Lesson 13 of 17
Objective: SWBAT determine the amount after interest when given the interest percent
Students enter silently according to the Daily Entrance Routine. Sprints are awaiting them at their seats, faced down. Students must write their names on the back of this sheet without turning it over. A 3 minute timer is set and students are started as soon as they sit down silently and have a pencil ready to go.
The questions included in this Do Now assignment involve calculating the percent of or fractional piece of a whole number. These also include benchmark percents and fractions that students should pushed to complete using mental math. Once the 3 minutes on the timer have expired, all students are asked to stop. Those who finished within these 3 minutes will have their paper picked up and re-distributed to another student who finished so that they can check the answers with a pen. I will review some mental math tricks, such as moving the decimal, with the help of students who may already know these tricks. For example, question 3 asks for 5% of 500. A mental math trick which can be used for this problem is to calculate 10% of 500 by simply moving the decimal (50). Then, we compare 5% and 10%; 5% is half of 10%. This means we can take half of 50, to get 25 as a final answer. A bar model could also be used to visualize this mental math trick.
We review the rest of the answers quickly. The class notes section for today’s lesson will require as much time as possible. Thus, if there is any extra time left over in this section, it should be given to the class notes section to ensure the check for understanding at the end of the next section.
Students receive class notes and the power point presentation is displayed on the board. Students must copy the aim at the top of their notes from the first slide in the power point. A student reads the aim and I move on to the next slide. Students are asked to copy the definition of “interest” as I read it to them, at least 3 times.
money paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt.
After copying this definition, I check in to make sure all students understand what we’ve reviewed so far. Students may inquire (or I may ask them) about the definition of the word “rate” in this context. I ask students to review their past notes to figure out the definition of the word rate (a ratio, or fraction) and I used this definition to explain that in this context, rate is being used to explain interest as a fee we pay for the use of money. The fee is determined by using a ratio, or rate, or a percent. The sample problem included in this slide may be used to give an example of a rate. To check for understanding, I ask for a volunteer to tell me “what is the rate given in this problem?”.
We move on to the next slide and define “simple interest” and the formula associated to its calculation. I explain to students that when you borrow money you are expected to pay it back in full, but you are also charged extra money for borrowing. This is sometimes a surprising fact to students and it is important to give them enough time to ask questions and talk to each other to fully understand this concept (1 – 2 minutes).
I move on, explaining that this fee we are charged for borrowing money can also work the other way. If we save money with a bank we will earn interest. While our money sits in the bank account, the bank will add on a percentage of what we keep in there as long as we let them keep it. So, when you take out your money, you may have more than you originally put in. I explain to students that we can call this an investment, and I ask them to write this into their notes.
Then, I introduce the simple interest formula as a way for us to calculate the amount of extra money we are either earning if we save it or paying back if we borrow it. When introducing this formula, it is very important to point out that “I” stands for the interest alone. It does not give us the total that would need to be paid back or the total earned n an investment. It is also important to point out that this extra money is also dependent on the amount of time the money was borrowed or saved, and that the formulas requires the time be substituted in years. The rate is the percent interest, and it must be converted to a decimal before we can use it to calculate in the formula.
The last word we will need to define is “principal”. It is the initial amount invested or borrowed, the amount you asked to borrow or the amount you began to save. Again, I use the same example to check for understanding as I ask, “what is the principal amount in Rita’s problem?” We also list all of the information we will need to solve the simple interest equation.
In the following slides I will be asking students to give me each step:
- Begin by writing the formula I = prt
- In the next line, what is the unknown? Which variable should I keep? I
- Then we write an equal sign, followed by what number? What is the principal? 500
- Now we multiply by r; what does r stand for? What is it? How should we write it? 0.035
- Next we multiply by t; what does t stand for? What is it? How should we write it? Why? 0.25, because 3 months is equal to a fourth of a year
Students will receive calculators to aid the multiplication and focus on the process. Students are warned however, that they must show all work the way we have done in the power point. I also make sure to review how “interest” will impact students’ future lives (real world examples).
There are two problems on the back of the class notes which students must complete and enter into Senteo clickers. They will have 5 minutes to do this independently and silently.
I will use the results to create heterogeneous groups of students working together on the task, first assigning the three available booths to groups of 4, and then asking other groups to use any left-over tables in the center of the room. Any students who did not complete the problems on the back or answered both questions incorrectly will be working in a group with me.
A 15 minute timer will be set for students to work in groups. Each group, including my own, will be assigned one problem to display on a piece of chart paper. Each group must elect 1 or 2 students who will explain the solution to the problem during the closing.
In our small group I will be focusing on students understanding what each letter in the formula stands for and the way in which numbers ought to be substituted (i.e. converting months to years, writing percents as decimals).
At the end of 15 minutes all students will be asked to return to their seats. If the problem assigned to the group was not completed on the chart paper, the 1 – 2 students assigned to present will need to tape their paper to the blackboard and finish the problem.
Each group will be given no more than 2 minutes to state their answer and explain why they substituted each number the way they showed on their paper. For example, students who had word problems where time was given in months will need to state how they figured out the number in years.
At the end of these explanations students will be given their homework and dismissed.