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STEP 2

• Point to the clock images in a random order and have children determine and speak aloud the times.

STEP 3

• Have children draw clocks showing each of these times.

Step 1

• Have children use physical objects to demonstrate and solve these exercises, such as an abacus, toys, or beans.

Step 2

• Have children write out each problem and solution in equation form. For example, children write ‘4 – 2 = 2’ for ‘How many are 4 less 2?’

Step 3

• Assess mastery by reading aloud the listed problems and having the children mentally compute and recite the solutions.
• If children have difficulties, work with physical objects again and then reassess.

STEP 1

Teach children that the numbers 1-12 mark the hours, the minutes, and the seconds depending on which hand is pointing at the number. Point to each number on the clock image shown below and have children recite the following:

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.

STEP 1

• Children separate a larger group of up to 18 objects into two smaller groups.
• Repeatedly separate a group of objects into smaller groups per the table below. For example, 9 pencils from 9 pencils leaves 0 pencils, 8 coins from 17 coins leaves 9 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 ten shoes?’ and ‘How many are nine frogs from eleven 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 ten?’ and ‘How many are four from thirteen?’
• 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 18 leaves 9
• 18 minus 9 is 9
• 18 – 9 = 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:

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

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.

Step 1

• Tell children seconds are the shortest unit of the three. Count a few seconds off with the children – say ‘One thousand one, one thousand two, …, one thousand five.’
• Tell children sixty seconds make up a minute. Count a whole minute off with the children – say ‘One thousand one, one thousand two, …, one thousand sixty’ etc.
• Tell children sixty minutes, or 3600 seconds make up an hour. Count a few seconds off with the children – say ‘One thousand one, one thousand two, …, one thousand five.’ Tell children you’d need to keep count to 100 36 times before an hour would pass.
• Tell children 24 hours make up a day. Count a few seconds off with the children – say ‘One thousand one, one thousand two, …, one thousand five.’ Tell children you’d need to keep counting all day and all night before 24 hours would pass.