The fifth and sixth graders all participated in two mini units to start the year. First the students studied and created tessellations. They looked at the work of M. C. Escher, and watched videos of teachers building tessellations. They learned that tessellation begins with a shape (like a square, equilateral triangle, or regular hexagon) that will tessellate. They cut and tape pieces of the shape to create their basic tessellating piece. Their work is on bulletin boards in the hallway and Mr. Fisher's room.
The second unit was from the web site, Youcubed.org. This website was created by Stanford University researcher Jo Boaler. She has done some groundbreaking and innovative research into how people learn math and how the brain grows. They have a "Week of Inspirational Math" on the site, which is free and open to parents, teachers and students. Each day for five days we did an interesting and engaging math activity. Here is what we did:
Day 1: Four Fours - Students must use four fours and the operations (+, -, X, /) to make the numbers from 1 to 20. For example, 4 times four plus 4 divided by four equals 17.
Day 2: Shapes - Students looked at 30 shapes built from arrangements of circles. They identified what number each shape represented, then looked for patterns. Some of the patterns they might have found included prime numbers, odd and even numbers, and multiples.
Day 3: Paper Folding - Students had to fold a square into another square with an area one-fourth the original square, and a triangle with one-fourth the area of the original square.
Day 4: Growing Patterns - Students examined a sequence of patterns of squares that increased in size in a predictable way. They had to come up with different ways of explaining the growth.
Day 5: Pascal's Triangle - Students completed a part of Pascal's triangle and looked for patterns.
You can go on the website for more info about the week of inspirational math and many other things. You can read Jo Boaler's research, find problems, get lesson plans, etc.
From here, the fifth graders will be focusing on factors and multiples, and multiplicative reasoning. Multiplicative reasoning is the understanding of when multiplication and division are appropriate operations to use in problem solving. And also to see relationships that are multiplicative (as opposed to additive).
The sixth graders will be doing a unit called "Prime Time." They will study prime numbers, factors and multiples, including greatest common factor and least common multiple, and how to use these concepts in problem solving.