Factors can be intimidating, but there are some tricks that help to understand them. Factors are numbers that are multiplied together to equal the final number. For example in the problem 2×4=8, the factors are 2 and 4. Although these are factors, they are not prime factors. Prime means any number greater than 1, and its only factors are 1 and itself. Some examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, and 43. If we go back to the problem 2×4=8, clearly 4 is not a prime number; therefore, we have to break it down until it is a prime number. To break down 4 into prime numbers we can start by finding a multiple of 4, which is 2 (2×2 = 4). Now we have all prime numbers: 2x2x2=8; this is the same as saying 2×4=8.
Factor trees help to find the prime factors of a number by first obtaining any two factors and then obtaining their factors. This may seem confusing, but it is actually quite simple. For example if we have the number 40, we can start by obtaining any two factors (8×5). Since 5 is already a prime number, we only need to obtain the factors of 8. These factors could be 4×2. Once again, 2 is a prime number; therefore we only need to break down the number 4. The number 4 breaks down into 2×2. Now we have all the prime factors of 40: 5x2x2x2=40. I have provided a picture of a factor tree to help visualize the problem.
A fun game that involves practicing factors is called Roast Turkey. This game helps to gain further knowledge of factors and helps to practice them. The game begins by letting the player choose what level you want. After you choose your level, it explains that you use your keyboard arrows and space bar to navigate “Professor Super”. Once you click the begin button, it will bring up a page that explains factors. Now it is time to begin the game; a question will pop up like: what is not a factor of 25. There will be three uncooked turkeys floating around your screen with different numbers in each one. You have to use the arrows to navigate “Professor Super” and the space bar to “fire” the correct turkey. This is a fun interactive factoring game!
Division can be a tricky, but understanding some basic terms can help. There are three basic terms to describe a division problem; they are dividend, divisor, and quotient. An example of this is 24/6=4. In this example the 24 is the dividend, 6 is the divisor, and 4 is the quotient.
There are two different concepts to find the solution to a division problem. They are the sharing concept and the measurement concept. The sharing concept uses the divisor to divide the problem into number of groups, and uses the quotient to determine how many parts are in each group. A great way to visualize this is by using fruit. For example, we have a total of 24 apples, and we want to divide them equally between 6 groups. How many apples will each group receive? According to the sharing concept the divisor, 6, is used to find the number of groups, and the quotient, 4, is used to find the number of apples in each group. This means we will have 6 groups with 4 apples in each group. On the other hand, the measurement concept uses the quotient to divide the problem into number of groups, and the divisor to determine how many parts are in each group. If we use the apple problem again, there would be 4 groups with 6 apples in each group. The picture provided may help to clear up any confusion about the concepts.
Drawing pictures is a great way to practice division, but I have also found a fun game that is great for practice. The game is called Alien Munchtime; in the game it allows you to choose the fact families that you need help with. The choices include 2 through 12. After you have chosen your fact families, an alien pops up and says she needs help serving lunch. Once you click the “lets go” button the game begins. Hungry alien students come through the lunch line with a division question like 88/8 and you have to serve them the answer like 11. This is a great way to get practice with division and have fun at the same time!
A very commonly used math concept is multiplication; it can be defined as repeated addition. For example, 2×4=8 can also be written as 2+2+2+2=8. This seems like a very simple definition, but can be confusing for young students. I can remember learning multiplication when I was in elementary school, and it took me a while to fully grasp the idea of it. I practiced my multiplication with flashcards all the time! Now that I am learning how to teach students multiplication, I think it is important to get them involved in math activities.
A great activity to help students understand multiplication is to draw chocolate chip cookies. In the drawing the chocolate chips stand for the number that we are multiplying and the cookies stand for the number that we are multiplying by. In the problem 2×4=8, the 2 is the number we are multiplying and the 4 is the number we are multiplying by; therefore, we would have 2 chocolate chips in each of the 4 cookies. When we add up all of the chocolate chips in the cookies the answer is 8. I think this is a fun and creative way to get students to understand multiplication.
The cookie activity is a great way to learn how to multiply, and Factortris is a great way to practice multiplication. Factortris is an online game that helps students who may struggle with their multiplication tables. It is also great practice for students who know their multiplication tables, and just need more practice. The idea of the game is to answer the problem before the time runs out. For example, it may say 54 and the player has to use the arrows on the keyboard to click the answer. In this case the player could use the down arrow and move it to 9, and use the right arrow and move it to 6. This would show up on the screen as 9×6 which is 54. Factortris is just one online game that focuses on multiplication practice, but I am sure there are many more.