# Designing Math Lessons for Adult Ed Using OER

Adult Educators do not have a lot of time to dive into dozens of resources spread all over the internet to try to find the essential items they need to create a high-quality lesson for their students.  This guide is designed to walk you through each step of creating a math lesson-plan with recommended OER that you can evaluate.

## How to Use this Guide

Each section has an element of a lesson plan with recommended OER, how to implement it in the adult ed classroom, and tips when appropriate.  While opinions vary about what do include in lesson plans, this structure should hit the essential elements as outlined below:

### Standards

Matching the lesson to at least one of the College and Career Readiness Standards

### Warm-up

Build up background and interest

### Introduction

This is a highly interactive step in which you model, demonstrate, and do a think aloud to show students necessary mental processes they will apply. Do not rush this step.

Show students how to do something then engage them in questions about it.  Modeling is active.

### Activities (Whole Class and Small Group)

What will the students do to engage and learn about the topic?

### Practice Exercises

Once students have learned about and explored a topic, they need to get some practice to ensure that they are understanding what they learned.  Exercises are also one way to do formative assessment.

### Formative Assessments

These are in-process ways of evaluating student learning and progress.  Grades are not attached to them. They assist in learning the material and letting the teacher know whether students are understanding.

To take a deeper dive into the difference between Formative and Summative Assessments, check out “Formative Assessment and What's Next: Cynthia Bell”

### Summative Assessments

These are a way of measuring student skill acquisition and learning at the end of a defined period of time such as the end of a lesson or unit or semester.  They are often graded and more conclusive.

## Finding the Standards

### Main Reference

• The math section is found on pages 44 - 84.
• I recommend starting with the standards you want to meet for your lesson, and then building from there instead of creating a lesson and then trying to match it to standards.  If you create the lesson first, you might find that you are only meeting part of a standard, or that your approach does not have a match within the standards.
• Lessons can often meet more than one standard, but try not to tackle too many at once because then you will be sacrificing depth for breadth.

## Sample Lesson on Pythagorean Theorem:  Finding the Standards

For this example, we will create a lesson on “Understanding and Applying the Pythagorean Theorem.”

We will use the level D standard found on page 76 of the CCRS which states:

“Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (8.G.7) Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.8)”

## Warm-ups

### Number Sense

To develop number sense and estimation skills try using http://www.estimation180.com/ at the beginning of class for several weeks.  These activities are appropriate for all age levels, they promote mathematical thinking, and they are wonderful for statistics and data analysis.  A sample found on OER commons is the “Clothesline Integers Game.”

• Low-tech option:  You can get ideas from the site and bring in the real items such as cheese puffs or toilet paper rolls or a jar of candy to have students practice their estimation/data analysis skills
• Digital skills extension:  You could have students practice using Google Sheets or Excel to explore their class responses to learn range, central tendency, population sampling, creating formulas or other relevant digital skills.

### My Favorite "No"

To promote a growth mindset and assess student thinking on any math subject, try using the low-cost activity “My Favorite No” (a 6 minute instructional video).  While this teacher is using the activity with children, it would also work well with adults.

### Number Talks

Think about using “Number Talks.”  An excellent primer is from Stanford Professor, Jo Boaler.  From Stanford Online's "How To Learn Math for Teachers and Parents": Number Talks

## Sample Lesson on Pythagorean Theorem: Warm-up

Using “My Favorite No” provide students the following problem:

If the total area of a square room is 144 sq ft, then what are the dimensions of the room?  (I chose this problem because it’s essential to understand squares and square roots to be able to understand and apply the Pythagorean Theorem.)

Extension Question:  What would be the distance from one corner of the room to the opposite corner (Round to the nearest whole number)?

## Math Introductions

### CK-12

CK-12 has adaptable online textbooks.  These are visual textbooks accessible from any device.  Hundreds of adaptations are available. One example that will be used in the sample lesson is Pythagorean Theorem (Student Edition) but you can search CK-12 on the search bar for OER Commons and come up with many more options to suit your specific needs.

No matter what the topic is in math, Khan Academy likely has something to get you started.  Type your topic in the search bar on his site and you will get videos and exercises that are relevant.

### YouCubed

You can find visual math tasks for all levels, including many “low floor/high ceiling” tasks at YouCubed, Jo Boaler’s project out of Stanford.  Go to “Tasks” and choose your filter.

## Sample Lesson on Pythagorean Theorem: Introductions

Have students watch visual proof with ball bearings and ask them what they notice.  Then ask, “What do you wonder?” Then proceed to the hands on activity.

Hands on activity:  Pair students up and give them grid paper.  Have them draw a 6x8 right triangle. Next give them grid square cutouts that are 6x6, 8x8 and 10x10.  Make them different colors for effect. Have them place the square on the sides of their right triangle.  Show how the area of each of the legs adds up to the area of the hypotenuse.

Critical thinking question:  Does this idea of adding squares work if the triangle is not a right triangle?  (using the cutouts have students make the legs into acute and obtuse angles and see what happens to the hypotenuse.)

Using the Pythagorean Theorem (Student Edition) from CK-12, show several of the proofs available.  Understanding the proofs is not critical. . . the point is to show the variety of methods, the creativity and visual nature of how different people have demonstrated that the the Pythagorean Theorem is true.

Watch the first 5 minutes of Khan Academy’s Pythagorean Theorem Intro(part1)

Pythagorean Theorem Intro (part 2)

## Model and Demonstrate

### PHET

When you don't have the resources for a full lab, try some simulations at PHET such as this one for graphing lines.

### Geogebra

Get creative with a graphing calculator or full interactive lessons at GeoGebra.  Here is a Geogebra tutorial on OER Commons that has resources for many topics in math.

### Desmos

Similar to GeoGebra is Desmos, which also has lessons for teachers with classroom management features as well as a versatile graphing calculator.  My opinion is that Desmos is a bit easier for the beginner to use -- the slope of the learning curve is not as steep. Desmos has classroom activities tutorials and tutorials on how to use their graphing calculator.

## Sample Lesson on Pythagorean Theorem: Model and Demonstrate

Using this Geogebra model show how the pythagorean theorem works. Play with the different sliders.  Feel free to jump into showing common “triples” and how they are similar triangles -- thus; proportional.

Or, you could use this Desmos Distance activity on a grid that incrementally walks the student to the pythagorean theorem.

## Whole Class Activities

Khan Academy:  Use the site’s search function to find relevant exercises and do problems as a class

### CK-12

Their flexible, online textbooks offer content in the following formats: activities, videos, audio, exercises, flash cards, text,and interactive graphs and pictures. Check out this full Algebra I Flexbook to get a feel for what you can use to engage the whole class in learning.

## Sample Lesson on Pythagorean Theorem: Whole Class Activity

Using the text and videos from CK-12 on Pythagorean Theorem work through the examples and watch the videos.  Lead a discussion about when it’s useful to use the Pythagorean Theorem.

## Small Group Activities

### Desmos

Desmos:  In pairs or triads, have students work on pre-designed class activities such as “Lines, Transversals and Angles.”  Desmos has many other activities to explore under “Desmos Classroom Activities” on their homepage.  These activities also have a wealth of classroom engagement and management tools for the teacher.

### PHET

Phet:  Once you make a free account, you get access to other teacher lesson plans and videos about how to implement the simulations in your classroom.  Even without an account you can access math simulations such as this Balancing Act simulation.

### Illustrative Mathematics

Illustrative Mathematics:  You can search for tasks by standard at Illustrative Mathematics and you will find activities such as 8.G.7 Running on the Football Field.  To find something useful, I highly recommend knowing the standards you are trying to meet, otherwise you will get too many hits and will have difficulty finding what you need.

## Sample Lesson on Pythagorean Theorem: Small Group Activity

Implement 8.G.7 Running on the Football Field from Illustrative Mathematics.

## Exercises

### Open-Ended

Make them open-ended:  Take exercises from any of the sites below or from textbooks and make them open-ended.  For example, ask students to make a word problem from 8n + 7 = 31 and to solve it by drawing a picture.  For an even more creative and engaging method for turning typical exercises into student-centered discussions and problem solving sessions, watch Dan Meyer’s “Math class Needs a Makeover.”

### OER Commons

OER Commons:  If you do a search on OERCommons based on the subject you want to teach, you will often find a variety of lesson plans, worksheets, videos and other resources that will help.

Khan Academy:  Once again, Khan Academy has math exercise for any math topic you would cover in an Adult Education setting.  Us the internal “search” in Khan Academy to find videos and exercises that you need.

### CK-12

CK-12:  Go to the exercises portion of the text.  For example, go to Pythagorean Theorem (Student Edition) and in the Table of Contents click on “4.0 Exercises.”

## Sample Lesson on Pythagorean Theorem: Exercises

A search in the OER Commons resulted in a handy worksheet from Madison Miller.  One option is to do half of it as a full class and then have partners do the second half.  If you think most people are understanding the concept, this could be done individually and utilized as a summative assessment.

An alternative would be to go to Pythagorean Theorem (Student Edition) and in the Table of Contents click on “4.0 Exercises.”

## Formative Assessments

### OER Commons

Check the assessments from lesson plans you find online.  Searching OER Commons is a good start to the process.  When I look through other lesson plans, I often don’t like the entire lesson.  I tend to adapt the pieces I like the most and then create the rest for my particular environment and teaching style.

### Kahoot!

Kahoot is an online platform for making quiz games for your students.  They can participate using any device, but it’s optimized for smart phones.  If you want a low-stakes, engaging game to see what student know, Kahoot is a good choice. (You will need to make a free account to search the collections for content or to make your own.)

## Sample Lesson on Pythagorean Theorem: Formative Assessment

Login to Kahoot with your free account and search for a Pythagorean Theorem quiz that has already been created.  Have students use their phones/laptops/devices to play at Kahoot.it where they put in your quiz code.

## Summative Assessments

### Mathematics Assessment Project

Mathematics Assessment Project Tasks.  Many are available in OER Commons

## Sample Lesson on Pythagorean Theorem: Summative Assessment

Use the assessment and scoring rubric about the Pythagorean Theorem from Mathematics Assessment Project