common core geometry unit 1 lesson 5 homework answers

Chapter 1, Lesson 1: Points, Lines, and Planes

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Curriculum  /  Math  /  5th Grade  /  Unit 7: Patterns and the Coordinate Plane  /  Lesson 5

Patterns and the Coordinate Plane

Lesson 5 of 14

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Plot horizontal and vertical lines on a coordinate plane and find patterns in their coordinates.

Common Core Standards

Core standards.

The core standards covered in this lesson

5.G.A.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).

5.G.A.2 — Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Draw horizontal and vertical lines in the coordinate plane. 
• Understand that horizontal lines are parallel to the x -axis and perpendicular to the y -axis and vertical lines are perpendicular to the x -axis and parallel to the y -axis.
• Discern the pattern that horizontal lines all have the same y -value and vertical lines all have the same x -value. 
• Name the coordinates of a point that lies on a horizontal or vertical line, including without needing or being able to plot that point.

Suggestions for teachers to help them teach this lesson

Lesson Materials

• Graph Paper (2 sheets per student)
• Optional : Quarter inch graph paper (2 per student) — This is optional in case you don't have graph paper.

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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Amiyah and Brian were playing Battleship. Brian guessed the coordinate pair (5, 8) and got a hit. What coordinates would you recommend Brian give for his next guess? Explain your reasoning.

Guiding Questions

Draw a line that passes through points  Y  and   Z .

a.   Plot one other point on the same line as  $$\overleftrightarrow{YZ}$$  and label it  X

b.   List the coordinates of  X ,  Y , and  Z  in the following table.

c.   What do you notice about the coordinates of points  X ,  Y , and  Z ? What do you wonder?

Grade 5, Unit 9, Lesson 3 (2017-2018) is made available by  Achievement First  as a part of their  Open Source web portal  under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed May 25, 2018, 3:30 p.m..

Use the table below to answer the following questions.

a.   Before plotting the points, what do you notice about their coordinates? What do you wonder?

b.   Plot the points on a coordinate grid. Then connect the points by drawing a line through all of them.

c.   Determine the coordinates of another point that would lie on this line.

Grade 5 Mathematics > Module 6 > Topic A > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US  license. Accessed Dec. 2, 2016, 5:15 p.m..

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Discussion of Problem Set

• In #1, what’s the relationship of line e  to the x -axis and y -axis?
• What do all of the points of line e  have in common in #1f? 
• In #2, how did you know that the points given in parts (a) and (c) were on a line that was not parallel to the x -axis? For the lines that were parallel to the x -axis, what was the distance of every point on those lines from the x -axis?
• In #3, how did you know that the points given in parts (a) and (b) were on a line that was not parallel to the y -axis? 
• In #4, what’s the relationship of line h  to the x -axis and y -axis?
• What pattern occurs in the coordinate pairs that let you know that line h is vertical in #4d?

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Use the following grid to answer Parts (a)-(f).

a.   Use a straightedge to draw a line that goes through points E and F .

b.   Which axis is parallel to the line you drew?

c.   Which axis is perpendicular to the line you drew?

d.   Plot two more points on the line you drew.  Name them G and H .

e.   Give the coordinates of each point below.

E :  ___________ F :  ___________

G :  ___________ H :  ___________

f.   Give the coordinates of another point that falls on the line you drew that isn’t shown in the coordinate plane drawn above. 

Student Response

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

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Word Problems and Fluency Activities

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Topic A: Introduction to the Coordinate Plane

Define a coordinate plane and identify the coordinates of given points. 

Construct a coordinate plane and plot points given their coordinates.

Construct a coordinate plane with non-unit intervals and use it to plot and identify points. 

Determine the interval needed to plot various points and practice plotting and identifying points on coordinate grids with various axes.

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Topic B: Drawing Figures and Shapes in the Coordinate Plane

5.G.A.1 5.G.A.2

Draw parallel lines on a coordinate plane (optional).

Draw perpendicular lines on a coordinate plane (optional).

Draw shapes on a coordinate plane.

Draw symmetric figures on a coordinate plane.

Topic C: Real-World Problems and Patterns on the Coordinate Plane

Understand that a coordinate plane can be used to represent real-world information and interpret coordinate values of points in the context of a situation.

Represent real-world problems by graphing information represented on a table in the coordinate plane and interpret coordinate values of points in the context of a situation.

Represent real-world problems by graphing information given as a description of a situation in the coordinate plane and interpret coordinate values of points in the context of a situation.

5.G.A.2 5.OA.B.3

Generate two numerical patterns using two given rules, plotting the points, and identify multiplicative relationships between corresponding terms.

Generate two numerical patterns using two given rules, plotting the points, and identify more complex relationships between corresponding terms.

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Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

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