# q2-day_53-extending_line_graphs

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```					                                  Mathematics Alignment Lesson
Grade 5 Quarter 2 Day 53
Common Core State Standard(s)                                              Alignment Lesson
5.G.1 Use a pair of perpendicular number lines,                                    Extending Line Graphs
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             1. Display Transparency “Extending Line Graphs” and
a given point in the place located by using an                  ask students how you could use the graph to answer
ordered pair of numbers, called its coordinates.                the question. If no one suggests it, suggest that you
Understand that the first number indicates how
far to travel from the origin in the direction of               extend the line to get the answer. Carefully model
one axis, & the second number indicates how                     how to extend the line on the graph by lining up your
far to travel in the direction of the second axis,              ruler. Then model how to find where 9 hours
with the convention that the names of the two
axes and the coordinates correspond (e.g. x- axis               intersects the line and go over to the y-axis to see
and x-coordinate, y-axis and y-coordinate).                     how much money Jack has made. Make sure
5.G.2 Represent real world and mathematical problems by               students understand that only a pattern that is
graphing points in the first quadrant of the coordinate
plane, and interpret coordinate values of points
consistent can be extended to solve a problem.
in the context of the situation.
2. Separate the class into pairs for the next activity.
Give each pair 3 copies of the Coordinate Grid (TRB
Standards for Mathematical Practice                              M36). Go over the directions on
Standard 4 Model with mathematics.                                    Transparency/Blackline Master- “Pattern Hunt
Directions and Recording Sheet”. Remind students
Standard 6 Attend to precision.                                       that they should draw a line that intersects more than
one point to help show a pattern. Allow students to
work in pairs to practice finding and extending
Materials Needed:                                      patterns using a line graph.
    Blackline Masters- “Coordinate Grid (TRB
M36) – 3 copies per student”                              3. Select student leaders from each group to share one
    Transparency/Blackline Master- “Pattern                          of the patterns they graphed and the real-world
Hunt Directions and Recording Sheet”                         context they created for the graph.
    Transparency- “Extending Line Graphs”
    Math Expressions Textbook (Vol. 2)                            4. Have students turn to page 368 in the Math
    Math Expressions Activity Workbook                               Expressions textbook or page 115 in the Math
    Math Expressions Teacher Edition (Vol. 2)                        Expressions Activity Workbook (Unit 8, Lesson 7 –
    Rulers                                                           Going Further; Teacher Edition page 858). Complete
the activity as outlined on in the Teacher Edition.
Assessment
Use the questions students Activity Workbook
page 115 as an informal assessment.                             Note: Be sure to emphasize throughout the lesson that only a
pattern that is consistent can be extended to solve a problem.

Homework                                  Source: NC DPI 5th Grade Unpacked Mathematics Content
Blackline Master, “Extend Line Graphs
& Math Expressions Unit 8, Lesson 7
Homework”

Vocabulary
Coordinate Plane – a system of coordinates formed by the perpendicular intersection of horizontal and vertical number lines.
x-axis –the horizontal axis of a two-dimensional coordinate grid
y-axis – the vertical axis of a two-dimensional coordinate grid
ordered pair – a pair of numbers that shows the position of a point on a graph
origin – the point (0,0) on a two-dimensional coordinate grid
Wake County Public School System, 2012
Transparency Grade 5   Day 53   Standard 5.G.1 & 5.G.2

Extending Line Graphs

Use the graph below to determine who much money Jack makes after
working exactly 9 hours.

Adapted from NC DPI 5th Grade Unpacked Mathematics Content (p. 43)

Wake County Public School System, 2012
Answer Key Grade 5   Day 53   Standard 5.G.1 & 5.G.2
Extending the Line Graphs – Answer Key

Use the graph below to determine who much money Jack makes after
working exactly 9 hours. – answer: \$24

Adapted from NC DPI 5th Grade Unpacked Mathematics Content (p. 43)

Wake County Public School System, 2012
Transparency/Blackline Master     Grade 5   Day 53    Standard 5.G.1 & 5.G.2

Pattern Hunt Directions & Recording Sheet
Directions:
1. One partner draws a line from (0,0) through 2 points on the grid.
2. The other partner carefully extends the line and writes the ordered pairs for the whole number
points along the line.
3. Working together, the partners write a pattern using the information on the graph and the
ordered pairs.
4. Working together, create a real-world context for the pattern
5. Exchange roles and repeat the activity as time permits.

Round 1:
Pattern

Real-world Context

Round 2:
Pattern

Real-world Context

Round 3:
Pattern

Real-world Context

Round 4:
Pattern

Real-world Context

Adapted from Math Expressions Activity Card 8-7 (Teacher Edition p. 859)
Wake County Public School System, 2012
Blackline Master Grade 5                    Day 53     Standard 5.G.1 & 5.G.2
Name: ________________________
Date: ________________________
Extend Line Graphs Homework

Sara’s Earnings
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1

0   1   2 3   4   5   6   7   8   9 10 11 12 13 14 15

Directions: Use the graph above to answer the questions that follow.

Sara earns \$2.00 for each chore she does and she saves all of her money.

1. Create a graph that shows the relationship between the hours Sara did her chores and the amount
of money she has saved. Make sure to label each axis.

2.    How much will she have after working 3 hours? Explain how you used the graph to determine
this amount.

3. How much will she have after working 5 hours? Explain how you used the graph to determine
this amount.

4. How much will she have after working 7 hours? Explain how you used the graph to determine
this amount.

5. What other information do you know from analyzing the graph?

Adapted from NC DPI 5th Grade Unpacked Mathematics Content (p. 43)

Wake County Public School System, 2012
Answer Key Grade 5            Day 53        Standard 5.G.1 & 5.G.2

Extend Line Graphs Homework – Answer Key

Sara’s Earnings
15
14
13
12
11
10
9
Amount Earned (in dollars)        8
7
6
5
4
3
2
1

0   1   2 3 4 5 6 7 8 9 10 11 12 13 14 15
Number of Chores Completed

Directions: Use the graph above to answer the questions that follow.

Sara earns \$2.00 for each chore she does and she saves all of her money.

1.   Create a graph that shows the relationship between the hours Sara did her chores and the amount of money she has
saved. Make sure to label each axis.

2.    How much will she have after working 3 hours? Explain how you used the graph to determine this amount. \$6.00; I
used the graph by going over to three on the x-axis (number of chores completed) and going up to where it met
the line graph I created and then over to see that it met with \$6.00 on the y-axis (amount earned).

3.   How much will she have after working 5 hours? Explain how you used the graph to determine this amount. \$10.00; I
used the graph by going over to five on the x-axis (number of chores completed) and going up to where it met
the line graph I created and then over to see that it met with \$10.00 on the y-axis (amount earned).

4.   How much will she have after working 7 hours? Explain how you used the graph to determine this amount. \$14.00; I
used the graph by going over to three on the x-axis (number of chores completed) and going up to where it met
the line graph I created and then over to see that it met with \$14.00 on the y-axis (amount earned).

5.   What other information do you know from analyzing the graph? The more chores Sara does, the more money she
earns. Sara the amount earned is always twice the n umber of chores completed. The points fall on a straight
line since Sara always makes the same amount per chore.

Adapted from NC DPI 5th Grade Unpacked Mathematics Content (p. 43)
Wake County Public School System, 2012

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