Operations with the Golden Beads

Subtraction 1


As for addition


To give an understanding of subtraction
To give the vocabulary: subtraction, minuend, subtrahend, and difference


4 1/2 years and older


A small group of children.  The material is arranged as for addition.  One child is in charge of the golden bead material, another the large number cards, and another the small number cards.  These subtraction problems will not involve exchanging.  The teacher may choose to use one or two subtrahends (the number being subtracted).  Below is how the following problem would be worked.
  4326   minuend
- 2112  subtrahend
- 1103  subtrahend
The teacher tells the children, "Today we are going to work subtraction problems."  The teacher makes the minuend, 4326, in golden bead material and the large number cards, and places them on the mat.  She makes the subtrahends, 2122 and 1103, in small number cards and puts them on two trays.

She gives a tray to each of two children, Mary and John.  She asks the children to read the numbers on their trays.  They do so in turn.  The teacher then indicates the bead material on her mat and says, "I have 4326.  I am going to let Mary subtract 2112 and I am going to let John subtract 1103.  Mary, will you subtract 2112?"  As the children have not worked subtraction before, she guides them through the process.  "How many units do you want, Mary?" "Two."  "Yes.  You can take two of these units."  Mary does so.  "How many tens do you need?"  "One."  "You can take one ten then."  Mary continues until she has subtracted 2112 in golden beads.  The teacher takes the small number cards 2112 off Mary's tray and puts them under the large ones which form the minuend at the top of the mat.  "Now, John, you may subtract 1103.   How many units will you take?"  John continues until he has subtracted 1103 in golden beads.



The teacher takes the subtrahend off John's tray, saying, "You have subtracted 1103."  She puts it under Mary's subtrahend at the top of the mat.



The teacher then asks a child to count the bead material remaining on the mat, and place the corresponding small number cards underneath.  "We have 1111 left."  She superimposes the small number cards, and places them underneath the subtrahends at the top of the mat to form the answer of the written problem.  The teacher then reviews the problem.  "We had 4326, and Mary subtracted 2112 from it, and John subtracted 1103.  We have 1111 left." 

Introducing the specialized vocbulary, the teacher may tell the children, "Today we did subtraction.  4326 was the amount we started with--our minuend.  From that we subtracted our two subtrahends, 2112 and 1103.  We call the answer to our problem, 1111, the difference."  Pointing to each set of numbers, she reviews, "Minuend, subtrahend, subtrahend, difference."  She further clarifies the terminology by continuing with the three period lesson.  "Point to the minuend.  Which one is the difference?  Point to a subtrahend.  Is there another subtrahend?"  Pointing to each set of numbers in turn, she asks the students, "What do we call this?"  The teacher will use this vocabulary when working additional subtraction problems with the children.