Wooden Hierarchical Material

Material Description:

Number Dimensions Forms Colours Coloured Lines

1 (1/2cm3) cube green none

10 (1/2cm2 x5cm) prism blue green

100 (5cm2 x ½cm) prism red blue

1,000 (5cm2) cube green red

10,000 (5cm2 x 50cm) prism blue green

100,000 (50cm2 x 5cm) prism red blue

1,000,000 (50cm3) cube green red

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  • golden bead unit, ten, hundred, thousand on a tray
  • supply tray (to write the notation for the children)
  • prepared cards or labels (notation is centred and same size paper):

Set 1: 1 – 1,000,000 (with commas) all the same size, not colour-coded

Set 2: For later work, a double-sided set with exponential notation on reverse


This is the first piece of Arithmetic material, beginning Elementary, it begins with the concrete, though the children may not use it for long, it is for all children because it introduces something new which is not given in Casa, the presentation is different.  The loose three period lesson is much more fluid and naturalistic than in Casa.  This is the first piece of material at Elementary.

Association with the Golden Bead Material

  • Lay them out in order, in a line, keeping them an equal distance apart, involving the children, (units on the right, million on the left for writing in columns)
  • Pair with golden beads


  • Count with the unit of the Wooden Hierarchical Material with the ten of the Wooden Hierarchical Material, use the ten to do the same with the hundred and then the hundred moving up the thousand, take the thousand and count along the ten-thousand (moving from right to left), count with the ten thousand along the side of the hundred-thousand (not on top) , then with the hundred thousand going up against the side of the one million cube

Loose three period lesson

  • With the children review the names of the newly learnt lesson
  • Begin the second period, missing up the material starting with the unit, concentrating on the new numbers, stressing their names
  • rearranging it with the children in order

Group the material into families

  • Set out the material again grouped into the Simple Family, Hundreds Family and Million Family, put them into a line like before with a gap in between them, give the names of the family to the child.
  • Ask, We only have the unit for the millions family, do you think there might be more?”  “Do you think it goes on forever?”
  • Ask the child, “What could we say about the colours of each family?” (the units are green, tens are blue and hundreds are green)
  • Ask the child, “What could we say about the form of each family?” (the units are cubes, tens are prisms and hundreds are square-prisms)
  • Ask the children to follow you moving away and having a look from a distance, ask the child, “What could we say about now about the geometrical aspect of each family?” (the units are point, tens are line and hundreds are surface), say, “The million would look like a point too, if we went a very long way away”

Writing the symbol

  • Usually straight after, with the material arranged in families, say, “We are going to write symbols or numbers to show these, you already know how to do this”
  • Nominate a child to write the numbers, 1,10, 100, in the centre of a slip and pair them.
  • Show the children how to write the others in a new way, ask the children what type of number the thousand is, write a one, say, “We put a comma to remind us it is in the family of thousands and three zeros”. To write the ten-thousand we ask the same questions, ask the children what type of number the ten-thousand is, write a ten, say, “We put a comma to remind us it is in the family of thousands and three zeros”.  For the hundred-thousand, ask the children what type of number the hundred-thousand is, write a hundred, say, “We put a comma to remind us it is in the family of thousands and three zeros”.  Say, “Now what have I come to, I’ve come to the family of a million, I have one million so I write a 1, then a comma for the a new family, three zeros for the thousand family and then I have to write a comma and three more zeros because I am moving into the simple family”.  After writing each number place it

Loose three period lesson

  • Pick up the paper slips, give them to the child and ask them to place it.
  • Pick them up again and ask the child to read it and place it
  • Continue till the children are comfortable with making the notation

Introduce possibility of Further Work

Give the children prepared labels for them to use or to make their own labels

Acknowledge the other set of prepared labels, saying that you will talk about them later.

Show the children how to put it away, starting with the Million


Key to reading and writing of large numbers


  • Gives children a graphic impression of the decimal system beyond one thousand
  • It is an extension of the work with the decimal system, leading to the reading and writing of large numbers, in families
  • It gives the names of the families and the number of parts in each family (3 parts, units, tens and hundreds and a comma separates each)
  • Suggests the infinite


  • Stress the continuation of the pattern and families, the stressing of the comma connects upto the number of zeros needed for the simple family, the thousands family and the simple family.

When to give the lesson:

When the Children come to the Casa, if the children do not know the names of the unit to one thousand stress the names of these too.  Give this after the Story of Arithmetic, which can take place int he fourth week before this the children can use the material (e.g. the deconomial) they are familiar with in Casa, you can observe them and they can learn their multiplication facts (so you can go to long multiplication straight away).

After the lesson:

Preparation for the Large Bead Frame, the next piece of material to be introduced

Follow up work:

powers can be given later when we use the Wooden Hierarchical Material in a different way., for work with exponential notation


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