Lesson plan

In this lesson, we’ll introduce the concept of dividing decimals to `6`th graders by using the standard algorithm for division.

Grade 6

Number System

6.NS.B.3

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Students will be able to divide decimals fluently using the standard algorithm.

- Teacher Slideshow
- Online Practice

Start the lesson off with a notice and wonder activity. Share slide one of the slideshow where students will discuss dividing decimals by multiples of `10`.

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Give students a few minutes to think about possible answers. Have them write down `3` notices and `3` wonders about the equations. Students may notice there are two division problems and there are two multiplication problems. They may notice the `7.2` is being used in all four equations or notice the patterns with multiples of `10`. Students can have a variety of responses for what they wonder as well. Responses could vary from why the decimal is moved in a specific direction to what would happen if you divided by a decimal instead of a whole number.

Give students a simple problem `48 \div 3`. This is a good time to review the steps in long division.

Ask them that if `48 \div 3` is `16`, what do they think would be the value of `4.8 \div 3`. This will lead to an interesting discussion of what should happen to the decimal point. But without getting into the procedure using long division, help students to build an intuition.

Hopefully, students will see that `4.8` is just `48` divided by `10` and therefore `4.8 \div 3` will have the same answer as `48 \div 3` further divided by `10`.

Then talk about what to do with the decimal point when they are doing long division.

The first example is dividing a decimal by a whole number. Show students that they need to bring the decimal point up to the quotient so it will be correctly placed once they start dividing. Emphasize that the decimal point has to be placed exactly above where it is in the number inside the house (the dividend). Then they can ignore the decimal and complete the long division. |

Try one more problem with students: `3.6\div 3`.

Ask students to look at the two expressions and figure out what is same and what is different in the two expressions.

Students are likely to say that the numbers are same but are not since there are decimal points in both. Some might point out that in both cases, the decimal point has moved one place to the left. Ask them what operation can cause a decimal point to move to the left - students will make a connection to the problems in the warm-up.

Once you have collected and discussed their answers, ask them if they both have the same value. Some students are likely to say that `4.8 \div 0.6` is smaller than `48 \div 6`, and some might think they have the same value. Ask students to explain their thinking. Hopefully, all be convinced that when you multiply `4.8` and `0.6` by `10`, you get `48` and `6`.. and that the `10`s cancel each other out (it is like multiplying by `1`).

`\frac{4.8}{0.6} \cdot \frac{10}{10}=\frac{48}{6}`

Give students a new problem: `2.4 \div 0.8` and ask them if they expect the answer to be more than `1` or less than `1`. Once you have established that the answer will be more than `1` (because you are dividing by a smaller number .. and both are positive:), ask them to do the division. Students will likely use the work they did earlier to rewrite it as `24 \div 8` and give an answer of `3`.

You can then move to a few more problems: `24 \div 0.12, 0.72 \div 1.2, and 5.4 \div 1.25`. Every time, you start the problem by asking them if they expect the answer to be more or less than `1`.

Pass out class whiteboards to students and have them work on each division problem. Once a student has completed the problem, have them hold up the whiteboard and check their work. Go over each problem as a quick discussion. You can have students volunteer to come to the board to show their work!

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of dividing decimal activities. Check out the online practice and assign to your students for classwork and/or homework!

Dividing Decimals Practice

Problem 1 of 4

<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><p>`34÷0.4`</p></selectivedisplay>

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