lesson 31 session 1 explore

©Curriculum Associates, LLC Copying is not permitted.647 Lesson 31 Understand the Coordinate Plane

LESSON 31

StartConnect to Prior KnowledgeWhy Review how a number line shows relationships between numbers to prepare students for exploring the coordinate plane.

How Have students answer questions about points on a number line.

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Start

Grade 5 Lesson 31 Session 1 | Explore the Coordinate Plane

Which point is closest to 0?

How far from from 0 is point E?

How would you describe moving from 0 to point D?

0 4 8

C D E

1 2 3 5 6 7 9 10

Solutionspoint C;9 units;Move 5 units right from 0.

MODEL ITRead the question at the top of the Student Worktext page. Remind students that they know how to use distance from 0 to represent numbers as points on a one-dimensional number line.

1 Tell students that they are going to use whatthey know about number lines to think about points in a two-dimensional space called the coordinate plane, determined by two perpendicular number lines that intersect at their 0 points. Then clarify the task and have students complete the problems.

Spend some time discussing the new vocabulary terms: x-axis, y-axis (plural axes), and origin. Because students are not yet looking at specific points in the plane or working with x- and y-coordinates, they may not understand the use of “x” and “y” as axis names. Let them know that they will find out more about using these names on the next page.

Common Misconception If students place their number labels in the spaces between the grid lines, then connect labeling the x-axis and y-axis to labeling a number line. Ask: Where do you place the number labels on a number line? [directly below the tick marks] Where do you think you place the number labels on the axes of the coordinate plane?

DISCUSS ITSupport Partner DiscussionEncourage students to refer to their coordinate plane as they discuss the similarities and differences between how they labeled the axes.

Look for coordinates planes showing:

• labels of 1–4 placed where the grid lines intersect the axes

• label of “O” placed at the origin where the x-axis and y-axis intersect

Support Whole Class DiscussionPrompt students to compare the coordinate plane to a number line.

Ask How are a number line and a coordinate plane similar and different?

Listen for A number line is one-dimensional and can be either horizontal or vertical. The coordinate plane uses both a horizontal and a vertical number line to form a two-dimensional space. A number line has tick marks to show the units, and the coordinate plane has grid lines.

Ask How are the x-axis and y-axis similar and different?

Listen for Both the x-axis and y-axis are number lines, but the directions of the axes are different, as the x-axis is horizontal and the y-axis is vertical.

Purpose In this session students explore theconcept of the coordinate plane. Students learn how to distinguish between the x-axis and the y-axis, identify the origin, and locate points inthe first quadrant.

SESSION 1 Explore

©Curriculum Associates, LLC Copying is not permitted. 647Lesson 31 Understand the Coordinate Plane

Learning Target• Use a pair of perpendicular number lines,

called axes, to defi ne 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 fi rst 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.

SMP 1, 2, 3, 4, 5, 6, 7

LESSON 31

Model ItComplete the problem below.

1 When a horizontal number line and a vertical number line are lined up so that the 0s intersect, a coordinate plane is formed.

y

x

Coordinate Plane

a. Label the numbers 1–4 on the x-axis, the horizontal number line.

b. Label the numbers 1–4 on the y-axis, the vertical number line.

c. Label the origin, the point where the x-axis and y-axis intersect, with the letter O.

What does a point in the coordinate plane represent?

DISCUSS IT• Compare how you labeled

the coordinate plane with how your partner labeled the coordinate plane. Are they the same? Are they diff erent?

• I think a coordinate plane is like a number line because . . . I think a coordinate plane is diff erent from a number line because . . .

SESSION 1

Explore the Coordinate Plane

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4

3

2

1

1 2 3 4 O


©Curriculum Associates, LLC Copying is not permitted.648

LESSON 31 EXPLORE

Lesson 31 Understand the Coordinate Plane

SESSION 1

Model ItComplete the problems below.

2 An ordered pair is a pair of numbers, called coordinates, that describes the location of a point in the coordinate plane. The coordinates of an ordered pair always appear in the same order: fi rst the x-coordinate and then the y-coordinate.

a. If you move only on grid lines, how can you get from the origin to point B in the fewest number of moves?

b. The ordered pair (2, 5) is a way to represent the location of point B. Use your answer to problem 2a to describe what the x-coordinate of an ordered pair tells you about the point’s location and what the y-coordinate tells you about the point’s location.

c. What is the ordered pair for the origin, O?

3 REFLECTThink about how you have heard the word origin used outside of math. Why do you think the point (0, 0) is called the origin?

y-coordinatex-coordinate

Ordered Pair(x, y)

5

4

3

2

1

1 2 3 4 5O

y

x

B

C

DISCUSS IT• How can you and your

partner fi gure out the ordered pair for point C?

• I know the x-coordinate of any point on the y-axis is 0 because . . .

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(0, 0)

Possible answer: You move 2 units right and 5 units up from the origin to get to point B.

Possible answer: The x-coordinate tells you the point’s horizontal distance from the origin. The y-coordinate tells you the point’s vertical distance from the origin.

Possible answer: Origin is a word that means where something begins.

The x- and y-axes on the coordinate plane begin at (0, 0), so it makes sense to

call this point the origin.

MODEL IT 2 Tell students that they will now think about how

to locate points in the coordinate plane. Clarify the task and have students complete the problems.

Common Misconception If students do not understand the concept of an ordered pair, then emphasize that an ordered pair tells the location of a point in the coordinate plane in reference to the origin. Emphasize that the first number inside the parentheses is always the horizontal distance from the origin and the second number is always the vertical distance from the origin.

DISCUSS IT Support Partner DiscussionEncourage students to refer to the coordinate plane as they discuss.

Listen for understanding that:

• the numbers in an ordered pair give horizontal and vertical distances from the origin to a point

• (0, 0) is the ordered pair for the origin

Hands-On ActivityWrite ordered pairs for points.

If . . . students are unsure about ordered pairs,

Then . . . use this activity to have them connect locating a point to the ordered pair for the point.

Materials For each pair: Activity Sheet Points A and B

• Distribute the Activity Sheet to pairs and have each student point to the origin, (0, 0). Write this ordered pair frame on the board: (move units, move units)

• Have one student use a finger to trace a path from the origin to point A, using first one horizontal movement and then one vertical movement, describing the movements out loud. Ask the other student to record the movements in the ordered pair frame. [(move right 3 units, move up 7 units)]

• Have the first student label point A with the ordered pair that represents it. [(3, 7)]

• Partners trade roles and repeat for point B. [(move right 8 units, move up 5 units); (8, 5)]

• Discuss the relationship between each point’s coordinates and the directions to get there.

Support Whole Class DiscussionPrompt students to describe how they figured out the x- and y-coordinates for point C.

Ask How did you find the x-coordinate for point C? the y-coordinate?

Listen for I counted 4 units to the right from the origin along the x-axis to find that the x-coordinate is 4. Then I counted 3 units up to point C to find a y-coordinate of 3.

Close: Exit Ticket

3 REFLECTLook for understanding that (0, 0) is the ordered pair that tells the location of the origin in the coordinate plane and for students to connect the word origin to starting or beginning.

Common Misconception If students do not reference the x-axis and y-axis in their explanations, then ask students to point to the origin in the coordinate plane on the Student Worktext page and explain that this is the place where both the x-axis and y-axis originate, or begin. Describing a point’s location in the coordinate plane involves describing movements that begin at the origin.


LESSON 31

©Curriculum Associates, LLC Copying is not permitted. 649

Name:


2 From the origin, you move three units to the right and six units up to point P. What ordered pair tells the location of point P?

1 Think about what you know about the coordinate plane. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.

Word In My Own Words Example

coordinate plane

x-axis

y-axis

origin

ordered pair

x-coordinate

y-coordinate

LESSON 31 SESSION 1

Prepare for the Coordinate Plane

649

Possible answers:

the space made when a horizontal number line and a vertical number line are lined up so that the 0s meet

the horizontal number line in the coordinate plane

the vertical number line in the coordinate plane

the point where the x-axis and the y-axis intersect in the coordinate plane

a pair of numbers, (x, y), that describes the location of a point in the coordinate plane

the first number in an ordered pair For (3, 2), 3 is the x-coordinate.

the second number in an ordered pair

For (3, 2), 2 is the y-coordinate.

y

x

4

5

3

2

1

1 2 3 4 5O

y

x

2

1

1 2 3 4 5 x-axisO

y

x

2

1

1 2 3 4 5

y-axis

O

y

x

2

1

1 2 OOrigin

(0, 0)

y

x

2

1

1 2 O

Ordered pair(1, 1)

(3, 6)

Solutions

Support Vocabulary Development

1 Read each of the terms in the graphic organizer. Ask students to work with a partner to talk about the meaning of each term.

Have partners compare and contrast the coordinate plane and a number line. Encourage students to think about how a point on a number line can be described with one number but a coordinate plane requires a pair of numbers.

Have partners write their definitions and examples for each word. Call on volunteers to describe their examples.

2 Clarify that each grid line on the coordinate plane indicates one unit. Demonstrate how to count units on the x- and y-axes. Have students read the problem with a partner and work together to determine the location of the point in the coordinate plane.

Supplemental Math Vocabulary• left

• right

SESSION 1 Additional Practice


Levels 1–3 Levels 2–4 Levels 3–5

English Language Learners:Differentiated InstructionELL

Reading/Speaking Have students read Model It problem 2 with partners. Have students work with partners to identify the meaning of each number in the ordered pairs for points D and E. Have partners discuss ways they can remember which coordinate comes first in an ordered pair. Invite students to tell their ideas to the class.

Reading/Speaking Have students read Model It problem 2 with partners. Display the following words: point, ordered pair, x-coordinate, y-coordinate, x-axis, y-axis. Have students work with partners to identify the parts of the ordered pair and coordinate plane. Invite volunteers to tell ways they can remember which coordinate comes first in an ordered pair. Support students in discussing the ordered pairs for points D and E with the following sentence frame:

• I know is because .

Listening/Speaking Read Model It problem 2 and have students follow along. Display, read, and have students chorally repeat the following words: point, ordered pair, x-coordinate, y-coordinate, x-axis, y-axis. Have students tell the meaning of each number in the ordered pairs for points D and E. Guide students to use their fingers to show the location of the x- and y-axis on the coordinate plane in problem 1. Have students work with partners to talk about the points using the following sentence frames:

• The ___-coordinate of point is .

• Point is above the number on the x-axis and to the right of the number on the y-axis.


Solve.

3 Look at the coordinate plane below.

Coordinate Plane

x

y

A

a. Label the origin with the letter O.

b. Label the numbers 1–9 on the x-axis.

c. Label the numbers 1–9 on the y-axis.

d. Explain what the ordered pair (7, 4) tells you about point A.

LESSON 31 SESSION 1

650

Possible answer: The x-coordinate, 7, tells me that point A is seven units away from 0 in the direction of the x-axis. The y-coordinate, 4, tells me that point A is four units away from 0 in the direction of the y-axis.

1O

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9

Prepare for Session 2Use with Model It.

3 a. Students should label the lower left corner of the coordinate plane with the letter O.

b. See the labels on the horizontal axis of the coordinate plane on the student page.

c. See the labels on the vertical axis of the coordinate plane on the student page.

d. See possible explanation on the student page. Students may also describe that you move from the origin to point A by moving 7 units right and then 4 units up.

Medium


LESSON 31


LESSON 31


SESSION 2

Model It: the CoordinAte PLANETry these two problems.

1 Points A, B, and C are graphed, or plotted, in the coordinate plane below. Use the graph to write the ordered pair for each point.

Point A

Point B

Point C

2 Plot the following points in the coordinate plane in problem 1. Label each point with its letter name.

Point D(1, 0) Point E(3, 2)

y

x

4

3

2

1

1 2 3 4 O

A

B

C

Develop Understanding of the Coordinate Plane

DISCUSS IT• Ask your partner to explain

how he or she determined the location of points D and E.

• I think plotting points in the coordinate plane is like plotting points on a number line because . . .

• I think plotting points in the coordinate plane is diff erent from plotting points on a number line because . . .

651

See the coordinate plane above. Note that students will graph point F in problem 3 on the next page.

(0, 2)

(2, 4)

(4, 1)

D

E

F

StartConnect to Prior KnowledgeWhy Support students’ understanding of ordered pairs.

How Have students identify the x- and y-coordinates of two ordered pairs.


Start

Name the x-coordinate and the y-coordinate for each ordered pair shown below.

(2, 7)

(0, 9)

Grade 5 Lesson 31 Session 2 | Develop Understanding of the Coordinate Plane

Solutions(2, 7):x-coordinate: 2; y-coordinate: 7(0, 9):x-coordinate: 0;y-coordinate: 9

Develop LanguageWhy Clarify the meaning of the word plot as it relates to graphing a point.

How Explain that the word plot refers to marking a location or a point on a graph, such as a coordinate plane. Have students find the word in Model It. Ask: What do you need to plot? What do you draw when you plot a point?

MODEL IT: The COORDINATE PLANE1 – 2 Present the problems and have students

complete. As students work, help them understand that they are being asked to identify the coordinates of points plotted in the coordinate plane and then plot points given the coordinates.

Common Misconception If students interchange the x- and y-coordinates when writing ordered pairs, then write (x, y) and (horizontal, vertical) on the board and discuss how x and y are in the same alphabetical order as horizontal and vertical. Encourage students to move from the origin to a point in “alphabetical order”—first move horizontally and then vertically, recording the numbers of units moved as (x, y).

DISCUSS ITSupport Partner DiscussionEncourage students to find even small differences in how they plotted and labeled points in the coordinate plane.

Support as needed with questions such as:

• Where did you start when you plotted a point in the coordinate plane?

• How did you interpret the y-coordinate of 0 for point D?

• How did you label the points you graphed?

Support Whole Class DiscussionFor each problem, have several students share their graphs and ordered pairs.

Ask Do you move both horizontally and vertically when you plot points on a number line? in the coordinate plane?

Listen for A number line involves moving in one direction, but the coordinate plane involves moving in two directions.

Ask What do you know about the coordinates of a point located on one of the axes?

Listen for One of the coordinates is 0 because you do not move either horizontally or vertically to get to that point.

Purpose In this session students identify the coordinates of points graphed in the coordinate plane. Then students graph points in the coordinate plane given ordered pairs or the x- and y-coordinates in a table.

SESSION 2 Develop



LESSON 31 DEVELOP


SESSION 2

Model It: Tables3 x- and y-coordinates can be organized in a table like the one below.

Point A B C D E F

x 1 3 4

y 0 2 3

a. Use the coordinate plane on the previous page to complete the table with the coordinates for points A, B, and C.

b. Use the coordinates given for point F in the table to graph point F in the coordinate plane on the previous page.

c. Explain how you can tell from the table which two points are located on the same vertical grid line in the coordinate plane.

Connect ItComplete the problems below.

4 How do the coordinate plane and the table represent points? How are the x- and y-coordinates of a point shown in each model?

5 Plot point A(1, 4) and point B(3, 0) in the coordinate plane.

y

x

4

3

2

1

1 2 3 4 O

DISCUSS IT• Compare your answers to

your partner’s. Do you agree or disagree?

• Looking at points in a table helps me see . . .

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0

2

2

4

4

1

Possible answer: Points C and F are on the same vertical grid line because they have the same x-coordinate. So, they are the same number of horizontal units away from the origin.

Possible answer: In the coordinate plane, a point is shown at a location determined by a horizontal distance from the origin (the x-coordinate) and a vertical distance from the origin (the y-coordinate). You see the coordinates as scale labels on the axes. In the table, points are shown with their x-coordinates in the first row and their y-coordinates in the second row.

A

B

MODEL IT: TABLES3 Present the problems and have students

complete. As students work, have them identify that they need to use information on the previous page to write the missing coordinates in the table and then use information in the table to graph point F.

DISCUSS ITSupport Partner DiscussionEncourage partners to connect the coordinates listed in the table to the points graphed in the coordinate plane on the previous page.

Support as needed with questions such as:

• How did you know what coordinates to write for points A, B, and C?

• How did you know how to locate point F in the coordinate plane?

Support Whole Class DiscussionFor each problem, have several students share their table and coordinate plane.

Ask How was it helpful to see the coordinates of point F in a table before graphing this point?

Listen for The labels in the table helped me identify the x- and y-coordinates for point F.

Hands-On ActivityMake a classroom coordinate plane.

If . . . students are unsure about locating points,

Then . . . use this activity to provide practice.

Materials For each student: 1 index card with an ordered pair written on it

• Arrange student desks or chairs in rows to represent the coordinate plane. Define where the origin, x-axis, and y-axis are located.

• Give each student an index card with an ordered pair on it. Then have students sit at the desk located at their ordered pair.

• Ask students to hold up their index cards to check that they are sitting at the correct desks.

• Ask volunteers to share how they found their seat.

• Ask students to compare their coordinates with the person next to them and discuss how their coordinates are related.

CONNECT IT4 Student responses should show understanding that the coordinate plane shows

the locations of points and the table shows the coordinates of the points.

Close: Exit Ticket

5 Look for recognition that the first coordinate in an ordered pair tells the number of units to the right from the origin and the second coordinate tells the number of units up.

Common Misconception If students reverse the x- and y-coordinates when plotting the points, then have students locate (1, 2) and (2, 1) in the coordinate plane. Discuss the importance of the order of the coordinates when plotting points.


LESSON 31


Name:


Study how the Example shows writing ordered pairs for points in the coordinate plane. Then solve problems 1–9.

ExampleWrite ordered pairs for the origin and point A shown in the graph below.

The x-coordinate tells how many units from the origin the point is along the x-axis. It is the fi rst number in the ordered pair.

The y-coordinate tells how many units from the origin the point is along the y-axis. It is the second number in the ordered pair.

The ordered pair for the origin is (0, 0).The ordered pair for point A is (3, 1).

5

4

3

2

1

1 2 3 4 5O

y

x

A

B C

D

1 Point B is unit(s) to the right of the origin and unit(s) up from the origin.

The ordered pair for point B is ( , ).

2 Point C is unit(s) to the right of the origin and unit(s) up from the origin.

The ordered pair for point C is ( , ).

3 Write the ordered pair for point D. Explain your answer.

4 Use the ordered pair (2, 3) to graph and label point E on the coordinate plane.

Practice with the Coordinate Plane

LESSON 31 SESSION 2

Vocabularycoordinate plane a two-dimensional space formed by two perpendicular number lines called axes.

ordered pair a pair of numbers, (x, y), that describes the location of a point in the coordinate plane, where the x-coordinate gives the point’s horizontal distance from the origin, and the y-coordinate gives the point’s vertical distance from the origin.

Origin

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1 3

3

3

3

5

1

5

(4, 5); Possible explanation: Point D is 4 units to the right of the origin, so the x-coordinate is 4. It is 5 units up from the origin, so the y-coordinate is 5.

See the coordinate plane above.

E

Solutions

1 Point B is 1 unit to the right of the origin and 3 units up; The ordered pair for point B is (1, 3). Basic

2 Point C is 5 units to the right of the origin and 3 units up; The ordered pair for point C is (5, 3). Basic

3 (4, 5); point D is 4 units to the right of the origin, so the x-coordinate is 4. It is 5 units up from the origin, so the y-coordinate is 5. Medium

4 Check that point E is graphed and labeled at (2, 3) in the coordinate plane in the Example. Medium

SESSION 2 Additional Practice

Fluency & Skills Practice Teacher Toolbox

Assign Understanding of the Coordinate Plane

In this activity students use ordered pairs to identify points on the coordinate plane. They also plot points using ordered pairs. They become familiar with conventions, such as the horizontal and vertical axes representing x- and y-coordinates respectively. Students may use a coordinate plane to make and interpret simple maps. Later they will use the coordinate plane to produce line graphs and scatter plots.

©Curriculum Associates, LLC Copying is permitted for classroom use.

Name:

Fluency and Skills Practice

Understanding of the Coordinate Plane

1 Write ordered pairs for the 5 points on the coordinate plane.

Point A Point B

Point C Point D

Point E

Plot the following points on the same coordinate plane. Label each point with its letter name.

Point P (3, 5) Point Q (5, 3) Point R (0, 7)

Point S (3, 1) Point T (7, 8)

Describe the location of point P compared to point Q in the coordinate plane.

2 In the table, write the coordinates for points

A, B, C, D, and E, shown in the coordinate plane.

Point A B C D E F G H J K

x 8 6 9 5 2

y 3 0 10 2 5

The coordinates for points F, G, H, J, and K are also shown in the table. Plot and label the points in the coordinate plane.

Which two points are located on the same horizontal grid line in the coordinate plane? Explain how you can tell by looking at the table.

3 Compare representing points in the coordinate plane and in a table?

O

A

C

E

D

B

1

1

2

3

4

5

6

7

8

2 3 4 5 6 7 8

x

y

A

B

C

D

E

10

1

0

2

3

4

5

6

7

8

9

10

2 3 4 5 6 7 8 9 10

x

y


Levels 1–3 Levels 2–4 Levels 3–5

English Language Learners:Differentiated InstructionELL

Speaking/Writing Have students read Apply It problem 4 with a partner. Ask them to make a list of terms and phrases they can use to explain the pattern.

Once complete, ask students to share and compare their list with another set of partners. Have groups work together to write an explanation using complete sentences.

Speaking/Writing Have students chorally read Apply It problem 4. Ask students to work with a partner to complete the table in Part A. Provide the following sentence frames to help students discuss the pattern:

• The points in the coordinate plane are on a straight line .

• Each point is 1 unit right and 1 unit up from the point before.

• In the table, each coordinate is 1 unit greater than the coordinate above it.

Have students write and share their sentences.

Listening/Speaking Have students chorally read Apply It problem 4. Ask students to work with a partner to complete the table in Part A. Display, read, and support understanding of the following words: unit, line, pattern, straight, up, down, left, right, more than, less than. Provide the following sentence frames for students to talk about the pattern:

• The points in the coordinate plane are on a straight line .

• Each point is 1 unit right and 1 unit up from the point before.

• In the table, each coordinate is 1 unit greater than the coordinate above it.


LESSON 31 SESSION 2

Use the table and coordinate plane for problems 5–7.

Point A B C D E F

x 3 4 5

y 4 4 2

5

4

3

2

1

1 2 3 4 5O

y

x

A

B

C

5 In the table, write the coordinates for points A, B, and C, shown in the coordinate plane above.

6 The coordinates for points D, E, and F are shown in the table. Plot and label the points in the coordinate plane.

7 Choose a point in the coordinate plane above. Describe its location compared to the origin.

Use the table and coordinate plane for problems 8 and 9.

Point R S T

x 3 4 5

y 5 0 2

5

4

3

2

1

1 2 3 4 5O

y

x

8 The coordinates for points R, S, and T are shown in the table. Plot and label the points in the coordinate plane.

9 Describe the location of point T compared to point S in the coordinate plane.

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0

3

1

5

2

0

Answers will vary. Possible answer: Point T is 1 unit to the right and 2 units up from point S.

D E

F

Answers will vary. Possible answer: Point D is 3 units to the right of the origin and 4 units up from the origin.

See table above.

See coordinate plane above.

See coordinate plane above.

T

R

S

Prepare for Session 3Use with Apply It.

5 See completed table on the student page. Medium

6 See plotted points on the graph on the student page. Check that each point is labeled. Medium

7 See possible answer on the student page. Challenge

8 See plotted points on the graph on the student page. Check that each point is labeled. Medium

9 See possible answer on the student page. Students may also answer that point S is 1 unit to the left and 2 units down from point T. Challenge


LESSON 31


LESSON 31


Apply ItComplete these problems on your own.

1 SHOWLook at the table at the right. Plot and label points M and N in the coordinate plane below. Then write the ordered pairs for points M and N and describe how to move from (0, 0) to each point.

5

4

3

2

1

1 2 3 4 5 6O

y

x

2 ANALYZEIrvin wrote the ordered pair (4, 3) for the location of point J in the coordinate plane at the right. Explain Irvin’s error.

3 CREATEChoose three points in the coordinate plane at the right to be the vertices of a triangle. Label the points with letters and draw the triangle. What are the ordered pairs for the vertices of your triangle?

5

4

3

2

1

1 2 3 4 5O

y

x

J

Refine Ideas About the Coordinate PlaneSESSION 3

PAIR/SHAREDiscuss your solutionsfor these threeproblems with apartner.

5

4

3

2

1

1 2 3 4 5O

y

x

Point x y

M 1 4

N 5 2

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M(1, 4). Point M is 1 unit right and 4 units up from the origin.N(5, 2). Point N is 5 units right and 2 units up from the origin.

Possible answer: Point J is 3 units right and 4 units up from the origin, which means the ordered pair is (3, 4).

Triangles will vary. Possible triangle shown on grid. Possible ordered pairs: A(1, 2), B(3, 1), C(3, 3)

N

M

A

C

B

StartConnect to Prior KnowledgeWhy Reinforce understanding of the coordinate plane and ordered pairs.

How Have students describe how to locate a point and then identify a point with the same x-coordinate and a point with the same y-coordinate.


Start

Grade 5 Lesson 31 Session 3 | Refi ne Ideas About the Coordinate Plane

Describe how to plot the point (5, 4) in the coordinate plane.

Name an ordered pair with the same x-coordinate as (5, 4).

Name an ordered pair with the same y-coordinate as (5, 4).

Possible SolutionsMove 5 units right from the origin and then 4 units up. Same x-coordinate: (5, 1); Same y-coordinate: (1, 4)

APPLY ITHave students work independently or with a partner.

1 SHOWLook for understanding of what the x-coordinates and the y-coordinates in the table represent. Both points should be labeled and the descriptions should include the direction of the movements, such as right or up.

Have a few volunteers explain how they plotted the points in the coordinate plane. Use the following to start a discussion:

• How is this table different from the tables you worked with in Session 2? [The coordinates of each point are in a row instead of in a column.]

• What is the x-coordinate of point M? [1] What does the x-coordinate tell you? [Point M is 1 unit to the right of the y-axis.]

• What is the y-coordinate of point N? [2] What does the y-coordinate tell you? [Point N is 2 units up from the x-axis.]

2 ANALYZELook for understanding that Irwin’s error is that he switched the x- and y-coordinates. Encourage students to plot the point (4, 3) in the coordinate plane on the Student Worktext page and compare it to point J.

3 CREATELook for understanding that students need to connect the three points with line segments to form a triangle.

Prompt discussion with questions such as:

• How did you find the ordered pairs for each point?

• Do you think a list of ordered pairs or seeing the points in the coordinate plane is more useful for identifying the figure?

• How do you think the three points would need to be placed to form a right triangle?

Common Misconception If students choose three points that are on the same grid line, then reinforce that the points should form a triangle, not a straight line, so at most two points can be on the same grid line.

Purpose In this session students demonstrate their understanding of the coordinate plane and ordered pairs as they talk through three problems. Then they use points graphed in the coordinate plane to complete a table and describe a pattern formed by the points.

SESSION 3 Refine



LESSON 31 REFINE


SESSION 3

Use what you have learned to complete problem 4.

4 Part A Use the coordinate plane below to complete the table.

x

y

1O

1

2

3

4

5

6

7

2 3 4 5 6 7

A

B

C

D

Point x y

A

B

C

D

Part B Describe a pattern you see formed by the points in the coordinate plane above. Then explain how the pattern is shown by the x- and y-coordinates in the table.

5 MATH JOURNALGraph and label point A(2, 3) and point B(3, 2) in the coordinate plane at the right. Then explain how you used the ordered pairs to decide where to place each point.

y

x

4

3

2

1

1 2 3 4 O

656

Possible answer: In the coordinate plane, the points are in a straight line, with each point 1 unit right and 1 unit up from the point to its left. In the table, the x-coordinates increase by 1 and the y-coordinates increase by 1.

Possible answer: (2, 3) is 2 units to the right and 3 units up from the origin, (0, 0). (3, 2) is 3 units to the right and 2 units up from the origin, (0, 0).

0

1

2

3

1

2

3

4

A

B

4 Before students begin, read through problem 4 as a class. Make sure students understand their task is to write the coordinates of the points in the table and then describe a pattern formed by the points as well as give an explanation of how the pattern is shown by the x- and y-coordinates in the table.

As students work on their own, walk around to assess their progress and understanding, to answer their questions, and to give additional support, if needed.

Have students share the pattern they described with a partner and confirm that the points follow the pattern their partner described. Ask them to try extending the pattern by plotting the next two points in the pattern and adding rows to the table for these points.

Scoring Rubric

Part APoints Expectations

2The table is completed correctly, indicating an understanding of the coordinate plane and ordered pairs.

1

An effort was made to complete the table. The table is partially incomplete or contains some errors, indicating some misconceptions.

0The table is entirely incomplete or it shows little or no understanding of the coordinate plane and ordered pairs.

Part BPoints Expectations

2

The response includes an accurate description of both the pattern represented by the points in the table and the points in the coordinate plane.

1Only one accurate description is included or the descriptions contain minor errors, indicating some misconceptions.

0There is no response, or the response shows no evidence of understanding of the pattern.

Close: Exit Ticket

5 MATH JOURNALStudents use their understanding of ordered pairs to graph and label point A and point B in the coordinate plane. Their responses should indicate an attention to precision by including direction, such as right or up, when describing how to locate each point.

Error Alert If students fail to recognize that an ordered pair indicates how far to move horizontally and vertically from the origin, then ask students if they could plot a point in the coordinate plane given the instructions that a point is 1 unit right and 4 units up without telling them where to start.

©Curriculum Associates, LLC Copying is not permitted.656a Lesson 31 Understand the Coordinate Plane

LESSON 31

Lesson Quiz Teacher Toolbox

1©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 31 Understand the Coordinate Plane

Name ___________________________________________________________ Date ____________________

Lesson 31 Quiz

Solve the problems.

1 Look at the coordinate plane at the right.

Which statements about the points in the coordinate plane are true? Choose all the correct answers.

K

L

J

x

y

1

1

2

3

4

5

6

O 2 3 4 5 6

� Point J and point K have the same y-coordinate.

� Point K and point L have the same x-coordinate.

� The x-coordinate for point K is 1.

� The y-coordinate of point L is 5.

� The y-coordinate of point J is 5.

2 Use the coordinate plane below. Match each point with its ordered pair.

Point Ordered Pair

A (1, 4)

B (3, 4)

C (3, 6)

D (4, 1)

(4, 3)

(6, 3)

C

B

x

y

1

1

2

3

4

5

6

O 2 3 4 5 6

A

D

(2 points)

(2 points)

Tested SkillsAssesses 5.G.A.1

Problems on this assessment form require students to be able to identify points given ordered pairs and identify the ordered pairs that name plotted points in the first quadrant of the coordinate plane. Problems also require students to plot an ordered pair as a point in the coordinate plane. Students will also need to be familiar with identifying and comparing numbers on horizontal and vertical number lines.

Alternately, teachers may assign the Digital Comprehension Check online to assess student understanding of this material.

Error Alert Students may:

• confuse the x- and y-coordinates.

• confuse the meanings of the direction words right, left, up, and down.

• not be able to identify or locate the origin.

Solutions1 B, E; Students could solve the problem by

recognizing that points K and L are both located 5 units to the right from the origin and that point J is located 5 units up from the origin. A is not correct because the y-coordinate for point J is 5 and the y-coordinate for point K is 1. C is not correct because the x-coordinate for point K is 5. D is not correct because the y-coordinate for point L is 4. 2 points 5.G.A.1, DOK 1

Multiple Select and Matching Scoring Rubric

2 points 1 point 0 points

All answers are correct

1 incorrect answer 2 or more incorrect answers

Short Response Scoring Rubric

Points Expectations

2

• Correctly identifies that the 3 in the ordered pair represents moving to the right 3 units and the 2 represents moving up 2 units on the coordinate plane. (1 point)

• Well-organized, clear, and concise explanation that demonstrates thorough understanding of how to plot a point in the coordinate plane. (1 point)

1

• Correctly states that either the 3 represents moving to the right 3 units, or the 2 represents moving up 2 units, while incorrectly stating the location of the other coordinate.

• Shows partial or good understanding of how each coordinate in the ordered pair tells the distance and direction.

0

• No attempt at finding a solution.• No effort to demonstrate an understanding of

coordinate pairs and the relationship to the coordinate plane.

Fill-in-the-Blank Scoring Rubric

2 points 1 point 0 points

• Both numbers in the ordered pair are correct.

• Demonstrates correct math procedures.

• One number in the ordered pair is correct.

• Demonstrates correct math procedure.

• Incorrect answers that do not demonstrate the correct math procedure.

©Curriculum Associates, LLC Copying is not permitted. 656bLesson 31 Understand the Coordinate Plane

Differentiated Instruction

RETEACH REINFORCE EXTEND

Teacher Toolbox

Enrichment ActivitiesStudents who have achieved proficiency with concepts and skills and are ready for additional challenges

Will benefit from group collaborative games and activities that extend understanding

Math Center ActivitiesStudents who require additional practice to reinforce concepts and skills and deepen understanding

Will benefit from small group collaborative games and activities (available in three versions—on-level, below-level, and above-level)

Tools for InstructionStudents who require additional support for prerequisite or on-level skills

Will benefit from activities that provide targeted skills instruction

2©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 31 Understand the Coordinate Plane

Name ___________________________________________________________ Date ____________________

Lesson 31 Quiz continued

3 What are the coordinates of point F?

G

F

E

x

y

1

12345678

O 2 3 4 5 6 7 8

� (1, 1)

� (6, 7)

� (8, 4)

� (7, 6)

4 What are the coordinates of point A in the coordinate plane below? Write your answer in the blanks.

x

y

1

1

2

3

4

5

6

O 2 3 4 5 6

A

( , )

5 Quentin wants to plot point B (3, 2) in a coordinate plane. What steps should Quentin take to correctly plot point B? Explain.

(1 point)

(2 points)

5 3

Possible answer: To graph point B (3, 2), Quentin should start at the

origin and move to the right 3 units. Then he should move up 2 units

and plot a point B.

(2 points)

2 Point A: (3, 6); Point B: (1, 4); Point C: (6, 3); Point D: (4, 3) 2 points 5.G.A.1, DOK 1

3 B; Students could solve the problem by identifying that point F is located 6 units to the right and 7 units up from the origin. A is not correct because the ordered pair (1, 1) represents the location of point E, not point F. C is not correct because the ordered pair (8, 4) represents the location of point G, not point F. D is not correct because the ordered pair (7, 6) represents a location 7 units to the right and 6 units up from the origin, and point F is located 6 units to the right and 7 units up from the origin. 1 point 5.G.A.1, DOK 1

4 (5, 3) 2 points 5.G.A.1, DOK 1

5 See possible steps on the student page. 2 points 5.G.A.1, DOK 1

lesson 31 session 1 explore

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