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Dividing Segments Proportionately

Judith Danter, Math Teachers' Adventure of ICT Integration, Oct 10, 2017

In this lesson plan the students can explore how to divide segments proportionately.

Lesson Plan

In this chapter you find the lesson plan, a description and didactic commentary on the included materials.

1. Lesson Plan - Dividing Segments Proportionately

Lesson Plan - Dividing Segments Proportionately

Lesson Information

[table][tr][td]Subject: [/td][td]Mathematics[/td][/tr][tr][td]Grade Level:[/td][td]7th[/td][/tr][tr][td]Duration:[/td][td]30 min[/td][/tr][tr][td]Technology:[/td][td]teacher computer with projector, computer for students[/td][/tr][/table]

Topic

Dividing segments into a certain proportion

Learning Outcomes

The students are able to divide a segment graphically into a certain proportion.

Lesson Objectives and Assessment

[b]Lesson Objectives[/b][br][list][*]The students are able to divide a segment graphically with pen and paper. [/*][*]The students are able to divide a segment into equal parts.[/*][*]The students are able to divide a segment into any given proportion.[/*][*]The students are able to explain how to divide a segment into a certain proportion.[br][/*][/list][br][b]Assessments[/b][br][list][*]The students are able to divide a segment graphically into a certain proportion and to solve different tasks.[br][/*][/list]

Teaching Strategies

The students work independently on the computer and explore the applet on the worksheet. After they have answered the questions below the applet, the students should solve examples in their workbook graphically. They can still use the applet if they need some help.

Technology Integration

The students need the computer throughout the lesson sequence.[br]No prior knowledge of GeoGebra is necessary for working with this worksheet. [br]Alternatively, this applet can also be demonstrated by the teacher on the projector and the construction steps can be discussed and elaborated together.

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Worksheet

In this chapter you find the worksheet for the students.

1. Dividing a Segment Proportionately

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Dividing a Segment Proportionately

Instruction

First, explore the GeoGebra applet and then try to answer the questions below. [br]To do this, follow the construction steps 1 to 4 and read the instructions carefully. [br][br]You can change the task by draging the sliders below and modifying the proportional ratio m : n. [br]Move point B and check whether the given ratio is still valid.

Which statements are accurate to divide a segment propotionately?

The division of a segment propotionately can only be done graphically and can not be calculated. To divide a segment you have to add the ratios and then divide the auxiliary segment into as many equal parts as the value of the sum. If the ratio is 3 : 4, the 7th auxiliary point is connected to the end of the segment and the parallel line through the 3rd point gives the correct division on the given segment. It does not matter how many parts the auxiliary line has.

Task

Now use your workbook and divide the segments into the given proportion graphically:[br][list=1][*]Divide the segment AB = 10 cm into the proportion 2 : 4.[/*][*]Divide the segment EF = 12 cm into the proportion 3 : 5.[/*][*]Divide the segment XY = 15 cm into the proportion 5 : 6.[/*][/list]Check your solution by calculating and measuring the length of the divided segments!

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