When my daughter started division in fourth grade, I knew we were in for trouble (and extra math practice at home). As a parent who learned math the “old” way, I had a really difficult time understanding the processes behind her math homework and word problems. (I am embarrassed to say that fourth grade division word problems are no joke.) I used Evan-Moor’s book Math Fundamentals to learn, practice, and review division strategies. The visual models and explanations provided a step-by-step learning process that reinforced what my daughter was learning at school and deepened her understanding. While helping my daughter master long division, I even discovered strategies behind the division process that deepened my understanding of the relationship between division and multiplication.
Division is one of those math skills that deserve lots of attention, explanation, and practice. Rather than teach math as a series of systems/steps to memorize, today’s math curriculum encompasses the fundamental thought processes behind every skill and strategy children are taught. Today’s math curriculum wants children to understand why they are doing those steps and to utilize that understanding of number relationships to solve problems more efficiently. If children know why they are doing specific steps, they can apply that understanding to solve various mathematical problems and understand number fluency at a deeper level.
Here are some of the strategies and concepts we practiced that helped both my daughter and me better understand division.
Beginning Division and Multiplication Facts
As your child begins to learn division, it is important for him/her to understand the relationship between division and multiplication. Children need to know their multiplication facts well. (If they don’t know their multiplication facts, practice fluency for a few weeks before beginning division.) Check out the additional links below for tips and ideas to learn multiplication facts.
Relationship between multiplication and division
Beginning division teaches the simple concept that in order to divide, you must multiply. Use visual examples of multiplication and division will help your child learn to recognize the difference between multiplication and division.
If you are used to the old method of dividing, this process may seem tedious, but it is important for children to understand the difference between multiplication and division. When the numbers and word problems get more complex, this foundational understanding will help them know when to divide and when to multiply.
Model how to find an unknown number with multiplication or division.
To find out if your child understands the basic relationship between multiplication and division, ask him or her:
- How can multiplication facts help you solve division problems?
Answer: multiplication and division facts are related. If you know one fact you can solve the other related fact.
Three Division Strategies
One aspect of the current math curriculum that I love is the focus on teaching multiple strategies and allowing children to decide which one works best for them. This approach allows children to understand and choose which method makes the most sense for their learning style. Trying different approaches can sometimes even make the difference between failure and success in math. Here are three different strategies to teach when beginning division.
1. Make connections with division patterns and break down numbers
This is number fluency at its finest. Teaching children to recognize and use patterns within number operations will make them very efficient problem solvers.
6,000 ÷ 3
6 ÷ 3 = 2
6,000 ÷ 3 = 2,000
Just think of 6,000 divided by 3 as 6 thousands divided by 3, and that is 2 thousands.
2. Breaking down numbers into “friendly” numbers using an area model
260 ÷ 5 = 52
Break down numbers into “friendly” numbers. Breaking down numbers into easily divisible numbers is important to learn for number fluency. This may seem a bit tedious, but understanding how to break large numbers into easier-to-manipulate numbers can build children’s mental math capacities.
Break down 260 into the “friendly” numbers 250 and 10. I chose 250 because it’s the divisor, 5, multiplied by a big number (50). I choose 10 because it’s the difference between 250 and 260. These go inside the boxes of the area model. Divide each one by the divisor to get the factors, then add the factors together.
3. Divide by subtracting groups
623 ÷ 4
I can make groups of 4 and subtract them from 623 until there isn’t enough left to make a group. I’ll start with 100 groups of 4. That leaves 223. Next I’ll subtract 50 groups of 4. Now I have 23 left. 5 groups of 4 will use up most of it; there is not enough left to subtract even 1 group of 4. Finally, I’ll add up the number of groups of 4 and write the remainder.
Long Division: dividing multidigit numbers with area models, partial quotients, and the standard algorithm
If I just lost you using phrases like “partial quotients” and “standard algorithm” don’t be alarmed. These are just mathematical terminologies for step-by step processes. A quotient is an answer, and a partial quotient is a partial answer. A standard algorithm is a step-by-step way to solve a problem. Long division uses these strategies to incorporate repeated subtraction to eventually find the answer.
Dividing multidigit numbers using an area model
We tackled this earlier with beginning division, but now the numbers are getting larger and a little more complex.
3,182 ÷ 15 = 212 R2
Division is just repeated subtraction. I’ll make groups of 15 and subtract them until there isn’t enough left to subtract. Then I’ll add up the number of groups. Since I ended up with a number smaller than the divisor, I’ll write it as a remainder.
3,182 ÷ 15 = 212 R2
Divide using partial quotients
Just like in the area model, I’ll find groups of the divisor and subtract them. Then I’ll add up the numbers of groups and write the remainder if there is one.
Divide using the standard algorithm
If you sigh with relief at this example, I completely understand. This is the traditional way of teaching division that most of us learned years ago.
This long division standard algorithm repeats itself with the steps of:
4. Drop down the next digit
*Many children get confused with steps 2 and 3 because you are not actually dividing but multiplying and subtracting to find a remainder.
3,182 ÷ 15 = 212 R2
Look at only one place at a time, starting on the left. Since 15 won’t divide into 3, I’ll go to the next place. Now I estimate how many times 15 will go into 31 and write that above the 1. I subtract and bring down the digit from the next place. I keep doing this across the dividend (number). When I run out of places, I’ll write the leftover number as the remainder.
The best way to help your child master the difficult skill of dividing is to practice, practice, and practice. Find out which method works best for your child and provide plenty of practice problems for him or her to work through. Also, don’t forget to tackle division word problems. Solving word problems can demonstrate how well your child understands the concept of division and how to use it.
For teaching tips on word problems and multiplication, check out these articles:
How to Solve Word Problems in 3 Simple Steps
Tips for Teaching Multiplication and a Free Multiplication Strategy Printable