Polygons in the Grid

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Objective

SWBAT use the coordinate grid to find polygons, area and perimeter.

Big Idea

Connecting the dots between Geometry and the Coordinate Grid

DO NOW

10 minutes

Students will be looking at ordered pairs to determine the lengths of the line segments.  This is something we have already covered so it is a review.  If you haven’t covered how to find the length of line segments, you may need to model one first.  I put a grid in their notes to help them  visualize the line segment for those that may struggle with just the numbers (SMP5: using tools strategically) Students could plot the ordered pairs and count the distance or they can look at the ordered pairs, determine the distance between the numbers that are different. For example, (-6,2) (-3, 2). Students would reason that this is a horizontal line because the y coordinates are the same.  Then they would say, the distance between -3 and -6 is 3 units (this also uses absolute value if you want to have them explain why the value is positive).  So the line segment is 3 units long.  The tricky line segments come when the values cross the axes because they have to add the coordinates together.  For example, (2, -6) and (2, 5).  This means that they will cross the x axis.  So they would have to add 6 and 5 together to get 11 units for the length of the line segment. By getting the students to talk about how and why this works, incorporates MP1: making sense of what is being asked, MP2: what do the numbers mean, and MP4: modeling the math by understanding which numbers to use to find the lengths of the segment.

Tools:  Polygons in the grid power point and notes

Review of the Grid

5 minutes

I’m going to do a quick review of the grid with the students to remind them of the quadrants and what types of ordered pairs are in each quadrant.  This can be used as a teaching tool if you have not covered the grid yet. I liked this illustration of the grid because it shows everything and will help with the discussion.

Tools: Polygons in the grid power point. 

The Grid and Geometry

25 minutes

I’m going to go through 3 problems with the students.  For each problem, they will be plotting the points on the grid to find the desired result.  I’m letting them use the grid to help them visualize the shape and then get them thinking about how they could find the missing piece without using the grid.  If students can make this generalization on their own, without the grid, you will have them working with MP7 and MP8. To get to this desired result, you will need to ask the students what they notice about this missing ordered pair? How does it fit with the rest of the ordered pairs?  Is it possible to find this ordered pair without using the grid?

Problem 1: This problem has them plotting all 4 ordered pairs to find the side lengths. I liked this problem because the students will be finding perimeter and area of their shapes in their practice problems.

Problem 2: This problem has them plotting the points and then finding the missing ordered pair to make the shape into a rectangle.  Students will need to know that a rectangle has opposite sides that are congruent and parallel and that it has 4 right angles. As students work through this problem, ask them to explain how they know their ordered pair is correct (MP3).  They should use their understanding of rectangles to support their answer or they can use their understanding of side lengths to support their answer as well.

Problem 3:  This problem has them plotting the points on the grid to determine the side length of one of the sides. Students will need to label their points with a letter so they are using the correct line segment.

Tools: Polygons in the grid power point and notes

Numbered Heads Together

25 minutes

I will be using the NHT activity as an informal assessment.  Some of the problems I have chosen are an extension to their learning.  They will be finding perimeter and area of shapes on the grid so it may be a good idea to review this with them before starting this activity.  Students will only need one whiteboard and marker for this activity because they will be using the grid to support their work and only writing their answer on the board.

Question 1:  Finds this side length.  Students should be able to do this independently and with no concerns. They can use the grid or use their mathematical understanding to support their answer.

Question 2: They will need to plot the points and find the area.  Students know how to find area by counting squares on the grid and they also know how to apply the formula.  Both strategies are fine to use.

Question 3: The students are finding the missing coordinate to make the shape into a parallelogram.  Students may need some help remembering the characteristics of a parallelogram. 

Question 4: The students are finding the missing coordinate to make a right isosceles triangle.  This question lends itself to several different solutions.  Again, students may need a reminder of what a right isosceles triangles looks like.   This is going to be a good one to listen to as the students discuss their solutions because the triangle can be created many different ways.

Question 5: This problem has them finding the perimeter of a shape. Some students may need a reminder about perimeter.

Tools: Polygons in the grid power point, white boards, markers, coordinate grid paper. 

Closure

15 minutes

For the closure, I’ve taken away the grid and am asking the students to find the area of the shape.  I would like students to make the leap by finding the length of the segments, using mathematical knowledge, and then using the formula to find the area.  Students will also be explaining in words how they know their solution is correct.  I’m anticipating that my lower students may struggle with this.  It’s ok to give them some struggle time.  Ask them to visualize the grid.  Can they tell which ordered pairs connect?  Can you then use this to find a length?  Can you draw your own visual to help you? Modeling the math is ok, if they need it.  Knowing which tool to use is implementing (MP5) 

Tools: Polygons in the grid power point and notes