lesson 7 homework practice graph on the coordinate plane

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Course: 5th grade   >   Unit 12

• Introduction to the coordinate plane
• Coordinate plane: graphing points

Graph points

• Identify coordinates
• Identify points
• Graph points review (positive numbers only)

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Maneuvering the Middle

Student-Centered Math Lessons

Coordinate Plane Activities to Try

The coordinate plane is a personal favorite of mine. It is hands-on, reinforces the ordering of rational numbers, and spans all of secondary education. If there is a unit that I look most forward to – it is this one!

Today I will share some tips for teaching the complexities of this grid and some engaging activities that you and your students will love.

Three Tips for Teaching

The most common misconception you will see is students moving up and down on the y-axis before moving right or left on the x-axis. There are many memory tricks like “you have to crawl before you can climb” or “you have to cross the street before you can get on the elevator” to help students plan their steps. Because graphing on the coordinate plane doesn’t require “showing work” like setting up a proportion, I have no problem asking students to annotate the coordinates. I will model and require students to write a tiny right or left arrow over the x-coordinate and a tiny up or down arrow over the y-coordinate every single time they encounter a set of coordinates. I also ask students to label their graphs with “x-axis” and “y-axis.”

Don’t overestimate students! It can be easy to think your 6th graders can graph on all 4 quadrants on day 1. Start by just graphing in Quadrant I on the first day. Then move to graphing on all 4 quadrants the second day. By the third day, you will be more successful graphing rational numbers.

Graphing on the axes can be particularly challenging. When I saw students mix up coordinates, it was usually because one of the coordinates was 0. Tip: remind students that if there is a 0 for that coordinate, then it won’t show up on that axis. For example, (0, 4) means that it cannot end up on the x-axis because it has a 0 for the x-coordinate. It has to end up in the y-axis. 

Coordinate Plane Activities

Coordinate Plane Unit – This 6th grade unit does an excellent job scaffolding instruction. Plus, student handouts, homework, a study guide, and an assessment are done for you!

Demos Coordinate Plane Activities – Desmos really delivers on this skill. I’ve linked the entire scope of their coordinate plane practice, but this Mini Golf Marble Slide is especially useful in plotting points, while incorporating error analysis. Battleboats is a play on Battleship, and I can visualize the engagement!

Coordinate Plane Digital Activities – Do you need practice for all of the 6th grade CCSS coordinate plane standards – introducing the parts of the graph, graphing, reflections, and distance? These digital activities cover everything, come with a 2-question exit ticket per skill, and include 16 total activities.

Stock the Shelves Online Game – I came across this website from a member of our Maneuvering the Middle VIPs facebook group. This is online practice for graphing integers on all 4 quadrants. I like that if a student is incorrect, they have to keep trying before they can move on to the next problem.

Design a Dorm Room Performance Task – This Coordinate Plane Performance Task can be a typical assignment, group project, or an extension.  It requires students to think outside of the box as they solve real-word and mathematical problems by graphing on the coordinate plane. 

Create a Coordinate Plane on your Floor – Our MTM team member and current teacher Marissa is a big fan of this activity. She pushes all of the student desks to the edge of her classroom, and uses painters’ tape to create a giant coordinate plane. Students are then asked to walk the graph as they would plot points (start at the origin, walk the x-axis and then move vertically along the y-axis). In this activity, she has students practice reflecting over the axes using a partner to represent their reflection. 

Coordinate Plane Scavenger Hunt – Students will move around a coordinate plane map of the city using the clues provided at each station. Hands-on and interactive!

Coordinate Plane Battleship – Students just need coordinate planes. Have them mark various points as their battleships. You call out various coordinates. Students say ‘hit’ when you say a coordinate that has one of their battleships on it. The student that still has a battleship at the end of the activity wins!

Flyswatter Game – The flyswatter game was perfect when I ended a lesson early or if I needed to inject some energy into my morning classes. Simply provide 2 students a flyswatter and give them locations to smack like:

• The various quadrants
• (5, -3) and more

What coordinate plane activities do your students love?

Digital Math Activities

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Lesson Plan: Coordinate Plane

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In this lesson plan, students will define a coordinate system and ordered pairs .

One class period or approximately 60 minutes

• a large space - gym, preferably, or a multipurpose room, a playground if necessary
• masking tape

Key Vocabulary

Perpendicular, Parallel, Axis, Axes, Coordinate Plane, Point, Intersection, Ordered Pair

Objectives 

Students will create a coordinate plane and will begin to explore the concept of ordered pairs.

Standards Met

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)

Lesson Introduction

Define the learning target for the students: To define a coordinate plane and ordered pairs. You can tell students that the math they’ll be learning today will help them succeed in middle and high school since they will be using this for many years!

Step-by-Step Procedure

• Lay out two crossing pieces of tape. Intersection is the origin.
• Line up at the bottom of a line we’ll call the vertical line. Define this as the Y axis, and write it on the tape near the intersection of the two axes. The horizontal line is the X axis. Label this one as well. Tell students they’ll get more practice with these.
• Lay out a piece of tape parallel to the vertical line. Where this crosses the X axis, mark the number 1. Lay out another piece of tape parallel to this one, and where it crosses the X axis, label this a 2. You should have pairs of students helping you lay out the tape and do the labeling, as this will help them gain an understanding of the concept of the coordinate plane.
• When you get to 9, ask for a few volunteers to take steps along the X axis. “Move to a four on the X axis.” “Step to the 8 on the X axis.” When you’ve done this for awhile, ask students if it would be more interesting if they could move not only along that axis, but also “up”, or over, in the direction of the Y axis. At this point they’ll probably be tired of just going one way, so they will probably agree with you.
• Begin to do the same procedure, but laying out pieces of tape parallel to the X axis, and labeling each one as you did in Step #4.
• Repeat Step #5 with the students along the Y axis.
• Now, combine the two. Tell students that whenever they are moving along these axes, they should always move along the X axis first. So whenever they are asked to move, they should move along the X axis first, then the Y axis.
• If time allows, have one or two students silently move along the coordinate plane, over and up, and have the rest of the class define the ordered pair. If they moved over 4 and up 8, what is the ordered pair? (4, 8)

Homework/Assessment

No homework is appropriate for this lesson, as it is an introductory session using a coordinate plane that can’t be moved or reproduced for home use.

As students are practicing stepping to their ordered pairs, take notes on who can do it without help, and who still needs some assistance finding their ordered pairs. Provide additional practice with the whole class until most of them are doing this confidently, and then you can move to paper and pencil work with the coordinate plane.

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Into Math Grade 8 Module 7 Lesson 2 Answer Key Solve Systems by Graphing

We included H MH Into Math Grade 8 Answer Key PDF Module 7 Lesson 2 Solve Systems by Graphing to make students experts in learning maths.

HMH Into Math Grade 8 Module 7 Lesson 2 Answer Key Solve Systems by Graphing

I Can solve a system of linear equations by graphing and check that my solution is correct.

Turn and Talk How can you check that you correctly determined any possible places where the trains might collide?

Build Understanding

Turn and Talk How can you tell just by looking at two given equations whether they must have a point of intersection?

Step It Out

D. A student claimed that the point of intersection of the lines is (\(\frac{1}{4}\), 3\(\frac{1}{2}\)). Is the student correct? How do you know? ___________________ ___________________

Check Understanding

B. Describe how can you check your solution. _______________________ Answer: The equations are representing the two streets. The first equation represents one street. The second equation represents the second street.

On Your Own

C. Explain how to check that you found the correct intersection point. Answer:

Question 3. The graph shows a system of equations.

B. Show how you can check that the point of intersection is a solution of the system you wrote. Answer: Yes, the point of intersection is the solution of the system. The lines are intersecting at the point (-1,-1)

B. Estimate the solution of the system and explain what it represents. ___________________ ___________________ Answer:

Question 5. Critique Reasoning Brianna was asked to use graphing to solve the system of equations y = 2x + 3.5 and y = 2.5x – 1.

B. Another student said the solution is (9, 21.5). Is he correct? Explain. Answer: Given that, y = 2x + 3.5 is an equation 1 y = 2.5x – 1.is an equation 2 In the equation 1 If x = 1 then y = 2(1) + 3.5 = 5.5. If x = 9 then y = 2(9) + 3.5 = 21.5 In the equation 2 If x = 1 then y = 2.5(1) – 1 = 1.5 If x = 9 then y = 2.5(9) – 1 = 21.5 The student said the solution is (9, 21.5). The (9, 21.5) is the solution of the equation because at this point also the lines are intersecting at each other.

I’m in a Learning Mindset! How was solving systems by graphing an appropriate challenge for me?

Lesson 7.2 More Practice/Homework

Question 1. Deshawn is using a coordinate plane to design a mural. Two of the straight lines on the mural are represented by the equations y = 2x + 8 and y = \(\frac{1}{2}\)x – 4.

B. At what point do the lines intersect? ________________ Answer: The two lines do not intersect because the two equations have different values. The first equation has the positive values and the second equation has the negative values. So, they do not intersect.

C. Reason Show how you can check that the point of intersection is a solution. Answer:

B. Estimate the solution of the system. What does the solution represent? Answer: The total cost of renting a paddleboat for 1 hour is 5 at Lake Mitchell. The total cost of renting a paddleboat for 1 hour is 7.3 at Lake Sutro. Both equations are intersecting at the point (3,8)

Question 3. Math on the Spot Use a separate sheet of graph paper to solve each system by graphing. Check your answer.

Spiral Review

Question 8. Construct a linear function that has a slope of -3 and passes through the point (-2, 3). Answer: Given that, The slope = -3 The points (x, y) = (-2, 3). The linear function of two variables is always a straight line. The standard form of the linear equation is y = mx + c Here m = slope y = -3x + c 3 = -3(-2) + c 3 = 6 + c c = 3 – 6 c = -3 The equation of the straight line is y = -3x – 3. So, the linear function is f(x) = -3x -3.

Question 9. Solve the equation 3(x – 1) = 27 – 2x. Check your solution. Answer: Given that the equation is 3(x – 1) = 27 – 2x 3x – 3 = 27 – 2x 3x – 2x = 27 – 3 x = 4

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Chapter 3, Lesson 7: Distance on the Coordinate Plane

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