Before Jacob was in kindergarten, he was showing an interest in adding and subtracting numbers. We spent time together; going over what it looks like visually with objects, and doing practice questions. He enjoyed the attention and the feeling he got when giving a correct answer.

At this time, I had the notion that introducing a math concept prior to the time he might see it in school, could be an advantage for him. Thus, shortly thereafter, we began to look at multiplication, which is essentially repeated addition. He made the connection fairly quickly. I then made him a multiplication table (10 by 10) and we made a game out of learning the product of numbers in the table. It didn’t take too long before he developed a reasonable level of proficiency.

He Was Not Ready Yet

When we moved to division, which was still quite some time before he would see it in school, he struggled  with making the connection between multiplication and division. He wasn’t yet ready, so we set that aside for the time being.

We then started looking at squares and square roots. I knew that many students in junior high struggled with knowing the difference between these two ideas. On short car trips, he would ask me to give him some verbal questions. I would bounce back between squares and square roots. We then delved into other roots, cubes, 4^th roots, 5^th roots and so on. He liked to use a calculator and draw on a white board to display these large values of squares and various roots.

Shortly thereafter, he was ready to revisit division.  We cut out little pieces of paper and formed groups. For example, we talked about the number of groups of 3 that can be made out of 6 pieces of paper. He could soon see that there is a connection between multiplication and division.

The number zero is very interesting. It becomes very important in high school. For now, I asked him to memorize that dividing by zero is not possible (I used the term undefined) and zero divided by anything is always zero. Although I tried to explain the reasoning behind this, I am quite sure he didn’t understand. But eventually he will, and hopefully he will remember this early work.

I thought it would be useful at this point to also mention that anything divided by itself is 1, and that anything divided by 1 is itself.

Negative Integers

The notion of a negative integer hadn’t yet surfaced in school when he and I started talking about it. One cold February when I was in Florida and he was in Alberta, we used temperature as an example. I said, “Our temperature here in Florida is 28, and your temperature is -20. How many degrees warmer are we than you?” We did this for several days and the process out of making sense of a negative number began. Soon after, we then went to adding and subtracting rules. Seeing an application prior to discussing rules can foster a deeper level of understanding. He is now quite confident in working with integers.

Fractions can be challenging for many students. Once again, we started the concept before he saw any classroom instruction. We used manipulatives to help him see the process. It did take a while to make progress. But, because his times tables were so entrenched, he was soon able to grasp the idea of equivalent fractions. He was then really able to move forward with the skill of adding or subtracting fractions.

When he was in grade 5 or 6, I picked him up for a short car trip to run some errands. He had his math scribbler with him. He wanted to show me what they were working on in class. He then said to me, “You know Grandpa, to you and me, this scribbler is like the holy grail!”

He learned how to play crib several years ago. This card game is an excellent way to work on mental math skills. Jacob is able to combine numbers to determine point accumulation in a very efficient manner. He quickly analyzes patterns. Playing crib is a wonderful way to develop and practice math related skills.

Jacob is currently in grade 9. His favourite subject is math. He believes that he is good at it, and he is. He understands it and it makes sense to him. He is also willing to work at improving his number sense. His foundation is solid. As long as he maintains a great attitude, works hard, and doesn’t give up when it gets a little challenging, he will continue to be a successful math student.

To summarize, my key points are:

• Learning the times tables as early as possible is extremely beneficial.
• Introducing concepts prior to seeing them in classroom instruction, can promote an early sense of confidence.
• Seek everyday opportunities to review and reinforce key ideas.
• Encourage and provide a significant amount of positive reinforcement.
• Use visual aids to help students see connections.
• Periodically introduce new ideas and give them time to grow.