Skip Counting

Materials:

  • The Bead Chain Cabinet 

  • Chains, squares & cubes (following the same color scheme as the Colored Bead Stair) for the numbers 12 through 102 and 13 through 103

  • Labels in containers for the short bead chains

  • Labels in containers for the long chains

  • (These are the same measurements as the labels for linear counting. They are the same color as their corresponding chains and show all the multiples up to the square and the cube of the number represented by the chain.)

  • A Rug 

  • The long linear counting underlay for the longest chains

Purposes:

  • Comparison of the squares and cubes of the numbers 1 – 10

  • To give the child another means for skip counting

  • More practice in linear counting

  • Indirect preparation for multiplication

  • Indirect preparation for squaring and cubing and for bases other than base 10

Age: 4 ½ - 5 ½

Preparation:  The child has worked with both the 100 and 1000 chains

Presentation: 

Part 1: Short Chain (Example: 5 Chain)

  • Invite the child to unroll a rug, and a tray with the short 5 (light blue) chain, the small box of tags, and one square for the corresponding chain.

  • Layout the chain on the rug.

  • Invite the child to count the beads in one bar.

  • Fan-fold the chain and count (one five, two fives, three fives….)

  • Pull the chain out and allow the child to fold and count.

  • Superimpose the square.  

  • Extend the chain on the rug. Place square at the end.

  • Remove the tags from the box, arrange face up, and begin counting each bead, placing the tags pointing toward each bead.

  • When the first bar is finished, remind the child tags will only go at the ends from now on. Allow the child to continue counting each bead aloud and place the corresponding tag.

  • Count only the wide tags forward and backwards.    

Note: If the child is successful with this chain, move to introducing the Long Chain for the same chain set.

Part 2: Long Chain (Example: 5 Chain)

  • Invite the child to unroll a second rug at the end of the first (this is ideal). If one is not available, see alternate arrangement below.

  • Bring the tray with the remaining squares, the cube, the large box of tags and the long chain.

  • Lay out the long-chain underneath the short-chain.  Leave some space between the chains.

    *Alternate arrangement: Lay the chain below the short-chain, neatly along the edge of the rug.

  • Comparison the two chains.  

  • Fan-fold the chain and count (one five, two fives, three fives….). Place a square above that section of the folded long chain.

  • Transfer to the child to do the rest. For the last set, take the square from the short-chain.

  • Stack up squares and compare them to the cube.  

  • Extend the long-chain, remove the labels, and place them face up.

  • Invite the child to count and place the tags.

  • When they get to 25, at the larger link, show how it’s a wider tag and that means it gets a square above that bar.

  • Child continues.

  • Once the last square is placed at the end of the chain, place the cube directly above the square.

  • Together with the child, count the wider tags (by 5s) forward from 5-125.  The child can count backwards if they want.

  • Invite the child to work with this as much as they want and to even write it.

Control of Error:  If the number counted does not correspond to a label.

Following Exercises:

  • Read the Labels Backwards.

  • Write the Numbers from the Tags: Write the numbers from the counted tags on a long roll/strip of paper.

  • Laying Out all the Short Chains: Lay out all the short chains, count/tag them, and look for similarities and differences.

  • Laying Out all the Long Chains: Move the furniture and have the children lay out, count/tag all the long chains, and notice the similarities and differences. 

Pedagogical Notes:

  • These can be called the square and cube chains.

  • There is no test for this area.

  • The child does not have to work through all the short chains first.  If they have counted to 1000, they can do whatever chain they like. 

  • Do not give a lesson on every chain.  After the child has been introduced to these chains, they can select whichever they like.  

  • The 5 chain has a nice rhythm to it, so it’s a good idea to start with this chain.

  • The long 7, 8, 9 chains are the most difficult and the child may need your help.  Best to try and stay close. 

  • We use unit labels on each bead at the beginning to indirectly show the number of units in the different number base systems.  For example:  in the 5 chain, there are 4 units in the 5 base system.

  • Adding machine tape is great to use for writing the numbers from the tags.

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Linear Counting: 100 and 1000 Chains