##
* *Reflection: Intervention and Extension
Basic Constructions - Section 3: Guided Practice

When I first taught this lesson, I underestimated the disparity among students with respect to how quickly they would learn to perform the constructions in this lesson. I thought all students would pick up the techniques in similar amounts of time given that I would be showing the steps for each construction and all they would have to do would be to watch and replicate.

As it turned out, I had students who finished quickly and others who seemed unable to make sense of what they were seeing and needed to have the demonstrations repeated over and over again before they felt comfortable trying them on their own.

The second time I taught the lesson, I dealt with this disparity by using a looser structure than I had originally planned to use. For the first demonstration of each construction, I had all of my students put their tools down so that they could pay attention to my narration. In that narration, I described each step, one at a time, pausing after each step, using academic vocabulary. I also explained the purpose for each step.

After that, I basically put the demonstrations on a loop to play continuously. As students were working, I walked around and saw what there was to see. If a student had already finished, I asked them to explain the steps to me from start to finish. This would allow me to see if they had truly learned the steps or if they had merely followed individual directions without learning the process as a whole. If I noticed that a student was having trouble, I gave assistance. It tended to be technical issues, such as how to keep the compass point from moving or needing to adjust the pencil height. For others, they just couldn't keep up with the pace of the demonstration. By the time I could see who these students were, most other students had already finished so I could slow the demonstration down by pausing it after each step.

In order to keep the class on pace, I decided to allow students who were lagging behind to finish the written explanation of steps at home so that we could move on to the next construction for students who were waiting. So basically, I tried to create a structure that allowed students to work at their own pace. I chose to make time the constant and amount of work finished the variable in the situation. However, I did require students who didn't finish all work in class to go home and finish it.

*Differentiation*

*Intervention and Extension: Differentiation*

# Basic Constructions

Lesson 9 of 14

## Objective: SWBAT perform the following constructions and informally explain why they work: Copy a segment; Bisect a segment; Copy an angle; Bisect an angle; SWBAT use measurement to verify constructions

#### Activating Prior Knowledge

*15 min*

**Where We've Been:** Students have learned to use correct geometric naming conventions, symbolic notation, and diagrams. They also know and understand basic geometric terminology.

**Where We're Going:** We're introducing geometric constructions for the first time in the course.

The goal of this section is to make sure that students have a solid understanding of the figures they will be constructing: congruent segments, congruent angles, segment bisector, and angle bisector.

To help with achieving this goal, I use the Activating Prior Knowledge: Basic Constructions resource. As students are working, I walk around doing some informal assessment. I give feedback to get students to be precise with their diagrams (e.g., using tick marks appropriately).

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#### Concept Development

*15 min*

Since this is our first time doing constructions, I have to introduce some fundamental concepts. So I give students the following notes:

**Classic Geometric Construction:** A method of creating geometric figures using only a **compass** and a **straightedge.**

**Compass**: A compass is a tool for making **circles** or **arcs** with a specific **radius**.

**Straightedge**: An object with a straight edge that is used only to make straight segments (i.e., it is not used as a measurement device)

**Circle**: The **locus** of points in a plane that are equidistant from a point called the center

**Radius:** The distance between the center of a circle and any point on the circle

**Arc**: A continuous part of a circle

**locus**: The set of all points satisfying a given condition

So a compass creates a set of points (an arc or circle) that are equidistant from the center of a circle. The center of the circle is marked by the sharp point of the compass. We set the radius of the compass to determine the distance from the center that all of the points will be.

Keep in mind when we are doing constructions that this is what the compass is doing.

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#### Guided Practice

*60 min*

For this section of the lesson, all students have a compass and straightedge. I also give each student four sheets of blank white copy paper.

For starters, I show students how to adjust the radius of the compass. We start with a radius of 2.5 cm. Then I ask them to draw a circles with radius 2.5 cm. Then I walk around to make sure that no one is having major compass complications.

Next I instruct students to give one of the sheets of white paper the heading "Construction: Copying a Segment"

I run the copying a segment demonstration several times so that students get a feel for it. Then I show the demonstration one step at a time so that students can perform the construction themselves. Next, I have students write down the steps of the construction and a short explanation of why it works. Finally, I have students to verify that the segments are congruent. If they are congruent, students should mark the diagram appropriately ( with the lengths and with tick marks).

We then repeat this same process for bisecting a line segment, copying an angle, and bisecting an angle.

#### Resources

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The resource Independent Practice: Basic Construction are the worksheets from mathopenref.com that were designed to accompany the construction demonstrations. I use these as independent practice on the day following this lesson.

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- UNIT 1: Community Building, Norms, and Expectations
- UNIT 2: Geometry Foundations
- UNIT 3: Developing Logic and Proof
- UNIT 4: Defining Transformations
- UNIT 5: Quadrilaterals
- UNIT 6: Similarity
- UNIT 7: Right Triangles and Trigonometry
- UNIT 8: Circles
- UNIT 9: Analytic Geometry
- UNIT 10: Areas of Plane Figures
- UNIT 11: Measurement and Dimension
- UNIT 12: Unit Circle Trigonmetry
- UNIT 13: Extras

- LESSON 1: Origins of the Geometric Universe
- LESSON 2: Line Segments
- LESSON 3: Distances in the Coordinate Plane
- LESSON 4: Exploring Midpoint Quadrilaterals
- LESSON 5: Investigating Points, Segments, Rays, and Lines
- LESSON 6: Formative Assessment Day 1
- LESSON 7: Introducing Angles
- LESSON 8: Angle Measurements
- LESSON 9: Basic Constructions
- LESSON 10: Measuring to find Perimeter and Area
- LESSON 11: Finding Perimeter and Area in the Coordinate Plane
- LESSON 12: Geometry Foundations Summative Assessment Practice Day 1 of 2
- LESSON 13: Geometry Foundations Summative Assessment Practice Day 2 of 2
- LESSON 14: Introduction to Transformations