*Contributor: Marlene Vogel. Lesson ID: 12930*

Where would art be without math? What do origami and isosceles mean? With ordinary paper, watch your geometry knowledge take shape with fun and fancy artwork as you make a geometric name for yourself!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Lion, Beaver

Grade Level

Intermediate (3-5), Middle School (6-8)

Lesson Type

Skill Sharpener

Mixing art and math skills makes learning fun! Come on and give it a "tri"! Watch these videos on how to make origami; you will be trying your hand at them later in this lesson:

This lesson will help you refresh your knowledge of both isosceles and equilateral skills.

Following the skill-sharpening lesson, you will have an activity to complete. Then, you can move on to the next section of the lesson, complete at least one activity in that section, and then to the final section, where you are required to complete one activity in that section.

**Refresh your memory**

The first thing you want to do is remind yourself of the differences between — and definitions of — isosceles triangles and equilateral triangles. It may be easier for you to describe the difference between the two triangles. Turn to your parent or teacher and see if you can define or describe the difference between the two types of triangles in your own words.

Were you able to explain to your teacher that the difference between the two different types of triangles is their sides? Excellent! I am sure you told your teacher that an isosceles triangle has two sides with the same measurement, whereas an equilateral triangle has the same measurement for all three sides. Great job and congratulations!

Make your teacher say “Wow!” one more time. Explain to your teacher that the fancy math word that means the same as sides of triangles having the same measurement is "congruent." If you say that a triangle has *two* congruent sides, then you are talking about an *isosceles* triangle. Of course, an *equilateral* triangle has *three* congruent sides.

**Activity 1**

Have you ever tried to complete a puzzle where you are asked to count the number of a geometric shape you see in a larger shape? For example, below is a large triangle with many triangles inside of it. How many triangles do you see all together in this puzzle?

- First, you will learn the steps involved in figuring out how to complete this type of puzzle.
- Then, you will be given another triangle with more triangles inside of it.
- You will need to use the following guide to help you complete that activity on your own:

- Look at the picture below. You will need a piece of paper and pencil to complete this activity and the next activity.

- You are now going to break down these triangles into their different sizes so that you can keep count of each one in this picture. The first size you are going to look for is known as a "4." What that means is, the side of a size 4 triangle is 4 times the size of the smallest triangle found in the picture. Below, you will see an example of what is the smallest triangle in the picture above.

- The green triangle in the picture below is considered the smallest-size triangle in the entire picture. Now that you know that, which triangle from the picture above would be considered a size 4? (Remember, a size 4 has sides that are four times larger than the green one.) See below for the answer.

- So, which triangle from the picture would be the size 4? It would be the largest triangle you can find in the picture (See below):

- On your piece of paper, make a table like the one you see below

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

- Great job! Now you are looking for triangles that are a size 3. This means that the sides of a size 3 are 3 times larger than the sides of the smallest triangle in the picture. Also, just to make it easier for yourself, stay with the triangles that have their point up for now. You will count upside-down and sideways triangles shortly (See below for size 3 triangles.):

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

point up | 3 | 3 |

- As you can see, there are 3 size 3 triangles. Two are located at the bottom and one is located at the top. Don’t forget to put that information into your table. Once you have counted all the triangles in the picture, then you will add all the numbers in your final column.

- Next are the size 2 triangles that have their points facing up:

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

point up | 3 | 3 |

point up | 2 | 6 |

- Now, it is time to count the size one triangles. Remember, you are only counting the ones whose tip is facing up

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

point up | 3 | 3 |

point up | 2 | 6 |

point up | 1 | 10 |

point down | 1 | 6 |

- Next, start counting the triangles that have their points facing down. Count the size 1 triangles with their points facing down:

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

point up | 3 | 3 |

point up | 2 | 6 |

point up | 1 | 10 |

point down | 1 | 6 |

point down | 2 | 1 |

- Time to count size 2 facing down:

Point Up / Point Down |
Size |
How Many? |

point up | 4 | 1 |

point up | 3 | 3 |

point up | 2 | 6 |

point up | 1 | 10 |

point down | 1 | 6 |

point down | 2 | 1 |

- There is only one size 2 triangle in the picture. Also, if you look closely, you cannot fit a size 3 or size 4 point down triangle anywhere in the picture.

- Add all the numbers in the third column under the title “How many?” Your answer should be 27.

**Activity 2**

It is now time to try this puzzle on your own. You will need the back of the paper you just used to make another blank table on, your pencil, and *Activity 2 - How many triangles are in this picture?* found in the **Downloadable ****Resources** in the right-hand sidebar.

In addition, your teacher will need the *Activity 2 – How many triangles are in this picture? Answer Key* (**Downloadable Resources**).

Good luck and have fun!

The *Got It?* section offers two opportunities for you to continue to sharpen your angle measurement skills!

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