 7 is the same as 10 + 6 (9 wants so badly to be 10 so that it "steals" one from 7);
• doubles and the accompanying addition facts;
• number rainbows and how to use them to practice subtraction;
• a structured drill for addition facts.
  

Enjoy!



Strategies for Addition and Subtraction Facts - Video

Timed drills for math facts?

Are timed math tests (drills) necessary and for what purpose? If necessary, how often should facts be tested? Are timed math tests recommended for students who have "math issues." , such as low confidence and slower progress.

I simply feel that timed drills are a tool among many, when it comes to learning math facts. Some kids will "thrive" on them, or in other words quickly learn when they are used. Perhaps they like racing against the clock or like the challenge. There exist computer games that are timed that can work very well for drilling facts. Check for example:

Math Magician games has a simple 2-minute countdown, and if you answer 20 questions in that time, you get an award.

Some of the games at Sheppard Software don't time you but give you more points the faster you go. That site is actually filled with several types of games just for math facts practice.

Yet for other kids timed drills may be counterproductive and end up in tears and frustration. The proof is in the pudding though. Just try them and see how it goes.

I feel timed drills are a good tool but not absolutely necessary. Kids can learn their facts so many ways. For example, some learn to use clever shortcuts such as "Since 7 + 7 = 14, then 7 + 8 is one more or 15" and actually perform that in their heads so quickly that you can't tell the difference if they memorized it or did some calculation. Some learn them by heart from much usage in problems, without being timed.

You're welcome to use timed drills with low-confidence students because you never know, perhaps a student like that has decent memory and can succeed with it. However, if you already know that a student cannot easily remember facts without context, then it might not work.

Number rainbows to learn subtraction facts

I thought some of you (those who teach second grade) might enjoy my NUMBER RAINBOWS. The idea is that you connect two numbers with an arc if they add up to the particular number, such as 13.



Then, the child can use it as a reference when subtracting from 13 or when doing subtraction drill. You could first drill subtraction facts WITH the rainbow (such as 13 − 4, 13 − 7 etc.) and then without.



You would also ask the child to reproduce the rainbow - and color it, of course! These make for quite pretty math facts practice, don't you think!

I'm going to add these to my Add & Subtract 2-A book.

A question on MathScore

Hi Maria - I am really enjoying your workbooks for the kids - I can't wait to get going on fractions.

I wanted to ask you do you see value in any of the online math practice programs for drill? I saw that HS Buyers Co-op is offering www.mathscore.com - at a discount and we are trying it out on trial - It's just pretty much basic drill for speed and accuracy. I don't want to waste the $$ on it - if that is not really important to math.
Thanks for any feedback.

I've personally visited and even reviewed Mathscore. Mathscore is not just about basic drill on addition or multiplication - they have basic word problems, geometry, etc. as well. It is more like a math practice system for any kind of basic problems.

Kids do need to learn their facts by memory. So "drill" is not bad in itself.

Obviously math instruction should not be only drill. You should just balance it all. Teach concepts, teach why something works, let them practice, and help them master their facts. Drill can be part of that whole package. Just don't rely on it.

For example, if you subscribe to MathScore, you could teach your kids a "normal" math lesson on one day, and the next day let them practice at MathScore. It is a tool, it can be very useful, but it is not essential if they get to do math problems some other way. Just try it out and see if the kids like it, but don't forget basic instruction on concepts.

My review
MathScore - direct link
Info on the discount at Homeschool Buyers Co-Op.

Do you need drill to learn multiplication facts?

Continuing on the same lines as my previous post, what about multiplication facts and drill?

Well, the principle is similar: show them first the concept and patterns.

Then can come some plain drill.

But, I want to share with you a few more detailed points.

1. The main "patterns" in various multiplication tables of course follow from the concept of multiplication. For example, table of 2 is counting by 2's. You get table of 4 by doubling the answers in table of 2. You get table of 8 by doubling the answers in table of 4.
   
   Table of 10 is counting by 10s. Table of 5 - just take half of what the 10 ×
   
   Here are some resources to give you ideas about these kind of patterns and little "tricks".
   
   * Michele's Math
   * Times Tables' factsheets
   
   


2. We ALSO need them to know the tables "backwards".
   
   Let me explain.
   
   It's not enough to know that 8 × 7 is 56, when someone asks what is 8 × 7. The students ALSO need to know that 56 is 8 × 7, when given just the answer 56.
   
   This is very important. Students need this fairly soon when they start learning division. Later on it will be important when simplifying fractions or factoring.
   



3. Since it's important to know the tables backwards, I do not feel it's enough if the child is able to "figure out" the multiplication problems. I feel they need to memorize them, period, and not just be able to count or use some other method to find the answers.
   
   It's fine initially, and indeed very helpful, if the child figures out 8 × 8 by first going 8 × 2 and doubling that twice.
   
   But this fact also needs memorized so that later on, when she comes to the problem 64 ÷ 8, it won't take her 10 seconds to find the answer.
   
   Now you might ask why is that important? Because of long division, for example. It's going to be a pain to learn long division if you don't know your division facts by heart.
   
   Here's another reason: soon the student is going to have fractions to simplify. If you know your division facts, then simplifying 35/56 will be a breeze, otherwise a pain.
   

See how it all builds on the previous topics? You need to get a good foundation, and multiplication facts "both ways" is part of that foundation.

I have posted online the entire guide to effective oral drilling from one of my books.

The guide explains how the teacher and student can achieve memorizing multiplication tables in this manner where they know the answers and they know which answer goes with which multiplication problem.

Check also a list of online games that practice times tables. These are great after you've done some basic drill and the child needs reinforcement (practice!!!).

How NOT to drill addition facts

Some people think "drill is kill", and many people think it's necessary.

And of those that use it, not everyone knows HOW to actually drill math facts effectively.

You know, this is NOT the most effective way:

Shuffle the flash cards and start asking randomly.

Why? Because you are not utilizing techniques that help our brain remember quicker.

For example, it is easier to remember when the mind can tie the fact into something already known.

This is the idea behind silly rhymes such as "five, six, seven, eight - fifty-six is seven times eight."

Besides those, we want to show our children the PATTERNS in math.

So this is how I start drilling math facts (whether addition or multiplication):

I make a list on paper, IN ORDER. For example, lately we've been doing this with my daughter:

8 + 2
8 + 3
8 + 4
8 + 5
8 + 6
8 + 7
8 + 8
8 + 9

We went through the answers and notice how each one is ONE MORE than the next! That's a pattern!

Then I would point to a fact and say the problem so she'd both see and hear it (using two senses). You can additionally MOVE her finger on the chart with yours - so she's using three senses. This should help the auditory, visual, and kinesthetic learners all.

When I'd point to a fact further down the list, automatically she'd know it's more than a fact that is up on the list. It's a visual pattern.

First, I drilled just a few of them, namely 8 + 3, 8 + 5, and 8 + 8 until she remembered those.

After that, I would go first to 8 + 8 which she knew, and immediately after that to 8 + 9, and she was able to deduce it from knowing 8 + 8.

I would gradually add new facts in a similar manner - using the known facts as "stepping stones" so that the new fact was one more or less than a well-known fact.

And so we go "round and round" on this chart.

NOTICE THIS:
= > The chart creates an organized context for the addition facts.

Obviously, the child is also associating the position of the fact on the chart with the answer, and so after this is well remembered, it will still take another effort to remember the facts when they're in isolated context, such as in a game, or in a math book, or on flash cards.

But at least it is a very good start, I feel!

What are your thoughts?