Comparing Unit Rates in Different Forms

Objective:

I can compare unit rates using tables, graphs, words, and equations.

I can create rate tables, line graphs, and equations to represent proportional relationships.

Part 1:  Comparing Unit Rates

In this part of the lesson, you will compare the unit rates of four different pizzerias.  The catch is that each pizzeria has represented their pricing structure in a different way.

Part 2: Representing Unit Rates

Now that you know how to find the unit rate in each of the four different representations, your goal is to convert each pizzeria's pricing structure into the different representations.  To do this, you can follow the instructions on this handout.

What you MUST do before next class:

• Relax and have a great Thanksgiving weekend.

2.1 and 2.2 Scaling and Using Unit Rates

Lesson Focus: The main goal for this lesson is to look at how to create and use unit rates as a strategy for comparing ratios.

Part 1: Comparing Rates

As a follow-up to our work last class, try to use one of the "comparing ratios" strategies from last class.  If you need a reminder, here is the list that we generated:

• Create a common numerator
• Create a common denominator
• Convert into percentages

Part 2: Creating and Comparing Unit Rates

One way to compare two ratios (or rates) is to make a unit rate by scaling each ratio to find the cost of one pizza.  If you want some additional practice with finding unit rates, you can watch the video below.


Now try to find the unit rate for each of the pizza specials shown below:

When you are ready, try to determine which jar of peanut butter is the "better buy".  Remember to give a reason for your final decision.

Here is what you MUST do before next class:

• ACE (11) p. 54
• "Ratios, Rates, and Unit Rates" on Math XL For School.

1.2 to 1.4 Comparing and Scaling Ratios

Lesson Objectives:

• Students will be able to create and use a table to scale ratios up and down.
• Students will be able to use a variety of strategies to compare ratios.

Part 1: The Language of Ratios

Remember that ratios are about comparing two quantities using the language of "There are ____ _____ for every ____ _____".

Look at the image below and see how many ratio descriptions you can come up with:

Part 2: Scaling Ratios

Take a look at your ratio statements.  Do you have any statements that are really describing the same relationship, but using different numbers?  For example:

• There are 2 pigs for every 1 sheep.
• There are 4 pigs for every 2 sheep.

These two statements are really the same but the second set of numbers has been "scaled" up by a factor of 2.  So what is "scaling"?

Scaling is the process of multiplying or dividing one ratio by a particular "scale factor" to create an equivalent ratio.

Work through the task below.  Be sure to clearly show your "scale factor".

Part 3: Comparing Ratios

While scaling produces equivalent ratios, other situations require that we compare ratios.  Complete the task below.  If you get stuck, try some of the following strategies:

• Rewrite each ratio so that the "cups of concentrate" is the same.
• Rewrite each ratio so that the "cups of water" is the same.
• Convert each ratio into a part:whole fraction.
• Convert each ratio into a percentage.

Here is what you MUST do before next class:

• ACE (10, 17, 18, 22, 23)
• Remember to set these up as a table when possible to make your work more organized.

Accentuate the Negative Assessment Day

The main goal for today is for you to show all of the "positive" growth that you have made during this unit.

After you have completed your assessment, here are a couple of things that you need to do:

• Complete the "Comparing and Scaling Readiness Test" that is on MathXL for school.
• Complete the "Learning Behaviors Reflection" for this unit:
  

Accentuate the Negative Review

The main goal of today is to finish preparing for the "End of Unit Assessment".

Here is what you SHOULD do before next class:

• Complete the Accentuate the Negative Study Plan on Math XL For School
• Complete the Accentuate the Negative Unit Test Review.

Remember to also check the "ASK Sign-Up Sheet"

4.1 and 4.3 Order of Operations

Focus Question: How can we ensure that we have clear communication when writing, evaluating, and interpreting number sentences?

The main goal of this lesson is to write and evaluate different number sentences that involve a combination of different operations.

Part 1: Do Now

For the do now task, you will need to complete "Check-Up #2" which focuses on your procedural fluency with all four integer operations.

Part 2: Dealing Up

Part 3: Evaluating Number Sentences

Part 4: Writing Number Sentences
In this part of the lesson, we will look at how to write number sentences to represent different "real-world" situations.  A couple of tips when writing number sentences are:

• Pay close attention to when it is appropriate to use negative integers.
• Remember that there are a couple of different ways to write the same number sentence.  Each different way tells a slightly different version of the story.

Here is what you MUST do before next class:

• Complete the "Order of Operations" assignment on Math XL For School.  
• Make sure that you show your work in your squarebook.
• Remember that you should get 100% on this assignment as you can redo each question until you get it correct.  Let me know if you get stuck.

Here is what you CAN do before next class:

• Complete the "Multiplying Integers" assignment on Math XL For School.
• Complete the "Dividing Integers" assignment on Math XL For School

3.3 and 3.4 Dividing Integers

Before we get started today, we are going to talk a little bit about home base.  Here is the link to the survey that I would like you to do afterwards.

Now...on to division.

Do Now:

Here is a quick modelling warm-up for you to get your math juices flowing:

Applying Division:

We are going to take another look at our math relay course from last class and try to develop some rules for dividing integers.  You can work through each of the examples below:

Creating Rules:

Using the number sentences that you have created for your models as well as the number sentences that you created for the relay race, see if you can create a set of rules that can be applied to dividing integers.

Practice:

Complete the "Zorna" page.  Check with me when you have completed it.

More Practice:

Find a partner at your table group who will play the Integer Game with you.  Click on the image below to take you to this game.

What you MUST do before next class:

• Complete the "Zorna" worksheet and glue it in your book.
• ACE (15-18) (36)
• Watch the video on Order of Operations and complete the notetaker.

3.1 and 3.2 Multiplying Integers

Focus Question: How do we determine the sign of the product when multiplying 2 or more integers?

In this lesson, we are going to explore some different ways to think about the meaning of multiplying integers.  Here is what we are going to do:

Part 1:  Modelling Integer Multiplication (and Division)

Using the picture below, you should be able to create 5 different number sentences and describe what each number sentence means in terms of multiplication, division, or addition.

Part 2: Developing the Rules For Multiplication

On page 55 and 56 of your textbook, there is a description of a relay race where students are running between (-50m) and (+50m) on a number line.  Work through Task A in order to help you develop the rules for multiplying integers.

Part 3: Applying The Rules

Once you know the rules, you should be able to predict whether the final product is either greater than zero (positive) or less than zero (negative) just by looking at the question.  Try this by using the image below:

If you want to look at the entire lesson, here is the slideshow:

This is what you MUST do before next class:

• Finish the "Famous Farmer Saying" worksheet.
• ACE (1-10) (28-31) p. 66