-
Math 8 Tasks
-
1. Pythagorean Theorem
- Distance Between Two Points
- Areas of Squares and Right Triangles
- Lengths of Squares and Right Triangles
- Discover Pythagorean Theorem
- Missing Side Lengths
- Trouble with Triangles
- More Trouble with Triangles
-
2. Angle Relationships
-
3. Transformations
This activity is also part of one or more other Books. Modifications will be visible in all these Books. Do you want to modify the original activity or create your own copy for this Book instead?
This activity was created by '{$1}'. Do you want to modify the original activity or create your own copy instead?
This activity was created by '{$1}' and you lack the permission to edit it. Do you want to create your own copy instead and add it to the book?
Math 8 Tasks
Tamara Willis, Apr 22, 2020
Distance learning activities for 8th Grade Mathematics.
Table of Contents
- Pythagorean Theorem
- Distance Between Two Points
- Areas of Squares and Right Triangles
- Lengths of Squares and Right Triangles
- Discover Pythagorean Theorem
- Missing Side Lengths
- Trouble with Triangles
- More Trouble with Triangles
- Angle Relationships
- Transformations
Pythagorean Theorem
I can understand and apply the Pythagorean Theorem and its converse.
-
1. Distance Between Two Points
-
2. Areas of Squares and Right Triangles
-
3. Lengths of Squares and Right Triangles
-
4. Discover Pythagorean Theorem
-
5. Missing Side Lengths
-
6. Trouble with Triangles
-
7. More Trouble with Triangles
Distance Between Two Points
Learning Goal
Students will explore distance between two points in a coordinate plane and learn how this relates to right triangles.
Visual 1: Click, drag, and drop the points to explore the distance between them.
Question 1: Use the visual to...
Find the distance between each set of two points:
- (0,0) and (5,0)
- (0,0) and (0,5)
- (7,3) and (5,3)
- (-6,-4) and (-6,4)
Font sizeFont size
Very smallSmallNormalBigVery big
Bold [ctrl+b]
Italic [ctrl+i]
Underline [ctrl+u]
Strike
Superscript
Subscript
Font colorAuto
Justify
Align left
Align right
Align center
• Unordered list
1. Ordered list
Link [ctrl+shift+2]
Quote [ctrl+shift+3]
[code]Code [ctrl+shift+4]
Insert table
Remove Format
Insert image [ctrl+shift+1]
Insert icons of GeoGebra tools
[bbcode]
Text tools
Insert Math
- 5 units
- 5 units
- 2 units
- 8 units
Question 1: Check your answer.
Visual 2: Click, drag, and drop the points to explore the distance between them.
Question 2: Use the visual to...
Find the distance between (1,1) and (8,6).
- What is different this time?
- Can this exact distance be found? Why or why not?
Font sizeFont size
Very smallSmallNormalBigVery big
Bold [ctrl+b]
Italic [ctrl+i]
Underline [ctrl+u]
Strike
Superscript
Subscript
Font colorAuto
Justify
Align left
Align right
Align center
• Unordered list
1. Ordered list
Link [ctrl+shift+2]
Quote [ctrl+shift+3]
[code]Code [ctrl+shift+4]
Insert table
Remove Format
Insert image [ctrl+shift+1]
Insert icons of GeoGebra tools
[bbcode]
Text tools
Insert Math
- This time the distance is not just horizontal or vertical, it's both. In other words, this is a diagonal distance.
- This distance can't be found by counting, because it doesn't line up perfectly with the unit squares, but it can be found in other ways.
Question 2: Check your answer.
Attention: Did you notice the right triangle?
Wherever there is a diagonal distance, there is also a right triangle.
- The longest side of the right triangle (called the hypotenuse) is the diagonal distance.
- The two shorter sides of the right triangle (called the legs) make up the horizontal and vertical components of the diagonal distance.
Visual 3: Click, drag, and drop the points and the lengths to estimate the distance.
Question 3: Use the visual to...
Estimate the distance between each set of two points in terms of the lengths of the hypotenuse and legs of the right triangle:
- (0,0) and (6,3)
- (-3,5) and (2,1)
- (-7,-4) and (3,-8)
- (4,-2) and (0,2)
Font sizeFont size
Very smallSmallNormalBigVery big
Bold [ctrl+b]
Italic [ctrl+i]
Underline [ctrl+u]
Strike
Superscript
Subscript
Font colorAuto
Justify
Align left
Align right
Align center
• Unordered list
1. Ordered list
Link [ctrl+shift+2]
Quote [ctrl+shift+3]
[code]Code [ctrl+shift+4]
Insert table
Remove Format
Insert image [ctrl+shift+1]
Insert icons of GeoGebra tools
[bbcode]
Text tools
Insert Math
- Leg lengths = 6 & 3, and 3 < 6 < hypotenuse length < 6+3=9.
- Leg lengths = 5 & 4, and 4 < 5 < hypotenuse length < 5+4=9.
- Leg lengths = 10 & 4, and 4 < 10 < hypotenuse length < 10+4=14.
- Leg lengths = 4 & 4, and 4 = 4 < hypotenuse length < 4+4=8.
Question 3: Check your answer.
Saving…
All changes saved
Error
A timeout occurred. Trying to re-save …
Sorry, but the server is not responding. Please wait a few minutes and then try to save again.