Purpose:
– To give the child all the possible combinations in addition.
The red line has the same purpose as the notched card in the snake game: to show how many went to make ten and how many units were left over.
– The red line teaches how many numbers are composed of a ten and a quantity of units bringing us that much further toward another ten.
– This is the mechanism of addition that has to be learned. The child is helped to see the entire structure of addition and to memorise the combinations.

Control:

Age:
5 – 6 years

Materials:
A board divided into 18 squares across from left to right and 12 squares from top to bottom.
Each square is 2 x 2 cm..
Above the grid are the numerals from 1 to 18.
Numerals 1 to 10 are in red, then a red line divides the board vertically; the numerals from 11 to 18 are in blue.
Two sets of numbered strips.
One set is blue with a numeral in red (1 to 9) at the end of each strip; the other set is red, divided into squares by blue lines, with a numeral in blue (1 to 9) at the end of each.
Squared paper and pencil.
Control Charts 1 & 2.

Presentation:

At a table, ask the child to read the numbers along the top of the board in random order.
Note the red line, the color of the numbers and the grid.
Remove the blue strips – arrange like the number rods to the left of the board.
In the same manner arrange the red strips to the right of the board.
The child chooses a blue strip ie. 6 or 7.
Place on the top line of the grid, aligned at left side.
Place the ‘one’ red strip directly to the right of the blue strip.
Read the board – ie. 7+1=8. The answer is found directly above the last section of the red strip.
Write the equation.
Remove and replace the red strip into the stair.
Repeat for each red strip, 2 through 9.
By the third or fourth equation the child may take over.
When finished, show the child how to check his work with the Addition Control Chart # 1.

Exercise:

As in the presentation the child works through all the tables.

Exercise 2A:

Ask the child to choose a number, ie. 6 or 7.
Write the number centerd on the page.
State the goal: to find all the pairs of numbers which make up that amount.
Begin with the ‘one’ blue strip – laying it on the grid as before.
Ask the child what is needed to add to ‘1’ to make the chosen amount. (The child may count the squares to find the answer.)
The child places the appropriate strip to the right of the blue ‘1’.
Read the equation, ie. 1 + 5 = 6. The child writes the equation.
Repeat the procedure until all the possible combinations are on the board.
Check the work with the Addition Control Chart #1.
The child continues through all sums 2 – 18.

Exercise 2B:

When the child has completed the above exercise, have him make a chart of all the numbers and their combinations on graph paper. ie. 2 = 1 + 1 3 = 1 + 2, 2 + 1 4 = 1 + 3, 2 + 2, 3 + 1
Check chart with Addition Control Chart #1.

Exercise 3A: Commutative Law

Write an equation, ie. 2 + 4 =.
The child uses the board to find the answer (the blue strip for the first addend, the red for the second addend) and records it.
Write another equation reversing the above addends, ie. 4 + 2 =.
The child uses the board as above to find and record the answer.
Ask if the same numbers were used to make the sum.
Check by comparing the strips (place equivalent strips underneath each other).
Note that it does not matter which side of the plus sign the addends are on the answer is the same.
Repeat with a few more examples.

Exercise 3B:

Using the chart the child made in Exercise 2b make a second chart which does not include duplicates. ie. 2 = 1 + 1 3 = 1 + 2 4 = 1 + 3, 2 + 2 5 = 1 + 4, 2 + 3
Check chart with Addition Control Chart #2.