Testing Bridge Length

Today we tested how the length of a bridge affected how much weight the bridge could carry. Students worked with their table groups to test bridges with lengths ranging from 4 inches to 11 inches to determine how many pennies the bridge could carry before breaking.

Although when students initially graphed their results, it initially appeared to many that there was not a clear relationship or pattern, when we combined the class data the relationship became more apparent. Unlike our previous bridge experiment, where students tested how the thickness of the bridge affected the carrying weight, the relationship this time could be better modeled with a curve than a straight line, as you can see for yourself below.

How does speed affect driving times?

Welcome Back!

Today in class we investigated a common question many drivers find themselves pondering, particularly when covering large distances: "How much time can I save if I drive faster?"(of course, drivers are also weighing out the costs of safety and potential speeding tickets when considering driving above the speed limit, while we in class today are solely focusing on the impact of speed on driving time). With 42.2 million Americans traveling over the Thanksgiving break, this problem offered a particularly timely application of studying patterns.

You may download the classwork and homework from the link below:

http://dl.dropbox.com/u/10516607/8th%20Handouts/CW_Testing_Driving_Fast_Pays.docx

Slope Intercept Rap

In honor of our work with the slope-intercept form of lines, I thought I would share this informative slope-intercept rap I found online.

http://www1.teachertube.com/viewVideo.php?video_id=101097

Have an idea for your own math rap or song? Let's record it and share it on the blog!

Using Linear Equations for Graph Models

So far in our study of linear equations, we have been focusing on situations that are neatly linear, which we can tell looking at a table or graph by identifying a constant rate of change. In the real world, often the data we encounter are not quite as "neat" and perfectly linear. Nonetheless, linear relationships do surround us in our world, even if the patterns are not necessarily as apparent as they may be on a crisp math worksheet.

Today we returned to a concept introduced over a month ago: the graph model. A graph model is a straight line or a curve that shows the general trend in a set of data. In todays classwork and homework, we worked with slightly "messier" data that did not lie in a perfectly straight line. After plotting the data, we were able to draw a line that reflected the general trend of the data and, from that line, create a linear equation.

Click the link below to download the classwork "Setting the Right Price" and tonight's HW (due Monday).

http://dl.dropbox.com/u/10516607/8th%20Handouts/Problem%201.4%20Setting%20the%20Right%20Price.docx

Quiz 2 on Linear Equations were returned today. Please take the opportunity this weekend to talk with your families about what areas you feel you have grown with linear equations and which areas are still challenging for you. Quizzes should be signed by a parent and brought to class Monday. Please see me tomorrow or Monday if you were absent to receive you quiz.

Writing Equations in Slope-Intercept Form Classwork/Homework

Here are the links to download today's CW/HW on Writing Equations in Slope-Intercept Form (a.k.a. y=mx+b). You may use either method (graphing the points or calculating the slope and substituting) to find the equations.

Medium Work

http://dl.dropbox.com/u/10516607/8th%20Handouts/CW_Slope%3AIntercept_Form.docx

Challenge Work

http://dl.dropbox.com/u/10516607/8th%20Handouts/CW_Slope%3AIntercept_Form_Challenge.docx

Make Up Quiz Monday 11/15

Students who missed our quiz Thursday on Linear Equations will be able to make up the quiz Monday after school. If this time is not convenient, please let me know of Monday another day next week (other than Wednesday) when you will be available to make up the quiz.

Week Summary 11/8-11/11

After developing an understanding of how we can find slope last week, by comparing the rise over run, this week we put all that we have been learning about linear equations together in writing equations based on different information that we are given.

On Monday students practiced finding the slope, y-intercept and equation if they were given a pair of numbers, such as (-2, 1) and (2, 3). Students first graphed the given points, which then allowed them to determine the slope by drawing a triangle between two points and comparing the rise over run. Students then were able to use their graph to help them identify the y-intercept and write their equations in the format of y=mx+b.

On Tuesday, students were introduced to Alphonso's Inheritance puzzle. Alphonso had received a check from his grandfather for his birthday. Alphonso decides to save a certain amount of his allowance every week to add to his savings from his grandfather. Alphonso's sister Maria wants to find out how much money he received, and Alphonso gives her a puzzle to solve.

A. Alphonso tells Maria he will save the same amount from his allowance each week. He says that after five weeks he will have a total of $175 and after eight weeks he will have $190. How much money is Alphonso planning to save each week?

B. How much money did Alphonso’s grandfather give him for his birthday?

Write an equation for the total amount of money Alphonso will have saved after a given number of weeks (M= money, W = weeks). Describe the reasoning you used to write your equation.

Students worked with partners and used different strategies (from graphing, to finding the difference and determining the rate saved per week) to determine that Alphonso was saving $5 per week. Based on the slope of 5, students were able to work backwards to determine the y-intercept which was $150, or how much he received from his grandfather. Students determined the equations to be: M = 5w + 150.

On Thursday took their Linear Equation Quiz to assess what they had learned so far about linear equations.

Next stop on the 8th Grade Math Train...non-linear relationships!

Week Summary 10/25-10/28

We continue to move ahead in our investigation and understanding of linear equations.

Following a week of graphing linear equations, last week students focused on how to solve linear equations symbolically, using 2 step algebraic equations, such as 90 = 5x +30.

Monday students investigated how they can use linear equations to solve problems through the problem 5.1 “Paying in Installments.” This problem describes:

The Unlimited Store allows any customer who buys merchandise costing over $30 to pay on an installment plan. The customer pays $30 down and then pays $15 a month until the item is paid for.

Students worked together to translate the written description into linear equation to find how long it would take to pay down different items (such as an iPod, for $195: $195=30+15m, where m = the number of months)

We also found that linear equations can describe the relationship between specific bones (radius, humerus, tibia and femur) and a person’s height. Students had the choice between working with equations with whole numbers or decimals in their analyzing bones classwork.

Although at the start of the week solving algebraic equations and showing their work was a bit tricky for students, by Thursday everyone was comfortable solving 2-step algebraic equations independently.