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

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

Wrapping Up Addition and Subtraction

The main focus for today was to wrap-up our work with addition and subtraction of integers.  In order to do this, we divided into a couple of different groups based on our individual current needs.

Part 1: Adding and Subtracting Quick Quiz

At the beginning of class, complete the Entrance Card on adding and subtracting integers.  This entrance card will be used to determine what group you are in for the rest of the class.  Your goal is to score at least 7 out of 10 for each section.

Part 2: What Do You Need?

If you meet expectations on the entrance card you will play a game called "Life On The Number Line" which will stretch your ability to work with integers as well as test your ability to describe integer relationships.

If you did not meet expectations of the entrance card, you will do some additional practice with adding and/or subtracting integers.

Here is what you MUST do before next class:

• Finish the "Find a Match" and "Daffynition Decoder" worksheets OR the "What Should You Do If You Are Surrounded By 20 Lions...." worksheet. (this should have been completed last class)
• Finish your TOFU for the Mid-Unit Assessment (this should have been completed last class)
• Watch the video on multiplying and dividing integers and complete the note-taker handed out in class.

Fall Break Refresher

Hey everybody, I hope that you are having a great fall break.  I know that some of you have asked to have somethings that you can be working on over the break.  Here are some Khan Academy activities that you can try in order to keep your integer skills fresh.

Integers Basics

• Negative Numbers on the Number Line
• More Negative Numbers on the Number Line
• Ordering Negative Numbers
• Number Opposites
• Interpreting Negative Numbers

Absolute Values

• Finding Absolute Values
• Comparing Absolute Values
• Interpreting Absolute Values

Adding and Subtracting Integers

• Adding Negative Numbers
• Adding and Subtracting Negative Numbers

Mid-Unit Assessment and Consolidation Day

The main goal for this lesson is to see where you are at in terms of your understanding of adding and subtracting integers.  To do this, we will do an in-class assessment.  Good Luck.

After the assessment, there are a couple of things that I would like you to do in order to tie your understanding of this unit and the last unit together.  Here they are:

• Log in to Math XL For School.  Make sure that you have completed the following four tasks
• Accentuate the Negative Readiness Assessment
• Accentuate the Negative Pre-Assessment
• 1.2 Extending The Number Line
• 1.3 From Sauna to Snowbank
  
• Check your math grade in PowerSchool and look for any missing homework assignments from the Shapes and Design Unit.  Most of these will be Khan Academy activities.  Finish these.
  
• Check your grade on your blogpost from this unit and if you would like, edit your blogpost to improved standards.  Here are a couple of examples of a blog post that meets expectations and one that are exemplary.

What you MUST do before you leave the room today:

• Complete the Mid-Semester Reflection Form

2.2 and 2.3 Subtracting Integers

Focus Question:  How do you determine whether the final result with increase or decrease when subtracting integers?

In this lesson, we will explore how to use models to subtract integers.  We will also look at how addition and subtraction are connected to one another.

Step 1:  Determine each of the differences from the two different sets.  If you need help, remember to look back at the "subtracting integers" video on the previous post.

Step 2:  Look at the results from the two different sets of differences and try to fill in the blanks below based on the patterns from above.  I'll give you a hint....use "Set 1" to answer the first two bullets, and use "Set 2" to answer the last two bullets.

Step 3: Watch the slideshow below to help you discover the connection between addition and subtraction when it comes to integers.  The statements above will also help.



What you MUST do before next class:

• ACE (18-40) Evens only, (67)
• Remember that we have a mid-unit assessment next class.

2.1 Adding Integers

Focus Question: How can we predict whether the sum of two integers will be positive, negative, or zero?

In this lesson, we will explore two different models for adding integers and then work as a group to develop some algorithms (rules) for adding integers.

Here is a final overview of the Integer Chip model for addition.  Remember that your notes should look like the notes that have been written on the image below.

By the end of this class, you should be able to do the following:

• Use either a number line or integer chip model to add integers.
• Add integers mentally
• Describe an algorithm for adding integers with the same sign (both positive or both negative) and an algorithm for adding integers with two different signs.

Here is what you MUST have completed before next class:

1. ACE (1-14) p. 44
2. Watch the video on "Subtracting Integers" and complete the note-taking sheet that goes with it.

Here is some extra practice with adding integers if you would like:

1. Adding Integers on Khan Academy

1.4 In The Chips

Focus Question:  How can you use a "Chip" model to add and subtract integers.

Overview:

In this lesson we are going to use a "chip" or "counter" model to help us develop some strategies for adding and subtracting integers.  Here are some key concepts that you will need to know for this lesson.

Opposites - two numbers that are the same distance from zero, but on opposite sides.  For example, +5 and -5 are opposites.

Zero Pair - When a pair of opposites are added together, the sum is always zero.
For example,  +5 + (-5) = 0

Add - to "add on to" an initial value

Subtract - to "take away" from an initial value

For this lesson you can use either a physical chip board or a virtual chip board.  The virtual chip board can be found by clicking the image below.

As a class we will work through a couple of examples together from each of tasks A-D.

This is what you MUST do before next class:

• Complete Tasks A-D (E and F are optional extension activities) on pages 18 and 19 (Should be done in class)
• Complete ACE (49-55) (Should be done in class)
• Make a Blog Post that answers the investigation 1 reflection questions on page 28.  Remember to label it. (Should be started in class)

1.2 and 1.3 - Using a Number Line

1.2 Focus Question:

• How can you use a number line to compare two numbers?

In this lesson, we will explore how to order and compare values using a number line.  We will also look at some informal ways to find the difference between two values on a number line.

Assignment:

• Complete "Inequalities on a Number Line"
• Complete Assignment 1.2 on Math XL For School
• Complete ACE Exercises 9 and 10

1.3 Focus Question:

• How can you use a number line to model a number sentence, and how can you write a number sentence to represent a change on a number line?

In this part of the lesson, we are going to explore how we can use a number line to determine the difference between two temperatures as well as how to write number sentences to represent the change in temperature.

Assignments:

• Complete Tasks A-E on page 16.  Remember to draw BOTH a number line model and write a number sentence.
• Complete Assignment 1.3 on Math XL For School
• ACE (36-45, 48) (76, 77)

Shapes and Design - Test Day

Yipee...today is your first chance to show all the great things that you have worked hard on learning in this unit.  Good luck.

After you have finished the unit test, you have a couple of tasks to take care of.  Here they are:

Learning Behaviours Unit Reflection:

One of our goals this year is to pay closer attention to "how we approach learning".  This is demonstrated through a variety of different behaviours.  A lot of research show that how students approach learning has a large impact on how much they learn.

At the end of each unit, you will complete a self-assessment that asks you to reflect on your learning behaviours for that unit.  Try to be as open and honest with yourself as possible.

Here is the Learning Behaviours Reflection

Next Unit - Accentuate the Negative:

Our next unit focuses on extending our knowledge of the four main math operations to include negative numbers.  In order to prepare for this unit, you will need to do a couple of things.

• Sign In to "Math XL For School".
• Remember that your username is your SAS email address and your password is "math1234"
• Do both of the Assignments that show up in the "My Upcoming Assignments" section.

Homework:

• Complete the "Learning Behaviours Reflection"
• Complete both of the Math XL Assignments
• Bring your "Shapes and Design" textbook next class.  Lost books will cost you SGD 20.

Review - Shapes and Deisgn

The main focus of this problem is for you to review and prepare for your upcoming test next class.  To do this, we will do three main things:

Part 1: Guiding Questions

Here are some guiding questions that you should be able to answer in order to be fully prepared for your upcoming test.

Part 2: Individual Review

You will work on a review package/practice test.  This is to be done individually for the first 10 minutes.  Afterwards, feel free to get some help from those in your group.

Part 3: More Individual Review

In order to keep practicing your skills, here are a list of Khan Academy things that you can do:

Background Skills

• Understanding Angles
• Recognizing Angles
• Angle Types
• Drawing Angles
• Naming Angles
• Measuring Angles
• Decomposing Angles
• Benchmark Angles

Skills from this unit

• Drawing right, acute, and obtuse angles
• Properties of Shapes
• Measuring Segments
• Congruent Segments
• Complementary and Supplementary Angles
• Vertical Angles
• Solving for Unknown Angles
• Quadrilateral angles
• Constructing Triangles
• Constructing 2D Figures

Games from this Unit:

• Bee Dance
• Quadrilateral Game

Homework:

1. Complete as many of the Khan Academy activities as you can.
2. Complete the Practice Unit Test
3. Your Unit Test is next class.

Using Deduction in Geometry

Objective:

The main goal for today is to piece together our learning from the unit so far especially in terms of how it relates to interior vs exterior angles, the sum of angles in a polygon and communicating our thinking about geometry to others.

Summative Assessments:

We now have two summative assessments under our belt which means that there is now a pattern that is forming.  I challenge you to take a look at that pattern and decide whether you are proud of that pattern, or not so proud of that pattern.

If You Are Proud of the Pattern:

• Keep up the great work
• Keep practicing your skills
• Keep allowing yourself to be challenged and keep taking mathematical risks.

If You Are NOT Proud of the Pattern

• You can do something about it such as....
• Redo your blogpost based on my feedback.  Some sample blog posts that Meet Expectations are HERE and HERE and some that are Exemplary can be found HERE and HERE.
• Complete your TOFU and redo your quiz
• Ask for help...it's my job to help you and I will help as long as you keep asking.

Digital Design Challenge

More Turtle Art....Yippee.

For this part of the lesson, you are going to try to replicate some designs that I have drawn using TurtleArt.  Pay close attention to the information that you are given in the design.  Write a single line of code for each shape on the same file and save it.

Homework:

What you MUST do:

• Complete TOFU for your quiz.  Even if you are not planning on redoing this assessment.
• Complete the front side of the Digital Design Challenge.

What you CAN do:

• Redo your blogpost by the end of the week.  Email me, if you have done this.
• If you are planning on redoing your quiz, check the calendar to see available time slots.  You will also need to do the following:
• Make sure that you have completed all previous HW assignments (Check PowerSchool)
• Have one of your parents sign your TOFU
• Bring the original quiz and your TOFU with you to the retake.

3.1 and 3.3 Building Triangles and Quadrilaterals

Objective:

The main focus of this problem is to explore what combinations of side lengths allow us to build different types of triangles and quadrilaterals.  In addition, we will determine if a given combination of side lengths forms a unique polygon.

3.1 - Building Triangles

Task A: Building the Triangles.

In this part of the problem, you need to try to build triangles using a variety of different side length combinations.  You will record your work on Labsheet 3.1. For each combination, you need to do the following:

• Try to build the triangle using lego or virtual polystrips.
• If it is possible to build a triangle, make a sketch of the triangle that you built.
• Label and name your sketches with the most appropriate name.
• When building, think of possible ways to make different triangles, these could include changing the order that you attach the sides, or possibly "flexing" the angles.  See what works and what doesn't.

Here are the first four triangle side combinations to try:

• 3, 4, 5
• 2, 4, 8
• 3, 3, 6
• 5, 5, 9

Task B: Looking For Patterns

Complete the three questions from Task B in your squarebook. (P.63)

EXTENSION:

Once you have tested the four combinations that I have given you, create three different sets of side lengths that meet the requirements that I have listed in the table.

3.3 - Building Quadrilaterals

Task A: Building Quadrilaterals

In this part of the problem, you need to try to build quadrilaterals using a variety of different side length combinations.  You will record your work on Labsheet 3.3. For each combination, you need to do the following:

• Try to build the quadrilateral using lego or virtual polystrips.
• If it is possible to build a quadrilateral, make a sketch of the quadrilateral that you built.
• Label and name your sketches with the most appropriate name.
• When building, think of possible ways to make different quadrilaterals, these could include changing the order that you attach the sides, or possibly "flexing" the angles.  See what works and what doesn't.

Here are the first four quadrilateral side combinations to try:

• 8, 8, 10, 10
• 3, 5, 9, 5
• 2, 3, 10, 4
• 6, 10, 3, 5

Here is the virtual polystrip site if you need it:

Task B: Analyzing Quadrilateral Patterns

When you are finished...Answer all of the questions from TASK B (pg. 66)

EXTENSION:

Once you have tested the four combinations that I have given you, create three different sets of side lengths that meet the requirements that I have listed in the table.

HOMEWORK:

1. Complete ALL TASKS from 3.1 and 3.3 described above.
2. 3.1 ACE Problems (1-5) (28)
3. 3.3 ACE Problems (10-14) (29-30)

2.4 - The Ins and Outs of Polygons

Objective:

The main focus of this problem is for you to be able to describe the difference between interior and exterior angles in a polygon, label polygons as being either "concave" or "convex" and to describe and use the relationship between interior and exterior angles.

Part 1: Launch

1.  Look at the two polygons pictured below and answer the following questions in your group:

• How are these two polygons different from the ones in the Shape Set?
• Look-up the definition of "convex" and "concave" polygons.  Which term describes the polygons below?  How do you know?
• In your square book, draw and label an example of a "convex polygon" and an example of a "concave polygon".

2.  Watch the video below and answer the following questions in your square book:

• How many sides does the track have?
• What is the sum of the "interior angles" of the track.  Clearly show your method.
• What is the relationship between the "interior angle" and the "exterior angle" for any one turn?
• What is the special name given to this special relationship?

Part 2: Explore

1. Work through Task A with your group.  Be sure to record your work on the handout provided in class: Labsheet 2.4 A.  Glue this page in your book.

2.  As a group, think about the following questions:

• What was the sum of the "exterior angles" for each polygon?
• Why do you think this is the case?  HINT - Think about which direction each cyclist is facing at the beginning of the race and at the end of the race.
• Work through Task C.  Be sure to show your thinking in your squarebook.

Part 3: Putting It All Together

1. Get a copy of Labsheet 2.4 D, glue it in your book, and answer the questions.  For each questions be sure to include the following:

• Write an equation to show the relationship between the sum of the three angles.
• Solve your equation using inverse operations and the property of equality.
• Use your solution to find the measure of each angle, be sure to show your work.
• Add the interior angles together to show that you have done your work correctly...be sure to think about what the sum of those angles should be.
• Use the "interior angles" to find the "exterior angles".  Add the "exterior angles" together to check your work...what should they add up to?

Part 4: Designing Stuff

1. Download and install a copy of TurtleArt found here.
2. Here are some basic tips on using TurtleArt.
3. Here are some advanced tips on using TurtleArt.
4. Try drawing the following polygons as an intro to TurtleArt
1. Square
2. Rectangle
3. Equilateral Triangle
4. Regular Hexagon

By the end of this problem, you should be able to do the following:

• Identify the difference between "concave" and "convex" polygons.
• Identify the difference between "interior" and "exterior" angles.
• Describe and show how to find the sum of the "interior angles" for any convex polygon.
• Know the sum of the "exterior angles" for any convex polygon.

HOMEWORK:

• 2.4 ACE (14, 15) (21) (25)
• Download and Install TurtleArt (the link is posted above)
• Quiz on Investigations 1 and 2 next class (that is everything in this unit so far)

2.2 Angle Sums of ANY Polygon

Objective:

To develop a formula to helps us find the sum of the interior angles for ANY polygon with n sides.

Last class we looked at a strategy that we could use to find the sum of the angles for regular polygons.  In this class, we are going to build on that idea and try to extend our pattern to include all polygons.

Do Now:

On the piece of paper provided complete the following tasks:

• draw an angle of 60 degrees
• determine the complement and supplement of the angle that you drew.
• measure all three angles of the triangle and add them together.  Compare with the others in your group.  What do you notice?

Explore:

What is the sum of the angles in a quadrilateral?  How can we use the "Angle Sum of a Triangle" to prove this?

Problem 2.2 Tasks B and C

Glue Labsheet 2.2 in your squarebook.  You will do all of your work for these tasks on this Labsheet.

Trevor's Method:

Casey's Method:

At the end of this Problem you should be able to do the following:

• Use a formula to determine the angle sum of any polygon.
• Explain the meaning of each formula discovered in this lesson.

Homework:

• ACE Problems (3, 4, 5 ,6, 7, 8,9 10, 11) (19) (23, 24)

MAP Testing

Objective:

The goal of the MAP test is to provide information about each students' relative strengths and areas for growth so that as a teacher I can help you improve to the best of my ability.  As a result, it is important that you try your best on this test as better data means I can provide a better experience for you this year.

Assignments:

When you finish the MAP test, there are a couple of things that you need to do.

1. Be sure to finish your blogpost for Investigation #1.  These were found on page 39.  Check the rubric that you were given in class.
2. Here are some more Khan Academy activities for you to do.
1. Benchmark Angles
2. One Step Equation Intuition
3. One Step Equations

2.1 Angle Sums in Regular Polygons

Objective:

The main idea of this problem is to look for patterns in finding the sum of all of the "interior angles" for a regular polygon with any number of sides.  Using the pattern, we should then be able to create a formula for finding the sum of the angles for any polygon as well as a formula for finding the size of any one angle in a regular polygon.

In this lesson, we will explore the following "regular polygons":

Using a protractor, carefully measure one of the angles for shapes A, B, C, and D and record them in the table below.  See if you can then determine the "Angle Sum" for the four polygons.

• See if you can find any patterns in your table.  If so, try to extend those patterns in order to fill out the rest of the table.
• Answer Questions 1-4 for Task A
• Discuss Task B in your group.
• The most difficult part of this lesson is trying to write a rule (formula) that would allow you to determine the "Angle Sum" based on the number of sides for any polygon (Task C) as well as the size of each angle in a regular polygon if you know the number of sides (Task D)

At the end of this problem you should be able to do the following:

• Calculate the "Angle Sum" for any polygon if you know the number of sides.
• Determine the "Measure of an Angle" for any regular polygon if you know the number of sides.
• Describe the difference between "regular" and "irregular" polygons.

HOMEWORK:

1. 2.1 ACE Problems (1, 2) (17, 18) (22)
2. Make a Blog Post to address the "Investigation 1 Reflection Questions" (pg. 39).  Be sure to label your blog post so that I can find it.  Check out the rubric here.

1.5 Design Challenge 1

Objective:

The main focus of this problem is for you to follow written directions in order to draw a variety of angles and polygons that meet specific requirements.  In order to do this, you will need to use a protractor and/or ruler.  If you want to see some examples of this being done, try watching the following video:

Part 1: Problem 1.5 Design Challenge

You will need to use a ruler and protractor to draw each angle and polygon that is described in this problem.

• Read the description of each polygon on page 23 of your textbook.
• Record your drawing on the handout provided in class.  This will be collected and assessed at the end of class.

HOMEWORK:

1. 1.5 ACE PROBLEMS: (58)
2. Remember to also do the ACE problems from 1.4

1.4 Measuring Angles

Do Now:

Use the protractor provided to find the measure of the 6 angles shown.

Objective:
The main focus of this problem is to give you hands on experience measuring angles using a protractor. This is hopefully a skill that you have practiced before, but if not, you can check out this video on how to properly use a protractor.

Part 1: Working on Problem 1.4

• Task E - Use a protractor or angle ruler to measure each of the angles on the pages provided.
• Task D - Supplementary and Complementary angles.  Write the pairs of these angles on the "Do Now" page.  If you need more practice with these, check out the Khan Academy task found here.

Part 2: Summarizing Your Learning As A Group

In your group, discuss the following questions.  Be prepared to share your thoughts with the class.

What things do you check to make sure you are making accurate measurements?

Do you prefer the protractor or the angle ruler?  Why?

FOLLOW-UP WORK/HOMEWORK

1. 1.4 ACE PROBLEMS (19-28)

Math Technology Tools

This year in math we will be making use of a wide variety of tools to help us gain a better understanding of math.  The main objective for today is to get everybody signed-up for these online tools.

Khan Academy:

Khan Academy is a great place to go to get some additional skills practice for both the current unit as well as areas from last year where you might need some additional practice.  To set-up your Khan Academy account, follow the directions posted here.

Class codes:
Block C -  YUGTSP
Block E -  B5HCRK
Block G -  BHTYCB

Dash Web:

Dash Web is on online version of your math book that also gives you direct access to some pretty cool math tools and resources.  You have already been set-up for this.  Your login is your regular SAS username.  Your password is "math1234".


Math XL For School:

Math XL is a another place where you can get some extra practice for the unit that we are currently working on.  The great thing about Math XL is that it directly ties to the exact units that we are doing in class.  To set-up your Math XL account, follow the directions posted here.

StatKey:

StatKey is a Google App that we will use later this year.  Download it and install it now.

Desmos:

Desmos is also a Google App.  It is an awesome graphing tool that we will use throughout the year.  Download it and install it now.

Homework:

1. Make sure that you have downloaded/installed/registered for all of the software listed above.  The exception to this is Block C who were unable to set-up Math XL.
2. Complete the following Khan Academy Tasks:
• Angle Types
• Measuring Angles
• Complementary and Supplementary Angles
• Recognizing Triangle Types
• Quadrilateral Types
• BONUS PRIZE for anybody who earns more than 5000 points before next class.
3. Be sure to complete the ACE Problems from both 1.2 and 1.3 if you did not do so already.

1.3 Estimating Measures of Rotations and Angles

Objective:
The main goal of this problem is for you to use your knowledge of benchmark angles to be able to estimate the measure of angles and to sketch angles with a given measurement.  One of the common difficulties with doing this is that students measure the wrong angle because they do not understand the system used when naming angles.

Group Work:

With your group, work through Tasks A-D on page 16/17.  Using a ruler will be a very important part of this unit, so make sure that you have one anytime you are doing classwork, homework, or other assignments.

By the end of the problem, you should be able to do the following:

• Identify, read, and label angles using proper notation.
• Estimate the size of an angle within 15 degrees.
• Sketch and label angles based on either a measurement (180 degrees), number of rotations (half a rotation) or description (two times the size of a right angle)

HOMEWORK:

1. ACE Problems: (10-11) (49, 51, 53, 54+)
2. If you would like some extra practice estimating angle sizes, try The Honey Bee Dance

1.2 In a Spin

Do Now:

• Complete the "Entrance Card" that is on your table groups.  This is to be done individually.
• Open your "Squarebook" to where you completed the homework for last class and be prepared to discuss questions 64 and 65 with your group/class

Objective:
The main focus of this lesson is to be able to identify some common "benchmark angles".  These are angles that are usually pretty easy to recognize such as 45 degrees, 90 degrees etc.  We are going to do this by playing a game and then estimating some angle sizes based on these benchmark angles.  As a quick introduction to angles and rotation.  Check out the videos below:

This one is going to hurt!!



Or check out this video from the 2014 Olympics.  How many spins do you count?  How many degrees of rotation is that?



I am a huge fan of ski aerials.  Watch this guy try to break a world record by performing 4 back flips and 4 full rotations in a single jump.



Group Work:

With a partner you are going to complete Task A which involves playing a game called "Four in a Row".

In this game, the objective is to get 4 places on the grid in a row.  Here is the game board in the event that you would like to practice more:

By the end of this problem you should be able to do the following:

• Recognize basic benchmark angles of 30, 45, and 90 degrees.
• Use multiples of benchmark angles to determine the size of other angles on a polar grid
• Find and label the location of a point on a polar grid.

HOMEWORK:

1. ACE Problems: (6-8) (45, 46) (67+)