## 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.

Here is a link to the handout.

## 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?

## 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 3-digit Divided by 1-Digit

I created scaffolded handouts for 3-digit divided by 1-digit as a follow up to the previous scaffolded handout of 4-digit divided by 1-digit. Here are links (Word, PDF).

## 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).