Learning Archives - Page 2 of 2

Building Mental Math Fluency

Mental math fluency is one of the most important basic math skills a child needs. Finger counting, skip counting, and using pencil and paper are inefficient ways to do simple calculations. When your child is faced with a more complex math problem, such as long division, it can be distracting, tiring, and lead to errors if they have to constantly stop and figure out small calculations. Also, building strong mental math skills helps your child deepen their understanding of numbers and how they work together.

Fluency develops from strong number sense (how numbers work together) and practice with mental addition and subtraction. There are a few easy ways to accomplish this and your child can quickly learn to add and subtract sums in their head. From there, your child can then move on to master multiplication fluency with a strong foundation and confidence. Start with the basics of numbers that make 10 and doubles facts.

Make 10

Knowing which numbers combine to make 10 is a very useful skill. It translates to adding larger numbers too. For example, if your child knows that 4+6=10, then figuring out 54+6 is not so challenging. Using the skill of making 10, your child will understand how far away the next multiple of ten is from a starting number. So if you are at 54 and you know that 4+6 makes 10, you know the next multiple is 6 away. Your child can use this thinking to break a problem apart into simpler components. For example, if the problem is 54+8, you can think “I know that I can use 6 of the 8 to get to the next ten, which is 60. Then there are 2 left. 60+2 is easy! The answer is 62”.

Doubles

If you know your doubles facts, you can quickly and easily solve pretty much any simple math problem. Work first with your child on memorizing doubles facts (1+1, 2+2, 3+3, 4+4, and so on). Then from there, you can practice addition problems similar to doubles facts, such as problems in which one of the addends is one more or one less that the other. Point out that the problem 3+4 is similar to 3+3. If 4 is only one more than 3, then the answer will be one more than the doubles fact 3+3.

3+3=6

3+4=7

This works for 3+2 as well. Once you know how to do this, you can move onto facts where the addends are two away from each other, such as 3+5. The idea is to make a connection with a math fact you do know, and work from there. Once your child practices this enough, they will start to see the connections and patterns and their math fluency will grow.

Making It Happen

I have found that the best way to build mental math fluency in these two areas is using flashcards and games. Another great tool for visual learners and hands-on learners is Cuisenaire rods. These simple colored blocks are useful in showing number relationships. The kit comes with a booklet detailing many activities for higher order math as well.

Games and flashcards make rote memorization fun and challenging in an exciting way. Your flashcards should feature the “make 10” or doubles fact on one side and the answer on the other. For example 6+__=10 is on the front, and 4 is on the back. You’ll want to have the fact in the opposite order as well on another card: 4+__=10. You can make flashcards for problems similar to doubles facts as your child progresses, such as 4+5, or 4+3. Practicing flashcards daily is the best way to become fast and fluent.

Some great, simple games to play include Go Fish and the Memory Game. With Go Fish you can change what makes a “pair” to numbers that make 10 (take out the face cards), or you can play it so that a pair is a double fact with one addend 1 more than the other (4 and 3 could be a pair, or 4 and 5 could be a pair). Have your child say that fact and the answer when they make the pair.

For the Memory Game, you can have the problem on one card and the answer on another. For example, if you’re doing all doubles facts, have all the facts (1+1, 2+2, 3+3, etc.) on cards and put the answers on separate cards. Place all the cards face down on the table. Players take turns flipping over two cards and trying to match the problem with its answer.

There are plenty of ways to get creative with math fluency. Think about your child’s learning style and interests and brainstorm some creative ideas to modify these activities or create your own! If your child is an artist, for example, let them make the flashcards colorful or interesting if it will help them remember better. If your child is struggling to develop mental math fluency despite your best efforts and you suspect there may be some learning challenges present, contact me to set up an assessment and get your child on the path to success!

When a Child Says “I Don’t Know”

I distinctly remember being a student in elementary and middle school and being chided for giving the answer “I don’t know” to a teacher’s question. It just simply wasn’t an option. I even remember hearing the response “That’s not an answer” from one of my teachers. It became engrained in me as well as my classmates that not knowing wasn’t an option. So what were you supposed to do if you really didn’t know? I suppose the idea was to encourage students to look for the answer, or to pay attention more in class. Maybe. I also recall the moment when I learned this wasn’t a practice unique to the school I attended. I was completing my pre-practicum to become eligible for graduate school and I was under the supervision of an elementary teacher at a school five minutes away from my college dorm. I was excited to be in the classroom, learning new techniques and getting a chance to interact with students. It was during a word study lesson that a student gave the answer “I don’t know” to the teacher’s question, and was quickly told that it wasn’t a satisfactory answer. Of course, being a young, impressionable teacher-to-be, I took this as the best way to respond to a child who really didn’t know, and this response would undoubtedly spark the desire for said child to open up a book and start searching for a better answer. Learning would be taking place! Right?

In Steven D. Levitt and Stephen K. Dubner’s book Think Like A Freak, this quote struck me: “It has long been said that the three hardest words to say in the English language are I love you. We heartily disagree! For most people, it is much harder to say I don’t know. That’s a shame, for until you can admit what you don’t yet know, it’s virtually impossible to learn what you need to.” This chapter goes on to detail the importance in our culture of trying to be an expert at everything or always knowing the answer. But is this a good thing? In my experience, I have found not. So many children are being taught from an early age that it’s not ok to say “I don’t know”. On top of that, we have a whole society of parents and teachers who have taken this lesson to heart and set the example for our younger generation. Children begin to think that mom and dad, their teachers, really any adult, must know more than they do. Adults always have the answer. It creates the false impression that children have everything to learn from adults, and adults have nothing to learn from children; they already know it all. It fact, I learn from children every single day. Even more damaging, children begin to grow into adulthood, finding that they don’t have all the answers, and feeling the pressure of having to pretend they do.

So what is a better way to encourage your child to be a thinker without creating a false sense that they have to always have the answer? I think one of the most important things that parents and teachers can do is model “not knowing”. I appraoch teaching and learning much differently than I had when I first made the decision to pursue education. Now, if one of my students asks me a question that I don’t know the answer to, I happily say “I don’t know. Let’s find out together.” Not only does this show the child that they don’t need to always have an answer, but it also shows them that they are capable of searching for their own answers to questions. It allows them to explore different sources of information and use their own judgement to determine what the most reliable answer may be. It is empowering. I believe it also shows children that there may not be an answer to every question. And that’s ok. In our society, we find that hard to accept. But the more we become used to this idea, the more open we will be to learning and discovering.