Step 1

• Children separate a larger group of up to 19 objects into two smaller groups.
• Repeatedly separate a group of objects into smaller groups per the table below. For example, 10 pencils from 10 pencils leaves 0 pencils, 8 coins from 18 coins leaves 10 coins, and 9 cars from 19 cars leaves 10 cars, etc.

• When children are ready, have them separate the object groups themselves.
• Children must perfectly master the operations listed in the table before proceeding to the next phase of the lesson.

Step 2

• Children separate groups of objects they can’t see, but can imagine (bears, mountains, trees).
• Using the table above as a guide, ask children to call out the answer to questions such as, ‘How many are one shoe from eleven shoes?’ and ‘How many are nine frogs from nineteen frogs?’
• Give numerous exercises on each number, with constant reviews, until children can recite each operation in the table with great accuracy and rapidity.

Step 3

• In this phase, do not mention objects. Children subtract numbers directly.
• Using the table above as a guide, ask children to call out the answer to questions such as, ‘How many are one from eleven?’ and ‘How many are four from fourteen?’
• Give numerous exercises on each number, with constant reviews, until children can perform each operation with great accuracy and rapidity.

Step 4

• Direct children to practice writing and reciting the subtraction problems listed in the table above. For example, they would write and then recite:
• 9 from 19 leaves 10
• 19 minus 9 is 10
• 19 – 9 = 10
• Repeat for each combination in the table until the children master the tasks.

Step 5

• 18 + 1 or 1 + 18 = ; therefore 19 – 1 = ; 19 – 18 =
• 17 + 2 or 2 + 17 = ; therefore 19 – 2 = ; 19 – 17 =
• 16 + 3 or 3 + 16 = ; therefore 19 – 3 = ; 19 – 16 =
• 15 + 4 or 4 + 15 = ; therefore 19 – 4 = ; 19 – 15 =
• 14 + 5 or 5 + 14 = ; therefore 19 – 5 = ; 19 – 14 =
• 13 + 6 or 6 + 13 = ; therefore 19 – 6 = ; 19 – 13 =
• 12 + 7 or 7 + 12 = ; therefore 19 – 7 = ; 19 – 12 =
• 11 + 8 or 8 + 11 = ; therefore 19 – 8 = ; 19 – 11 =
• 10 + 9 or 9 + 10 = ; therefore 19 – 9 = ; 19 – 10 =

Step 6

• Assess mastery by reading aloud the word problems below and having the children mentally compute and recite the solutions. If children have difficulties, repeat the prior phases and then reassess.