Proportions: Calculating Simple Interest

Starter:



Finish the team worksheet activity from last week. You'll be given 6 cards with tables. Determine whether each table is proportional (P) or not proportional (NP) and copy the table to the indicated chart on the worksheet. Then graph the points from the table and connect the dots to show why the graph is or is not a proportion. Finally, if the table does show a proportion, give the equation for the proportion: the form of the equation is y=ax where a is the constant of proportionality. If the table does not show a proportion, no equation is needed.

Watch this short video about calculating interest:

Practice calculating simple interest as follows:
Find the total value of the investment after the time given. Remember to convert percentages to decimals, e.g., 10% = 0.10.

1. $40,000 at 16% simple interest for 3 years.
2. $1,160 at 11% simple interest for 3 years.
3. $5,500 at 13% simple interest for 7 years.
4. $560 at 12% simple interest for 2 years.
5. $56,000 at 15% simple interest for 4 years.
6. $300 at 6% simple interest for 6 years.

Assessment Day

Login to Canvas and complete the module labeled "Tests: Expressions, Equations, and Inequalities."

Proportions as Equivalent Ratios

Complete today's starter:

Proportions as Equivalent Ratios
Proportions can be written as equivalent ratios, and since ratios look like fractions, you can use the same strategies you learned to calculate equivalent fractions to calculate proportions.
The simplest way to calculate a missing value in a proportion is to cross multiply then divide, as shown on slides 2-5. Use that strategy to complete the exercises on slides 6 and 7 from the starter.

CTE Day; Math Review

Starter:
Go to your Canvas Calendar and put it in Agenda View.
Click on the assignment title: 

NS1 Assessment #1 Quarter 2.

Complete the test. This will be included on your grade.

Proportions: Equations, Tables, and Graphs

Starter: Work on incomplete assignments in Canvas modules.

Review: Slides 1-7
Whole Group Practice: Slides 8-10
Small Group Practice: Slide 11. Materials provided in class.

Test day: Equations and Inequalitites

Students took their second graded test on equations and their first graded test on inequalities.

Proportional Equations, Tables, and Graphs

Starter: Complete the following on paper.


As a class, study slides 1-6 in the following:

Notes on Proportions

Copy the following into your notes. The rest of the class period will be spent viewing examples of proportions.

1. Definition: A proportion shows a relationship between two varying quantities where the ratio between the two quantities remains constant.
2. Characteristics:
1. Proportions have a constant ratio of y/x.
2. The graph of a proportion will pass through the origin.
3. The points on a graph of a proportion are collinear.
4. The equation of a proportion is in the form of y=ax, where a is the constant of proportionality.
5. The graph contains the point (1, a), where a is the unit rate.

Unit Rates: Canvas Modules

Students worked on Canvas to complete a sequence of assignments involving unit rates. Nov. 7-9.

Unit Rates with Tables and Graphs

Smaller type gives information for today's guest teacher. Presentations and larger type are intended for student viewing.
3rd period is my prep time; all other classes are Math 7.

Advisory:
Students should read silently throughout Advisory today. Students who didn't bring reading material may read a copy of the public domain story, The Magic Fishbone by Charles Dickens. Copies are on the front table. They can eat breakfast while they read, and they must be reading the whole time. Remind them to save their conversations for between classes or lunch time.

Check the "Daily Plans" binder for information on Breakfast in the Classroom. You will need to go to the cafeteria to pick up the crate for breakfast. Set the crate outside the door when everyone has had a chance to take breakfast: someone will pick it up later.
There is a special garbage liner for breakfast in the classroom. The garbage can next to the door already has a liner in it; breakfast should be cleaned up by 8 AM. You can send a student with the garbage bag to find a garbage can (there should be one in the south hallway). *Someone volunteered today and I told them OK, but I've forgotten who it was.

TAs:
TAs can participate in the lessons if they’d like, but since most of the work I have for them is online and they can’t use Chromebooks with a sub, I told them to bring something to work on quietly.
I didn’t include them on my seating charts: please leave a note on the seating chart to let me know if they were here. I have one TA in each of my first 3 classes (1st, 2nd, and 4th); they sit in the older student desk in the back of the room. I have 2 TAs in 5th: one of them sits in the aforementioned older student desk, the other sits in the desk nearest to that. I also have 2 TAs in 7th period: they sit in the empty team in the back near the window.

All math classes:
Click on the full-screen icon as each class leaves so the incoming class can work on this between classes. The slides should automatically change every minute, and the presentation will restart after the last slide. The answers will begin showing on the third slide.

• We are just beginning to study ratios, rates, and proportions. Yesterday, we learned to calculate unit rates by filling in a table of values. The students came up with 5 steps for calculating unit rates. 
• Ask students to compare their notes from yesterday with this list and make any changes they think are necessary. First and second periods will need time to copy.

Review: Steps for Calculating Unit Rates

1. Understand the problem: identify the kinds of numbers needed to answer the question.
2. Identify the units given in the problem.
3. Identify the rate or rates given in the problem.
4. Do the math: multiply or divide to calculate the unit rate.
5. Contextualize: give the answer in the context of the problem.

• I didn't use slides during 1st and 2nd period yesterday, so the following will not be familiar to them. Please take some time to help them understand how the information is organized into the tables. 4th-7th saw all of this information in tables, but these slides are in a different format.
• None of the classes saw graphs: they are new today. Take a moment to explain how the columns in each table represent each coordinate on the graph.
• The most important thing I'd like students to get from this today is that the coordinates (1,y) show the unit rate on a graph.

Again, you'll probably want to use the full-screen mode to present.



For guided practice, I often call on students randomly and ask them to explain the next step in the sequence. Using the steps outlined above, 5 students would take turns explaining how to solve one problem. You can use my method, or you can have students work together in teams to solve the problems. Either way, have them write out their work on a piece of paper. Check to make sure they're actually writing, but tell them to keep their work in their binders: I will collect it when I return.

Open the link below and go to the fourth page to find the guided practice. If time allows, they can work in teams to complete the independent practice on the 5th and 6th pages.

Practice: Use the steps in your notes to solve problems involving unit rates. 

Homework:

1. What coordinate on a graph shows the unit rate?
2. What ideas have you learned before that were helpful in solving some of today's problems?

Unit Rates with Tables

Rates and Unit Rates:

1. Review these two examples. 
2. Pause often to describe and label each step.
3. At the end of each example, summarize the process used.
4. Use the steps you labeled and described to try one on your own.

Almost every class came up with the exact same steps. These are:

1. Identify the kinds of numbers needed to answer the problem.
2. Identify the units given in the problem.
3. Identify the rate or rates given in the problem.
4. Multiply or divide to calculate the unit rate.
5. Give the answer in context of the problem.

Homework:

1. In your own words, explain what a unit rate is.
2. Explain how to calculate unit rates.

Solving Inequalities Day 5

We will be taking a Formative Assessment in class today to see how students are doing with solving inequalities: calculators are allowed. Please come after school on Monday for make-up tests.