Addition, subtraction, and multiplication... most Math teachers have a standardized approach to teach the basics. That standardized approach may not always be the best approach. Every student has different needs. Regardless of whether I am working with adults who simply need help learning, students who are learning English as a foreign language, or children, I often start my #virtualtutoring sessions by asking my students, "What did you do for fun this week?" The answer to that question often defines the context for the lesson. Sometimes asking, "What do you want to talk about today?" will provide the foundation for the lesson.
Think about how often you use math on a day-to-day basis. I know many people say they hate math, but we all use it every day! With basic math tutoring it is often helpful to apply the concepts within an environment familiar to the student. With a little bit of creativity math lessons are completely customizable. You can easily take students from basic boring math lessons focused on counting to applying math to subjects that are important to them and suddenly have the students adding, subtracting, and multiplying. You may be talking about farm animals with one student and buying a fancy dress with another!
How is this possible? Let’s start with a basic math lesson… This is a true story.
I was tutoring a woman with learning challenges. She wanted to talk about numbers. I was not sure what she knew about math, so we started with basic counting, 0 to 9. I created a series of columns on the whiteboard by setting up the single digits in a column on the left side of the screen. Once we counted all the way to the bottom of that column, we talked about two-digit numbers and set up a second column just to the right of the first column. This time I started with 10 at the top of the second column going all the way down to 19. By repeating this process all the way up through 99 students can start to see the pattern that is presented on the screen. The first column had only one digit. All other columns had 2-digit numbers. As you move to the right in the table, the first digit increased by one. The first row of numbers all ended with zero. Reading through that row is like counting by 10s. The second row ended with one, etc. Over time, the same table can be used to talk about counting by twos, fives, tens, or 20s.
When my older students and adults feel comfortable with this level of math, I have them start thinking about it being applied to dollars and cents. They all understand what it means to go shopping and have to pay for what they want to buy.
I put graphics on the screen that represent $1, $5, $10, and $20 bills. We then go through the process of counting $1 bills $5 bills $10 bills and $20 bills creating a stack of each of them, until each stack contains $100.
We know how much money is in each stack because we discuss adding the bills as we create the stack.
This process also provides a convenient context to start discussing multiplication concepts.
If you have to put five $20 bills into a stack to reach $100, students quickly grasp the concept 5 X $20 = $100.
Counting $10 bills and putting them all into one stack helps the students see that 10 $10 bills equal 100, or 10 X $10 = $100.
One of my ESL (English is a second language) students surprised me one day when I asked him what he had done for fun. Instead of replying “Work!”, he said he played with his goats! Goats?! I had no idea he lived on a farm. I asked him, "How many goats do you have?". The surprise answer was 30. I asked him what other animals do you have? He told me chickens! How many chickens? He said he used to have 10 but now he only had seven. What happened to the other three? He said the foxes got to them. I told him, “That's a subtraction problem 10 - 3 = 7.” I asked him what other animals he had. The answer was four cats and three dogs. I told him this was turning into a big addition problem and asked him how many animals he had all together. We did the math: 30 + 7 + 4 + 3 = 44. He asked me if we could multiply. I told him multiplication would not answer that question, but we could use multiplication to answer another question.
If you have seven chickens and they lay a total of 10 eggs every day, how many eggs do you have at the end of the week?
We first did this an addition problem 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70. This made it easy for him to understand the calculation as a multiplication problem: 7 days x 10 eggs = 70 eggs at the end of the week.
We also looked at how many eggs he would have at the end of multiple weeks. For example, if his chickens continued to lay 10 eggs a day for 4 weeks he would have (10 x 7) x 4 = 280 eggs! My student quickly got the concept of when to use multiplication.
I worked with another adult student with some learning challenges. She happened to have a birthday around the time we were talking about math. She told me about getting birthday cards with money in them, typically $10 or $20 bills. So, we used her birthday money as a way to count by 10s and 20s and to do multiplication problems. For example, we talked about how much money she would have if she had four $10 bills; it's like adding 10 + 10 + 10 + 10 = 40. Or, saying four times $10 bills equals 40. We did similar kinds of exercises with the $20 bills. Then, we talked about something that she wanted to buy and how many 10 or $20 bills it would take to make the purchase. From there we did the subtraction problem to see how much money she would get back when she paid and double checked by adding the change to what she owed to see if it equals the amount she paid.
Several months after our tutoring sessions ended, I got a message from her guardian saying that they had gone out to buy clothes. My former student found a dress that she really liked but she could not decide if she wanted to buy it. The guardian asked her how many $20 bills she would have to give up to buy that dress. When the woman figured out how many $20 bill she'd have to give up she decided the dress was not worth it.
The moral of the story? When you are teaching basic math skills, talk to your students and find out how they use math. When they realize it is relevant to things that are important to them, and they use math every day, you might find your students getting very engaged in the lessons. This approach is not limited to addition and subtraction. I have also had students telling me how they use division and geometry in their everyday activities (see Using Math to Divide and Conquer)!
