Where We Are in Place and Time- Analysing Evidence

Students in grade 5 have been busy investigating ancient civilisations and plotting major events on a timeline.  Through research, students discovered that the Egyptian pyramids were built about 4,500 years ago, farming in the fertile crescent began around 12,000 years ago, and pottery has been around at least 20,000 years.  This led students to wonder:

 “If the first written languages didn’t arise until 5,000 years ago, how do we know the age of things older than that?”

This was the perfect time to dive deeper into our 3rd line of inquiry: Processes involved in collecting, analysing and validating evidence.

Students were led through a series of activities to explore how scientist date artefacts.

The first step involved students recalling what they learned from a previous inquiry into properties of matter. Students recalled some basic information about the periodic chart and the structure of atoms. 

In the first activity, students learned about carbon-14 dating.  As a class, we watched a segment of the documentary, Hunting the Elements (link here, 22:30) in which scientists explain how they use the radioactive isotope of carbon-14 to help find the age of fossils and artefacts.  Students then broke into groups to watch a brain pop video and define some key terms. 

Students watch videos and define key vocabulary

After getting a better understanding of how carbon-14 dating works, students set out to explore the concept of a half-life. Students used M&Ms to help with this.  On an M&M, there is a small ‘M’ on one side of the candy.  This was used to show a carbon-14 atom. After starting with a known number of M&Ms (Carbon-14 atoms) students shook them up and dumped them onto a plate, some of the M&Ms would appear with ‘M’ side up others with the ‘M’ side down.  If the ‘M’ was not showing, this would indicate that the radioactive carbon-14 atom had decayed and turned into something else.  

Here is Rosa explaining how Carbon-14 dating works.

Students carried this out for 5 rounds. Afterwards, we found the average of all the groups.  We knew that about half should decay each round, but also knew that not every group would have exactly half each round.  Here we explored the idea of sample size- that with enough trials we would move closer and closer to the statistical result of exactly half. 

Exploring half-life with M&Ms

Firmly secure in their understanding of half-life, students began creating a graph of carbon-14’s half-life.  The graph can then be used to find the age of a fossil or artefact.  The only information needed to construct the graph is the starting number of carbon-14 atoms  in the artefact (at age 0), the remaining number of carbon-14 atom in the artefact, and the half-life of carbon-14 (5,700 years). 

In this example, the sample contained 48 Carbon-14 atoms (M side up) at the start. After a certain amount of time, some have decayed and no longer have an M. 27 atoms have decayed and only 21 Carbon-14 atoms remain.

Using this Carbon-14 half-life graph, students can plot the data along the curve. If 21 Carbon-14 atoms are remaining, that means the sample is 7,500 years old.

With all this knowledge, students were ready to take the next step and apply these skills to actually dating a fossil. 

Very simply, students were given a fossil of a bone and asked to find out how old it was.

An elaborate story was told of finding a small pyramid in the park, exploring it, uncovering an ancient burial ground inside, removing the bones, and bringing them to school for students to analyse.  More or less, nobody believed this story and quickly realised that the 'bones' were actually baked dough with grains of rice inside.  In this case, the rice represented carbon-14 atoms.  

To find out the age of the bone, students meticulously picked through the sample to find out how many Carbon-14 atoms were remaining. By finding out how many were remaining, they were able to determine how many had decayed from the original sample. They were then able to plot this information on a half-life graph and determine the age of the fossil.

Here are the young archaeologists hard at work.

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.

New Year, New Maths

Students came back to school well rested and full of enthusiasm for the second half of the year. After sharing stories from the holidays-skiing trips, movies, ice skating, play dates and trips to Grandma’s house- we set about investigating a new strand of mathematics. 

Central Idea

Range, mode, median and mean can be used to analyse statistical data

The following questions are being used to guide students through this investigation:

How can we manipulate data?

How can we interpret data?

How can we present our data effectively?

As a getting started activity, students explored the power and versatility of graphs by looking at Hans Roslings' graph of 200 countries over 200 years. Students pondered the question, "Was this data presented effectively?" You can visit the interactive graph here.

To construct meaning, student were asked to investigate the following question: 

                                  Do you have good balance?

As a class, we brainstormed the different aspects of data handling: 

Planning

Collecting data

Recording data

Organising data

Analysing data

Presenting data

Students worked their way through this investigation, pausing along the way to learn different methods of organising data and to practice calculating landmarks to help analyse the data. Finally, students used the collection of data to answer the question. Of course they used the landmarks to help justify their answer. Students experimented with different graphing options to best present the data and highlight the answer to the question.

Here are some students working through the investigation.

Week in Review

Readers’ Workshop

Students in 5B have a begun reading a class novel, Esperanza Rising. Although all students are reading the same book, we have broken up into smaller groups to work on different skills and strategies while we read and respond to what we read.  After reading, students are responsible for completing one of the following tasks: analyzing Esperanza’s character, creating high quality discussion questions in regards to the chapter, visualizing an important event, writing a summary, finding an important quote from the chapter, and researching the historical event from the chapter. In addition, using clues from the texts, everyone records their predictions on what they think will happen later in the story.

Students working on the various tasks after reading

Some students read along to an audiobook, some read orally in a group, some read in pairs, and one reads individually

Our working board. Students translated key proverbs from the story into their native languages. Can you recognise any of these languages or sayings?

Mathematics

Central Idea:

Patterns can often be generalized using algebraic expressions, equations or functions.

Students started with a tuning in game to help construct meaning around this idea. Students were given 7 two-sided chips. The goal is to flip all the chips so the other colour is showing. However, you must flip exactly 3 chips at a time.  What is the least number of rounds it takes to have all chips flipped? 

Students experiment with finding patterns

After experimenting and playing with possibilities, students came to the conclusion that 3 rounds was the least possible number of rounds.  Students then continued this challenge with 8 chips, 9 chips, etc...  Students began to record their results in a function table and were asked to look for patterns and try to predict what is the least number of rounds needed for 16 chips? 100 chips?

Students begin to organise their results in a function table which will help to see the pattern

Students use the function table to see and explain the pattern. The next step is to express the pattern mathematically-in an algebraic equation

Unit of Inquiry

How we Organize Ourselves is coming to an end and students are applying their learning and going further in their inquires. 

As a class we played a game to investigate our second line of inquiry, food production and distribution. Specifically, we looked at the challenges subsistence farmers face as they try to grow enough food for their families as well produce a small surplus to sell. 

Students were organized into small groups of farming families.  Each season, students must produce enough corn for their families’ to eat. Any surplus food could be sold to the global market for a small price. In addition, farmers can choose to harvest coffee fruit. However, to sell coffee to the global market farmers must first process the fruit and package it, and purchase an expensive export license. 

Students work hard to harvest their crops and sell the surplus so they can buy fertilisers or possible an export license

After this activity, students reflected where on the SOLO Taxonomy this fit. Some students classified it as a level 4 Connecting Ideas activity. They noted that they were comparing different strategies and explaining the effects of their actions.  Some thought it was a level 5 Going Further activity as they were planning a strategy, reflecting on its success and revising and improving on it in later rounds.

Students highlighted the thinking skills they used during the activity

Mei and Jeong Yeon take action to Go Further in their learning by designing an experiment to test organic and conventional fruit. They were curious to know if their was any difference in taste or quality. The results were surprising! They will write up a full lab report over the weekend and share it with the class next week. We are all looking forward to it.

Students perform a test to see if they can taste the difference between an organic banana and a conventional banana.
What is your hypothesis?

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