A quick Bio
Michael Calderbank graduated in 2010 with a math degree and completed his Masters in Teaching in 2011 from the University of Chicago. He joined Lindblom Math and Science Academy in Chicago in 2012. He is currently thinking about how students can create and answer their own mathematical questions about the world around them.
Rice on a chessboard
My amazing teaching moment takes place in a 9th grade Algebra 1 classroom. The lesson illustrates with tactile and visual examples how exponential and linear models differ .
The lesson begins with a story. A king is so impressed with his soldier’s bravery on the battlefield that he decides to give him an ornate chessboard. The soldier instead requests a more modest reward, to help feed his village. 1 grain of rice for the first square, 2 grains of rice for the second, 4 grains of rice for the third, etc.
After we all hear the story, students create a table based on the composition of the chessboard, and are asked how much rice they think there will be on the 64th square? Will it actually fit? It’s time to introduce some math! Students identify the pattern of growth and see that the repeated multiplication leads to exponents.
Now that students are hooked into the process, I give students some rice and a square inch of paper. They try to include as much rice as possible in a square inch. Once we come to a class consensus, it’s time to scale. With unit conversions, we can look at square feet, comparing it to the size of the classroom. Then, we can look at larger units, like square miles. Once we see just how large it is, they see that the story is really just a legend, but it opens up other avenues of study.
As a small group exercise, students can choose one another aspect to study this exponential growth: volume, cooking time, or cost, and share their results with the entire class. As an additional extension, we can even consider how much cumulative rice there is for the entire board, including all the previous 63 squares.
I am a big fan of this lesson because it gives a visual and a tactile example for exponential growth. Humans are not really that great with processing huge numbers, so the work with unit conversions and area gives them a scale to measure the enormous growth. Afterwards, we can look at other ways to measure the growth.
Hashtags: #rice , #chessboard , #exponential , #algebra1 , #volume , #area , #math
Big 5 Themes of an amazing STEM lesson:
1. Hands On Engagement: Students have easy access to the lesson immediately by playing with manipulatives to discover patterns, relationships, and to wonder in order to develop conceptual understandings.
2. Inter-Disciplinary Activity: The activity inspires other teachers to bring their content knowledge/focus into the activity; promotes rich cross-curricular connections.
3. Real World Connections- Students have opportunities to connect their learning to how the human race has used these same tools to evolve into the society we are today.
4. Prior Knowledge - Teachers assess their students’ prior knowledge while simultaneously introducing new content and drawing on their students’ previous experiences as a point of engagement.
5. Collaboration- Students work interdependently to solve problems bigger than themselves and benefit from each individual’s perspective rooted in their diverse cultural, experiential, and socio-economic backgrounds.
My amazing teaching moment takes place in a 9th grade Algebra 1 classroom. The lesson illustrates with tactile and visual examples how exponential and linear models differ .
The lesson begins with a story. A king is so impressed with his soldier’s bravery on the battlefield that he decides to give him an ornate chessboard. The soldier instead requests a more modest reward, to help feed his village. 1 grain of rice for the first square, 2 grains of rice for the second, 4 grains of rice for the third, etc.
After we all hear the story, students create a table based on the composition of the chessboard, and are asked how much rice they think there will be on the 64th square? Will it actually fit? It’s time to introduce some math! Students identify the pattern of growth and see that the repeated multiplication leads to exponents.
Now that students are hooked into the process, I give students some rice and a square inch of paper. They try to include as much rice as possible in a square inch. Once we come to a class consensus, it’s time to scale. With unit conversions, we can look at square feet, comparing it to the size of the classroom. Then, we can look at larger units, like square miles. Once we see just how large it is, they see that the story is really just a legend, but it opens up other avenues of study.
As a small group exercise, students can choose one another aspect to study this exponential growth: volume, cooking time, or cost, and share their results with the entire class. As an additional extension, we can even consider how much cumulative rice there is for the entire board, including all the previous 63 squares.
I am a big fan of this lesson because it gives a visual and a tactile example for exponential growth. Humans are not really that great with processing huge numbers, so the work with unit conversions and area gives them a scale to measure the enormous growth. Afterwards, we can look at other ways to measure the growth.
Hashtags: #rice , #chessboard , #exponential , #algebra1 , #volume , #area , #math
Big 5 Themes of an amazing STEM lesson:
1. Hands On Engagement: Students have easy access to the lesson immediately by playing with manipulatives to discover patterns, relationships, and to wonder in order to develop conceptual understandings.
2. Inter-Disciplinary Activity: The activity inspires other teachers to bring their content knowledge/focus into the activity; promotes rich cross-curricular connections.
3. Real World Connections- Students have opportunities to connect their learning to how the human race has used these same tools to evolve into the society we are today.
4. Prior Knowledge - Teachers assess their students’ prior knowledge while simultaneously introducing new content and drawing on their students’ previous experiences as a point of engagement.
5. Collaboration- Students work interdependently to solve problems bigger than themselves and benefit from each individual’s perspective rooted in their diverse cultural, experiential, and socio-economic backgrounds.