Step 1

• Children separate a larger group of up to 17 objects into two smaller groups.
• Repeatedly separate a group of objects into smaller groups per the table below. For example, 8 pencils from 8 pencils leaves 0 pencils, 8 coins from 12 coins leaves 4 coins, and 9 cars from 17 cars leaves 8 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 nine shoes?’ and ‘How many are nine frogs from seventeen 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 nine?’ and ‘How many are four from twelve?’
• 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:
  • 8 from 17 leaves 9
  • 17 minus 8 is 9
  • 17 – 8 = 9
• Repeat for each combination in the table until the children master the tasks.

Step 5

• Have children copy, solve, and recite the following table:
  • 16 + 1 or 1 + 16 = ; therefore 17 – 1 = ; 17 – 16 =
  • 15 + 2 or 2 + 15 = ; therefore 17 – 2 = ; 17 – 15 =
  • 14 + 3 or 3 + 14 = ; therefore 17 – 3 = ; 17 – 14 =
  • 13 + 4 or 4 + 13 = ; therefore 17 – 4 = ; 17 – 13 =
  • 12 + 5 or 5 + 12 = ; therefore 17 – 5 = ; 17 – 12 =
  • 11 + 6 or 6 + 11 = ; therefore 17 – 6 = ; 17 – 11 =
  • 10 + 7 or 7 + 10 = ; therefore 17 – 7 = ; 17 – 10 =
  • 9 + 8 or 8 + 9 = ; therefore 17 – 8 = ; 17 – 9 =

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.