(To be deleted at a later date)

2. Design and Develop Digital Age Learning Experiences and Assessments

Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating
contemporary tools and resources to maximize content learning in context and to develop the knowledge,
skills, and attitudes identified in the NETS·S.

a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote
student learning and creativity
b. Develop technology-enriched learning environments that enable all students to pursue their individual
curiosities and become active participants in setting their own educational goals, managing their own
learning, and assessing their own progress
c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources
d. Provide students with multiple and varied formative and summative assessments aligned with content
and technology standards and use resulting data to inform learning and teaching
EDMA 658 Math Maniacs: How to Integrate Differentiate Geometry Throughout the Grade Levels with Technology
Purpose:The purpose of the Math Maniacs page is:1) To design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity. 2) Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants setting their own educational goals, managing their own learning, and assessing their own progress. 3) Customize and personalize learning activities to address students' diverse learning styles, working strategies, and abilities using digital tools and resources. 4) Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching.


Grade 5/6: Using www.shordor.org to Differentiate How to Find the Volume and Surface Area of a Solid

Objective: To teach students how to find the suface area and volume of a solid object .

Standards: All standards are in regard to Alaska Standards for the fifth grade, and are as follows:

The student solves problems (including real-world situations) using perimeter or area by:

[5] G-6 estimating or determining area or perimeter of rectangles using a key, ruler, or given measures (M5.2.4)

The student communicates his or her mathematical thinking by

[6] PS-3 representing problems using mathematical language including concrete, pictorial, and/or symbolic representation; or using appropriate vocabulary, symbols, and technology to explain mathematical solutions (M8.2.1, M8.2.2, & M8.2.3)


Graph paper, Pencil, Eraser, Ruler, Stacking cubes (centimeter), Access to shordor.org website listed above


Introduce Situation:

We are going to construct real life 3d figures with these blocks. You will draw each face of your object, record the dimensions, calculate the surface area, and find the volume. You will then check your work by constructing a model on the webpage provided for you.

The student needs to:
1) construct a solid rectangular figure using their stacking cubes, 2) record the visual image of each side of the shape on the graph paper, 3) label the measure of each side to find the surface area of each side, 4) add all surface areas together to find the total surface area, 5) calculate the length x width x height of the solid figure.

Guided Practice:
1) Practice "playing" with the blocks, and describing the length, width, and height with each other, 2) review how to find the area of shape, and what surface area is, 3) review how to find the volume of an object, 4) ask students to watch the video below, and show them how to access it for later review as necessary.

Check for understanding by asking students to name specific lengths, widths, and heights of the figures they have designed. Ask them how they would find the surface area, and volume of their own shapes.


Students will work in partners to create their projects, draw their projects, and record the results on their graph paper. They will perform the necessary calculations to discover the surface area and volume. If the figure does not match the one they built or the calculations are incorrect they must trouble shoot where the error was made. They will then take the time to check their work by constructing figures with the same dimensions in the applet. Once the applet reports their dimensions are accurate they report back that they are done, and I will check their work via LanSchool remotely viewing their desktop.


Students will construct their own shapes, perform the necessary calculations (they must record a visual of the figures on the graph paper as well, just as before), recreate their figure in the applet, and print the screen once they are satisfied with their work. They will turn in the printout with their names on the page. If students have calculated the area and volumes correctly they have met the standards at a 3. If they are mostly correct they have met the standards at a 2. If they have failed to comprehend or show the concepts either on their graph paper or on the printout they have met the standards at a 1, and require further small group intervention.


Transformations in 3rd Grade

One important part of geometry in 3rd grade is learning transformations. Technology is very helpful in learning about slides, turns, and flips. The
Smart Board is particularly useful in doing quick lessons on slides and turns. You can make a shape, drawn or from the shape tool, and click on it. You can slide the shape in whichever direction would like. You can also turn it by grabbing onto the green circular arrow at the top of the shape when it is highlighted.

One outstanding resource that comes with the Smart Board is the Smart Exchange. It has an incredible amount of lessons to use on the Smart Board. I searched 3rd grade, mathematics, and typed in “slides, turns, and flips” and got several lessons. I also made the search narrower by asking for lessons that included the Smart Response question sets. The lesson I ended up with was excellent, but it did cost $3.99 from Onboard Academics.

First, it goes through explaining what slides, turns, and flips are with examples. It has short animations that shows each happening. Here is the animation for a turn. There were also ones for slides and flips.

Then there were a few questions to ask altogether. At the end, it had eight questions to be answered with the clickers.

I was really impressed with the clickers. I had to set up my class before hand, giving each student a number. They could use any of the set of clickers and type in their number. This will be their number for the year. As you can see below, when the questions were being answered, it showed how many had answered. If I wanted, I could click on the (show) next to “Who isn’t finished” and it would list out names of those who still needed to answer. This was helpful as the students were just learning the system and needed to know if they had put in an answer yet.

quiz shot.png

My favorite part is after the kids have done theirs. You can get all sorts of data from the answers they chose. For differentiation, this tool is outstanding because it can quickly and easily tell you who needs more help on certain topics. For example, I can tell at a glance of the graph below, that one student in particular needs more instruction on transformations. (I left off the key that had names paired with colors for confidentiality.)


I could also find out which questions were answered incorrectly. A very valuable tool is tagging questions. For example, on this question set about transformations, the questions could be tagged slides, turns, or flips. Then I could pull up data about those individually.

There are many different reports and graphs that can be made from the students’ answers.

I am so excited at the ease of the system and am looking forward to using it lots more!

Jennifer McCarty


Identifying geometric shapes in Kindergarten

Alaska Math Standards

[K] G-3. Geometric Relationships: The student demonstrates an understanding of geometric relationships by identifying triangle, circle, rectangle, and square (M5.1.1)

[K] G-6. Construction: The student demonstrates a conceptual understanding of geometric drawings or constructions by drawing, copying, or describing triangles, squares, rectangles and circles (M5.1.7)

Identifying geometric shapes seems pretty simplistic and basic. Kindergarteners learn the different shapes by using them in their art projects or by using pattern blocks to make designs. Learning comes from personal experiences. Technology is just another way to give students the exposure they need to learn in a different way. One way that I use technology is with my Mimio interactive white board. Using the Mimio notebook is a lot of fun for my class. It helps keep their attention and gives them a variety of ways to learn. I use the MimioConnect.com to get a lot of ideas for my lessons. Sometimes I don’t have to create a lesson because someone already has made one. I can just download it and use it immediately.

After students have practiced and played with shapes, I like to give them an assessment on what they know. I recently learned how to use Mimio Voters. It is another piece of hardware to go along with the Mimio Board. The students think its another game that we can play. Plus, everyone gets to do it at the same time and no one has to wait their turn. I created a math class using Mimio Gradebook. I assigned each student a number. When it is time to play a game, the students can grab the voter that has their number on it. When the assessment is given, the Mimio voter sends the scores to the grade book! No need for me to grade papers. The following video is an example of how Mimio Voters work.

Mimio Vote is connected to the gradebook as stated earlier. I can see who has the basic idea of shapes and those who do not. This is a very fun activity for the students. They love to see the results from their "test". They always want to get 100%. They cheer and shout when everyone gets the correct answer. But, we also take time to see what happened when someone chose the wrong answer. I like it because none of the students can see who got the wrong answer, but everyone can help explain why the other answer was the correct answer.



Shape Exploration/Manipulation
Shapes are an integral part of geometry kindergarten students encounter and are required to understand by the time they enter first grade. At the very least they expected to be able to name basic shapes regardless of their orientation in space. They are required to know that a triangle is a triangle regardless of how it is rotated, enlarged, shrunk, or moved. Furthermore, they are required to be able to differentiate between shapes based upon the characteristics of the shapes.
Teaching kindergarten students shapes has to be engaging in order to maintain their short attention spans. Therefore, it is vital to vary the manner in which it is taught. Using manipulates might engage students one day and carry little interest to them on the next. One medium that never seems to get old or dull for students however, is technology. The use for technology is far reaching, even at the kindergarten level. One such technology tool I found that could be useful in teaching shapes is Graphics Toolbox, which is a software program that allows users to create, manipulate, color, move, resize, and ultimately explore shapes!
Below is a lesson that does just that with kindergarten students, explore shapes.

Grade Level: Kindergarten

Lesson: Shaping Up

Alaska State Standards:

K.G.1 Describe objects in the environment using names of the shapes and describe their relative positions

K.G.2 Name shapes regardless of their orientation or overall size

K.G. 5 Build shapes and draw shapes

K.G. 6 Put together two-dimensional shapes to form larger shapes

Technology Standards:

A2: use technological tools for learning, communications, and productivity

E2: discriminate between responsible and irresponsible uses of technology


Students will be able to identify four basic shapes: triangle, rectangle, square, and circle

Students will be able to create, manipulate, resize, color, and alter shapes.

Students will be able to use the computer to create and manipulate shapes.

Students will be able to work with peers to create shape people.

Teacher Instructional Materials:
Document Camera
Shape cutouts
Shapes Toolbox Software

Student Materials:


Students who may have difficulty understanding the context of written language or oral directions for the assignment will have their needs met through alteration of words/language or presentation of the content.

Students with vision or hearing problems will be placed closer to the teacher to ensure their needs are met.

Students who are having or who have behavior issues will be placed closer to the teacher so they focus on the lesson.

Instructional Sequence

Anticipatory Set:
As students enter the group meeting area have the following shapes displayed on the document camera: triangle, rectangle, square and circle. Ask students to turn to a partner to discuss what these things are on the document camera. When they finish they can share out their thoughts. They should hopefully discuss that these are shapes!

Activate Prior Knowledge:
Access the prior knowledge of students about shapes by asking the following questions:
What is a shape?
Where have you seen shapes before?

Introduce vocabulary: triangle, rectangle, and circle
Give examples of each

Teacher Modeling:
Introduce Shapes Toolbox software
Demonstrate how to create a triangle, rectangle, square and circle
Demonstrate how to use the tools on the right side to add color to each shape, move each shape, and alter the sizes
Show students how the tools assist in the creation of a shape person

Guided Practice:
Invite a few students to come up to the computer to demonstrate for their peers how to interact the shapes toolbox software to create shapes and to change the color.

Independent Practice:
Pair students up and have students go to a computer, collaborate to create shapes using shapes toolbox, create different colored shapes, and manipulate their shape creations with their partner. Encourage students to change the colors, change the size, and move their shapes about the computer screen.

With their partners have students create shape people using the shapes toolbox software. Since there are two in each group, have students create two shape people, one for each. When they are finished and satisfied with their creations have groups save their work and print out the finished product. With the finished product they can then share out with other groups how they created their shape people.


The work they would be printing would give a glimpse into their understanding of shapes. In addition to this I would bring student’s attention back to the document camera where I would display various images and have them discern whether they were shapes we were learning about or not. For example, I would display a frog and they would give a thumbs up or thumbs down to let me know if it was one of the four shapes we were learning about. I would do this with 15 images to make sure they had a grasp on identifying rectangles, triangles, squares, and circles by sight.

Robert Dean Meili

Tech For Teachers
Assignment 2: Design and Develop Digital Age Learning Experiences and Assessments
Robert Dean Meili
8th Grade Pre-Algebra

For this assignment, our group chose Geometry, and my portion will be on Pythagorean Theorem. I wanted to find ways for students to use smart phones to not only engage themselves in the class, but begin to take ownership of their learning. Whether we like it or not, we are a smart-phone-using society and though they’ve historically been problematic in the classroom, their benefits far outweigh their drawbacks, which can be managed with few easy strategies.
I’d like to begin with a few things that help students take ownership of their learning environment. The first is making a shared list of notes on Google Form. My students enjoy the use of their notes on a test, so are happy to take notes during a lesson. I like to model taking notes by doing it on the Smart Board (whiteboard). Students and parents will have access to this through the teacher’s webpage, which has the form embedded. The page could also be a place for students to post links to videos and websites for the unit we happen to be working on. The final bit of ownership will be the use of FaceTime for students who are absent. Very often students are absent due to illness, but still have access to the web from home. Parents will very likely be thrilled that their child has access to the classroom via the web. This can be done by setting up any of the laptops from any of the mobile laptop carts in the classroom and making it face the area from which I teach the lesson (usually the front of the room in front of the Smart Board).
Students who have smart phones will load the free app “Boss T Math’s Pyathgorean Theorem and It’s Converse”. This is a simple and engaging app that teaches Pythagorean Theorem and includes exercises. After the student completes the exercises, it gives a percent of mastery. The cool part of this (besides that it’s free and reasonably fun to do) is that the exercises are different every time the student opens the app. This allows the student to improve over time.
Assessment of this concept is a typical test or quiz administered during class.
I’ve been incorporating the use of smart phones in my classes for several months now with positive results. However, this is a tool that must be managed. My students have developed a rule that is easy to follow, and will keep them from losing their smart phone privilege: No texting.
I didn’t come up with this rule. When I asked the students from each class period what might be the number one reason for loss of this privilege, they responded with a unanimous ‘texting’.
The school has a frequently abused policy against the use of cell phones during school hours, so they get satisfaction from ‘secretly’ using it during math class.

Alaska State Standards
M2.3.3 Use a variety of methods and tools to construct and compare plane figures.
M2.3.4 Describe and apply the relationships between dimensions
of geometric figures to solve problems using indirect measurement; describe and apply the concepts of rate and scale.
M5.3.1 Identify, classify, compare, and sketch regular and irregular polygons.
M5.3.6 Use coordinate geometry to represent and interpret relationships defined by equations and formulas including distance and midpoint.

Technology Standard
A: A student should be able to operate technology-based tools.
C: A student should be able to use technology to explore ideas, solve problems, and derive meaning.

Alice Kangas
Grade 9-12th


Many students do not have enough experience with angles when, at the beginning of a geometry class, we tell them how to use a protractor. Students find this difficult because they most of time they do not understand what they are measuring.

  1. Students will be able to understand angle basics.
  2. Students will be able to measure and classify angles.
  3. Students will be able to construct angles.

Student involvement:
1. To use their account on Khan Academy to improve their mathematics skills by setting and tracking their goals for learning about angles,
2. Work through geometry labs 1-5

Teacher (and/or parent) involvement: track students learning, guide students to lessons and units to help them achieve their goals

Materials needed: pattern blocks, templates for the labs, calculator, a compass, a ruler, a protractor, assorted types of paper: unlined paper, graph paper, and grid paper, and computer. An Ipad, Ipod, and/or smart phone can be used too.

Knowing about geometry will help you in many ways. Any time you read a map, loot at a floor plan for a house, or set up a baseball diamond, you are using the basic idea of geometry. Every day, carpenters, graphic designers, architects, engineers and many others use geometry in their jobs. In what ways do we use geometry in the Inupiaq culture? How do we use angles is our culture?
Teacher will use smart board to go through angle basics and terminology.

Activity 1: Students will work in groups of 2 or 3 on these hands-on labs.
Geometry labs 1-5
  1. Angles around a point
  2. Angle measurement
  3. Clock angles
  4. Angles of pattern block polygons
  5. Angles in a triangle
Teacher will be walking around the classroom-helping student when needed.

Activity 2: Khan academy
Log into their Khan academy accounts and go to Geometry and select angles
Students will watch the videos and work on problems all about angles. Students can spend as much time as they need on each topic about angles. The teacher can keep track of their progress because he/she is assigned as a coach.

Activity 3: Depending on if the student has an ipad, ipod and/or smart phone they can download some geometry apps:

Video Geometry Tutor

Video Geometry Tutor brings geometry class to your smartphone or tablet. Offering more than 80 videos in 15 different categories, you can find a refresher course on nearly any geometry topic. The videos have been designed with teens in mind and are focused on making geometry instruction a little more interesting and engaging to help students understand some of the more difficult concepts.

HMH Fuse Geometry

With the HMH Fuse Geometry app, students get help exploring geometry concepts and are presented with real-life problems to help build their knowledge and skills. Included in the app is a place to work out problems and multiple images to help illustrate important concepts. The app also connects geometry skills to other areas of math, such as algebra and statistics to help students really understand math as a whole.

Geometry Stash

Geometry Stash is a must-have app for students who need to brush up their knowledge of geometry terms or a handy reference guide to consult while doing their homework. Each term in the guide is illustrated and contains a detailed description. The app is designed to allow students to quickly find the terms and information with alphabetical lists and a handy search feature.

Pocket Geometry

Pocket Geometry serves as a geometry calculator for your smartphone or tablet. The app is designed to calculate measurements such as perimeter, area and volume of nearly any shape. It also calculates measurements for tricky 3D shapes and provides visual images to help students understand concepts.

Math Geometry Standards:
GCO.1. Demonstrates understanding of key geometrical definitions, including angle, circle, perpendicular line, parallel line, line segment, and transformations in Euclidian geometry. Understand undefined notions of point, line, distance along a line, and distance around a circular arc.
GCO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
GCO.12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
GSRT.6.Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
GMG.1. Use geometric shapes, their measures, and their properties to describe objects.
Technology Standard

A: A student should be able to operate technology-based tools.

C: A student should be able to use technology to explore ideas, solve problems, and derive meaning.
Hands-on assessment of the building of geometry angles with geo boards, pattern blocks and/or the computer. Each lab activity has several discussion questions to be answered. Khan academy keeps track of how the student is doing on the goals he/she set for themselves. Of course there will be a test similar to a standardized test so the high school student will be prepared for the SBAs and HSGQE.
Extension for high achieving students:
Lab 6-10: materials needed: circle geoboard, circle geoboard paper, cardboard, soccer angles worksheet, soccer circles worksheet, scissors and straight pins
  1. The exterior angle theorem
  2. Angles and triangles in circle
  3. The intercepted arc
  4. Tangents and inscribed angles
  5. Soccer angles