Task 1 attempt 3
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Western Governors University *
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AUA2
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Mathematics
Date
Jan 9, 2024
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Kyle Clinedinst
Student ID-001029234
BDM2 Task 1: Understanding and Teaching Ordered Pairs and Graphing
A: Study the ordered pairs and graphing content standards for your state and do the following:
1. List three content standards from your state that apply to ordered pairs and graphing for grades K–6. The three selected standards must represent three different grade levels.
Grade 3: “3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.” -
Ohio Learning Standards/Mathematics Grade 3
Grade 5: “5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of
numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the
two axes and the coordinates correspond, e.g., x-axis and x-coordinate, y-axis and y-
coordinate.”
-Ohio Learning Standards/Mathematics Grade 5
Grade 6: “6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.”
-Ohio Learning Standards/Mathematics Grade 6
2. Write a sample problem for each
of the three standards to illustrate the evolution of student understanding.
Grade 3
: 3.NBT.1
Round the following number to the nearest 100. Use the vertical and horizontal number
line. 529 ~______
Grade 5
: 5.G.1
Mystery Picture
Plot the following points on the coordinate plane. Connect each point in the sequence. When you read a Stop
, stop connecting and start the next sequence. (5,30)
(3,28)
(3,24)
(5,22)
(9,22)
(11,24)
(11,28)
(9,30)
(5,30)
Stop
(21,30)
(23,28)
(23,24)
(21,22)
(17,22)
(15,24)
(15,28)
(17,30)
(21,30)
Stop
(2,12)
(5,8)
(8,6)
(13,6)
(18,6)
(21,8)
(24,12)
(21,12)
(17,19)
(13,9)
(9,9)
(5,12)
(2,12)
Stop
A Coordinate Grid will be supplied for the students. A picture of the grid and the solution will be in part 1c.
Grade 6
: 6.NS.6
1.
If the point P=(6,-4) is reflected across the x-axis, what are the coordinates of the
new point P’? ___________
a.
Plot P’ on the coordinate plane.
2.
If the point D=(6,-4) is reflected across the y-axis, what are the coordinates of the
new point D’? ___________
b.
Plot P’ on the coordinate plane.
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3. Provide a solution for each
problem that demonstrates each
step or explains the thinking process involved in determining the solution.
Grade 3
: 3.NBT.1
Round the following number to the nearest 100. Use the vertical and horizontal number
line. 529 ~__
500
__
Thinking: To solve this problem, students will need to make 2 number lines, one vertical and one horizontal. When rounding to the nearest 100, the students will need to think about where 529 falls on a number line. 5 hundreds and 6 hundreds. Or 500 and 600. Next, they need to think about which hundred is closer. Also, the students will need to know that a number line can be vertical or horizontal. This will help them in the future when they work on coordinate pairs. An example is below. Grade 5
: 5.G.1
Mystery Picture
Plot the following points on the coordinate plane. Connect each point in the sequence. When you read a Stop
, stop connecting and start the next sequence. (5,30)
(3,28)
(3,24)
(5,22)
(9,22)
(11,24)
(11,28)
(9,30)
(5,30)
Stop
(21,30)
(23,28)
(23,24)
(21,22)
(17,22)
(15,24)
(15,28)
(17,30)
(21,30)
Stop
(2,12)
(5,8)
(8,6)
(13,6)
(18,6)
(21,8)
(24,12)
(21,12)
(17,19)
(13,9)
(9,9)
(5,12)
(2,12)
Stop
Thinking- For this problem, the students are given multiple coordinates to plot. They will
need to understand the x and y axes are number lines. The students will need to know the first coordinate number is the x-axes, and the second is the y-axes. To help with this, I will teach them to think of the grid as a hotel. You must go into the hotel before you go up the elevator. “In the hotel, up the elevator.” Students will plot each number
in the set and connect the points. After all three sets are plotted and connected, a picture will be created if done correctly. Grade 6
: 6.NS.6
3.
If the point P=(6,-4) is reflected across the x-axis, what are the coordinates of the
new point P’? ___
(6,4)
____
c.
Plot P’ on the coordinate plane.
4.
If the point D=(6,-4) is reflected across the y-axis, what are the coordinates of the
new point D’? _____
(-6,-4)
___
d.
Plot P’ on the coordinate plane.
Thinking- For this problem, students will first need to know how to plot numbers on a coordinate plane. They will rely on their prior knowledge of the 5th grade standard above. Next, students will need to know that when a point is reflected, it is the mirror image. When a point is reflected on the x-axes, the x stays the same and the y is negated. When negating a negative number, students will need to know that number becomes positive. The same process will apply when reflecting on the y-axes. The y stays the same and the x is negated. An example is below.
4. Discuss how the chosen standards and problems build student understanding of ordered pairs and graphing across the three K–6 grade levels selected previously.
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I chose these standards + problems because they help build the student’s understanding of ordered pairs and graphing. I started with the 3rd grade problem because I wanted to show when students start using vertical and horizontal number lines. Once they understand numbers can go from least to greatest from left to right and down to up, they start to build the foundation needed for graphing. Next, the 5th grade problem has students find positive ordered pairs. They do so by first learning that
the first number in the ordered pair is the number on the x-axis, and the second number is the number on the y-axis. Finally, the skills learned from grades 3 and 5 helps students plot numbers on a coordinate plane. Once students can plot positive and negative numbers, they then can learn that a reflection is a mirrored image. A reflection
on the x-axes means the first number stays the same and the y number is negated. The opposite is true with a y reflection. Part B:
Watch the “Teaching with Game over Gopher” video and do the following:
1. Explain the role of the teacher when using the technology-based game as an instructional strategy to support instruction about ordered pairs and graphing using examples from the video.
The teacher was the facilitator during this technology-based instruction. She started with a quick “initial discussion” where they discussed vocabulary, and shared what they already knew about ordered pairs. Next, the teacher had them get started with the game. During this time, the teacher walked around listening to the students share their ideas and strategies. This allows the students to take a lead in their learning and the teacher becomes the facilitator. She would ask questions when needed to help support their learning. Finally, the teacher had them take a break from the game to share ideas and strategies. This helps support the students who may be struggling by having them listen to ideas from their peers. 2. Explain how the teacher used different types of games to support instruction about ordered pairs and graphing using examples from the video.
The teacher used 2 different types of games to support instruction about ordered pairs and graphing. The first was an online game and the second was a “real world” game where the students had to manipulate the “Connect 4” pieces. For the online game, the students had to plot ordered pairs correctly to win. During this game, students were working together and shared ideas while the teacher was the facilitator. During the real world “Connect 4” game, the students tried to get 4 plots in a row. During this activity, some students were the “plotters” while others were the “graphers.” The plotters had to write the coordinates in which they wanted to put their game piece. The graphers had
to plot the game piece in the correct spot. This works on both writing ordered pairs and plotting ordered pairs. a. Explain how each
type of game helps to meet the needs of different learners.
Both games help meet the needs of different learners. First, the online game has students working together. This would help students at all levels because as we know, students learn best from their peers. The teacher could pair students who are below level with students who are on or above level. The students who are below level can rely on their partner for support. Also, the students who are above level get a chance to
express their thinking in words. The “Connect 4” game was very visual, helping visual learners. The students were also
outside the classroom which connects the activity to the real world. The students were also up and moving around which helps most students become engaged in their learning. 3. Discuss how teaching ordered pairs and graphing can be improved through the use of technology-based games, using a credible source for support.
Teaching ordered pair and graphing can be improved through the use of technology-
based games in a couple of ways. First, in the video, the students were very excited about playing a technology game. This gets them motivated to learn. Also, it allows the
students to manipulate a coordinate grid system in different ways. Like it says in “Elementary and Middle School Mathematics, Teaching Developmentally,” “In some cases, the electronic version allows users to interact with a manipulative in a way that is
difficult or impossible to do with hands-on tools, and it may be accessed at home.”-(Van De Wallie & Karp & Bay-Williams, 2012, p.26) Finally, in the video the teacher said the students could play at home. This would be a great tool for homework or extra practice for students at home. 4. Discuss one potential limitation of using technology-based games as an instructional strategy for teaching ordered pairs and graphing.
One potential limitation for using technology is that some students may struggle who are
not familiar with technology. These students may understand the math concept, but may not be able to show what they know because of technology limitations. For example, when graphing ordered pairs, students may struggle using the touch pads on a chromebook or laptop and this could lead to them clicking the wrong spot on the coordinate plane. Or, students may struggle with typing in the correct coordinates if they
are unfamiliar with the keyboard. That being said, these students do need to learn how to use technology in today's world, so it would be good for them to learn. But, they may
struggle and the teacher wouldn’t know if it was because they don’t understand the concept or if it’s that they don’t understand how to use the technology.
Part C:
Prepare to create an original lesson plan on ordered pairs and graphing by doing the following:
1. Describe an evidence-based instructional strategy that will be incorporated into your original lesson plan.
The evidence-based instructional strategies that I will be using are the “think-pair-share”
for my whole group and vocabulary portion and a “mystery picture” for the guided practice. When we discuss what we know about ordered pairs and the vocabulary needed to be successful, students will work with their partner to share ideas. When they are doing the guided practice, students will work on plotting ordered pairs to create a mystery picture. They can use their partners for support as I would be circulating the room listening for ideas and strategies. a. Explain why the chosen instructional strategy would be beneficial in a lesson on ordered pairs and graphing using evidence from a credible source to support your selection.
For this lesson, I will be using the “think-pair-share” strategy. As described by Van De Wallie & Karp & Bay-Williams, I will start the lesson going over the needed vocabulary to be successful. Teachers should “recognized the potential language confusion and allowed students the chance to talk about it before becoming confused by the task.” -
(Van De Wallie & Karp & Bay-Williams, 2012, p.70) To address all language concerns, the students will discuss needed vocabulary with a partner before the start of the task. I will first lead with a saying that helps the students remember which number represents the x-axis and which number represents the y-axis.
“In the store, up the elevator.” Then I will ask them to think about what the saying means, pair with their partner, and discuss their ideas with their partners. (The meaning of this saying is to remember to plot the x-axis first, then the y. The x-axis representing in the store, and the y-axis representing up the evaluator.) During the model portion of the lesson, I will be prompting students with questions such as “what number represents
the x-axis,” “Can you share with your partner one thing you noticed about the graph/graphing process.” After modeling and verbal prompting, the students will work together to plot a mystery picture. While doing so, they will repeat the saying and share
ideas about graphing coordinate pairs. “Peer-assisted learning” -(Van De Wallie & Karp & Bay-Williams, 2012, p.100)
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Part E
:
Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.
Ohio Learning Standards Mathematics
. (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/
Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx?
lang=en-US
Bay-Williams, J.V.D.W.K.S.K.J. M. (2012). Elementary and Middle School Mathematics: Teaching Developmentally, VitalSource for Western Governors University (8th Edition). Pearson Learning Solutions. https://wgu.vitalsource.com/books/9781256957669