Week 25

Dear Parents,

I hope your students enjoyed their President’s Day holiday, and I hope that those of you who were off enjoyed your break as well.

This week in science class, we are continuing our study of geology by continuing to study the inside of the earth. We will talk about plates and plate tectonics as the cause of earthquakes and other disasters. We will also demonstration in the lab how heat convection can cause the motion of plates.

In math, we will continue our discussion of fractions, focusing especially on mixed fractions, improper fractions, and the relationships between the two. We do also have a test on order of operations on Friday. Your students’ Friday folders from last week should have contained the worksheet on order of operations they completed last week. Most of the students did extremely well, but if you wish to review further with your students, here is a study guide:

Math Study Guide on Order of Operations

Order of operations is a list of rules that mathematicians have agreed upon in order to decide what operation to perform first, second, third, etc. in problems with multiple operations. Changing the order you perform operations changes the answer you get, so mathematicians have come up with an agreed upon order of operations in order to avoid having two correct answers to the same problem. This order is: 1. Parentheses  2. Exponents  3. Multiplication and Division  4. Addition and Subtraction

It is helpful to think of order of operation in as a list of ranks with 1 being the highest rank and 4 being the lowest rank. Operations are performed in order of rank from highest to lowest. For example:

70 – (4 x 5) x 3 becomes 70 – 20 x 3 and then 70 – 60 = 10

 If there is more than one operation of the same kind in a problem you perform the operations of the same kind from left to right:

(75+9) – (24-4) – (5x5) becomes 84 – (24-4) – (5x5) then 84 – 20-(5x5) then 84-20-25=39

One of the tricky parts of order of operations is the fact that multiplication and division are together on the same rank, and addition and subtraction are together on the next rank lower. What does it mean to have two operations on the same rank? It means that after exponents and parentheses have been evaluated, you evaluate multiplication and division in whatever order they happen to appear from left to right. Similarly, after multiplication and division have been performed in the order they appear from left to right, we perform addition and subtraction in the order they appear from left to right.

Here are some examples:

1. (35 - 30) x 50 ÷ 10 x 3 ÷ (10 + 5)

 5 x 50 ÷ 10 x 3 ÷ (10 + 5)

5 x 50 ÷ 10 x 3 ÷ 15

250 ÷ 10 x 3 ÷ 15

25 x 3 ÷ 15

75 ÷ 15 = 5

2.  5 x 5 -10 + 40 – (30 + 7)

5 x 5 – 10 + 40 – 37

25 – 10 + 40 – 37

15 + 40 – 37

55 – 37 = 18

Some students remember order of operations with the acronym PEMDAS. That is okay as long as they understand that multiplication and division are on the same rank, and addition and subtraction are both on the next lower rank. We do not perform multiplication first from left to right and then division first from left to right. We perform them in whatever order they appear in from left to right. Simialrly with addition and subtraction…

These are all the notes I have for you for the week! As always, you can contact me with any questions, comments, or concerns at rwycklendt@archwaytriviumeast.org.

Sincerely,

Miss Wycklendt