Math 6 Honors ( Periods 1, 2, & 3)

The Tangram Story
(One of the activities we did while students were at Astro Camp)

Once upon a time, long, long ago, in a faraway magical land lived a little boy named Tan. The emperor of the land had entrusted Tan with a very special task. The emperor had given Tan a magical square tile and asked him to deliver it to one of the emperor’s subjects who lived in the countryside. Tan was instructed to go directly to the subject’s house and not stop along the way. But, along the way, Tan encountered a group of his friends playing along the river. Tan thought he would stop for just a few minutes to rest and play … when alas; the tile flew out of his pocket and broke into seven pieces. Tan and his friends were so upset that they tried for days to put the tile back together again. They were able to form many beautiful designs of birds and animals and flowers but never the square tile. His designs have been handed down form generation to generation for over 3000 years and are known as Tangram puzzles.
If you would like to enjoy creating some of these puzzles or are interested in how to create your own tile, come in before or after school.

Math 6 Honors ( Periods 1, 2, & 3)

Proportions 7-7
We used fictional numbers for the middle schools in our district
AEWright 6th grade 160 students and 10 teachers
ACStelle 6th grade 144 students and 9 teachers
We looked at the teacher to student ratios of both schools and found
10/160 = 1/16
and
9/144 = 1/16

so 10/160 = 9/144
An equation that states two ratios are equal is called a proportion
10, 160, 9, and 144 are called the terms of the proportion.
Let's say LCMS has 192 students. How many teachers will be needed if the teacher- strudent ratio needs to be the same?

Let t = the number of teachers
10/160 = t/192

Using cross multiplying we discovered that
160t = 192 (10)

160t = 192 (10)
160 160

t = 192/16
or t = 12

12 teachers

we found that when
a/b = c/d and b is not equal to 0 and d is not equal to zero
then
ad = bc


3/8 = 12/n
3n = 8 (12)
3n = 96
3n/3 = 96/3
n = 32

what about 4/3 = n/7
3n = 4(7)
3n = 28

3n/3 = 28/3

n = 9 1/3

3/75 = 2/n
n = 50

3/m = m/27
m² = 3 (27)
m² = 81
so m = 9

49/n = n/4
n² = 4(49)
n² = 196
n = 14