Operations of the Decimal System: Multiplication

Materials:    

• Large quantity of golden bead material

• Large number cards 1 - 9000

• 3 sets of small number cards 1 – 3000

• Multiplier cards (small unit cards 1-9 with green symbol)

• Trays with bead cups

• Small tray with bead cup for making exchanges 

• A large tray with bead cup for doing the operational process

• Tables or Underlay Mats for laying out the small cards 

• 2 rugs

Purposes:     

• To show the process of multiplication as putting together equal quantities which result in a larger quantity

• Preparing the child to see that multiplication is the addition of like quantities

Age:    4 – 5 ½  

Preparation: The child has been introduced to addition and subtraction with the decimal bead materials

The child has probably done some skip counting with the bead chains

Parallel: The child will continue working with addition and subtraction.  The child will continue skip counting in the bead chains

Note:  It is not necessary to do static

Presentation: Dynamic Multiplication

Layout

• Invite three children for the lesson.  They will need to help set up:

  • Two rugs, one horizontal and one vertical.

  • Each will need a small mat to lay out on a table, a small box of cards set up on their mats, and a math tray.

  • Lay out the large cards on the vertical rug.

• Secretly tell each child the same number to get from their cards and then the matching quantity. 

• The Guide brings the exchange tray and an extra set of unit cards in a dish.

Operational Process

• Ask each child to put their cards together and to tell what they brought.

• Ask them what the notice about the quantities (they are all the same).

• Have the children place their quantities on the large tray. 

Calculation

• Move the children’s small cards to the left side lined up vertically.

• Let the children know they get to count the quantity.  Remind the children to STOP at ten to exchange.

• Allow each child a turn one by one to count a category stopping them at ten and talking through the exchange as in the addition exercise and to get the large card to match.  

Story Summary of the Operation

• Example: Point to each child’s number, “You brought (say the number conventionally), and you brought (say the number conventionally), and you brought (say the number conventionally) and when we put all the beads together, we got a bigger quantity.  We got (say the product.) 

  • Point to the small cards, “We have XXXX one time, XXXX two times, XXXX three times.  Since you all brought the name number, we only need to say it once.” Stack the multiplicands as you count them so only one remains.

  • “There is a little card to tell us how many times we brought the number.” Remove a three-unit card from the dish (multiplier) and place it to the right (child’s view) of the multiplicand. 

  • “We had XXXX three times (point to the multiplier) and then we had XXXX” (move the product to the right of the multiplier so they are in a line).  “When we take the same quantity more than once and put it together, we get a larger quantity, that is multiplication!”  

Control of Error: None, accuracy of the result is not the purpose.

Pedagogical Notes:

• The child doesn’t need static multiplication because essentially it is addition.  They have worked the operational process before. We start with dynamic to encourage their independent work.  

• Don’t keep the children working at the static level too long.  

• When children are independently working with addition, they may all decide to bring the same quantity.  You can introduce the multiplication story spontaneously then.

• If the children multiply a really large number, they can make a 10,000 card themselves.