Comparing and Scaling Assessment Day

After you have completed your assessment, it is time for you to complete the final Learning Behaviors self-assessment for the semester.

Here it is:



Here is what you MUST do before next class:

Nothing...have a great holiday.

Unit 3 Consolidation Day

Main Objective:

The main goal for today is to consolidate our understanding of ratios, proportions, and percentages in order to be prepared for our unit test on Wednesday.

Part 1: Do Now

Try to answer each of the questions below in your squarebook.

When you are finished, try to think about how each of the two questions are connected to each other in terms of how you work with percentages.

Part 2:  Preparing for your assessment

One of the main problems that students encounter when preparing for a math assessment is that they engage in only PASSIVE studying when what they need to be doing is ACTIVE studying.  Below is a list of things that would be considered PASSIVE and ACTIVE studying techniques.

Passive Studying Techniques (20% of your time)

• Reading your notes
• Reading blog posts
• Reading your textbook
• Watching YouTube videos

Active Studying Techniques (80% of your time)

• Doing the Review Package handed out in class
• Working through the MathXL For School Study Plan
• Redoing the questions from your Mid-Unit Assessment
• Working through ACE questions

What you MUST do before next class:

• Complete your preparation for the Unit Test on Wednesday
• Here are the answers to the Review Package.

Working With Percentages

Focus Question:

How can we use proportions and the constant of proportionality to solve problems involving percentages?

Part 1:  What is a Percentage?

So...remember that a percentage is just another type of special ratio.  The key characteristics of a percentage are:

• It is a part to whole ratio.
• The "whole" is always equal to 100.

Part 2: How to Solve Percentage Problems?

There are a couple of different ways to solve problems involving percentages.  We can set-up a pair of part to whole ratios, we can use a table to organize our thinking or we can construct equations in the form y=kx where "k" represents the percentage written in the form of a decimal.

For the problem below, try to set-up a table to organize your thinking.  Be really thoughtful about how each value is connected to the other values. (This is where the percentage work comes in).  In case you are not familiar with the language, here are some definitions to help you out:

• Purchase Price - the amount that Carla paid to get the car.
• Markup - the amount that Carla has increased the price of the car by in order to make a profit.  In this case, the markup is equal to 10% of the purchase price.
• Selling Price - the amount that Carla is going to sell the car for.  This is usually equal to the purchase price + markup.

Now, try to write an equation for each of the following relationships.  Remember that "k" is the percentage as a decimal.

• The markup based on the purchase price.
• The selling price based on the purchase price.
• The selling price based on the markup.

What you MUST do before next class:

• Finish TOFU for your Mid-Unit Assessment
• ACE (1-6) (11 OR 12) p. 71

More Constant of Proportionality

Objective:

The main focus for today was to consolidate our learning from the last couple of classes in terms of how to find the constant of proportionality from various different representations.

In case you missed class, here are the notes that we took during the first part of class:


For the final hour of class, we worked in our groups through a booklet that combined a lot of different representations of the constant of proportionality (k).  Here are the solutions to the problems in the booklet.

Here is what you MUST do before next class:

• Complete the work in the booklet
• We have a quiz next class that focuses on unit rates, best buys, and the constant of proportionality

The Constant of Proportionality

Focus Questions:

• What is the relationship between the constant of proportionality and a unit rate?
• How do we determine the constant of proportionality from a table, equation, or graph?
• How do we represent proportional relationships using an equation?

Do Now:

Which pizzeria is the best buy?  How do you know?

Who is the fastest runner?  How do you know?

Part 1:  Connecting Unit Rates and the Constant of Proportionality

The constant of proportionality is another name used to describe the constant ratio that exists between two different quantities.  In all cases, this is the same as the ratio expressed in lowest terms. In most cases, this is the same as the "unit rate".

Look back on your work from last class, "The Four Pizzerias" and determine the equation to find the Total Cost at each pizzeria.

Notice that each equation has a constant multiplier that we had previously identified as the unit rate.  This is also known as the "constant of proportionality"

Part 2:  Determining and Using the Constant of Proportionality

As a group, work through the "Constant of Proportionality" assignment that you will be given in class.  If you get stuck, look through your notes or ask for help.

What you MUST do for next class:

• Complete the "Constant of Proportionality" assignment handed out in class.
• Complete the "Constant of Proportionality" assignment on Math XL For School