Exploring the common core:Algebra I activities

Elana ReiserSt. Joseph’s College

Module 1, lesson 3: Graphs of Exponential FunctionsPay It Forward

•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.

•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.

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.

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

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.

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

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.

Find the missing numbers and signs and then explain any patterns you find:

Fill in the blanks to eventually get a squared term on the left:

Manipulate the following equations to get a squared term on the left:

The method you just did is called completing the square.Come up with a list of steps you need to follow in order to complete the square.

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