Let's Make A Deal!

 This week's game was also based on a television game show: Let's Make a Deal!  It is a review game that covers unit rate and leads into constant of proportionality. 

Students are given two choices (which eventually evolve to three or four choices) for which is the better deal.  They then use unit rate strategies to calculate which is the better deal based solely on math. This is an important filter. We actively discuss that in real life people think about other factors besides cost - taste, quality, and so on - but for our purposes, the only factor is the cost.

Students then calculate the better unit rate and explain in a sentence, using my model if they are having trouble wording an answer. 

I then wander the room and check work.  Students know I've picked a random student and that student needs to have their work shown as well as a sentence explaining which is the better deal including the unit rate.  

If students are correct, that is if the secretly chosen student is correct, they get the point. If not, teachers get the point. 

Generally students write in cost per item ($3 per pound, $2.29 per gallon.  When they calculate the cookies, they get 0.23, which they generally write as 23 cents per ounce for Oreos. When students calculate the problem above, they get 1.69/250 = .00676.  Students are often confused how to write numbers correctly when values get more precise than two decimal places. How does it get represented? It is a great question since we never (rarely) use this many decimals for money in real life.

What does .00676 mean?  Well, .01 is one cent, so this value is less than a penny per napkin... that seems to make sense; napkins aren't that expensive... so that means it is part of a penny per napkin. So we can write it as $0.00676 per napkin or we can round and say six-one thousandths of a dollar, or six-tenths of a penny per napkin. What we wouldn't write is 6.76 cents per napkin. We then establish a class agreement that the cent sign will no longer be used, and everything will be written in terms of dollars since that is the calculation result we would get. 

I show students this real image and ask, "If you were buying things from this toy bin, how many toys can you get for $5?"  Most answer 5 toys, since the cost is 99 cents each, which is about $1.  We then look at the photo in more detail and notice that it doesn't say 99 cents, but .99 cents.  This is read ninety-nine hundredths of a cent. This means each toy is less than a penny! 

We redo the math: $5 broken into $0.99 each would be 5 parts with a little left over.  But $5 broken into part of a cent each... $5 / .0099 = 505 toys!  What a bargain!  

Not sure who would need 2600 bananas for $5... but if you are looking...

Welcome to ... The Price is Right

Good morning, readers! Currently our eighth grade class is working on estimating the value of non-perfect square roots and placing them on a number line.  This is a difficult concept for many of our students as we are introducing them to the idea of irrational numbers. Additionally, many students have the misconception that the square root means "divide by two." 

To help with this, we play a game based on a VERY popular game show - The Price is Right. 

Here is how we play.  Students are given an imperfect square (such as 40) and asked to estimate the square root.  We have a double-number line tool card which was developed by a teacher at my school to help students visualize where they are on the integer number line. Using this card, they identify the two perfect squares that the imperfect square is between. They then decide which perfect square is closer to the imperfect square.  The initial goal is for them to identify if the imperfect square is larger or smaller than the half mark.

For example, if they had the square root of 40, students would identify the square root of 36 and 49, decide that they are closer to the square root of 36, which means the value is larger than 6 but less than 6.5.  We would get estimates that range from 6.1 to 6.4. 

Once we have done a few practice problems, the game begins!

I randomly call four students to the front with their tool cards. I play the music as they 'come on down' and then display the 'fabulous new prize'

It is the BEAUTIFUL square root of 10!

The four contestants then start their work while the 'studio audience' (other students) do as well. After 90 seconds or so, I have the students in the audience start calling out bids, much like the actual game show. Contestants up front can listen to the suggestions or stick with their answer. 

Each contestant shares their answer with me and I write their estimate on the board.  I then reveal the correct answer, usually to three decimal points.  Students then have to decide who is the winner - the person that is closest without going over. 

We do this for a number of rounds and the winner of each round gets to go into the showcase showdown at the end of class.  This determines our daily winner.

It is amazing how good students get at estimating values. At first they start with one decimal point but after some time, practice, and friendly competition, they start going out to two and three decimal points. 

This strategy and game has really increased our students accuracy as well as confidence. They never use a calculator during the entire lesson and are able to estimate the square root of imperfect squares with amazing precision!  The results of the final round are below: 

After the game, we do return back to the learning target - estimating the square root of non-perfect squares. It is important to return to this, because student "H" in the image above didn't win as they had an answer that was 'over', but all four answers met the target of the lesson.  It was a good day!

#MarburnCon21

This week got to experience the wonder of #MarburnCon21.  This virtual conference hosted by my school, Marburn Academy, focused on the theme of "Closing the Gap."  It brought together researchers from across the country as well as England and Australia to share the most recent best practices, techniques, and strategies to help students that learn differently or in non-traditional ways. 

What I really love about conferences is being able to take information from these experts and filter them into two buckets - what can I do to change my own classroom in the long term and what can I get from these presentations that I can bring back to the classroom on Monday.  MarburnCon21 gave me a good opportunity to reflect on my current teachings.

Day One

The Keynote speaker, Dr. Carl Hendrick, shared so many good thoughts. He reminded us that memories are built around schema - that words in context could have different meaning and memory depending on this schema. Vocabulary is built based on this schema and novices need lots of practice as well as explicit practice to build memories - much more so than people that have previous connections. 

Dr. Hendrick also talked about authenticity in four parts: Expertise in the subject, passion, unicity (the purposeful linking of the teacher's experience with students), and building rapport. 

One takeaway from Dr. Hendrick for Monday connected to feedback. The purpose of feedback is to improve the student, not the assignment. Improving the one assignment will not transfer, but improving the student has a stronger chance of transferring to the next activity. 

Another speaker that left an imprint on me was Dr. Sarah Powell. Dr. Powell spoke on helping students with word problems - a very important part of my everyday teaching world. She opened up with ineffective word problem practice.  When I say ineffective, I mean based on long term studies, not based in opinion. 

Dr. Powell shared that attaching keywords to operations in word problems is not an effective practice. For instance, teaching students if they see "all together" they should always add. What research has shown is that students will scan for numbers, key words, and then use the clues to solve the problem without reading the context.  She shared that in norm-referenced tests, key words led to correct answers between 25 and 50 percent of the time. With multi-step word problems (the type seen in late elementary to middle school) this accuracy dropped to less than 10%.  

Instead, we have to teach our students attack strategies and help build their schema to recognize how problems should be solved. Dr. Powell also shared a great visual for students in a round table discussion after her presentation.  

Day Two

Day two continued first with Dr. Erica Lembke sharing her knowledge of data based learning decisions. Much of her presentation fell into the bucket of long-term thoughts and how I could revise my progress monitoring on various skills and, more importantly, have students track their own growth over time. 

Her presentation was followed by an amazing language acquisition presentation by Dr. Pamela Snow. First, her dedication to helping educators was shown off by the fact she is located in Victoria, Australia, meaning she was presenting to us at 2:00 am local time.  Amazing.

Dr. Snow led us down a conversation of components of language including form, use, and content. She went into biological vs. non-biological forms of language, the explosion of vocabulary between ages five and eight, and the different tiers of vocabulary from everyday oral vocabulary (expression of feelings or needs) to general contextual reading (knowing words for comprehension), to lexicon in specific classes (hypotenuse, quotient.)  

I finished my MarburnCon21 experience with information from Dr. Amber Ray as well as Dr. Elizabeth Hughes. Both of them shared many ideas that I plan to incorporate into my lessons over the next few weeks. Dr. Ray spoke on SRSD as an approach to writing, while Dr. Hughes talked about the importance of precision of vocabulary in the classroom. Dr. Hughes had many connections back to Dr. Snow as well as Dr. Hendrick, and I reflected on how as a math department we have spent the past couple of years focusing on our vertical alignment of vocabulary.  It is a great feeling now when students join us in seventh grade and say, "I'm going to plus 5 and 9" and I hear a cry of "You don't plus numbers, you ADD them!"

Thank you to all of the organizers, presenters, and behind-the-scenes members that made this event possible!