Students learn partial quotients division with remainder.
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The students learn partial quotients division with a number to 100 with remainder.
Students will be able to use partial quotients to divide a number to 100 with remainder.
On the interactive whiteboard there is a short story. Using this story, the students must make the correct division problem and then solve it using partial quotients.
Explain that with partial quotients division you split the problem up into pieces and solve it in this way. You write down the problem and then draw a line underneath it. Next you can use a helping row made from the table of the number that you are dividing by. In this row you don't have to include every problem. For example, you can double or halve problems to get more. After this you solve a problem step by step by seeing how many times 4 fits into 49. After each step you write down how much you have left over. Sometimes you have a number left over that you can no longer divide by 4. This number is your remainder. Next you add up all the numbers that give how many times 4 fits into 49 (10 and 2) and give how many you have left over (1). Have the students practice solving a few problems on their own using partial quotients. Have them write down the problems on graphing paper, and remind them that they can also write down a helping row if they need to. Next you explain that you can also solve problems with larger numbers using partial quotients. The students also practice solving this type of problem. Ask various students what steps they took to solve the problem. Encourage the students to take the largest steps that they can when solving a problem.
Check whether the students can divide using partial quotients by asking the following questions:
- 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: 67 ÷ 4.
The students test their understanding of partial quotients division with a number to 100 with remainder, through ten exercises. Each of the exercises is a division problem that must be solved using partial quotients. The students can first write out each of the problems on graphing paper, and they can also write down a helping row if needed.
You discuss once again with the students that it is important to be able to divide using partial quotients with a number to 100, because that is how you can solve problems in a quick way. Check if the students know that with partial products you solve a problem in steps and that they can use a helping row to assist in their calculations. Have the students work in pairs. Both students come up with a division problem. Next they solve their partner's problem. After this they discuss how they did it. Are the steps they took similar, or did one person take bigger steps than the other?
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 a problem step by step, with no remainder. Look carefully at the steps that the students make and try to encourage them to take bigger steps (not 10 × 3 = 30 and 10 × 3 = 30, but in one step 20 × 3 = 60). After this they can practice with problems for which there IS a remainder.
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