The Radix Endeavor - Congruent Triangles

GM1.7: Closing the Window

slindgren — Sat, 18 Jan 2014 00:34:09 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.6: Measure Five Times, Cut Once

Summary:

Ember send you back to Transom to continue on geometry adventures.

Recommendations:

Begin this quest line before introducing the concept of congruence and congruent triangles.

Learning Objectives:

None.

Connecting Questions:

None.

Additional Resources:

None.

GM1.6: Measure Five Times, Cut Once

slindgren — Sat, 18 Jan 2014 00:32:42 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.5: Measure Four Times, Cut Once

Next Quest:

GM1.7: Closing the Window

Summary:

REPEAT OF PREVIOUS QUEST WITH A DIFFERENT COMBINATION OF FRAGMENTS AND A DIFFERENT CONGRUENCE POSTULATE/THEOREM.

Ember has a pile of unsorted glass fragments (sides and angles from triangles). Find three pieces that match the second window from the left, place them into the Triangle Template to cut a new glass panel. Fit the new panel into the window using the Architect's View.

Recommendations:

Begin this quest line before introducing the concept of congruence and congruent triangles. In using the broken angle and side fragments to create new glass panels, they are determining the necessary pieces that make two congruent triangles and in effect are learning about congruence postulates/theorems (SAS, SSS, ASA, AAS).

Learning Objectives:

Players will be able to use congruence postulates/theorems in order to create congruent triangles

Tools:

Architect's View

Triangle Template

Connecting Questions:

How did you determine which fragments to use to create the new glass panel?
Did you try any combinations that didn’t work?
Did it matter what order you put them in to be able to cut the correct piece?
What orders did you try? Which ones worked? (this is where connections should be made to the theorems i.e - using three side fragments to create the triangle = SSS congruence postulate)

Additional Resources:

These resources can give students additional practice on congruent triangles:

GM1.5: Measure Four Times, Cut Once

slindgren — Sat, 18 Jan 2014 00:31:29 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.4: Measure Thrice, Cut Once

Next Quest:

GM1.6: Measure Five Times, Cut Once

Summary:

REPEAT OF PREVIOUS QUEST WITH A DIFFERENT COMBINATION OF FRAGMENTS AND A DIFFERENT CONGRUENCE POSTULATE/THEOREM.

Recommendations:

Learning Objectives:

Players will be able to use congruence postulates/theorems in order to create congruent triangles

Tools:

Architect's View

Triangle Template

Connecting Questions:

How did you determine which fragments to use to create the new glass panel?
Did you try any combinations that didn’t work?
Did it matter what order you put them in to be able to cut the correct piece?
What orders did you try? Which ones worked? (this is where connections should be made to the theorems i.e - using three side fragments to create the triangle = SSS congruence postulate)

Additional Resources:

These resources can give students additional practice on congruent triangles:

GM1.4: Measure Thrice, Cut Once

slindgren — Sat, 18 Jan 2014 00:30:06 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.3: Measure Twice, Cut Once

Next Quest:

GM1.5: Measure Four Times, Cut Once

Summary:

REPEAT OF PREVIOUS QUEST WITH A DIFFERENT COMBINATION OF FRAGMENTS AND A DIFFERENT CONGRUENCE POSTULATE/THEOREM.

Recommendations:

Learning Objectives:

Players will be able to use congruence postulates/theorems in order to create congruent triangles

Tools:

Triangle Template

Connecting Questions:

How did you determine which fragments to use to create the new glass panel?
Did you try any combinations that didn’t work?
Did it matter what order you put them in to be able to cut the correct piece?
What orders did you try? Which ones worked? (this is where connections should be made to the theorems i.e - using three side fragments to create the triangle = SSS congruence postulate)

Additional Resources:

These resources can give students additional practice on congruent triangles:

GM1.3: Measure Twice, Cut Once

slindgren — Sat, 18 Jan 2014 00:28:43 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.2: A Perfect Fit

Next Quest:

GM1.4: Measure Thrice, Cut Once

Summary:

Recommendations:

Learning Objectives:

Players will be able to use congruence postulates/theorems in order to create congruent triangles

Tools:

Triangle Template

Connecting Questions:

How did you determine which fragments to use to create the new glass panel?
Did you try any combinations that didn’t work?
Did it matter what order you put them in to be able to cut the correct piece?
What orders did you try? Which ones worked? (this is where connections should be made to the theorems – using three side fragments to create the triangle = SSS congruence postulate)

Additional Resources:

These resources can give students additional practice on congruent triangles:

GM1.2: A Perfect Fit

slindgren — Sat, 18 Jan 2014 00:27:18 +0000

Quest Line:

Window of Opportunity

Previous Quest:

GM1.1: Builders Wanted

Next Quest:

GM1.3: Measure Twice, Cut Once

Summary:

Match the glass panel from Ember to the correct window. Use the Architect’s View tool to determine the correct window.

Recommendations:

Begin this quest line before introducing the concept of congruence and congruent triangles. In this first quest players are learning how to use the tool and how to fit matching shapes.

Learning Objectives:

Players will be able to understand congruence by overlaying matching shapes

Tools:

Architect's View

Connecting Questions:

How did you determine if your shape matched?
What does it mean for two triangles to be congruent?

Additional Resources:

These resources can give students additional practice on congruent triangles:

GM1.1: Builders Wanted

slindgren — Sat, 18 Jan 2014 00:25:30 +0000

Quest Line:

Window of Opportunity

Next Quest:

GM1.2: A Perfect Fit

Summary:

Transom wants you to go see Ember and help her install windows at the medical clinic.

Recommendations:

Begin this quest line before introducing the concept of congruence and congruent triangles.

Learning Objectives:

None.

Connecting Questions:

None.

Additional Resources:

None.

Window of Opportunity

slindgren — Fri, 17 Jan 2014 23:53:58 +0000

Ember is trying to finish construction on a clinic in Baobab Village. The construction workers in charge of the windows have abandoned the project and the player needs to help finish the project by cutting and fitting correctly shaped triangular glass pieces.

Standards Covered in Quest line:

CCSSM Practice 1: Make sense of problems and persevere in solving them
CCSSM Practice 2: Reason abstractly and quantitatively
CCSSM Practice 4: Model with mathematics
CCSSM Geometry Standard G-CO, 6-8: Understand congruence in terms of rigid motions
CCSSM Geometry Standard G-CO, 12: Make geometric constructions

Topic:

Geometry

Subtopic:

Congruent Triangles

Walkthrough:

Quests:

GM1.1: Builders Wanted

GM1.2: A Perfect Fit

GM1.3: Measure Twice, Cut Once

GM1.4: Measure Thrice, Cut Once

GM1.5: Measure Four Times, Cut Once

GM1.6: Measure Five Times, Cut Once

GM1.7: Closing the Window