Sunday, March 29, 2015

Exploring Surface Area

We spent a couple of days exploring surface area recently! We haven't done much with surface area in past years, so approaching this was new for me, a well as for the students. We started out with various shaped boxes (rectangular prisms) and I asked the students to visualize and then draw what the boxes would look like if they were taken apart and laid flat (without all the separate flaps and such). Most students took about 5 minutes to complete their drawings, depending on how detailed they chose to be, and for the most part, they did a very good job drawing their nets. They then spent a few minutes comparing their nets with their group members, deciding whether they were correct (even if they were drawn differently), and determining whether anyone appeared to be missing anything (some students did draw only five sides, and their group members were able to help them figure out what was missing).


After drawing their nets, the groups had two tasks - to find the surface area of their particular box and to determine a formula for the surface area of rectangular prisms. We have already studied area, so the only thing we discussed before they set upon their tasks was the actual meaning of the term surface area. So, they set off measuring (asking if they should measure in centimeters or inches - I said it was their choice) and calculating.
Most groups determined their surface area by the end of the class period, but none of the groups were able to decide upon a formula. We continued the next day, and while some groups were able to write a formula that reflected a correct understanding of the concept (though not written correctly "variable-wise"), others were stumped. Even though they were stumped about writing a formula, the "stumped groups" were able to explain to me HOW they had found their surface area. Most of them explained that they found the front and multiplied by 2 because the back is the same, and that they found the top and multiplied by 2 because the bottom was the same, (and the same idea for the sides), and then they added those three sums together. Other groups found the area of all six surfaces and added them all. One group found the area of the 3 different sides, added them and then multiplied by 2.  Based on our conversations, I know that they all had a correct way to find the surface area, but writing a formula was difficult. Some groups were very close with their formulas, but had to be guided toward naming the length, width, and height with different variables.



One group actually finished fairly quickly (correct formula and all!), so they then worked on determining the surface area of a triangular prism (I had a Toblerone box on hand to use)....they found that surface area fairly quickly too!


In the end, several groups wrote good formulas, which were shared and discussed with the class. The students really seemed to enjoy this activity - it was challenging but achievable:)  Giving the students the chance to explore the concept and to construct a formula based upon their understanding of surface area was a great use of class time!


Saturday, March 21, 2015

Fundraiser for Diana!

What happens when hundreds of wonderful TpT sellers decide that a fellow teacher is in need?
Click to see one of the fabulous bundles!
A MASSIVE fundraiser happens! That's what!
We call it Teachers Helping Teachers, and it came about after TpT teacher-authors heard the story of Diana Salmon, a New York teacher who lost a leg in a tragic hit and run accident.
Diana is an inspiration to all who know her, sending a message of strength and resilience by returning to the classroom just months after the accident.
Unfortunately, the extensive injuries Diana sustained require an expensive bionic knee for her to be at her dynamic best. This is where Teachers Helping Teachers comes in.
Diana's fundraising store, Bionic Teacher, is now the home of TEN limited edition resource bundles promising HUGE savings to all who purchase one. There is a bundle for everyone, and they all contain the most amazing products from top sellers! Best yet, 100% of the profits go to Diana's fund!
Visit Bionic Teacher, download the freebie for Diana's Story, and take a look at the bundles. You will be happy you did!
https://www.teacherspayteachers.com/Store/Bionic-Teacher


Friday, March 20, 2015

Learning to Love Math - Chapter 3

Chapter 3 - Examples of Differentiated Planning for Achievable Challenge

 I took notes on this chapter last week, on a bus ride to NYC (to see Aladdin!), but it has taken me until today to actually write this post:)

As the title of the chapter suggests, the author offers examples of differentiated planning and activities. In each example, students are learning the same basic concepts, but at different levels of challenge, which should lead to their maximum success and should minimize their frustration. There are several different examples, so I'll highlight a few in this post and the next.

The first activity, which involves working with shapes, is called "Draw My Shape," which the author says is a good activity for Map Readers. The steps for the activity are as follows:
1) pair student that have similar abilities in shape recognition and in naming shapes, OR pair a high mastery/low communication student with high communication/low mastery student
2) give each pair a set of manipulatives in a variety of shapes
3) the partners should sit opposite from each other with a divider between them so that they can't see each other's work
4) partner 1 gives verbal directions to partner two for how to draw a certain shape, and then the students switch
5) older students should be expected to use more descriptive, specific mathematical vocabulary.

A second activity involves estimating volume (with the goals of building estimation and prediction skills, adapting to new evidence, building math communication skills, number sense skills, and conceptual awareness):
The "low complexity" group follows this procedure:
1) the group is given a large pitcher of colored water
2) each group member fills an 8 ounce cup from the pitcher and predicts how high the water will reach when it is then poured into clear bottles that have different dimensions; students should mark their predictions with a marker before pouring and then discuss the result after pouring
3) student do the same thing with a second cup of water, making and marking new predictions before pouring

The "medium complexity" group, which the author labels as "Early Conceptual Thinking," does something similar to the first group, but they are expected to design the experiment themselves. They are given the materials and told that the goal is to make predictions, but are not given a procedure to follow. They are to keep group or personal records of their predictions, results, and explanations.

The "high complexity" group, labeled as " More Abstract Conceptual" would incorporate metric conversions and would look at the ounce markings on a measuring cup. In this case, students design  the experiment, complete it, and then pour the water from the 8 ounce into a metric cup. Students are expected to analyze, predict, test, adjust, and develop correlations about the relationship of cups, liters, ounces, and milliliters, as well as how to find conversion factors.

When finished, groups should share their findings with the rest of the class. Willis advises that homework should then be differentiated, based on the activities completed in class.

More examples next time...:)



Thursday, March 19, 2015

March Mayhem

Picture
Click to go to free bundle!
I have to be honest and say that I don't spend much time watching basketball (sorry!), but when some collaborators came up with a fun way to follow the NCAA Men's Basketball Tournament (AND offer some free products), I thought it sounded like a great thing to do! 

Our collaborative group, "Tools for Teaching Teens," (Brittany Naujok from the Colorado Classroom, Technology Integration Depot, Math Giraffe, Leah Cleary, History Gal, and myself) has put together a set of brackets to go along with the tournament! Each basketball team has been connected with a set of resources for middle school and high school teachers, and you can get some of these resource for free! Here's what you can do:

1.  For now, you can go here to download your free kickoff package.  The free bundle includes 6 resources, in different subject areas.

2.  Check out the "Mayhem" brackets here and root for your favorite items! (Some of these are high priced items from our stores).  When the tournament champion is crowned, the winning set of products will be made free to EVERYONE, not just one lucky winner!

3.  Follow our pinterest board for a many ideas and blog posts, all for teaching teenage students.

4.  Check out the links below to get acquainted with the whole "Tools for Teaching Teens" team!

5.  Remember to come back at the end of the tournament, to see which set of great resources made it to the end!  You will be able to access a free download of the paid items by re-downloading the original freebie bundle - at that time, it will be updated to include the winning paid resources!  May the best products win!



Click to download the free bundle!
 

Wednesday, March 18, 2015

Workin' On It Wednesday

Last Wednesday got away from me because I was workin' on watching Aladdin on Broadway! I almost forgot about today, too, because my son was scheduled for a root canal, so that was on my mind. Anyway, here is this week's Workin' On It Wednesday - I hope you will link up below!







Sunday, March 15, 2015

"Ace the Test" Test Prep Giveaway!

It's the test prep time of year, and there is a fantastic giveaway you can enter, to help you with your test prep needs! You can enter to win a Middle School ELA bundle, High School ELA bundle, and Secondary Math bundle. Click below either image to go to the giveaway.  Good luck!

Click to go to giveaway!


Click to go to giveaway!




Tuesday, March 10, 2015

Learning to Love Math -Chapter 2 continued


Chapter 2 - Understanding and Planning Achievable Challenge

Differentiating instruction is the key to creating  achievable challenges for students, through instruction, homework, multimedia support, etc.

In order to differentiate instruction, students' learning strengths must be understood, and Willis shares two general categories for students: Map Readers and Explorers. According to Willis, Map Readers like to work independently, and are most comfortable when they have specific instructions or procedures to follow. Map Readers have characteristics of the linguistic and logical-mathematical intelligence groups proposed by Gardner (1983), as well as learning styles of auditory, sequential, and analytic learners. They prefer problems with definite answers and procedures, they prefer new skills to be modeled by the teacher, process information in “parts-to-whole,” are comfortable with logical, orderly, structured approaches, and are good at using words to understand information, but may prefer written responses. They want to practice before sharing ideas and answers, appreciate early and frequent feedback, enjoy working independently and do not usually respond well to mixed-ability groupings. Map Readers take more time and work deliberately, showing all their work on homework and taking detailed notes.

Explorers are learners that want to skip instructions and jump into figuring things out with trial and error. Explorers share characteristics of spatial and bodily-kinesthetic groups and Gardner’s learning styles of global, big-picture, exploratory learners. They want to use their imagination, prefer discovery and exploratory learning where they can experiment, create, construct, and explore topics before there is direct instruction or modeling. These learners process information best when it’s introduced as “big picture” and then broken down; they use visualization memory strategies, enjoy choice and opportunities for innovation, find it helpful to draw diagrams, use graphic organizers, or make models and then add their own elaborations. Explorers recognize a pattern and then find thematic and cross-curricular links beyond math; they relate to inquiry projects that are open-ended.  Explorers work well in various groupings, and respond well to models or manipulatives that help see direction of instruction; they construct mental patterns to connect prior learning with new knowledge.

Using students learning strengths
To help find students' strengths and interests, Willis suggests introducing each new unit by offering the different categories of learners (Map Readers and Explorers) at least one, specific, targeted activity. You can then observe what elicits their interest and participation. She also suggests using interviews and written inventories to determine students’ interests and strengths.
Willis suggests using multisensory input - rather than lecturing and writing on the board, she suggests playing music at some point during the day, drawing diagrams, graphs, or sketches, and showing pictures or video clips, as well as offering hands-on experiences with manipulatives and using students to demonstrate concepts. For younger students, she suggests varying the presentation of information by stimulating several senses, like speaking in a rhythmic cadence, rhyme, or rap key phrase.

In attempting to differentiate instruction, it's important to avoid boredom. To avoid the stress of boredom,Willis states that teachers should limit excessive repetition once mastery is clear. For those students that finish quickly and correctly, teachers should have appropriately challenging or higher-level conceptual problems ready for them. This idea of too much repetition should be applied to homework as well – it is a turnoff and a stressor. Willis suggests individualizing students' math homework.
To help gifted math students show work (which is often difficult because they do it so quickly in their heads), give them more challenging problems that will require them to show the work in order to figure out the answer.

It is clearly difficult to individualize for all students and all lessons, so Willis suggests that teachers find their own achievable challenge in terms of differentiating for their students. Start by focusing on individualizing for just one or two students, or focus on trying one unit that engages students according to their learning strengths and interests. By doing so, she states that you will “stimulate and strengthen your own neuronal network for differentiating and planning for achievable challenge, and these approaches will become more and more automatic.”

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