Materials Spotlight: The Wooden Hierarchical Material
The Wooden Hierarchical Material takes up a great deal of space in our primary and elementary classrooms, and for good reason! This key math material helps children understand the hierarchy of numbers and physically represents units through millions.
The Concrete Material
The Wooden Hierarchical Material comprises cubes, prisms, and squares that vary in size and color according to the different place values they represent. Units are green. Tens are blue. Hundreds are red. This pattern continues throughout the families or categories, so unit thousands are also green, ten thousands are blue, hundred thousands are red, and then unit millions are green. Units are represented as cubes, tens as prisms (or a line of ten units), and hundreds as squares (constructed from ten tens side-by-side). Due to this repeated pattern that is reinforced through shape and color-coding, children can visualize the structure of our decimal system.
The Presentation to Children
When we present the Wooden Hierarchical Material, we first connect with other math materials children have used, like the golden beads and the stamp game. In this way, children can build upon their prior knowledge of place value and how 10 of one category are exchanged for one of the next category (e.g. ten units become one ten).
The material is constructed to reinforce the relationship between base-ten numbers in concrete form. As we place the blue ten bar to the left of the small green unit, we remind children how when ten units get together, they make a ten. We also point to the little green marks on the bar and use the unit to count that ten of the units make up the ten bar. Young children love double-checking this correspondence!
We repeat this process to show how ten of the blue ten bars correspond to the ten sections on the red hundred square. Then how when 10 hundreds get together, they make a thousand. When we place the green thousand cube to the left of the red square, we leave some extra space between them because we are starting a new family (or category). This green thousand cube is units of thousands, and we can continue the process with tens of thousands and hundreds of thousands. Children love getting to the green unit of the millions cube and often want to try to imagine or represent ten million, hundred million, and beyond!
The Many Benefits
Because children can physically explore how ten of the thousand cubes make a line that represents 10,000, just like ten of the unit cubes make a line that represents a 10, they develop a strong understanding of the hierarchical value of numbers and their position in the decimal system. Similarly, they can experience how ten 10,000s make up a 100,000, and ten 100,000s make a million! This physical manipulation helps them better grasp abstract mathematical
