How Tall is That? Using Similar Triangles

 

The figure above shows a problem of: How tall is the flagpole?  Our 8th grade Math investigation showed a way to find out the height of a cliff using similar triangles like the ones pictured above.  It is important to remember that similar figures share corresponding sides and corresponding angles.  Corresponding angles have equal measures, while corresponding sides have the same ratio.  In the picture above, the corresponding sides on the base of the similar triangles show a ratio of 15.5/4 which equals 3.875

Several eighth graders discovered a strategy to figure out the missing side by using the ratio multiplied by the corresponding side.  For example if we wanted to find the height of the flag pole, this strategy says we take 3.875 times 3, which gives the height of 11.625.  

If you want to find out more about how to use this method to find the height of familiar objects, such as skyscrapers, trees, or towers check out the website Connecting Geometry   

Another fun pair of links to sharpen your math skills are Math Videos at Khan Academy.  Check out the video links below and more great videos on Khan Academy.

 All about Circles  and Testing out Similar Triangles

Interactive Integer Flash Cards and Slope Practice

Try your skill at integer operations.  Solve the integer operations flash cards.  Check your answer by clicking the card after you solve the problem.  Then move the flash card to the correct or incorrect pile.  Try again and see how many you can get correct. 
Afterwards, add a comment below and some strategies you like to use for solving integer operations. 



More flashcards and educational activitites at StudyStack.com

Click on the Link Below to practice finding the slope of a line
Interactive slope of a line from Mathwarehouse.com

Popcorn Friday's: 8th Grade Fundraising

Eighth grade graduation fundraising has involved the business minded skills of the students selling taffy apples, buttons, and popcorn.   The sales will off set some of the costs for eighth grade graduation activities.  Students show teamwork by working together towards their goal of reducing graduation costs.  Friday popcorn sales involve the students measuring ingredients, collecting money, keeping records of sales, and problem solving for optimal sales each week.

What are some ways that math is used as students help manage a fundraiser?  Problems and questions often surface when we are popping away, or looking back at the figures.  For example, this week sales of popcorn were a total of $146 dollars combined between the early morning and afternoon shifts.  The first shift sold ten dollars more than the second shift.  How much money did each of the shifts make during their sales? 

The overall sales of shift 1 (x) and shift (2) y, equalled 146 dollars.   The equation is expressed as x+y=146
Another part of this problem involves the money earned by the second shift. y= x+10.
Solving a pair of equations can be done by solving for x algebraically, using guess and check, or a host of other strategies.  The equation way will substitute the second equation into the first equation.  Namely, x+(x+10)=146.   2x=136, x=68.   Then if x=68, y+68=146.  So y=$78.  Check involves 78+68= 146. 

The math involved in figuring out this equation likely relates to other situations or questions that have come up in managing events like a fundraising.  It'd be great to hear from you.  Share some ways that you have seen math being used.