Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Wednesday, 2 May 2018

CSI Meets Newton's Law of Cooling

Creating scenarios that allow students to use skills and knowledge to solve real world problems is a great way to make learning stick. Our Advanced Functions (MHF4U) class did this recently through an activity where they played the role of detectives examining a crime scene.

Students worked in teams to solve the puzzles
Students were divided into three teams, assembled in one of our breakout rooms and given a puzzle to solve in three stages. In the first stage, students worked together to use prior knowledge to solve a series of exponential and logarithmic functions. Once they had these answers, they used them and Newton’s Law of Cooling to determine the time of death of the body found at the crime scene.
 
The timer counting down added excitement to the activity
With the correct time in hand, three members of the team escaped from the breakout room to find a website URL that had been hidden in the classroom. Once the site was located, the remainder of the team left the breakout room and together the team used graphing software to create a function that reflected the function related to the time of death.
Each team worked in a separate breakout room
Rich performance tasks like this one enable students to develop valuable critical thinking and problem solving skills, and learn how to work effectively in teams, all of which are vital skills for the future.

Monday, 27 November 2017

Supporting Self-Directed Learning


Giving students opportunities to self-direct their learning within the classroom is a tremendous way to enhance student engagement and confidence.
Most of our high school math classes use an approach that allows students some choice in how they learn. Students can work individually using an online lesson prepared by Greenwood teachers or in small groups.

Some of our math classes are co-taught, which means there are two teachers in the room. This approach allows students to get direct instruction from one teacher, while the other teacher facilitates group learning. This approach is effective, as students use class time efficiently and learn in a way that meets their individual needs.


According to our students, having input into how you learn makes learning engaging. Our alumni tell us that this approach equips them with the high level of independence required to succeed in postsecondary studies.


  

Thursday, 1 June 2017

Drawing Conclusions in Advanced Functions

The CN Tower was one image students could choose to recreate with the graphing
software Desmos.

Math has lots of applications, but you may not have known that drawing pictures was one of them.

A big part of truly understanding mathematical functions is understanding what they look like. How does an adjustment to a function affect how it looks on the page?

Our Grade 12 Advanced Functions classes recently got more familiar with visualizing functions by doing something you might not expect: drawing. Each student was challenged with replicating one of several existing sketches in the graphing software Desmos using functions alone. Students applied their knowledge of what each function looked like to get just the right series of lines and curves to create images from butterflies to the CN Tower.

“We used this as a fun assignment last year, and the students not only enjoyed it, but found it to be really valuable,” says Advanced Functions teacher Megan Clark. “We formalized the assignment this year as a great way to get students more comfortable with visualizing functions.”



One student chose this especially complex "extension" image for her project (and she
made sure she didn't miss any of those eyelashes!)


The project is the perfect lead-in to the class’s upcoming short culminating evaluation. Each student will create a roller coaster path, but this time they’ll do it algebraically.

As Megan explains, the drawing assignment also allowed students to group themselves by readiness. “Each student chose a ‘Level 3’ or ‘Level 4’ image to replicate,” she says. “They then had the option to add difficulty to their chosen picture based on their comfort level. For example, some students opted to add more complex functions to their pictures.”

No matter which image they tackled, students were excited to take on this new challenge. One student even affectionately named her function-elephant “Peanut.”

“Everyone was really into it!” Megan says.


This student even took the time to graph out her elephant's name.



Thursday, 30 March 2017

Disaster DIY

After reading a book about a natural disaster, students teamed up to help their novel's
main character survive his or her ordeal.

Your town has just been devastated by a massive earthquake. The phone lines are dead, there’s no running water and supplies are running out fast. All you have is a few household objects and your ingenuity. How do you make it out alive?

Our Grade 7 classes tackled this tough question through a week-long integration project from March 6-10. After reading one of three books by Canadian YA novelist Eric Walters about a natural disaster - an earthquake, a tsunami or a flood - students teamed up to help their novel’s main character survive his or her ordeal.

To be successful, students had to draw on knowledge from four core subjects:

  • Science: Students invented a survival device that helped the characters purify drinking water, keep warm and dry or signal for help.

  • Math: Students used mathematical reasoning to predict how long the device will help the character survive until assistance arrives. (One group created a giant air bubble and did detailed calculations to determine how long that oxygen would last!)

  • Social Studies: Students needed to understand the specific characteristics of the area where the disaster took place, and to understand how humans acquire, manage and use natural resources based on their environment..

  • English: Students produced an oral or written explanation of how their survival device works, as well as a series of journal entries written from the perspective of their novel’s main character.

Students used a design thinking approach throughout this process: understanding what the end user needs, making sense of their research and resources and generating ideas and prototypes. By using design thinking, students learn that the process of trial and error is a good way to solve problems.


To work collaboratively students need space. Our learning community classrooms are not
only spacious but allow lots of flexibility.


What Did Students Invent?


Students’ creativity shone through in the wonderful use they made of their available resources. Some examples of devices include:

  • A water purifier made from a plastic bottle, coffee filters, curtains, sticks and a plastic bag
  • A giant “Help” sign made from glow sticks
  • A canopied raft made from debris and a tarp


How Did Our Expanded Building Support This Integrated Project?


To work collaboratively students need space: ample room to meet in small groups, spread out their materials and build their prototypes. Our learning community rooms fit the bill perfectly: they’re not only spacious, but their flexible furnishings allowed students to configure the room in the way that worked best for them. Our teachers also had plenty of space to circulate through the room and support teams as needed during work periods.

Our performance theatre also played a key role in the project. Its drop-down screen allowed the Grade 7s to view multimedia materials and go through short lessons as a large group. When it was time to present their projects, the theatre provided an ideal venue for this activity.


When it was time for Grade 7 students to present their finished prototypes, our
performance theatre provided an ideal venue.


Student Feedback


What did students like most about this project? Here’s what a few of them had to say:

“I liked that the whole week was connected to one main idea. I was really proud of our final product, because it worked and we had a clear view to why we made it.”

“I enjoyed using different ideas to help my character and put myself in the character's shoes.”

“I enjoyed going to different rooms and learning about survival if you were caught in an earthquake.”

“I’m proud of the final product because even though we disagreed at the beginning, we came together and worked through it, resulting in an awesome prototype.”

Thursday, 1 December 2016

Apprentice Teacher in Action: Kelly Murphy

As an Apprentice Teacher, Kelly Murphy has many opportunities to work one-on-one
with students during class time.

Greenwood’s year-long Apprentice Teacher fellowship is an induction program for qualified teachers who have recently graduated from a teacher education program. Working alongside an experienced teacher, Apprentice Teachers further develop classroom management skills, strategies that support personalized learning, technology integration and assessment strategies. These teachers also have opportunities to support Greenwood’s mission through coaching in the school’s athletic program and supervising our weekly Service Learning program in Regent Park.

There’s no better way to learn these skills than with hands-on experience. For Apprentice Teacher Kelly Murphy, her experience supporting Christine Joannou’s Grade 7 math classes has already been valuable.

“I get to focus purely on teaching, and on developing relationships with the students,” Kelly says. “I’m also learning a lot of classroom management skills - a big part of my role is understanding how I can help each individual student to get the most out of every class.”

Apprentice Teachers hone many valuable skills during their year-long fellowship,
including classroom management and assessment strategies.

Kelly has many opportunities to work with students one-on-one during class time. “If a student has a question while Christine is teaching, they can quietly ask me on the side without stopping the lesson,” she says. In cases where Christine is away, Kelly leads the class. “It’s wonderful to have opportunities to teach where I’m so familiar with the material,” Kelly says. “It’s also great for the students, because they’re working with a teacher who knows them really well even when Christine can’t be there.”

For Christine, having Kelly in class has been very positive. “Grade 7 is a year where students are building so many of the math skills they’ll need in high school and beyond,” Christine says. “Having Kelly’s support helps ensure that every student develop confidence and a strong foundation.”

Friday, 14 October 2016

Adding Flexibility to Advanced Functions

Math teachers Megan Clark and Kelly Smolinski used the flexible features of one of
our Learning Communities to allow greater customization in Advanced Functions.

A key piece of Greenwood’s customized approach to learning is giving students the power to choose how they learn. Some students prefer a teacher-directed lesson; for others, an online video lesson, which allows them to self-pace, is most effective. This knowledge inspired the design of Greenwood’s new Learning Communities - flexible rooms that easily reconfigure to support many different types of instruction.

Choice in Grade 12 Advanced Functions


Math teachers Megan Clark and Kelly Smolinski recently made excellent use of one of our Learning Communities to support their Grade 12 Advanced Functions class. After a “warm up” activity, students had a choice: they could continue with a teacher-directed lesson from Megan, or do a self-paced lesson through an online video. Based on their choice, students dispersed to three different locations in the room:

  • Those listening to Megan’s lesson remained at the front of the room.
  • Students who wanted to complete the video lesson in a small group chose one of the breakout rooms, where the sound wouldn’t interrupt the teacher-led lesson.
  • Students who wanted to complete the video lesson individually headed to a small nook by the window, where they used earphones.

The Benefits of a Bigger Space


Both teachers allowed these options in previous years, but co-teaching in a larger space with flexible furnishings offers Megan and Kelly even more opportunities to customize lessons.

“While Megan taught, I frequently checked in with students who chose the self-paced option, answering their questions and clarifying concepts,” Kelly says. “This resolved the issues that may have come up in the past, when it was more difficult for a teacher to answer questions from self-pacing students because they were also teaching a lesson.”

Thursday, 26 May 2016

Integration Projects Offer a New Take on Culminating Activities

Final evaluations are fast approaching, and the Grade 7 & 8 Integration Team is hard at work developing a second round of interdisciplinary integration projects. Each grade will participate in a four-day task designed to provide an authentic opportunity to apply a year’s worth of subject knowledge and skills to a real-world problem. (Read about the first Grade 7 and Grade 8 Integration Projects.)


As subject teachers, we have always been encouraged to create culminating tasks that would have students play a role and apply their subject knowledge to make real-world decisions. These integration projects are a perfect opportunity to take these individual subject role-playing tasks to the next level.

This second round of integration projects are designed to primarily assess skills and learning from the year, rather than teach new content. The development of these culminating integration projects therefore present their own unique set of strengths and challenges. There is more time within the schedule for students to focus in on their task, since less time is allotted to teacher-facilitated instruction. 


The actual project design has been more challenging this second time around. Our goal is to develop an authentic problem that requires a year’s worth of subject knowledge and skills, touching upon essential learning from at least four different courses. All of this while remembering, of course, that the problem-solvers are Grade 7 and 8 students - not yet ready to take on the complex problems that actually do require this level of integration. “Please draw upon your understanding of science, math, social studies and English to solve the problems in the Middle East.”

As teachers, it is causing us to reflect upon the curriculum in our own individual subjects in a new way. We are asking ourselves questions such as “If it is difficult to find a place for a particular concept or skill within a real-world, integrated project, how essential is it to begin with?”.

As we reach the final stretch, we are excited to see these culminating projects in action.This first year of Grade 7 and 8 projects have certainly be making all of us, teachers and student alike, think and reflect in new directions.

Samantha Moser
Grade 8 Science Teacher

Thursday, 21 April 2016

Grade 7 Integrated Project: Designing for Disaster


Shannon, Megan and Taylor with
their disaster survival prototype.
In March, Grade 7 students were challenged to ‘Design for Disaster’. The students’ goal was to use their scientific knowledge and understanding of resources to design a device that would allow their literary character to survive a natural disaster.

In the process of completing their prototypes, students were challenged to integrate subject knowledge, think creatively and develop their teamwork skills.

Students had the opportunity to create diverse products that covered several curriculum expectations. Project tasks were designed to provide appropriate structure, while being open ended to foster critical thinking and capture student interest. Students could choose how they demonstrated their design process, what they built, what supplies they used and even where they worked.

Choice served to empower our students’ thinking and creativity. Taylor Davis ('21) commented that “getting to be creative and build things without a written plan pre-given” was really rewarding. While reflecting on connecting her school subjects in one project, Zoe Starnino ('21) stated that she “really liked doing all of the science and math parts because it was kind of like you were solving a mystery, or going on an adventure, and you just kept discovering all these things”.

Learning should go beyond curriculum. A collaborative approach to design thinking was used throughout the week. This allowed students to learn from each other, as well as problem solve in a team.

Working in teams was a highlight for many of the students. Toby Bower ('21) stated that “sometimes we didn’t agree”, but as the project progressed they enjoyed  “coming together as a group”. Callum Thomson ('21) thought “it was really fun working with the same people. Splitting the jobs up worked really well for us because we got the work done quickly.”

Students experienced successes and failures throughout the week. While no two groups took the same path, all students realized their design goals in creating final products they were proud of.

Students and teachers are looking forward to the second Grade 7 Integration Project in June!

Elysia Jellema & Erin Klassen
Grade 7 & 8 Teachers

Thursday, 11 February 2016

Leveraging Technology to Monitor Student Learning & Streamline Assessment

Hapara allowed teachers to reinforce
positive behaviour and promote
digital citizenship through encouraging
collaborationon shared documents.
In December, Grade 8 students immersed themselves in Toronto City Council business and municipal politics with proposals to improve City of Toronto drinking water treatment. We were able to leverage Hapara, an online education platform, throughout the project to help improve student learning and streamline teacher assessment.

Throughout the learning process we shared templates and resources with students in their Integrated Project Folders on Hapara. Students used these same folders to develop their ideas and create their proposals. All Grade 8 Teachers had access to the folders and we could monitor individual progress to prompt deeper learning and identify students who required additional support. This technology also allowed us to reinforce positive individual and group behaviour, and promote digital citizenship through the collaboration process with shared documents.

Once the Grade 8 students completed their final proposals to the City of Toronto and presented their ideas to City Council, the integrated project was complete. Each student’s proposal included curriculum expectations for mathematics, English, Canadian Social Studies and science. Teachers worked together to mark the final products. Hapara significantly streamlined the assessment process as teachers from different disciplines could efficiently access students’ products to mark the appropriate curriculum expectations.

In the integrated project, students created products that examined a social issue with improved breadth and depth by looking with different subject perspectives. The careful design and implementation allowed curriculum expectations from four disciplines to be effectively addressed. Using technology, we were able to help ensure each student was supported and challenged throughout the process, and student products could be efficiently evaluated.

Elysia Jellema
Grade 7 & 8 Math and Science Teacher

Erin Klassen
Grade 7 & 8 Math and Learning Strategies Teacher

Want to read more about our Grade 8 Integrated Project? Read a student's perspective and a teacher's perspective.

Thursday, 21 January 2016

Grade 8 Integration Project: The Student Perspective

Group work was a major component
of the Integration Project.
Last week, teacher Kathryn Connelly shared her thoughts on our Grade 8 Integration Project. This week, Grade 8 student Graham Palmert provides his perspective on the same project.

During the week before the December holidays, the Grade 8 students were involved in an Integration project which drew from our four core subjects; math, English, science and social studies.

Each class contributed to a different aspect of the project. The beginning of the project was related to science and social studies. We had to pick substances or elements, such as fluoride or lead, and explain:

  • How the substance gets into our water system,
  • How it affects us, and
  • Ways to solve this issue. 

For English we wrote a final proposal, which outlined the research behind the issue we chose, how the issue affects humans, and potential solutions.

In relation to math, we completed a data analysis.

All of the subjects blended really well together and we required knowledge from all of them, such as:

  • Knowing the water system,
  • Taking data and turning them into graphs, and 
  • Knowing human settlement patterns. 

Each group chose their own topic to explore, such as how microbeads affect the water systems in Toronto. My group, which included Owen Bates and Jackson Cowie, learned about where lead comes from, how it affects us, and solutions to solve the problem of lead in our water system.

The two most astonishing facts that we learned were:

  1. Next year, the World Health Organization estimates that 143,000 people will die from lead poisoning.
  2. Lead pipes themselves elevate the risk of health issues for Toronto 35,000 households.

This project was a change from a regular classroom that provided different challenges. One challenge we faced was balancing working in a group, and dividing up how much each person had to do. The project itself was more challenging than the regular classroom work we are used to because we had to use knowledge from all four subjects instead of just one.  It was also different than a classroom because the whole week we worked in small groups, and I usually do not have class with some of my group members.

The final product had two different components:

  1. A proposal on what the problem was and how we can fix it. 
  2. A visual component. Our group decided to make a Google slides presentation on how lead affects us. Other groups used videos or poster boards. 

Upon completing the project, we showed our work to a Toronto city councilor, Jaye Robinson. Hopefully she will consider our ideas and make our water cleaner.

This was an interesting week for me as a student, which I thoroughly enjoyed. Take aways from the week were that Toronto’s water isn’t as clean as everyone thinks it is, and that working in a group requires a lot of patience.

Even though it was difficult, at the end, I think we all felt rewarded for the hard work that we had accomplished.

Graham Palmert
Grade 8 Student

Thursday, 14 January 2016

Grade 8 Integration Project: The Teacher Perspective

This December, Greenwood piloted a unique project for Grade 8 students: an integration task involving math, science, social studies and English components. This problem-based learning activity requiring the students to look at a water issue in the city of Toronto and examine how this issue has either impacted human settlement OR is impacted by human settlement.

How did this project go? Teacher Kathryn Connelly shares her thoughts. Next week, we'll bring you a student perspective on the same project.

The Grade 8 Integration project took flight on the week of December 14-17, 2015, with great success!

The Project


Students` visual and verbal presentations
highlighted their proposed solutions for
the water issue they studied.
The students were introduced to the project by going on a field trip to the RC Harris Water Treatment Plant. They took a tour of the facility and learned about where our water comes from, how it is treated, and what Toronto’s challenges are in terms of water treatment.

Back at school, the students were placed into small groups and were presented with a problem statement: How does human settlement impact the physical environment and sustainability of water resources in Toronto? What are possible solutions to this problem?

The Process


In small working groups, the students chose from a variety of topics directly related to the science, social studies, math and English curricula. In teams, the students researched, summarized and identified the connection between the science behind water quality issues in Toronto and how human settlements have impacted these issues.

The students were engaged and energized through their investigation and new knowledge of the relevance of water issues in Toronto, and worked collaboratively to think critically about their research and data, while also thinking of potential solutions to their chosen issue. The ideas that the students came up with were innovative and inventive. Throughout the collaborative process, the students were extremely engaged and active problem solvers. They worked well within their groups, divided the work effectively, and worked together to find the most relevant research and data. As a teacher, it was most impressive to observe their minds at work!

The Presentation


As a group, the students created a visual component that reflected each of their written proposals, which were completed individually. The goal of the project was exhibited through the presentations, as the students visually and verbally presented upon the history behind their issue, their analysis of the present situation and predictions of future trends of their issue, as well as the possible solutions/recommendations.

On the last day of the project, Toronto City Councillor, Jaye Robinson, listened to each group passionately present their discoveries and solutions to Toronto’s water quality issues.

Overall, it was an extremely successful integration project which the Grade 8 students embraced with open arms. Through a problem-based approach to the project, the learning became wholly student-centered, which enabled the students to work to their full potential. This project enabled the Grade 8 students to embark on a different type of learning than they were used to, allowing for more flexible and innovative thinking. The students thrived, showing them that hard work and dedication to a relevant issue leads to a heightened sense of accomplishment.

The project also gave the team of integration teachers an opportunity to communicate and collaborate outside the classroom walls, which was enriching and energizing. The first integration project helped solidify the value of student-centered learning, which will continue to be a focal point in future Grade 7 & 8 integration projects.

Kathryn Connelly
English & Learning Strategies Teacher

Monday, 13 January 2014

Personalizing by Readiness - A Grade 9 Math Approach

Personalizing by readiness can take many forms and have many functions. During the "Solving Equations" unit in Grade 9 math, students were given a chance to self-pace through a series of two lessons. Some students grasp how to solve equations quite readily, while others take more time and practice. Allowing students to self-pace in this topic gave us the ability to stretch some and support others.

During these lessons, students in my class worked through the following learning cycle:
  1. Watched a video created by Greenwood teachers and took notes as they followed the examples given. Students were able to pause and replay as desired.
  2. Completed several practice problems from the textbook. 
  3. Completed a Check for Understanding.
  4. Showed the Check for Understanding to me for feedback. Students used this feedback to correct their work.

Next, students moved on to a second video teaching a slightly more challenging concept within the unit, and then followed the same cycle of notes, practice, and a Check for Understanding.


This whole process spanned two classes. Students who finished before the end of the two classes were given extension problems. Students who needed more time to complete the tasks were identified and supported throughout the process, allowing them to finish within the two-lesson time period.

In speaking with the students about this process, there were several common reactions. Some of the stronger students expressed how they really liked being able to race ahead and work on more challenging questions after the basics were covered. Other students expressed how they liked being able to pause and replay the videos, as well as receive more one-on-one attention from me throughout the process.

Using self-paced lessons to teach solving equations allowed me to meet the needs of individual students within my class.

Megan Clark
Teacher, Mathematics and French