Specify the number of exercises N. You are given the option of between five and twenty. Then choose the largest number of summands K allowed for all N of the exercises. The number K must be between two and ten.

The child and parent should start with five exercises for the first few days, then gradually increase the number of exercises to twenty. During that initial time, the largest number of summands allowed should be two. After being able to do twenty exercises with ease, the child should continue to the next cycle. Together, repeat the cycle for K=3 to K=10 while remembering to gradually increase the number of exercises from five to twenty. All these nine cylces will be collectively referenced as Phase I. Notice the two checkboxes labeled addition and multiplication. By default, only the addition checkbox is checked for access to the Phase I cycles.

Access to any of the nine cycles which make up Phase II are given when only the multiplication checkbox is checked. The order of doing the cycles of Phase I should be repeated for Phase II.

Decide from two approaches for Phase II. The first approach is to periodically choose an exercise after the child has given the answer and ask how many times the number was added. The second approach is to have your child tell you for each exercise from the beginning until the middle of Phase II the number of times the number was added. The middle can be somewhere close to when N=8 and K=5.

Phase III consists of the cylces from when both checkboxes are checked. Instead of asking the question from Phase II for the first half of Phase III, read the exercises with summands that repeat in term of multiplication. For example, read the expression 5+5+5+5 as four times five. Notice that the first number read is the number of times five repeats. It could have alse been read as five times four. Be consistent which number is read first--the repeating summand or the number of times it repeats. How should you read the exercises in Phase III whose summands aren't all the same but which have some summands which do repeat? Well, read something like 1+3+3+7+9+9 as one plus two times three plus seven plus two times nine. At this point, it becomes a light memory game requiring concentration.

Mathematics notation should be introduced with paper and pencil during the second half of Phase III. Let us say we are doing the cycle for when N=18 and K=8 and are given the exercise 3+3+3+3. To introduce notation, write the expression using the symbol for multiplication. Then write it equal to the original exercise and have the child compute it. So it be written as 4*3=3+3+3+3=12.

An expression such as 1+3+3+7+9+9 gives an opportunity to introduce the use of parenthesis. Begin writing the expression with groups of repeating numbers within parenthesis. Write it equal to the expression where each pair of paranthesis is replaced with the multiplication notation. Then let the child compute it. For our example, we'd have 1+3+3+7+9+9=1+(3+3)+7+(9+9)=1+(2*3)+7+(2*9)=1+6+7+18=32.

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addition multiplication