Solving Multi Step Equations: Bringing It All Together (Day 4 of 4)

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Objective

SWBAT solve problems based in real world scenarios using multi-step equations.

Big Idea

Students will understand that a linear equation can be created in order to find an unknown value in a real world situation.

Do-Now

10 minutes

Students will complete the Do Now in their notebooks.

Many of my students have math anxiety, and can can be very trepidatious when taking the initial steps necessary in solving a problem. I provided the class with a small reminder on the side of the Do-Now to encourage them to push through their apprehensions.  

Six students will come up to the whiteboard to show their work and solutions for the class to review. Next, a student will read the objective to the class: SWBAT solve problems based in real world scenarios using multi-step equations.

Guided Notes + Practice

20 minutes

We will explore a number of different problems that have a basis in real world phenomena to help students gain a better understanding of the utility of algebraic equations. The Word Problems PowerPoint provides visual resources supporting the introduction of several of the problems.

Slide 2: We begin today's lesson by watching the video for the first example. Students should watch the video twice. Initially students should simply watch, and the second time they should record all of the important information as well as a mini summary of what happened on their notes. I will ask a student to restate the question posed at the end of the video for the class: "How many minutes,m, will it take for the two cups to contain the same amount of water"?

I will ask the class to decide what additional information they will need to figure out the answer to this question. Eventually, a student will say they need to know the rate at which the water is being poured out of the cup (Cup A 6ml per minute, Cup B 10ml per minute). Using the rate and the initial amount of water in the cup, we will come up with the equation 500 - 10m = 300 - 6m.  I will ask students why the slope is negative, and what a positive slope would imply.

For the next three examples, I will only show students the picture and wait for the class to decide what information they will need to solve the problem

Slide 3: Shawnee the cat has eaten four frooties, and is eating at a rate of 1 frootie per minute. Ms. Davis has eaten 2 frooties and is eating at a rate of 3 frooties per minute. After how many minutes will they have eaten the same amount of candy?

Slide 4: Shawnee is on page 50 and is reading 10 pages per hour. Ms. Davis is on page 200 and is reading 5 pages per hour. How long will it take for them to catch up to each other and be on the same page of their respective books? 

Slide 5: Ms. Davis has typed 100 words and is typing 30 words per minute. Shawnee is on his own laptop, and is erasing 10 words a minute from the 900 word autobiography that he typed.  

Slide 8: This example is an ode to our last class, and a great way to help students understand why "no solutions" is sometimes necessary in Algebra.  I ask student to think why it makes sense in the real world for this equation to be unsolvable (the containers are leaking at the same rate, so they will never catch up to each other).

Group Activity

40 minutes

Activity Preparation
I made four copies of the group activity cards for a class of 25 students. The cards should be laminated and cut up before class begins. I then placed all of the cards inside of a bucket at the front of the classroom.

Activity
Students will work in pairs to answer the questions from inside the bucket. Each group may only work on one card at a time. When they are ready, students will form a line in front of Ms. Davis to check their answer. If their solution is correct, the pair will write their names on the board (Slide #7) for the corresponding number of the problem.

The pair that finishes the most questions before the end of class is the winner!

Closing

10 minutes

I will ask one student to summarize what we did today. I will then challenge a student to create a real world dilemma for the class that can be solved with a multi step equation.   Students will then complete the exit card.