Partial quotients division with a number >1,000 with remainder

General

The students learn partial quotients division with a number greater than 1,000, with remainder.

Standards

CCSS.Math.Content.5.NBT.B.5

Learning objective

Students will be able to use partial quotients to divide a number greater than 1,000, with remainder.

Introduction

Have the students name a number to 1,000. You put this number on the blue line. Next you spin the upper wheel. Put the resulting number on the orange line. Then spin the lower wheel and put that number on the green line. The digits on the orange and green lines form one two-digit number. Next the students solve the problem that you have made.

Instruction

Explain that with partial quotients division you break up the problem into pieces and solve it in this way. You write down the problem and then put a line underneath it. Next you can use a helping row from the table of the number that you are dividing by. You don't have to put every problem in this row. You can double or halve problems, or imagine a 0 at the end of them. After this you solve the problem step by step to determine how many times 26 fits in 1,247. After each step you write down how much you have left. Sometimes you still have a number left at the end that you can't divide by 26. This number is your remainder. Next you add up all of the numbers that give how many times 26 fits in 1,247 (40, 5, and 2) and give how much you have left over (25). Explain that you will sometimes be asked for the remainder, while there is no remainder in the problem. In that case, you write a 0 as the remainder. Have the students solve a few problems using partial quotients. Have them write the problems down on graphing paper, and include a helping row if they need one. Next have the students practice in pairs. They discuss with each other how they would solve each problem using partial quotients. After this you have the students solve a few more problems on their own using partial quotients. Ask various students what steps they took. Encourage the students to take as large steps as they can.

Check whether the students can use partial quotients division by asking the following questions/assignment:
- Why is it useful to be able to divide using partial quotients?
- What aid can you use when dividing using partial quotients?
- Solve this problem using partial quotients: 1,619 ÷ 80

Quiz

The students test their understanding of partial quotients division with a number greater than 1,000 with remainder through ten exercises. The students can write down and solve the problems on graphing paper, and include a helping row if they need to.

Closing

You discuss once again with the students how it is important to be able to divide using partial quotients with a number greater than 1,000 with remainder, because that is how you can solve problems in an easier way. Check if the students know that with partial quotients division they solve pieces of the problem in steps and that they can use a helping row to do so. On the interactive whiteboard there are darker and lighter covers over numbers. The number that is under the dark cover is the first part of the problem. The number under the lighter cover is the second part of the problem. Have the students solve the problem using partial quotients division.

Teaching tips

When students have difficulty with partial quotients division, you can have them make helping rows of the table of the number that they are dividing by. Have them solve the problem step by step, for a problem without remainder. Carefully check each of the steps that the students take, and try to encourage them to take larger steps (not 100 × 3 = 300 and 100 × 3 = 300, but in one step 200 × 3 = 600).