Set of all linear counting beads

Linear Counting

Materials

Presentation 1:
The hundred chain consisting of 10 bars of 10.
The hundred square
An envelop containing arrowed labels:
- Green labels marked 1 – 9
- Blue labels marked 10 – 90
- A red label marked 100
- A large sized mat or runner

Presentation 2:
A thousand chain consisting of 100 bars of 10
Ten squares of ten
The thousand cube
An envelop containing arrowed labels:
- Green labels marked 1 – 9
- Blue labels arrowed 10 – 990
- Red labels from 100 – 900
- A large green label marked 1,000
- A large sized mat or runner

Presentation 1

The 100 Chain

• Bring the child to the chain cabinet.
• Show the child the bars on the shelves and discuss with the child if he has seen bars like these before.
• Begin counting with the child starting from the unit to the 10 bar.
• Have the child unroll the runner just a little ways.
• Show the child how to hold the 100 chain by both ends and have him lay it vertically at the bottom of the mat.
• Have him place the tray below the 100 chain.
• Slowly fold the chain together to create the hundred square.
• Notice that it looks like the hundreds square.
• Place the hundreds square on top of the folded ten chain to show that they are the same.
• Remove the hundred square and have the child gently re-straighten the ten chain.
• Take out the unit tickets (green) and tell the child what they are called. Line them in a vertical line to the left of the ten chain.
• Show the child the ten tickets (blue) and place in a vertical line above the unit tickets.
• Label the first ten by using the unit tickets and placing them on the left of the chain.
• Count with the child 11-20. At the 20 mark, place the ticket that has 20 on it to the right of the 20 bead.

Presentation 2

1. • Counting by units, continue placing the ten tickets until you reach 100. Have the child place the red 100 ticket next to the 100. Tell the child: “You have just counted to 100.”
   • Ask, “How many beads are in this chain?” (100) Point to the hundred square, “And how many are in this?” (100)
   • Count with the child all of the tickets: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
   • Then count backwards: 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.
   • Have the child replace the tickets into their correct envelops and then replace the rest of the material.
   • Tell the child that today we are going to look at an even longer chain than the 100 chain.
   • Have the child unroll the runner all the way.
   • Show the child how to hold the 1000 chain.
   • The directress carries the chain to the runner, with all of the strands laid out straight.
   • Have the child bring over the cube and the large box on a tray over to the runner. Also bring over the hundred squares.
   • Tell the child that you are going to try to fold the chain just like you did with the 100 chain.
   • Make a hundreds and ask the child what you made. Place a hundred square next to the one you just made.
   • Repeat until the whole chain has been folded in hundred squares. (The child can begin to make them after a while)
   • Place each of the hundred squares next to the hundred square you have made with the child.
   • Then place the hundred squares on top of the hundred squares you and the child have made.
   • Count with the child to see how many hundred squares there are.
   • Have the child place each hundred square on top of each other.
   • Notice that it looks just like the cube. When we have 10 hundred squares, we know that we have 1000 beads
   • Place the cube next to the ten hundred squares (placed on top of one another) to show this to the child.

   Purpose

   Direct
   - To consolidate the child’s knowledge of counting. Up
   until now, he worked with tens and hundreds in the decimal system. With these Exercises, he becomes familiar with the sequence of numbers from 1 through 1,000.
   - Counting is a restful activityand tends to become mechanical. Through repetition, the child establishes the mechanism of counting.
   - When the two chains are placed parallel to each other, they show in a striking and sensorial way the difference between the square and the cube of ten. In this way, the decimal system relationships are further established by the child.

   Control of Error
   As the labels have to be placed at the end of each bar, the child easily perceives he has made a mistake in counting.

   1. • Have the child gently pull the 1,000 chain straight. (Have him keep the chain near the left side of the runner.
      • Have the child lay out all of the tickets.
      • Count each bead and place the correct ticket when needed as in Presentation 1. When you get to 100, place the ticket as well as a hundred square next to the 100th bead. Repeat this for every hundred. (Even at the 1,000th bead)
      • At the 1,000th bead, also place the cube.
      • Stand at the beginning of the runner and walk all the way to the end. Stand at the end and look at the work of the child.
      • Go back to the beginning and count: 100, 200, 300, 400, 500, 600, 700, 800, 900.
      • Ask the child how many he had at the end: 1000.
      • Go back to the beginning and count the tens. 10, 20, 30, 40, 50, … 100, 110, 120, … 400, 410, 420, … 980, 990, 1000.
      • Then have the child count by tens backwards.
      • Then child can then put the material away.

      • Skip Counting - Chains of Squares and Cubes
        
        Materials
        - A cabinet of cubes, squares, and chains ranging from 2 to 9, including the unit bead:

      • Chains of 1 in red with corresponding labels in red marked 1.
      • Chains of 2 in green with corresponding labels in green marked 1, 2, 4, 6, and 8.
      • Chains of 3 in pink with corresponding labels in pink marked 1, 2, 3, 6, 9 up to 27.
      • Chains of 4 in yellow with corresponding labels in yellow marked 1, 2, 3, 4, 8, 12 up to 64.
      • Chains of 5 in light blue with corresponding labels in light blue marked 1, 2, 3, 4, 5, 10, 12 up to 125.
      • Chains of 6 in purple with corresponding labels in purple marked 1, 2, 3, 4, 5, 6, 12, 18 up to 216.
      • Chains of 7 in white with corresponding labels in white marked 1, 2, 3, 4, 5, 6, 7, 14, 21 up to 343.
      • Chains of 8 in brown with corresponding labels in brown marked 1, 2, 3, 4, 5, 6, 7, 8, 16, 24 up to 512.
      • Chains of 9 in dark blue with corresponding labels in dark blue marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 27, 36 up to 729.

      • - A large sized mat or runner

      • Presentation

      • As an introduction to the other chains, begin with a chain from the middle such as the 6 chain.
      • This is to be presented in the same way as the 10 chain and 1,000 chain.

      • The photograph below shows the 5 square chain folded next to the five square:

        The photograph below shows the 5 cube chain folded with five 5 squares next to it:

      • The photograph below shows that five cube chain folded into squares, the five 5 squares on top of each other to show that it is the same as the 5 cube:

        
        Note
        The Child does not need to be shown each of the chains.
        
        
        Exercice
        The child can then work with any of the chains.

        Purpose

        Direct
        - To give the child other means of counting than by one by one
        as they did in the chains of one hundred and one thousand (respectively, the square and the cube of 10)
        
        Indirect
        - For squaring and cubing. The child comes to realize the different quantities in the square and the cube as a number.
        - Also the relation of the square of a number to the squares of other numbers and of the cube of a number to the cubes of other numbers,
        - An indirect preparation for multiplication e.g. 5 x 2 = 10, etc.

        Control of Error
        The Child's own knowledge

      •