“Is It A Pattern?”
Students in the Fours constructed their own rules for what makes a pattern, and then used those rules to create patterns with different attributes of color, size, and direction. The students determined that “With a pattern, you always know what comes next”, and that patterns “Repeat again and again”.
Where’s the Differentiation?
A Size Pattern Was Posed As An Open Problem
Students created their own patterns independently, and then tested their pattern against the rules. Does my pattern repeat? Do I know what comes next? This open problem resulted in a range of work that served as a formative assessment for how well children understood the concept of patterns. This approach was also a useful way to differentiate the needs of the math learners in the class. Teachers could observe students as they worked, and support or challenge them by asking targeted questions based on the individual patterns the children were creating.
Thinking of Numbers to Represent a Size Pattern:
“Two big squares, two medium squares, two big, two medium…”
(Click picture to view video)
Thinking of Letters to Represent a Size Pattern
“B, B, A… B, B, A… B, B, A…”
(Click picture to view video)
Is It Still a Triangle if it’s Not Pointing Upward?
Triangle is rotated to expand students’ concept of a triangle.
When young children are first introduced to shape categories, like the triangle, they are presented with symmetrical models such as an equilateral triangle (all sides and angles equal in measure). Children are usually shown the equilateral triangle positioned only one way- with one vertex pointed upward, and a horizontal base.
However, research suggests that as soon as these typical examples are introduced, a variety of different positions and sizes should also be shown to children so that their notions of triangles don’t become rigid and limited to only one type of triangle, or a single example of a shape. “Children two to three years of age are not too young for this type of learning” (NCTM, 2010).
“There’s lots of ways you can make a triangle”
Examining various triangles and determining whether or not they are, in fact triangles, leads children to grapple about specific attributes that define what a triangle is (three sides, three corners, straight lines, etc.). As children experience a broader variety of each shape, they begin to build more accurate geometric concepts and ideas. Through this investigation process, the Fours are laying the foundation for geometric discussions that will take place in later grades, such as transformations (rotations, flips, slides), symmetry, and angles.
Observe the Fours as they explore and debate what it is that makes a triangle a triangle, and in the process, redefine their ideas of triangles.
What can a student in the fours do when they run out of a certain sized block?
They can use the “recipe” or conversion chart they made to create the block size they need from other blocks.
Students in Pre-K used classroom blocks to estimate, and then test, how many of each of the same size smaller blocks it would take to cover one double unit block. The class worked in pairs on this investigation, and then the class created posters of their mathematical conversions. They have found this conversion chart, or “recipe” useful to refer to when they run out of a certain block size because they can now create the size they need by combining (composing) other blocks. Continue reading