This document contains summaries of modules and lessons from an algebra course. It outlines activities for students on topics like graphs of exponential functions, solving simultaneous equations, distributions and their shapes, functions, and completing the square. For one lesson, students are asked to model a "pay it forward" scenario with a function and graph the results. Another lesson uses a word problem about the area of different regions of land to have students derive an answer using simultaneous equations. The document promotes exploring mathematical concepts through hands-on activities and invites interested teachers to a professional development course on creating such activities.

1. Exploring the common core:
Algebra I activities
Elana Reiser
St. Joseph’s College

2. Module 1, lesson 3: Graphs of Exponential Functions
Pay It Forward

3. •The top row is the original good doer but hasn’t helped anyone yet
so call that row 0, or x = 0. The next row, x = 1, has three people
who received a good deed so its value is 3. Use this to model with a
function. Find different values of the function.
•Draw a tree diagram similar to
the one in the movie and guess #
rows needed for everyone at
school to have received a good
deed.

4. •Share answers and how you got them. Check the original guess
about # of rows needed to have everyone in the school receive a
good deed. Is it what you expected?
•Plot the points you got earlier and sketch a graph.
•On the same set of axes draw a graph for if each person only
helped 2 people. 4 people.

5. Extra Challenge: Change the original scenario to two friends have
the idea together but one friend does it the same as Trevor while
the second friend only helps one person and asks his help-ee to
also only help one person.

6. Module 1, lesson 22: Solution Sets to Simultaneous Equations
Rectangular Land Problem
A man owns a rectangular piece of land that is divided into four rectangular
pieces, Region A, B, C, and D (see figure). One day his daughter, Nancy, asked
him, what is the area of our land? The father replied: I will only tell you that
the area of Region B is 200 ft2 larger than the area of Region A; the area of
Region C is 400 ft2 larger than the area of Region B; and the area of Region D is
800 ft2 larger than area of Region C. What answer to her question will Nancy
derive from her father’s statement?
Taken from Holistic Math Problems at University of California, San Diego

7. Module 2, Lesson 1: Distributions and Their Shapes
•Pick a company name and 3 products that your company produces.
•Your company needs to produce a year-end sales report. Make a pie chart showing what percent of
total sales each product is.
•Think of scenarios where your company would want to include a dot diagram then draw it.
•Pick your favorite product. We want to see how much it sold for in different stores. Take a random
sample of 15 of the stores your product is sold at and list the price at each store. Draw a histogram
and a boxplot for this data.
•Put all your work together to create a report and include a summary of everything you found.
•Present your findings to the class.

8. Module 3, Lesson 9: Functions
Brainstorm properties of this relation
What is the domain and range?
Change example to make it not a function
It’s not in this lesson but 1-1 & onto can also be brought up

9. Module 4, lessons 11-12: Completing the Square
Which of these is easier to graph and why?
x2 -4x+7 or (x-2)2+3
Explain why they are actually the same.

12. Interested in seeing more activities and creating
your own?
The last 2 weeks of July St. Joseph’s College is
offering a 3 credit course on this topic
Email ereiser@sjcny.edu for more info
Slides at http://tinyurl.com/limacon14