OVERVIEW The following math shortcuts will help students master some of the more difficult concepts by presenting a simpler method or helpful way of understanding the processes. The methods have been used successfully in the fourth grade math curriculum. Students have shown a substantial gain in understanding and retaining the learning.
OBJECTIVE(s) The philosophy behind these shortcuts is to relate the new learning more closely to previously learned materials with the idea that elementary students are like computers and must be reprogrammed each time new learning is attempted unless a way can be found to tie the new learning to the old in a quick and easy way.
|
58 x37 |
(5+8=13, 1+3=4) (3+7=10, 1+0=1) |
4 x1 |
1. "Add the digits of each factors till each reduces to a one-digit sum and then multiply. |
|
406 +1740 |
(4+0+6=10, 1+0=1) (1+7+4+0=12, 1+2=3) |
1 +3 |
2. "Add the digits" of each products till each reduces to a one digit sum and then add. |
| 2146 | (2+1+4+6=13, 1+3=4) | 4 | 3. "Add the digits" of the final product till it reduces to one digit sum. |
4. Check that the results in steps 1-3 above are the same (in this case 4).
PURPOSE To teach students the initial concept of division by one digit, without the confusion of the long division form.
ACTIVITIES AND PROCEDURES This method has been used very successfully to introduce the concept of division in relation to multiplication. Students who have mastered the multiplication facts should have no difficulty with one-digit division. The long-division form is taught after the students understand the short-division form and can divide any number by one digit.
Rationale From first grade, students have learned to add and subtract problems from right to left starting with the ones place. The long-division form attempts to teach students to work from left to right, which goes counter to all previous learning. Also students must master a series of steps (divide, multiply, subtract, bring-down, remainder) which uses several difficult math concepts and the concept of "bring down" which can be very confusing. With short-division the student uses the multiplication facts to break the number and find how many are left over. *Note / denotes division
3/7 = 2
3/7 = 2 r1
3/72 = 2 r12
3/72 = 24
4/6375
The problem is now complete To check ( 159354 ) + 3 = 6375 All major calculations were done by the student as "headwork". This procedure works with any number divided by one digit. The long division form should be introduced after students have mastered short division. These shortcuts have helped my class tremendously. My post-test average for division was 94%.
SUGGESTIONS/MODIFICATIONS
- As not to confuse the students be sure they have mastered the skills before introducing the shortcuts.
- Be sure that the students understand the shortcuts are for checking their work only.
- Ask the students to come up with other ways to check their calculations and test them to see if they work.