Introduction to Division

My focus is on working with students with special needs. Many struggle with rote memorization, including for multiplication facts. I find that skip counting, with scaffolded support in the learning process, provides them access to multiplication and therefore division. To access division, I use an approach of skip counting to find a missing factor and then connect this to division. This post provides details of a handout using this approach.

Overview

This handout focuses on connections to prior knowledge of skip counting and finding a missing factor. The students then make an explicit connection by rewriting division problems as missing factor problems. The handout is linked at the bottom.

Skip Counting

If students are struggling with multiplication, they are likely having trouble with skip counting. I start with a warm up on skip counting with the numbers that are easiest for students to skip count. Note: you can start with 2, 5, 10 only if necessary.

Factor Tree

I have students solve a missing factor problem using a provided skip counting row. Then they are shown that the problem can be rewritten as a division problem which has the missing factor as the answer. That is, division is another way to write a missing factor problem. You can use factor tree handouts and have students practice rewriting the problem as a division problem. Note: I see that most worksheets are used for prime factorization. Use the first two branches as shown in the image below.

Missing Factor

The students are then presented a math sentence only for missing factor. They are to solve for the missing factor. Then they rewrite the math sentence into a division sentence and solve again. I have a separate column to help emphasize that they are lookin to solve a division problem. They have to see the division problem in isolation and then write the quotient.

Division Problems

Finally, the students are presented division problems and rewrite as a missing factor problem. Their mental process can be as follows: “2 times what gives me 10?” and then they skip count by 2s until they reach 10. This can be supported with multiples rows as shown in the factor tree page. A blank page is provided. You can give students a division worksheet and have them copy the problems into the handout.

Access to Handout

Here is a link to the handout.

Partial Quotients Too?!

There is a difference of opinion on what is essential to teach in math. Partial Quotients algorithm (and the Standard Algorithm for division) are topics I believe are worth discussing regarding the need to master these beyond a single digit divisor.

In response to the post on the value of teaching Long Division by muli-digit divisor, there were several responses that cited the value of Partial Quotients. I like that approach much more but the same question still arises. Are students grasping the concept or do they not see the forest among the trees? What is the cost-benefit analysis for this? What do they gain, besides practicing skills?

Long Division: Should it be Long Gone?

I have seen many students struggle with long division (especially the Standard Algorithm but also the Partial Quotients Algorithm). Similarly, I have seen many teachers lament this lack of proficiency. I suggest that it is prudent to conduct a cost-benefit analysis for learning these algorithms for division beyond 1-digit divisors.

If students understand the concept of division and perhaps can do long division with 1 divisor, what is the purpose of teaching long division with a multiple digit divisor (or the partial quotients algorithm).

For a long time square roots were computed using a lengthy algorithm, similar in nature to long division. We don’t teach that any more.

Sharp came out with a scientific calculator in 1978. It had a square root button. No more algorithm.

Long Division – Scaffolded Handout

Many teachers shared that long division is one of the hardest math topics to teach. A major factor is likely related to a lack of mastery of multiplication facts. I have posted about some strategies related to multiplication. Here is a handout my initial attempt at scaffolding long division (WORD, PDF).

There are 4 versions: with and without arrows and with or without all squares. I am interested in feedback and would revise as needed. (Update, if you accessed the files before 8:30AM EST on Dec 4 you will see that I changed the wording in the left columns.)

I did not attempt to include using “R” to identify the remainder as my focus is on the steps.

The handout has a full page of each type. (partial pages shown).