Mid-Year Student Check-In Survey

It seems like only yesterday you were filling out your last google survey, introducing yourself to me and what your hopes, concerns and goals for the year were. I hope you have enjoyed the last 4 months as much as I have--variables, linear equations, inverse relationships oh my! :) As we approach the end of 2010 I wanted to take an opportunity to hear from you again and see how the year is going, what you are enjoying, what is challenging, and hear any ideas from you on how we can make our time together even more valuable in 2011. Additionally in January we are considering changing A/B groups and I wanted to get your input on what sorts of groupings you prefer. Thank you for taking the time to fill out this survey thoughtfully and honestly. I look forward to reading what you have to say. -Marcella

Please click the link below to complete the survey.

https://spreadsheets.google.com/viewform?formkey=dHgzRXMxS1VDU2xNZWw3cGlrSFh3QWc6MQ

Inverse Relationships

Today in class we defined the relationships we have been looking at this past week, from calculating the driving time to LA (360/Speed = Time), the relationship between the length of a bridge and its breaking weight, to determining the relationship between the area of a rectangle and its length and width (Ex. For a 24 square inch rectangle, 24/length=width). These relationships, which are graphically represented in a curve in which the difference is greatest when the x-value is low and the y value is high and then the difference dramatically decreases as the x increases. These relationships are distinct from our previously studied linear relationships and are called inverse relationships, in which as one value increases the other decreases (or experiences an inverse).

The relationship between two variables, x and y, is an inverse variation if:

y= k/x

or

xy = k

where k is a constant not 0

Students had a choice for homework today, 1 that is similar to what we have been doing in class, or taking a challenging option in which they are extending the applications of the inverse relationships we have been examining. The link for the homework is below (The first 2 pages is the standard homework and pages 3-4 are the challenge option). The homework is due Monday.

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

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.

Week 10/18-10/22 Summary

This week we investigated linear relationships in real-world situations.

On Monday, we examined how different walking rates affected the walking time of different students to the Bread Workshop, if the Bread Workshop is 750 meters away from school. We found that fastest walking rate (Catey's, at 2.5 meters per second) had steepest slope.

On Tuesday, we examined how different pledge plans would raise different amounts of money for a walkathon. One students plan, Tien's, would raise $2 per mile. Ylva's plan would raise $4 a mile. Aden suggested donor's pledge $10 and $0.50 per mile. After comparing money raised for different distances using a table and graph, students found that Aden's plan would raise the most money for the first 3 miles, but after that point Ylva's plan would raise the most money. This investigation gave us opportunities to discuss the intersection of different lines and use the graph to interpret data. We also discussed how Aden's suggestion of an initial $10 donation would be reflected on the graph (as the y-intercept) and how that shows up in the equation (y=0.5x +10).

On Wednesday, we looked at a situation between Erika and her younger brother (who I mistakenly named as "sister" in the worksheet), in which Erika is racing her brother. Erika has a walking rate of 2.5 meters per second, while her brother has a walking rate of 1 meter per second. If Erica gave her brother a 45 meter head start to the race, students worked together to find an appropriate distance to make a close race, in which either her brother or Erika narrowly wins. Students had the option of a more open ended problem, in which they worked with partners to generate a plan to solve, or a more structured approach to this investigation, which provided a table and encouraged students to create a graph first to help them interpret the problem. Students found that they would tie after 30 seconds at 75 meters, so a race that was 74 meters long would allow her brother to win in a close race, and a race that was 76 meters would allow Erika to just barely win.

On Thursday, we reflected on what we had learned about linear equations through the different investigations. After discussing with their table groups, students had time to begin their Math Reflection in class, and are finishing their reflections at home this weekend. A link to download the math reflection can be found below:

http://dl.dropbox.com/u/10516607/CW_Math_Reflection_Linear_Relationships.docx

Following our work this week with graphs and tables, next week we will focus on answering questions by writing and solving linear equations.

10/12-10/14 Week Summary

For our short week together, students were introduced to linear equations (y=mx+b) and interpreting what different parts of the equations tell us (m=the slope, b=the y-intercept).

Wednesday was spent reviewing key concepts we have been studying this year so far (exponents, order of operations, functions, graphing and linear equations) to prepare for Thursday's quiz.

This weekend students have received their second practice SSAT test to work on for homework (and as much as possible to be completed in simulated testing conditions: 30 minutes, no calculator, in a quite location).

HW the Week of 10/12

By request, here is an overview of this weeks homework (subject to change)

Tuesday 10/12-Linear Equations Worksheet

Wednesday 10/13-Finish Review Sheet and Study from notes, worksheet and homeworks

Thursday 10/14-In-class Quiz, HW-SSAT #2

Week 10/4-10/7 Summary

This week we began on Monday looking at functions by playing "What's My Rule," where students chose either a 1-step (ex. guess x 5 = result) or 2-step rules (ex. guess x 5 -1 = result) to develop an understanding of functions. A function is a pairing of 2 sets of numbers so that each number in the first set corresponds exactly to 1 number in the second set

Ex.

x 1 2 3 4 5

y 5 10 15 20 25

We then practice how we could turn our "rules," or functions, into equations using the variables x and y (ex. y=5x).

On Tuesday, we reviewed coordinate graphs, identifying coordinate pairs and placing coordinate pairs on a graph. We also had the opportunity to graph some of the functions we worked with on Monday.

Wednesday was our investigation day, where students worked in their table groups to determine "How does the thickness of a bridge affect its breaking weight?" using paper bridges and pennies as their loads. Based on the results collected for thickness of 1, 2, 3, 4 and 5 sheets of paper, students predicted how much their bridge would hold if it was 6 or 7 layers thick.

Thursday we shared our data and found the class averages for each thickness. We discussed how sometimes our data may not be perfectly linear, however we can use a graph model (or a straight line or curve that shows the trend in the data) to make predictions based on our data. Students created graph models of the class data and used their graph models to make predictions about the breaking weights of different thicknesses. Students also created graph models for different data sets in which the points were often less linear than those of our class data and compared/contrasted with their table mates as they discussed how they developed their graph models.

Coming up...Linear equations!

Different Ways to Solve the Bikes and Skateboard Problem

This week we have been working on developing characteristics of successful problem solvers as we working on the bikes and skateboard problem:

"A bike shop sold only bikes an skateboards.

All skateboards have 4 wheels and all bikes have 2 wheels.

There were 20 vehicles with a total of 52 wheels in the shop.

How many skateboards and bikes were in the shop?"

On Monday we discussed the importance of being persistent, and not giving up in the face of a challenge. On Tuesday, students finished working on their mini-posters and had a chance to participate in their first gallery walk, where they walked around and had a chance to view different ways of solving the problem and become more flexible in approaching problems in different ways. For homework tonight, students are asked to choose a different method (such as using a table, guess and check, making a drawing, writing an equations, etc), other than what they had tried in class. Here are a few examples of different ways students solved the bike and skateboard problem.

Bike and Skateboard Problem Solving Assessment

Please follow the link below for the Problem Solving Assessment:

https://spreadsheets.google.com/viewform?formkey=dHgzWEpGeVlqSmtLUXoycy05aFF5bWc6MQ

The week of 9/13 notes

This is my first time trying this out...let me know if this works

http://dl.dropbox.com/u/10516607/8Math_09_13_10.notebook

Cool Site of Math Puzzles

I just found this online site filled with interesting and stimulating math puzzles and problems. Check them out. Just think how sharp your brain would be if you took 15 minutes out of your day that you spend online or watching tv to try these.

It's a workout for your brain!

http://www.transum.org/go/default.asp

Checkerboard Reflection

Please click on the link below to access the Checkerboard Partnership Reflection (due Monday Sept 13)

https://spreadsheets.google.com/viewform?formkey=dDA3QkdTdjAtZVhHNVhPTUo0c2Zya0E6MQ

The Checkerboard Problem

Today we discussed the advantages of working within a group and began our first challenge in a partnership: the checkerboard problem.

How many squares are in a standard checkerboard?

We made a K-W-C table of what we

1) KNOW for sure

2) WANT to find out

3) Any special CONDITIONS

HW: Work on the Checkerboard Problem for 20 minutes and have an idea or strategy to share with your partner in class tomorrow. You are not expected to solve the problem, simply try out 1 or more strategies for 20 minutes and notice what worked and what did not.

Math Interview

Please follow the link below to access your first homework assignment, your Math Interview.

I look forward to hearing about your experiences and learning in math!

https://spreadsheets.google.com/viewformformkey=dGJDWHZET0EwYmxMRmlkc29uWFlPU1E6MQ

Welcome!

Welcome to an exciting new year together in 8th grade math!

This year we will continue to build and expand off concepts you began exploring in 7th grade, including working with variables, linear equations, and exponential growth. We will learn through a combination of hands-on investigations, based on the Connected Math Curriculum you have used in 6th and 7th grade math, where you work together to develop new understandings, and from traditional algebra text books that explain directly how and why we solve certain problems in different ways.

Our year together in math will be focused on the journey to understanding, rather than just getting the "right answer." I am excited to welcome a class of unique students and appreciate that each of you has your own strengths, and ways of understanding math, as well as your own challenges. This year we will focus on how can we share our thinking and understanding with one another to become better problem solvers.

I am very happy to welcome you to the beginning of our special journey together this year in 8th grade math!