#### Material

A collection of colored bead bars, boxed (minimum of five colored bead stairs).

Golden 10 bars, boxed (minimum of 25).

1 set of black and white bead bars, from 1 to 9, boxed.

A ‘bridge’, which may be a notched card.

A felt underlay – standard black or color-coded red.

All items fit on a tray.

#### Presentation

- Invite the child to the lesson.
- Show him the addition snake game.
- Ask him to bring the tray to a table.
- Ask him to unroll the red underlay.
- Place the lid under the black and white box.
- Take the black and white beads out of their box and randomize them on the underlay.
- “Let’s build a stair with the black and white beads.”
- Watch as the child counts and builds a stair in the top left.
- Open the colored bead box.
- “We are going to build a long, sinuous, snake. Sinuous means it goes up and down.”
- Place a few colored beads in a sinuous formation.
- Ask the child to add some beads.
- Continue adding beads together in this sinuous snake formation.
- “We are going to count the beads in this snake, and make it gold. I’ll show you what I mean.”
- Pick up the counter and place the notched part in between beads as you count, moving the counter with each bead.
- Count to ten with the counter, leave the counter where it is, and place a 10 bar above the beads that were counted. (take the lid off the box and put it back on every time)
- “These are the same!”
- “We’re going to take these colored beads out, but wait! There’s some left over that we need to save for counting!”
- Count what it is left over past the counter.
- Place the black bar of that number above the colored beads.
- Pull down the colored beads a few inches.
- Close the snake by putting the golden 10 bar and black beads in the colored beads spot.
- “The colored beads are going into this empty box. (the black and white bead box) The black ones just go back in the stair!”
- “We want our whole snake to be gold, so we just start counting right after the gold bar.”
- Continue the same process, counting the black bead and colored beads to make a 10.
- After three of four of these golden 10 bar exchanges, hand it off to the child and stay with the child.
- Watch to be sure that the child is performing the exercise correctly.
- Once everything is counted and exchanged, admire the snake with the child.
- “Can you carefully place the 10 bars back in their box?”
- “We will use this box of our colored beads that made the snake another time, for now, just put them back in the colored bead box with the rest of them.”
- And now you just need to put the black and white beads in their box which is empty right now.”
- Ask child to take tray to shelf.

##### Isolating the Bead Bars

- Invite the child to the lesson.
- “I’d like to show you something different with the addition snake game! Will you build a snake and then invite me over when you are done building it?”
- Isolate the first two bead bars by pushing them up on the underlay.
- Name the first two bead bars, such as 4 and 8, and count to 10.
- Place the marker where you stopped.
- Place a 10 bar above the colored beads.
- Place the black bead for the leftover beads above the colored beads.
- Point at the 10 bar and black bar.
- Say, for example “Ten and two make twelve.”
- Point at the colored beads, for example, 4 and 8.
- “Four and eight make twelve!”
- Move the colored beads down to the bottom of the underlay and then place them in the empty box.
- Close the snake with the golden 10 bar and the black beads.
- Continue the process as before in the original presentation, repeating these new steps of isolation when you have two colored bead bars that make at least 10.
- Hand it off to the child after a couple exchanges.
- Clean up as before.

##### First Proof

- Invite the child to the lesson.
- Ask the child to make a snake.
- Ask the child to count it as before and make it a gold snake.
- “When you are done, come get me. I want to show you something new!”
- Once the child finishes he will get you.
- “There’s a way for you to check that you counted the right number. It’s called a proof!”
- Place a few of the 10 bars vertically on the bottom left of the underlay.
- Ask the child to place the rest of the 10 bars.
- “Let’s put these colored beads over here.”
- Place a few of the colored beads, from the black and white bead box that is used to place the colored beads that made the snake but were exchanged for golden 10 bars, vertically on the bottom right of the underlay, from longest to shortest, left to right.
- Ask the child to place the rest of the colored beads.
- Pick up the longest colored bead and place it adjacent to the first 10 bar, such as a colored bead of 9.
- “What number bead do you need to make this 9 a 10? Right, one!”
- Place a 1 bead under the 9 in the same column.
- Repeat this process until you need to add a bead which you don’t have, for example, you have 7 and need a 3 but don’t have a 3.
- “We need 3 but don’t have a 3. I’ll show you what to do!”
- Take the smallest colored bead that can be exchanged for the number you need.
- For example, “We’ll take this 5 and exchange it.”
- Place the 5 bead horizontally near the top middle of the table.
- Take a 3 bead out of the colored bead box.
- Place it below the 5 bead.
- Take a 2 bead out of the colored bead box.
- Place it next to the 3 bead.
- “Three and two make five!”
- Place the 5 bead in the colored bead box.
- Place the 2 on the right with the colored beads.
- Place the 3 under the 7, adjacent to the 10 bar.
- Exchange a couple more times this way, then hand it off to the child.
- Stay with the child until he finishes.
- The colored beads should match exactly the golden 10 bars, in so far as not being a single bead more or less.
- “You did it! You got the same number, you got the right number! That’s how you check with the proof.”

##### Second Proof

- Invite the child to the lesson.
- “I have something new to show you.”
- Pick the beads that the child will use, but don’t make it obvious, for example: two 9’s, three 8’s, three 7’s, and four 4’s.
- Ask the child to make a snake, count it, and make it gold, just as before.
- After the child is done, say “I’ll show you how to check in a new way!”
- Place the 10 bars vertically in the lower left, and place any black-white beads with the 10 bars after all the 10 bars have been placed.
- Take the colored beads that made the snake out of the box.
- Organize them into horizontal columns based on number, biggest to smallest, on the right side of the table, for example:

first comes two 9’s horizontally, then three 8’s horizontally, and so on. - Demonstrate how to count them, starting with the first with in the column on the top, left to right, with the handle of the counter opposite of its usual direction, so that you can better see the whole column of beads.
- Once you get to 10, leave the counter where you stopped, place a 10 bead vertically below the column.
- Count the rest of the column, for example, “one, two, three, four, five, six, seven, eight.”
- “We don’t have an 8, but I know where we can get one!”
- Pick up a gold 10 bar from the left and place it horizontally at the top of the table.
- Find an 8 bead in the colored bead box and place it above the 10 bar.
- “What do I need with this 8 to make a 10? Right, a 2!”
- Find a 2 bead and place it next to the 8 bead.
- Place the 10 bar in the 10 bar box.
- Place the 8 next to the 10 bear in the first column.
- Place the 2 bead on the left with the other beads on the left.
- Count the vertical beads first. “1, 2, 3, … 18.”
- “Nine taken two times is eighteen!”
- Repeat this process for the other columns, hand it off to the child when he is secure, guide him as needed.

#### Exercises

Child works independently for all presentations and proofs.

#### Direct Purpose

Different ways to make 10.

Memorization of the combinations of addition.

To give subconscious knowledge that no two unit bars together make more than 18.

To reinforce the knowledge that addition and multiplication are the same concept.

#### Indirect Purpose

To introduce memorization of the multiplication combinations.

#### Age

5

#### Notes

For the first presentation, you can plan to make it so that the exchange results in all 10’s; if you take out an 8, put a 2 in your palm, or if a child takes out a 4, put a 6, casually so it just seems natural.

A golden snake might have a black “tail” or “head.”

Second proof comes much later after the first.

Second proof: black and white beads get exchanged, they don’t go vertically under columns for the proof.