MD10 - Division: One-digit divisor, 2,3 & 4 digit dividend, NO remainder

Instructor reads bold-faced words; student says words not in bold, and italics indicate directions to the instructor.

Notes on the Activities:

In Activity 1, the student manipulates the Base 10 blocks while the teacher models how to record the steps. In Activity 2, the student practices recording the steps while the teacher models with manipulatives. The Practice Script at the end allows students to transition from the concrete (manipulatives) to the abstract (written notation.)

Activity 1 -- Modeling Long Division with Manipulatives

Materials needed:

Mat 19 -- Blank division mat in sheet protector

Dry erase markers

Base 10 Blocks

Whenwe multiply, we first multiply the ones, then the tens, then the hundreds. With division we use a similar process, but in reverse.

Write the problem 96  3 horizontally on your mat. Student writes “96  3 =” in the upper left section of Mat 19. Write 96  3 as a fraction. Student writes 96/3 on the mat.

Now write the problem vertically. Student writes problem vertically, using the division symbol on the mat. Check to make sure that the studenthas written it correctly.

In division we start with a total and divide that into equal-sized groups. Look at the problem. What does the 96 tell us? (how many all together) What does the 3 tell us? (how many equal-sized groups)

Put the total number on the mat using your rods and cubes.Students put 9 tens rods and 6 ones cubes in the space on the left below the division problem.

Look at the problem. How many equal-sized groups? (3)

In most math, we start at the right. But in division, we start at the left, with the largest place value. Look at the dividend, or the total. What is the largest place value in the dividend? (tens)

How many tens? (9)

How many equal groups? (3)

What divided by what? (9 divided by 3)

Make it.Students make3 groups using the tens rods. Use the large portion of the mat on the right.

How many tens in each group? (3) Teacher writes 3 in the answer, above the 9 in the tens place. It’s important for teachers to model this step, so that students know how to stay in place value alignment.

What is 3 times 3? (point) (9) Teacher writes it below the 9. This shows us that we have used 9 tens so far.

Now we subtract. What is 9 - 9? (0) Teacher writes 9 – 9 = 0 in the problem. The 0 shows us that we do not have any more tens. Point out that there are no tens left on the side of the mat; they have all been separated into the three groups.

Our next digit is 6, so we bring that down and write it after the 0. Teacher draws and arrow and writes the 6. This shows that we have 6 ones. Point to the 6 ones on the side of the mat.

Now we’re at the ones part of the problem. How many ones? (6) How many equal groups? (3) Show it. Students move the cubes on the mat into 3 groups. Place the cubes next to the rods in each group. Each group should have 2 cubes.

How many ones in each group? (2) Teacher writes 2 above the line over the 3. This shows that 3 goes into 6two times.

What is 2 x 3? (point to the numbers in the problem)(6) This means we’ve used 6 ones. Teacher writes 6 below the 6 in the problem.

Do we have any ones left? (no)

Write in the subtraction and equal sign to show 6 - 6 = 0.

Can we go any farther in our problem? (no – there’s nothing left to bring down) So we’ve finished the problem.

Read and say the problem and the answer. (96 divided by 3 equals 32).

This means that 96 separated into 3 equal groups makes 32 in each group. Point to both the manipulatives and the written problem.

Practice with additional problems until the student is comfortable. Include problems that have “internal remainders,” such as 84  3 (see video).

Practice Problems:

36  3 =48  2 =78  3 = 38  2 = 65  5 =
Activity 2 – Recording and Practice

Materials:

Dry erase markers

Mat 20 --1-digit divisor sheet with lines

Base 10 Blocks

In this activity, the student practices recording long division on a mat. First, the teachers models using manipulatives while the student writes. When the student is ready, he can practice solving problems symbolically, without manipulatives.

Write the following problem horizontallyin the top corner of your sheet. (963 =). Write it as a fraction. (96/3 ) Now write it vertically in the other section of your sheet. Check that student uses correct place values.

This time the student will write the parts of the problem and the teacher will demonstrate using the manipulatives.

In division, we separate a total into equal-sized groups. What is our total? (96) Teacher shows 96with rods and cubes.

Which place value do we start with? (on the left, in the tens)

How many tens? (9) How many equal groups? (3) So it’s 9 divided by 3.

Teacher uses9rods to form 3 equal groups.

How many in each group? (3) How many times does 3 go into 9? (3) Write it in the tens column (above the line over the 9). Student writes 3 in the answer; check that it is in the correct place value.

Now multiply. What is 3 x 3? (9) Write that number under the 9.

That’s how many rods we’ve used so far. Point to the 9 the student just wrote.

Now subtract. What is 9 – 9? (0) Write it. Student writes to show that 9 – 9 = 0. Check that student includes minus sign and equal sign.

The 0 shows that there are zero tens left. But there are some pieces left. Where do we go next? (the ones)

Look at the problem. What is the ones digit? (6) Bring it down and write it after the zero. Student writes. What number is under the line now? (6)

The six is the ones part of the problem. Teacher points to the cubes. We have a total of 6 cubes and they need to be divided evenly into 3 groups. Teacher uses the cubes to show 3 groups of 2.

How many in each group? (2) Write it. Check that student writes “2” in the answer in the ones place, above the 6. This shows that six divided by three is two.

Now multiply. What is 2 x 3? (6) The 6 represents the 6 ones that have been used. Write 6 under the 6. Student writes.

What is 6 – 6? (0) Show it. Check that student uses minus sign and equal sign to record that 6 – 6 = 0.

Have we finished all parts of the problem? (yes – there is nothing else to bring down)

Do we have 96 all together? (yes) Is the 96 separated into 3 equal groups? (yes) How many are in each group? (32) So96 separated into 3equal groups makes 32 in each group.

Read the problem and the answer. (96 divided by 3 equals 32)

Continue with additional problems. See video for example of 84  3.

Practice Problems:

44  4 =64  2 =84  3 =76  4 = 32  2 =

When students are ready, use the script on the next page to practice solving problems symbolically, without manipulatives. See video for an example of 848  4 solved symbolically.

Checking Division with Multiplication

Students should know how to use multiplication to check a division problem. When students are ready, introduce this step.

Division is the reverse of multiplication. We can use multiplication to check our division answers. Let’s check 96  3.

What is 32 x 3? (96; if students struggle with multiplication, they could check their work with manipulatives.)

Is your answer the dividend we started with (96)?

  • If Yes, your division answer is correct. YEA !!!!
  • If No, check your multiplication.
  • If still No, check your division and make any corrections and check again.

PRACTICE SCRIPT

Materials:

Dry erase markers

Mat 20–1-Digit Divisor Sheet with Lines in sheet protector

Use the script below to practice problems such as these:

876  6 306  9 496  4 510  5 1712  8

(146) (34) (124) (102) (214)

SCRIPT:

Read the problem aloud. Student writes the problem on Mat 20. Check that digits are in the correct place value.

  1. Look at the sign. What kind of problem is it?
  1. Where do you start?
  2. What goes into what? (What divided by what?)
  3. How many times?
  4. Write it in the answer. Check for correct place value.
  1. What times what? How much? Write it.
  2. What minus what? Write the answer. Check that student uses minus sign and equal sign.
  3. Anything to bring down? (If Yes, Do it).
  1. Where do you go next?
  2. What goes into what? (What divided by what?)
  3. How many times?
  4. Write it in the answer. Check for correct place value.
  1. What times what? How much? Write it.
  2. What minus what? Write the answer.
  3. Anything to bring down? (If Yes, Do it).
  1. Is the problem done? If Yes, go to Step 17. If No, go to Step 9.
  1. Do we have anything left over?
  1. Read and say the problem and the answer.

When appropriate, have student check their answer using multiplication.

MD10 Script – Divide by one digit, no remainder1 of 5

HuronIntermediateSchool DistrictApril, 2011