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.