Tutor profile: Kristin N.
What strategies can we use to solve for x in the following problem? x – 18 = 12
There are several different strategies we can use to solve the above equation. The first strategy is inverse operations. Inverse operations are basically opposite operations that undo each other. If we wanted to use inverse to solve the above equation we would have to use addition. Addition and subtraction are inverse operations because they undo each other. In order to use inverse operations we would rewrite our subtraction problem in reverse using addition. Therefore, x - 18 = 12, would become 12 + 18 = x. Once I rewrite using inverse operations and then solve, I have my value for x. In this case, x = 30. A second strategy we can use is isolating the variable. This strategy is all about keep our equation balanced, but also requires the use of inverse operations. We need to picture our equation on a scale, (x - 18 would be on one pan and 12 on the other). At all times our scale must remain balanced. Therefore, if I make any changes to one pan, I have to make those same changes to the other pan in order to make sure my scales stays balanced. As I said earlier the goal of this strategy is to isolate our variable (which means to get our variable all alone). In order to get variable isolated, I need to undo whatever is next to it. In this case, next to my variable I am subtracting 18, in order to undo subtraction we need to use the inverse operation which is addition. So instead of subtracting 18 I need to add 18. If I am adding 18 on one side I need to the same thing to other. Remember -- keep the scale balanced. One the left pan/side, I am left with x now. Subtracting 18 and adding 18 leaves me with 0. On the right pan/side i am left with 18 + 12 which equals 30. Therefore, I am left with x = 30. Here is visual of the explanation above x - 18 = 12 + 18 + 18 x = 30
Subject: Basic Math
How do powers of 10 relate to dividing decimals?
When we divide decimals we need to be able to move the decimal point as needed. In order to move the decimal point we need to multiply by powers of 10. For example, if we are dividing 2.56 divided by 0.8, before we can actually begin the process of long division we need to turn our divisor into a whole number. In order to turn 0.8 into a whole number, we need to multiply it by 10 (or move the decimal point one space to the right). After multiplying, 0.8 by 10 it becomes 08 (or more simply 8). Now since we have made changes to our divisor we need to change our dividend. This keeps the problem balanced. We cannot change the value of one without changing the value of the other. Since we multiplied 0.8 by 10 we are going to do the same thing to 2.56. After we multiply 2.56 by 10, it becomes 25.6. Our new problem is now 25.6 divided 8. Now that we have made our divisor into a whole number by multiplying by a power of 10, we can divide normally.
Subject: Early Childhood Education
Why is it important to expose students to various strategies when teaching them basic math skills?
When students are learning early math skills they are still developing their basic understanding of numbers, what they are, how they work and what they represent. They are building their foundation of the place value system. When we introduce them to various strategies for skills such as addition, subtraction, multiplication and division they are able to make connections and deepen their foundational understanding. In addition, this is a form of differentiation. Students learn in different ways. Each of these strategies presents different visually, or requires the use of different models. By exposing them to different strategies, they are more likely to develop a deeper understanding. When they have a deeper understanding of foundational skills they are more likely to be successful in their future math endeavors.
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