In order to learn division, the student must first have a good understanding of multiplication. The child doesn’t need to be perfect but should know the majority of the facts or have a reasonably quick strategy to figure out the answer.
When teaching division, we will be going in steps.
Step 1: Have the student understand the concept of division and be able to solve division problems with manipulatives.
For example: Given 12 pennies. Have the student evenly divide the 12 pennies among 2 people. From that practice writing the division statement 12 / 2 = 6 and have student explain the meaning: “12 pennies divided into 2 groups gives 6 in each group.” Then have the student divide the 12 into 3 groups and repeat the math sentence and the explanation. Next, divide 12 into 4 groups, then 6 groups. Repeat with other numbers such as 16 (divide into 2, 4, and 8 groups) until the student shows mastery of the concept and writing the corresponding math sentence.
Step 2: Have the student understand the concept of a remainder. You will continue with manipulatives in this exercise. Give the child 5 pennies. They have to share the pennies among 2 people. Let them try, if they split the pennies into 2 and 3 then discuss how that isn’t fair. If they divide it 2 and 2 with 1 left over, explain that happens sometimes with division: we don’t have an even amount to divide and therefore get a remainder. Have the student write the problem as: 5 / 2 = 2 with Remainder 1. Continue this process with other numbers: 9 divided by 2. 11 divided by 3, etc.
Step 3: Have the student understand the link between multiplication and division. Go back to your manipulatives and have them show you 3 x 4 = 12 with manipulatives. Remember that multiplication should have been taught as the x means “groups of” so 3 x 4 means 3 groups of 4. Put your 3 groups of 4 equals 12 to the side. Now have them take 12 and divide it 3 groups as you did in step 1. 12 / 3 = 4. Show them that their result is the same as their multiplication piles they made. In the end they have 3 groups of 4 items. Have the student write the fact family: 12 / 3 = 4; 12 / 4 = 3; 3 x 4 = 12; 4 x 3 = 12. Show them how if you read a division problem “backwards” you have a multiplication problem. Also show them that they can think of 12 / 3 as “what times 3 equals 12?” Continue with practice – 1) writing fact families and 2) finding missing factors: 4 X ___ = 16 (After they get the answer, convert to a division problem – 16 / 4 = 4).
Step 4: The next step is to teach the long division process. The key here is that we are focusing on the process, not on learning division – although doing the practice will help reinforce the concepts of division. Print out and cut the division cards, you will need to use these are you teach the process.
Example: 215 / 5.
We actually start with a 3 digit number because it shows the repetitive process. Get out the X5 division card. On a white board, write the problem. The steps to the division process are:
1. Look at the first number, 2, does 5 go into 2? No, 5 is too big.
2. Look at the first 2 numbers together: 21. Looking at the division card, find the number closest to 21 without going over. You see that the number is 20.
3. Write the number to the left (blue number) above the 1 on top. Write the number to the right (red number) below the 21. So, a 4 goes on top and the 20 goes below.
4. Now, subtract 21-20. You get 1. Using an arrow (make sure they use the arrow) bring down the 5 so it is next to the 1, making 15.
5. Repeat process: find a number as close to 15 without going over. We find 15 in the table. The red number (3) goes on top above the 5. The blue number (15) goes below the 15, now subtract. We get 0. Note, there are no more numbers to bring down and since we ended with 0, we have no remainder.
Example: 3426 / 5
1. 5 doesn’t go into 3.
2. Find closest to 34 on chart without going over: 30 (5X6=30).
3. Put 6 on top and 30 under the 34.
4. Subtract, get 4.
5. With arrow, bring down the 2, to get 42.
6. Find the closest to 42 without going over: 40 (5X8=40)
7. Put the 8 on top and the 40 under the 42.
8. Subtract, get 2.
9. With arrow, bring down the 6, to get 26.
10. Find the closest to 26 without going over: 25 (5X5 =25)
11. Put the 5 on top and the 25 under the 26.
12. Subtract, get 1.
13. Since that was our last number, 1 is the remainder.
14. The answer is 685 Remainder 1.
Keep practicing with different divisors until the student can do it independently with the division cards.
Step 5: The student now knows the concept of division and the process of division. Now they need to practice division without the help of the division strips. First give them problems with one of the easy divisors such as 2 or 5 and a 2 digit dividend. Even if it goes in evenly such as 5 into 25, make sure they write out the 25 underneath and show the remainder goes to 0. Give them remainders that go to zeros and ones that don’t so they get practice taking the problem to the end.
Step 6: Once the student is successful with 2 digit dividends with divisors of 2 and 5, have them work with 3 and 4 digit dividends but still use the divisors of 2 and 5.
Step 7: Expand with new divisors one at a time. Do 2 digit dividends first and then expand to 2or 4 digit dividends before moving onto a new divisor.
To view division strips visit: http://www.apex-math.com/teaching-division-to-children