Bracing For Brackets Alignment Lesson

1. Bracing For BracketsAlignment Lesson Day 75

2. Let’s review what we learned yesterday about Order of Operations

4. 25 – 4 + 4 x 3 • Using what you have learned, solve the expression above. • Explain your thinking

5. 25 – 4 + 4 x 3 • With your elbow buddy, insert parentheses into this same expression to create a new problem with a different solution. • We will have a few student leaders share their group’s expression and explain their solutions.

6. Discuss the following questions with your elbow buddy… • How do parentheses change an expression? • What do they do to an expression? • Once you have had a chance to discussion these questions, we will share your responses with the class.

7. Can an expression have more than one set of parentheses? • Try and prove whether or not this is true or false by making up a few expressions of your own. • Once you have had the opportunity to find an answer the above question, we will share your expressions for the class to solve.

8. 2{5[12 + 5(500-100) +399]} • What do you notice about this problem? • Parentheses, brackets and braces all serve the same sort of purpose in an equation: they are used to group and separate parts of the problem. • We solve these grouped items together before grouping them with the rest of the problem. • Let’s not solve this expression quite yet!!!

9. Hierarchy of Order Parentheses ( ), brackets [ ] and braces { } all serve a specific purpose within a problem. Each one functions as a grouping to separate a part of the problem to do it in a certain order.

10. We use these different “groupings” for a variety of reasons, the most common being to solve problems that could be part of a set. Check out this problem… • Sally’s mom gives her 5 cookies each day for her lunch at school. Each day she eats all but one of them and shares the last cookie with her teacher. If we wanted to find out how many cookies she gives her teacher in a school year, we would have to consider some other factors. • In order to solve this we are going to make some “norm” statements. Each week there are 5 school days and each month has 4 weeks. There are 10 months of school.

11. Here’s how we could use ( ), [ ] and { } to solve this problem. • We want to find out how many cookies are left for the teacher each day first, so this information would need to be in ( ). • Mom gives her 5 cookies and she eats all but one of them, so we know she eats 4 cookies. (5-4). • Then we know that there are 5 school days so this can be represented with 5(5-4). • Then we need to represent that there are 4 weeks in a month [4 x 5(5-4)].

12. Here’s how we could use ( ), [ ] and { } to solve this problem. • Finally, we need to represent that we are multiplying this by 10 months for a whole school year {10 x [4 x 5(5-4)]}. • We could solve this problem by doing the ( ) first: • (5-4) = 1. • Next we multiply 5(1) = 5. • Then we multiply [4 x 5] = 20. • Finally we multiply {10 x 20} = 200. • This shows that Sally gives her teacher 200 cookies in a school year.

13. 2{5[12 + 5(500-100) +399]} • Now….try and solve this expression! • Let’s use “Think-Pair-Share” • First, you will take a few minutes to “think” on your own. • Next, “pair” up with a partner and “share”. • Write out each step you take to solve the expression. • You may use calculators to help with the calculations.

14. Find Day 75, “Bracing for Brackets” • We will solve a few of these problems together and then you will practice a few on your own. • Homework: Day 75, “Order of Operations with Brackets Homework”