Function Carnival

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Two years ago I taught 7th grade.  I wrote about how there was a disconnect between classwork grades and assessment grades and our class “town hall” type meeting to help me gain so understanding. (There’s a Disconnect). On of the biggest takeaways for me was how I helped students review for assessments. 

This school year, I’ve been very intentional about selecting interactive games and activities as well as create study guides which encompass strategies and ideas we discussed as a class. We’ve played musical chairs, Kahoot, Quizizz, a math version of Heads Up and many other things. As we prepared for our Unit 6 Introduction to Functions assessment, I wanted to keep our review engaging but also fresh. So, in a bit of desperation, late on a Thursday night I reached out for help https://twitter.com/mrsjenisesexton/status/824811795839856640

To my dismay, I was left to figure this one out on my own. This is what I came up with:


Identifying Functions Fun House. Similar to a fun house at a carnival where there are multiple mirrors all around, this fun house held multiple tables showing relations. The tables had to be adjusted so that each would reflect a function. All red cards were the x values and the black cards were the y values. 


A game of Clue. Students were given 10 different guess who statements. Based on the clues provided, they needed to identify the vocabulary word which matched the clues. 



Graphing Memory Match mixed the concept of a memory or concentration game with matching graphs to appropriate stories. Side note: students made this activity better by deciding to place all of the graphs on one side and all stories on the other. It helped with the flow of the game. 



Determining Rate of Change War. Using scenarios which compared rates of change, I created two stacks. One stacked is numbered while the other is lettered to avoid mixing the cards. The numbers and letters are ordered the same to ensure the scenarios matched one another. Students played in regular I Declare War fashion, the the card with the greater rate of change being the winner. 

Students were required to work with a partner to compete against or collaborate with another partner pair. This allowed for continued support to build understanding of the concepts within our Function Carnival. 

We Should Do This More Often

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Our last unit ended with a bang!  Unit 5 Pythagorean Theorem and Volume was opened with act 1 of Dan Meyer’s Taco Cart.  As with most 3 act tasks, this one began with the notice and wonder component. Students’ ideas exceeded what I expected. 




The blue notes the notices, the orange notes the wonders and the black were thoughts added during our discussion about estimations. 

We decided to answer “Who got to the Taco Cart faster?” but said we would come back to answer: are they going at the same speed, was one person running and will they get there at the same time?  The conversation around the estimation became intense. ​​​

​To prove our theories we used anglegs and color tiles to mimick the right triangle created by the path Ben and Dan walked to determine the length of the legs using the length of squares. Even as we were building a student kept repeating, “there has to be a part 2 to this, there just has to be”.  As students concluded the area of the legs combined or the path Dan walked was the same as the area of the square on the hypotenuse or Ben’s route, the excitement grew even more. 

Many thought their estimation of the guys getting to the cart at the same time was correct after the hands on activity. Others held on to the fact that time would play a key role in who got there faster. So I revealed the information for part 2. I love that many students had already developed a rate for the sidewalk to sand speed. Those who shared their conjectures believed the rate was 2 to 1. From the provided information it was determined it was 2.5 to 1. 

“I know you are not about to do this to us.”

Then I decided to press the pause button on the task. After students recorded the speed and distances provided on their recording sheet, I instructed them to put the papers in their porfolios to which a student exclaimed, “I know you are not about to do this to us!” Can you say completely hooked?!

We finished the day completing a practice task from Hands-on Standards:


The next day, students came in asking, “Are we doing Taco Cart today?!” Each time I told them, “No, but I promise we will finish it this week.”  The suspense grew and grew. Everyday they came in asking the same question. We worked through a few more concept development tasks from the GA Math Frameworks before returning to Taco Cart on Friday. 

Students had an opportunity to use everything they learned during the week along with the information obtained in part 2 to work out the problem and develop a conclusion. Some students remained stuck in estimation mode (which was disappointing) 


Others focused on using their understanding of the Pythagorean Theorem to form their conclusion but did not factor the time element:


While others were able to make the connections:


This was the best part:


After the screaming subsided, a young lady shouted, “that was intense. We should do this more often!”  

Musical Chairs

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We’re nearing the end of our unit on exponents and scientific notation. This means it’s time to prepare for our common assessment. What better way to do this than with a game of musical chairs. 👍🏾

Last year, I had the pleasure of attending a session at GCTM conducted by educators from Hart County, Georgia. They discussed engaging ways to implement practice in the math classroom; perfect for me as practice was my area of instructional weakness when I taught 7th grade two years ago. 

Musical chairs was one of the activities presented where you setup chairs in traditional musical chairs style. In each chair, a question is placed face down. The music is played, I used Keep Your Head Up, Good to be Alive and Run, and students circle the chairs. My 8th graders were gitty and circled the chairs in suspense of the music stopping. When the music stopped, the quickly sat down and began solving the problems in their seat. Once finished I would check their answer and offer feedback. We repeated this process over and over until class ended. 

Students played as if someone could be eliminated, one student continuously asked, “how do people get out?!”  I never answered mainly because I had not thought about that aspect. Students answered about 6 questions from their study guide, received immediate feedback and it would’ve been more if time had allowed. Everyone was engaged and excited. Everyone worked to answer the questions. 

Hindsight, take time to answer questions myself before the game to avoid solving them mentally during the game. Develop a way for students to get “out” but keep them engaged in the game. 

So I Tried Clothesline Number lines

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I was introduced to clothesline number lines through the #MTBoS.  I inquired more about it and was provided these resources (1, 2, and 3) by @mr_stadel.  After doing some research and making sense of the instructional idea for myself, I decided to try it.

We’re focusing on scientific notation, not just converting and operations but ordering and comparing.  On my first try with clothesline number lines I provided each student with a card.  I asked half of the class to record any number in standard form and the other half of the class write any number in scientific notation.  The goal was to order the numbers from least to greatest.

Students took about 90 seconds to place their numbers on the number line, sliding cards and shifting cards where they felt necessary.  As a whole group, we took a step back to analyze the cards and one student said aloud, “Which end is the least and which is greatest?”  I though to myself, great thinking and we briefly discussed how an empty number line can start and end with any number.  From that part on, while in the heat of the moment, I thought the lesson was an epic fail.  Students remained focus only on the order of the number in scientific notation and did not consider how they compared to the numbers in standard form.  As I tried to draw their attention to this oversight, I noticed some students began to check out of our discussion.  So I summarized our discoveries and moved on to the next activity.


Later as I reflected upon this activity, I noticed the beauty in the oversight.  Although students were able to convert between the two ways to represent large and small quantities, they had not yet been able to apply this understanding.  I also realized students did not have a full understanding of the magnitude of the number when written in scientific notation.  Perfect, I knew exactly what I needed to target!

On the high of the benefits of using clothesline number lines, I quickly developed a plan to present this within a professional learning session I was slated to conducted for other math teachers within my district.  This time, the focus concept would be expressions and equations.


Teachers said their biggest take-aways were:

  • ability to assess students’ number sense when using variables
  • ability to discuss equivalent expressions using the number line
  • connecting kinesthetic number lines to the clothes line number line
  • making the connection to solving equations using the clothesline number line

Many teachers committed to trying this idea within their classrooms within the upcoming week.

Put My Strategy Up There

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I have a habit of not saying anything a kid can say.  So when students present a strategy, even if it is the ultimate strategy I wanted to present, I give the student credit.  Here are a few examples of thoughts students have provided.  We can it their strategy and refer to their suggestions often.

 

 


It has become such a habit, when a student stated her strategy for converting a large number from scientific notation to standard form she yelled, “Put my strategy up there, I want my own strategy!”  And so I did.

Having Fun with Scientific Notation Part 2

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I can’t really say students traditionally struggle when using operations with scientific notation.  Some of my students were apprehensive about the concept as we transitioned from converting to computing.  Again the saving grace was beginning with the conceptual using base ten blocks.

Students were able to see the quantities being added having the same blocks like when we were adding (6 x 10^3) + (3 x 10^3) or related blocks like with (6 x 10^3) + (3 x 10^2).  The discussion of regrouping blocks to add unlike blocks went over well allowing a student to conclude this:

 

We used a combination of concrete manipulatives and virtual manipulatives.

By the end of the lesson a student stated, “Is it really that easy?  I thought scientific notation would be hard!”

Having Fun with Scientific Notation Part 1

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I’ve been enjoying my year teaching Introduction to Algebra.  This portion of Unit 3 isn’t any different as we are working with scientific notation.  Last year, I wrote a post about how teachers have traditionally discussed this concept in this post and this post.  Therefore, I wanted to do my very best at presenting this concept through the lens of place value understanding.


Our first activity was connecting base ten blocks, powers of 10 and decimal notation or standard form through the context of a number line.  Hindsight, this would have been a great bridge to implementing clothesline number lines.  What we actually did was create a human number line.  As we transitioned from concrete to representational, we constantly referred back to our physical number line and the equivalent values.


Looking at the numerical representation, students were able to identify patterns among the powers of 10 and exponents.  Beginning with base ten blocks made the transition to converting between decimal notation and scientific notation very simple.  We looked at 3 cubes and determined not only did they represent 3,000 but also 10^3 three times or 3 x 10^3.   We tried a few examples using the blocks we actually had before extending it out to the millions.

By now you may be thinking, how did we discuss exacting how to convert a number in standard form to scientific notation.  Of course the topic of the decimal point moving can up, mainly because students heard this terminology within their science class.  I used a draw place value chart to demonstrate how the digits shift and the decimal stays put.  Later, I was introduced with this site which helps to illustrate my point.  During our discussions, I would explicitly state when the digits shifted and how many spaces and connect it to a pattern previously identified by a student.

Another benefit of the base ten blocks:

3 flats is 3 x 10^2

6 flats is 6 x 10^2

9 flats is 9 x 10^2

10 flats is 10 x 10^2 which students were able to determine was equivalent to 1 x 10^3.  We were able to conclude is scientific notation is written with a whole number coefficient less than 10.  Students had a conceptual understanding of why it is a whole number less than 10.