Context for this Lesson
GENERAL TOPIC: Simplifying formulas with PEMDAS (Parentheses, exponents, multiplication/division, addition/subtraction)
FOCUS: How can we help students remember the order for simplifying formulas, and how can we apply the order to formulas?
MATERIALS: 6 note cards with parentheses, exponents, multiplication, division, addition or subtraction written on them, several equations to use during lesson
ENGAGE (HOOK): Today we are going to review how to simplify math formulas, and work together to solve several equations.
REVIEW: Can I have six volunteers to go first? Give six volunteers one of the six note cards with PEDMAS written on them. Please order yourself according to the rules of formula simplification we learned this semester. Give the other students in the class an easy formula that needs to be simplified while the students with note cards order themselves. Once the note cards are ordered, ask the students in the class if the note card order looks correct. If anyone in the class has a suggestion, let them re-order the note cards. If no one has a question about the order, ask the students in the class to solve their given equation using the order of the note cards. You can walk through the first iteration with the students, going through each note card step by step. The key here is to take the students’ suggestions. Even if the note cards are ordered incorrectly, let the students figure this out by solving the equation. The equation should only get one correct answer if the order of the note cards is correct. If the students’ answer is incorrect, discuss with them what different orders yield different results, and stress the importance of the PEMDAS order. Once the students have correctly solved the first equation, switch groups. The students who solved the last problem now get the note cards, and must again correctly order themselves. The students who formerly had note cards now have to solve their given equation. This time, the equation can be a little more complicated, since the students will most likely remember the order. Review this only once or twice more, to make certain the students remember the order, and then move on to the next activity.
Explore: One-Word Storytelling:
This is a variation on a dramai game called “One-Word Storytelling.” Let’s all sit in a circle. Explain that the group is going to solve equations together, keeping in mind the PEMDAS order they have just been drilling. Place an equation in the middle of the circle. For example: 3 x 3 + 2 + 4 / 2 – 1 = x The facilitator begins the equation “story” by stating the first part of the equation and simplifying: Three times three… And the next student: equals nine. The facilitator can write this part of the equation down for clarity: 9 + 2 + 4 / 2 – 1 = x The next person continues with the equation, simplifying the next part correctly: Nine plus two… And then next student: plus four divided by two… …Equals nine plus two plus two. Again, the facilitator can write the equation down for clarity, making it easier to see what needs to happen next. 9 + 2 + 2 – 1 = x Students continue in the same manner until the equation is solved. They can work together, and if one student doesn’t know the correct answer, or if they are struggling, encourage the other students to help. Always make sure the student whose turn it is, however, answers the question, even if it only means repeating another student’s prompting. Hopefully, this will reinforce the PEMDAS order for all students. Once the students have solved one equation, continue to “tell” other equation stories with each other.
1. Describe what we did.
2. What things did we do to help one another? What could we have done?
3. Why might we solve problems together like this? What was our biggest struggle? How did we figure this out?
4. How might we make solving these equations more efficient? How can we remember these for the TAKS tests?