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!

The Amazing (Review) Race

For a final review in term two I decided to host an Amazing Race activity.  This review would use the TV show as inspiration to review concepts in the major content areas.

The students walked in to a dimmed room with the opening theme to The Amazing Race playing on repeat.  We watched a quick clip to help orient students that have never seen the show before and then I explained how it was going to work today.

• Students were on teams of three or four. 
• Each team was assigned a color and symbol.
• Clues for each team were in envelopes with their symbol. 

The Teams

Unlike the actual amazing race, the goal wasn't necessarily to be the first team to finish. Instead it was a point-based game where you can earn points for various tasks:

• Completing a route: 20 points
• Completing a road block: 15 points + points for creativity, quality, and originality
• Bonus points: 5 points each (given at the end of the match, similar to Mario Party)

Students were also told there were ways to lose points.  I really wanted to focus on them working together and using each other as a resource:

• Getting help from an adult or other team: -5 points
• Running or unexpected hallway behavior: -5 points
• If your group is split up / not together: -10 points
• Opening the wrong envelope: -10 points

We also talked about 'sabotage' and how it wasn't allowed (for instance, seeing someone else's envelope and moving or otherwise interfering with other teams.) 

That is a great haiku about China - but you didn't talk about the government... ROAD BLOCKED

After that I put them in their groups and said their first clue was in the commons.  They left the classroom, found their clue and the game began.  

We played a total of 4 route cards and one road block.  The route cards reviewed skills from all the major subjects that my partner teacher and I presented in term two.  To add to the game I bought some programmable padlocks from amazon.  Certain route cards led you to a locker number with a lock. The clue also had the combination to that lock embedded in the clue.  A few groups came up to me for clarification, but when I used the phrase, "is this an official asking for help question?" many of them chose to figure it out as a group rather than lose the five points. 

$10 on Amazon. Great purchase.

After the game was finished, students completed a reflection / feedback survey.  The results were very positive.  Students rated their partner's helpfulness at 3.2 out of 4, Fun rated a 3.3 out of 4 and 93% of students said they'd want to do this again.  It took quite some time to create this, so I'm glad that it went so well!

I really enjoyed this activity for a number of reasons. Students were encouraged to ask each other for help rather than asking a teacher. Only two groups asked a teacher for help throughout the entire game, and that was after they realized they all were stuck.  I got to incorporate a mix of topics - science, social studies, math, and language arts were all represented.  On top of academics, the social pieces - communication, team building, and all the skills that go with that were also emphasized.  I'll be excited to try this again in term three!