Operations of the Decimal System: Addition

Materials:    

• Large quantity of golden bead material

• 1 Box of Large Number Cards 1 - 9000

• 3 Boxes of Small Number Cards 1 - 3000

• Three trays with bead cups

• Small tray with bead cup for making exchanges 

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

• 2 Rugs

• Tables or Underlay Mats for laying out the small cards 

Purposes:     

• To show that the operation of addition is putting quantities together to form a larger quantity

•  To understand the role of changing

Age: 4 – 5 ½  

Preparation: Formation of Numbers, the Change Game, Teens and Tens Boards

Presentation 1: Static Addition

Layout

• Invite a small group of children (2-3) 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.

• The guide will go to each child and tell them a number to get from their cards (no exchanges).  Recite the number conventionally and invite the child to get the quantity from the shelf. 

• When they have cards and quantity to match, they will bring their tray and sit at the horizontal rug

• The guide brings the large tray.

• Each child will verify each category of quantity on their tray and then read their number conventionally.

Operational Process

• Line up the numbers vertically on the left side of the rug (from the child’s perspective) and the children will place their quantities on the large tray.  

Calculation

• Tell the children they will count to see what is on the tray.

• Assign each child a quantity category to count and to in front of them.  Start with the units.

• Once counted, they will go to the right side (from the child’s perspective) of the large tray in a cup.

• Ask the child to get the large card to match and place on the tray below the cup.

• Repeat for the rest of the categories.  After they are counted, they will be in the appropriate order on the large tray from the child’s perspective.

• When all the cards are on the tray, stack them and do the Magic Slide.  Lay the large cards below the smaller cards.

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 sum). When we put smaller quantities together, we get a larger quantity and that’s called addition. You did addition!”

Note:  As long as the children are working at this level, they are dependent on the guide for numbers.  Once they get the hand of the operation, move them to Dynamic Addition.  

Presentation 2: Dynamic Addition

Layout

• Same as above with the addition of the exchange tray and only give the children larger numbers 

Operational Process

• Same as Static Addition

Calculation

• Assign each child a category and ask them to place the quantity in front of them.

• Remind the children that if there are more than ten to say, “Stop!” so we remember to exchange.

• The units will be lined up like a ten as they are counted.  When ten are counted, the child stops, give a reminder of the exchange, “What do we do with 10 units?”  The units go onto the exchange tray and are exchanged at the store for a ten.  The ten is given to the child who is assigned the tens.

• When the units are exchanged as far as they can, the child will get the large card to match what is left and place it on the tray as in the last presentation.

• Repeat for the tens, then hundreds lining them up to mirror the category above and exchanging as needed.

• Stack the cards, Magic Slide, and place them below the small cards.

Story Summary of the Operation

• Same as in Static Addition

Note: The child can now get their own numbers and solve independently.

Control of Error: None.  Accuracy of the result is not the purpose.

Pedagogical Notes:

• The purpose of these exercises is about the process of the operation, not the correct answer.  The child just needs to engage in the process in the right way.

• Children should be encouraged to create their own addends. If they need the adult to help with the story summary, that is okay. 

• We give a powerful visual impression to the child by using smaller cards for the addends and larger cards for the sum.

• You may hear these presentations called The Collective Exercises.