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!