Even Steven, or Odd Todd? Mathematics in Year 4
Learning is a consequence of thinking. Retention, understanding, and the active use of knowledge can be brought about only by learning experiences in which learners think about and think with what they are learning.
– Cultures of Thinking, Harvard Graduate School of Education
As we design learning experiences for our students, the development of thinking is always forefront of mind. Here is an example which highlights how students are developing as thinkers, and therefore growing their retention, understanding and ability to apply their knowledge.
In mathematics, we have begun a new unit focusing on addition and subtraction. To begin with, we have explored the properties of odd and even numbers. We played a game called ‘Even Steven vs. Odd Todd’, in which students played against a partner. Each player nominates to either play as Even Steven or Odd Todd. Two dice are rolled – if the total is even, Steven gets a point. If the total is odd, Todd gets a point. Simple right? Well, what if you were asked the question…
If you had first choice, would you prefer to play as evens or odds?
After playing a round of the game, we used the thinking routine, ‘Claim, Support, Question’ to scaffold their thinking. This routine sees students make a claim about who they would play as if given a choice, to find supporting evidence for their claim, and then ponder any questions that arise.
Student 1 – The game is fair; there is no skill in rolling a dice.
Student 2 – Even is better than odd; it is luckier.
Student 3 – There are more odds on a dice, so it is better to be even because two odds make an even.
Student 4 – On a ten-sided dice there are actually an equal number of odd and even numbers. On a dice, if it starts with an odd, it will end on an even.
Student 5 – If you are odd, you get 7 which is one of the most likely numbers.
Student 6 – You should choose to be Steven because there are more ways to make even. E+E=E, O+O=E and O+E=O.
After making these claims, alongside others, students were given the opportunity to find supporting evidence to prove or disprove, their own or other student's claims.
Student 7 – On an eight-sided dice, there are more possibilities to roll an even total. There are 12 possibilities to roll an odd total, and 16 possibilities to roll an even total. It supports my claim.
Student 8 – We were surprised that there are actually an equal number of odd and even on the different dice.
Student 9 – We rolled heaps of times and odd won so it doesn’t always matter.
Student 10 – On a ten-sided dice, we think there were 23 combinations to roll even, and only 13 to roll odd.
Student 11 - Is zero an even number?
With a clear goal in mind – a deeper conceptual understanding of the properties of odd and even numbers - this inquiry enables students to BE mathematicians: making hypotheses, testing their claims, finding supporting evidence, and readjusting their thinking. The question posed at the end provided another chance for students to inquire using the same thinking routine – can you find supporting evidence to prove that zero is an even number?
Follow up lessons included adjusting the game to use subtraction, adding more dice and using different types of dice.
Please enjoy some photos of our students as they explore the meaning of the equals sign through a card game.
Unit of Inquiry
For our second unit of inquiry, Where We Are In Place and Time, our student inquired into the central idea that innovations in technology have changed the way people live their lives.
To finish this unit of inquiry, our students were challenged to follow the design process to identify and solve a real problem that exists in the world, exploring how their own innovations may be able to help people in their lives; using a social justice lens to help elevate their thinking around this central idea.
For our next unit of inquiry, Sharing the Planet, we will inquire into the central idea that living things are connected to the places in which they live. Stay tuned!
This term, the Year 4 students are embarking on a journey into imaginative texts. A central part of this inquiry is our student-led book club. Book club is an inclusive approach in which students choose a book to share with their peers and are responsible for taking notes and bringing discussion points to their regular meetings. Each student has a role to undertake for each session, helping build their comprehension and communication skills, alongside their self-management skills. To learn about these roles, and the protocols for running discussions, we’ve been practising with rich picture literature. Please enjoy the photos of our students and their thinking as they engage in lively discussions about these books, and a couple of examples of how students engage with their roles.
JAMES CLAPHAM Year 4 Teacher