Integrating Maths into the Unit of Inquiry

As the grade 5 move into the How The World Works unit of inquiry and begin to investigate properties of matter, it seemed like a natural fit to start a mathematics unit on measurement.

During their first trip to the science lab, with the help of Mr. Johnson, the lab technician, students set about to investigate the question, 

"Does mass change as a material goes through a phase change?” 

Students carefully measured the mass of a beaker with ice and sent the ice through a phase change using a hot plate. When the ice was melted, students remeasured the mass to find if their was any difference.  

After completing the first investigation, students reflected on their results. Many students were surprised to find that the mass of the water was less than the mass of the ice. It seemed the answer to the question was, "Yes, mass is lost during a phase change." Upon further reflection, many students wondered if their measurements were accurate enough. Perhaps there is a way to get more reliable results? Students then designed another experiment with more variables controlled and a more precise method of measuring the mass of the water- in all its phases.


Most groups concluded that some of the water was being lost as a vapour so they were unable to measure its mass. Students know that one property of a gas is that it wants to spread out and fill the open space. Groups came up with a variety of ways to trap the gas so it could be measured along with the liquid water.  In Rosa and Limie's experiment, they used a balloon on top of a beaker to trap the gas. Based on their results, a tiny bit of gas may have escaped. They found a difference in mass of 0.2 grams. Not bad for only the 2nd try.

Here is Jian, Tanatswa and Sunaina talking about their investigation.

In addition, students did a bit of research into this topic on the conservation of mass. We watched a short- yet very dramatic- video about Antoine Lavoisier. Widely considered the father of modern chemistry, Antoine Lavoisier is credited with proving the conservation of mass. Students were surprised to learn he did over 1,000 experiments before he was confident his measurements were correct. We're hoping 2 is enough for us! 
Click here to watch the dramatic video. 

Besides the practical application of measurement through science investigations, students are also working on measuring the different attributes of shapes and events- specifically perimeter, area and volume.

After spending some time constructing a definition of area and perimeter, and developing a method for calculating the area and perimeter, students were given the following 2 questions to investigate:

Students worked out the answer in a variety ways and explained the thinking and process in their notebooks. However, being scientists, we need proof!

Method 1                                                                Method 2     

After working individually and conferring with a few partners, students reflected on this activity by consulting their deep mathematical thinking checklist in their notebooks. As a class, we have been exploring the concept of growth mindset and what that looks like in a maths class. We came to the conclusion that getting the correct answer isn't nearly as important as testing out ideas, persevering, making connections to previous learning, and defending your position-to name just a few. As class we decided which of these attributes we were using while investigating these questions. 

For an overview of growth mindset, the science of learning math, the importance of perseverance, the multiple ways to 'see' math, visit the youcubed.org website. This comes from the research of Jo Boaler from Stanford University. It is filled with great information for parents, students, and teachers.

Parent Sharing Session

For 2 hours on Tuesday, January 24 the fifth grade classrooms and drama room were filled with parents actively participating with their daughters in a range of learning activities. The session was split into 2 parts, the first focusing on mathematics and the second focusing on changes that occur during adolescence.  A bit more on the mathematics session:

Students broke into groups of 2 or 3 to demonstrate a mathematics concept studied in the first semester. Students led parents through an inquiry activity, stopping along the way to explain relevant concepts, algorithms, strategies, and tips to help develop the tools necessary to solve the problems. Here are a few of the inquiries students led parents through.

Here are some photos of parents and students in action

After the mathematics session wrapped up, we switched our focus to explore changes that occur during adolescence. A main goal of this session was for parents and daughters to have fun and work together to develop some strategies that could be used to maintain healthy relationships with each other during the changing years of adolescence.

Firstly, a list of 10 changes was given to each group. We asked groups to rank these changes in terms of most important, concerning, biggest, surprising, etc... Parents and daughters were able to share their perspectives with each other and talk through the changes in more detail.


Next, we role-played a few scenarios to help promote dialogue between parents and daughters. To add a bit of perspective, we had everyone switch roles; parents played the part of daughters, and daughters played the part of parents.



We finished with parents and daughters offering each others bits of advice to remember moving forward.

We want to thank everyone for taking the time to come out and share in these activities with us.  It was clear that everyone learned something and enjoyed themselves.

We look forward to our next session on March 2 when we share our science investigations with parents.

Mathematics

Grade 5 is just wrapping up a unit in mathematics exploring the idea that:

Fractions, decimals and percentages are ways of representing whole-part relationships.

Students started off the unit with a pre-assessment to help answer the questions:

How am I doing?

Where to next?

Students used the information from the pre-assessment to set goals for the unit, and the teachers used this information when planning learning activities.

As a tuning in activity and discussion starter, students briefly reflected on the question of “What is a fractional part, and what isn’t a fractional part?" 

Students used the image below to decide which shapes were divided into fractional parts and which weren't.

Which shapes are divided into fourths? Why are the others not considered to be fourths?

Throughout the unit, students had many opportunities to work both independently and collaboratively to construct meaning on a variety of concepts related to fractions.  Here are students constructing a fraction strip to help investigate fractional relationships.

After students had opportunities to sort out ideas and construct meaning, they were given more challenging problems to apply what they had learned.  Here are a few students discussing their problem solving strategies.

              

                                   

Below, Amy, Rosa and Limie use all they know about fractions, angles, measurement and ratio to follow a detailed set of blueprints to construct a house of precise dimensions. 

A few of the details:

-The length of the front wall of the house is 9/16 of the length of the paper.

-The roof angles in at 40 degrees from each top corner of the house. The top of the roof is parallel to the top of the front wall.

Applying what they know. Perhaps they should join the school renovation meetings.

We finished the unit with an assessment to check student progress and note areas we still need to work on. Students plotted their score and progress on our

Growth Mindset Graph. 

As you can see, most students land in the top-right quadrant, which is the high growth-high achievement quadrant-exactly where we want to be!

Ask your daughter which dot is hers.

Students discussed which dot represented the "best" score. It was a lively discussion with the verdict split between the far right dots and the dots at the top.  In fact, it inspired Limie to coin a new phrase:

"Improving makes good learning." -Limie Sanada 2016