2012-13 and 2013-14 Transitional Comprehensive Curriculum
Grade 6
Mathematics
Unit 7: Rational Numbers
Time Frame: Approximately four weeks
Unit Description
The focus of this unit is on working with rational numbers. Number lines, both horizontal and
vertical, are used to represent rational numbers and their opposites. Rational numbers represent
values above and below zero, to the left and right of zero, and are used to solve problems in real
world applications. Coordinate grids extend beyond the first quadrant to include the full x- and
y-axes, including positive and negative x- and y-coordinates and their reflections.
Student Understandings
Students should have a conceptual understanding of positive and negative numbers and how they
relate. They plot and write ordered pairs where x and y can be positive or negative rational
numbers. Students interpret situations with positive or negative rational numbers.
Guiding Questions
1.
2.
3.
4.
Can students interpret and represent rational numbers on a number line?
Can students calculate the distance from zero on a number line?
Can students locate, order and compare rational numbers on a number line?
Can students interpret absolute value as magnitude for a positive or negative
quantity in a real-world situation?
5. Can students identify the four quadrants on a coordinate plane and determine in
which quadrant a point will lie?
6. Can student plot ordered pairs on a coordinate plane and reflect the point over the xand y-axes?
7. Can students solve real-world problems by graphing points in all four quadrants of
a coordinate plane?
MATH: Grade 6 Grade-Level Expectations and Common Core State Standards
Grade-Level Expectations
GLE #
GLE Text and Benchmarks
Algebra
8.
Demonstrate the meaning of positive and negative numbers and their
opposites in real-life situations (N-3-M) (N-5-M)
28.
Use a rectangular grid and ordered pairs to plot simple shapes and find
horizontal and vertical lengths and area (G-6-M)
Grade 6 MathematicsUnit 7 Rational Numbers
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CCSS for Mathematical Content
CCSS Text
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.
a. Recognize opposite signs of numbers as indicating locations on
opposite sides of 0 on the number line; recognize that the opposite
of the opposite of a number is the number itself, e.g., –(–3) = 3, and
that 0 is its own opposite.
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.
c. Find and position integers and other rational numbers on a
horizontal or vertical number line diagram; find and position pairs
of integers and other rational numbers on a coordinate plane.
6.NS.7
Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative
position of two numbers on a number line diagram. For example,
interpret –3 > –7 as a statement that –3 is located to the right of –7
on a number line oriented from left to right.
b. Write, interpret, and explain statements of order for rational
numbers in real-world contexts. For example, write –3 oC > –7 oC
to express the fact that –3 oC is warmer than –7 oC.
c. Understand the absolute value of a rational number as its distance
from 0 on the number line; interpret absolute value as magnitude
for a positive or negative quantity in a real-world situation. For
example, for an account balance of –30 dollars, write |–30| = 30 to
describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements about
order. For example, recognize that an account balance less than –
30 dollars represents a debt greater than 30 dollars.
6.NS.8
Solve real-world and mathematical problems by graphing points in all four
quadrants of the coordinate plane. Include use of coordinates and absolute
value to find distances between points with the same first coordinate or the
same second coordinate.
ELA CCSS
Reading Standards for Literacy in Science and Technical Subjects 6–12
RST.6-8.4 Determine the meaning of symbols, key terms, and other domain-specific
words and phrases as they are used in a specific scientific or technical
context relevant to grades 6–8 texts and topics.
College and Career Readiness Anchor Standards for Writing
6.W.4
Produce clear and coherent writing in which the development, organization,
and style are appropriate to task, purpose, and audience.
CCSS #
6.NS.6
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Sample Activities
Activity 1: Rational Numbers Vocabulary Awareness (CCSS: RST.6-8.4)
Materials List: Rational Numbers BLM, pencil
Before beginning the unit, have students complete a vocabulary self awareness chart (view
literacy strategy descriptions). Provide students with the Rational Numbers BLM. Do not give
students definitions or examples at this point.
Word
absolute value
axis
coordinate plane
horizontal
integer
negative number
ordered pair
origin
positive number
rational number
reflection
vertical
+

– Example
Definition
Ask students to rate their understanding of each word with either a “+” (understands well), a
“” (some understanding), or a “–” (don’t know) and write in examples and definitions to the
best of their knowledge. During and after completing the activities throughout this unit, students
should return to the chart to revise and fill in examples and definitions in their own words. The
goal is to have all plus signs at the end of the unit. After all the students have completed the
chart, have them share their examples and definitions with each other to check for accuracy.
Activity 2: Are You Positive? (GLE: 8; CCSS: 6.NS.6a,c; 6.NS.7a,b)
Materials List: thermometer, Are You Positive? BLM, pencil
Show the students a Fahrenheit thermometer and ask: “What is the temperature on a hot, sunny
day?” Have a student point out a degree on the thermometer. Ask a few other questions similar to
this making sure the answer would be a positive number. Ask students what it means for the
temperature to be 5 degrees below zero and show where this is on the thermometer. Explain that
a negative sign is needed to write this number since it is below zero. Next, ask them where 20
degrees below zero would be on the thermometer, and then ask them whether it is hotter or
colder than 5 degrees below zero. Since 20 degrees below zero is colder than 5 degrees below
zero, negative 20 is less than negative 5. This can be written as -20 < -5.
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Display a thermometer similar to the one below. Have students make up problems using the
thermometer. It was 32.5 degrees during the day. Graph the temperature and its opposite on a
vertical number line.
Students should see a connection between positive and negative numbers and the world around
them through the use of problems embedded in contexts such as the temperature problems. Have
students brainstorm (view literacy strategy descriptions) a variety of situations where positive
and negative numbers would be required. Some examples are distance above or below sea level,
and banking (deposits and withdrawals), football gains and losses.
Present the following problem to the class. Metairie, LA is 5 feet below sea level. Terrytown,
LA is 3 feet below sea level. Have students draw a number line, mark each city’s elevation, and
write a comparison statement in words and symbols about the two locations.
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8
6
4
2
0
•
•
-2
Terrytown
-4
Metairie
-6
-8
Terrytown is located above Metairie on the number line, so Terrytown has a higher elevation
than Metairie. 3 feet below sea level is higher than 5 feet below sea level. -3 > -5
Ask, “What is the opposite of -3?” (3) Have students place an X on the number line at the
opposite of -3.
8
6
x
4
2
0
•
•
-2
Terrytown
-4
Metairie
-6
-8
Have students draw a horizontal number line and locate the following situation and its opposite
on the number line. Place a point on the number line to represent the problem and an X to
represent its opposite.
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Jenny lost 3.25 pounds last week.
•
x
3 4
-4 -3 -2 -1 0 1 2
Distribute the Are You Positive BLM to the students. Have the students complete the activity in
groups or independently. Discuss the answers as a class. Have students respond to the following
prompt in the math learning log (view literacy strategy descriptions). Name and give examples
of 4 real-life situations in which rational numbers can be used. Allow students time to share their
responses with a partner or the class. Students should listen for accuracy and logic.
Activity 3: Comparing Numbers (GLE: 8; CCSS: 6.NS.6c; 6.NS.7a,b)
Materials List: Planets BLM, pencil
Present the following problem to the class: A meteorologist recorded low temperatures for five
cities in Alaska. List these cities in order from lowest temperature to highest temperature.
Cities in Alaska
Anchorage (A)
College (C)
Fairbanks (F)
Juneau
(J)
Wasilla (W)
Temperature
-5º F
-10° F
-8° F
-3° F
6° F
Tell students that since the temperatures are given as integers, a number line will help solve this
problem.
10
Horizontal Number Line
C
A
F
J
•• ••
-10
-8
-6
W
-4
W
-2
0
2
4
•
6
•
8
10
6 Vertical Number Line
4
2
8
10
0
J
A
F
C
Grade 6 MathematicsUnit 7 Rational Numbers
•
•
•
•
-2
-4
-6
-8
-10
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2012-13 and 2013-14 Transitional Comprehensive Curriculum
Ask questions such as the following:
 What happens as you move to the right on the horizontal number line? As you move to the
right on the number line, the numbers increase in value.
 What happens as you move to the left on the horizontal number line? As you move to the
left on the number line, the numbers decrease in value.
 What happens as you move up on the vertical number line? As you move up on the
number line, the numbers increase in value.
 What happens as you move down on the vertical number line? As you move down on the
number line, the numbers decrease in value.
 Which city had the highest temperature? Wasilla
 Which city had the lowest temperature? College
Have students write an inequality to compare the temperature in Anchorage to the temperature in
Fairbanks.
-5 > -8
-5 > -8 is interpreted as -5 is located to the right of -8 on a horizontal number line.
In this situation -5 > -8 means -5°F is warmer than -8º F.
Have students write an inequality comparing the temperatures in College and Juneau, and
interpret and explain the inequality.
Example: -10 < -3
-10 < -3 is interpreted as -10 is located to the left of -3 on a horizontal number line.
-10 < -3 means -10°F is colder than -3º F.
Distribute the Planets BLM. Have the students work together to complete. Discuss the answers
as a class.
Activity 4: Line Up (CCSS: 6.NS.6a,c; 6.NS.7a)
Material List: Opposites BLM for each group students, Opposites Record BLM, scissors
Run the Opposites BLM on stock paper, cut out the cards, and shuffle each set of cards. Each
pair of students will need a set of cards. For the first part of the activity, take one set of cards and
distribute one card to each student. Have students line up in order from least to greatest, without
talking, to create a human number line. Have each student read his/her number starting with the
smallest number. Have students listen to see if the numbers are in order from least to greatest.
Have students pair up and sit with their opposite. Have pairs explain why they are opposites.
Distribute the Opposites Record BLM to each pair of students. Have the students play the game
of “war.” Each pair will split the cards evenly between the two players. Both players lay down a
card and the one with the higher card wins both cards. In each round of the game, have students
make up a real world scenario, create a statement of inequality (e.g., -8 < 3) and interpret the
statement by writing the inequality and its meaning in a sentence or sentences. An example is,
last Wednesday the low temperature in Breckenridge was -8ºF and the high temperature was 3ºF.
Negative 8 is less than positive 3 means that negative eight is to the left of positive three on the
number line. Have students share their scenarios, inequality statements and interpretations.
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2012-13 and 2013-14 Transitional Comprehensive Curriculum
Activity 5: Who’s Farther? (CCSS: 6.NS.7c,d)
Materials List: paper, pencil
Present the following problems:
Problem 1:
Sal and Jan were at school. Sal lives 2 miles west of the school and Jan lives 2 miles east of the
school. Who lives farther away from the school?
Tell students that a number line can be used to represent the problem. 2 miles to the west can be
represented as -2 and 2 miles to the east can be represented as 2. The school is at 0.
S
-4
-3
•
-2
J
-1
0
1
•
2
3
4
Both numbers are 2 units from zero on a number line. Explain that this is known as absolute
value, and it is written |2| or |-2|. The absolute value of a number is the distance from 0 of that
number. Sal and Jan both live the same distance from the school in opposite directions.
Problem 2:
One of the thermometers shows -2°C and the other shows -4°C. Which thermometer shows
which temperature? Which is the colder temperature? How much colder?
Have students write an inequality to show the relationship between the temperatures and explain
how the model shows this relationship.
The thermometer to the left shows 2 degrees below zero and the thermometer to the right shows
4 degrees below zero. 4 degrees below zero is colder.
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2º colder
• •
-4 < -2 - 4 is located to the left of -2 on the number line. -4º is colder than -2º.
-4
Problem 3:
-3
-2
-1
0
1
2
3
4
We went deep sea fishing in the Gulf of Mexico. The depth of the gulf where we fished is –1500 feet.
What is the absolute value of -1500? | –1500| = 1500. 1500 is used to describe the distance below sea
level. We fished in water with depths > -1500 feet. This means that we did not fish below a depth of 1500
feet below sea level.
Activity 6: Solve It! (GLE: 8; CCSS: 6.NS.6c; 6.NS.7a,b,c,d; 8.NS.8; 6.W.4)
Materials List: Solve It! BLM, paper, pencil
Distribute the Solve It! BLM. Have students work with partners to solve each situation. Discuss
each situation with the students.
Situation 1:
The highest and lowest temperatures ever recorded in Louisiana are –16 ºF in Minden and 114 ºF
in Plain Dealing. Which temperature is colder? -16 ºF
Show the temperature change on a number line.
16º
•
-20 -10
114º
0 10 20
30
40 50 60 70
80
90
•
100 110 120
How much colder? -16 is 16 units from zero on the number line and 114 is 114 units from zero
on the number line. So |16| + |114| = 16 + 114 = 130. It was 130 degrees colder.
Write an inequality to show the relationship between the temperatures. . -16 < 114 or 114 > -16
Situation 2:
Ms. Jones sponsors a school club. After their pizza party last week, the bookkeeper informed her
that the club account has a balance less than 25.50 dollars. Is the club’s debt greater than or less
than 25.50 dollars? The club’s debt is greater than 25.50 dollars.
Situation 3:
The highest point in Louisiana is Driskill Mountain at 535 feet above sea level. The lowest point
in Louisiana is 8 feet below sea level in New Orleans. Represent each number as an integer. 535
and -8
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2012-13 and 2013-14 Transitional Comprehensive Curriculum
Show the elevations on a number line.
•
550
500
450
400
350
535 feet
300
250
200
8 feet
•
150
100
50
0
-50
How much higher is Driskill Mountain than New Orleans? -8 is 8 units from zero on the number
line and 535 is 535 units from zero on the number line. So |8| + |535| = 8 + 535= 543. It is 543
feet higher.
After discussing the solutions to the problems above, have the students create a text chain (view
literacy strategy descriptions). Put students in groups of four. On a sheet of paper, ask the first
student to write the opening sentence for the math text chain. For example, a student might begin
the chain with this sentence.
Last week it was -3 ºF.
The student then passes the paper to the student sitting to the right, and that student writes the
next sentence in the story, which might read:
Today it was 7 ºF.
The paper is passed again to the right to the next student who writes the third sentence of the
story.
How much cooler was it yesterday?
The paper is now passed to the fourth student who must solve the problem and write out the
answer. The other three group members review the answer for accuracy.
Answer: |-3| + |7| = 3 + 7 = 10 so it was 10 degrees warmer.
Grade 6 MathematicsUnit 7 Rational Numbers
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This activity allows students to use their writing, reading, and speaking skills while learning and
reviewing the concept of integers. When text chains are completed, be sure students are
checking them for accuracy and logic. Groups can exchange text chains to further practice
reviewing and checking for accuracy.
Activity 7: Newspaper Comparisons (GLE: 8; CCSS: 6.NS.6a, 6.NS.7b,c,d)
Materials List: newspapers, paper, pencils
Have students use sections from the local newspaper to create scenarios comparing rational
numbers. The weather page contains both positive and negative temperatures. Have students
choose one section and make up scenarios using the information found in the charts. For
example: Show the relationship between yesterday’s highest and lowest recorded temperatures.
How far are the temperatures from zero on a number line? Be sure students include comparison
statements to describe their temperatures.
These scenarios will be used as the student pairs present their scenario using a modification of
questioning the content (QTC) (view literacy strategy descriptions). In this case, instead of
students questioning a text they read, they will question each other as authors of these scenarios.
As the authors of the scenario, the pair will be involved in a collaborative process of building
understanding with integer situations. Students should develop a model of their situation and
represent the situation mathematically. Once the student pairs have developed their scenario, the
pair begins answering the questions from classmates about their scenario and solution. Strive to
elicit students’ thinking while keeping them focused in their discussion. The pair will answer
questions that the class asks about their scenario and justify the mathematics involved in the
solution.
Students should be able to answer the following questions about their scenarios.
1. What are your rational numbers?
2. Which number is larger?
3. What is the absolute value of each number?
4. Give a comparison statement to describe your numbers.
Activity 8: The Fly On The Ceiling (GLE: 28; CCSS: 6.NS.6c, 6.NS.8)
Materials List: The Fly on the Ceiling, Coordinate Points BLM, pencil
The book The Fly on the Ceiling by Julie Glass, Random House Books for Young Readers
(1998) offers delightful insight into the mathematician Rene Descartes and to the Cartesian
coordinate system. Read the story to motivate the students and let them become familiar with
point plotting.
For an introduction to the coordinate plane, The Math Forum offers a graphic representation that
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presents an understanding of points on a line, finding and graphing points in a plane, and
estimating points. The Math Forum is located at http://mathforum.org/cgraph/cplane/.
Tell students that points in a coordinate plane are represented by ordered pairs in which the first
number is the xcoordinate and
the second
number is the ycoordinate. In
the graph below,
point k is
represented by
the ordered pair
(4, 2). The xcoordinate shows
how far to move
left or right from
the origin and
the y-coordinate
shows how far to
move up or
down from the
origin.
y-axis
j
f
k
Up 2
x-axis
origin
Over 4
Ask, “What are the coordinates of point j?” (3, 6) Have students graph (7.5, 4) and label it as
point f.
Grade 6 MathematicsUnit 7 Rational Numbers
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Distribute the Coordinate Points BLM. Have students work with partners to answer the
questions. Discuss the answers as a class.
The history of the coordinate plane, how it was invented, and who named it is at
http://mathforum.org/cgraph/history/.
Activity 9: Quadrants (CCSS: 6.NS.6b,c; 6.NS.8)
Materials List: Coordinate Graph BLM, Ordered Pair Cards BLM, Ordered Pair Record BLM
pencil, scissors, glue
Graphic organizers (view literacy strategy descriptions) help students learn concepts by
organizing information in a manner that makes it easier to understand and learn. Distribute the
Coordinate Graph BLM. Have students cut along the dotted line and then fold each flap in. The
fold line should be at the left and right edge of the coordinate grid.
Cut along dashed line on both sides of the coordinate grid. This allows the students to focus on
one quadrant at a time.
Fold the top and bottom flaps along the edge on each side of the coordinate grid. Label the
coordinate plane, including quadrants, origin and axes.
Quadra
nt
II
Quadra
nt
I
Quadra
nt
III
Quadra
nt
IV
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Have students label the x- and y-axis and the origin.
y
•
x
Origin
(0,0)
Have students label Quadrant I. Discuss that points that fall in Quadrant I must have positive x
and positive y values. Have students plot point (4, 3) and label it point A. Have them plot point
(2, 1) and label it point B.
y
Quad I
(+, +)
•
Points in
Quad I
•
•
A(4,3) B(2,1)
x
Origin
(0,0)
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Have students label Quadrant II. Discuss that points that fall in Quadrant II must have negative x
and positive y values. Have students plot point (-4, 3) and label it point C. Have them plot point
(-2, 1) and label it point D.
y
Quad II
(-,+)
Points in
Quad II
Quad I
(+, +)
•
•
•
C(-4,3) D(-2,1)
Points in
Quad I
•
•
A(4,3) B(2,1)
x
Origin
(0,0)
Have students label Quadrant III. Discuss that points that fall in Quadrant III must have negative
x and negative y values. Have students plot point (-4, -3) and label it point E. Have them plot
point (-2, -1) and label it point F.
y
Quad II
(-,+)
Points in
Quad II
•
•
•
C(-4,3) D(-2,1)
Quad III
(-, -)
Points in
Quad III
Quad I
(+, +)
•
•
Points in
Quad I
•
•
A(4,3) B(2,1)
x
Origin
(0,0)
E(-4,-3) F(-2,-1)
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Have students label Quadrant IV. Discuss that points that fall in Quadrant IV must have positive
x and negative y values. Have students plot point (4, -3) and label it point G. Have them plot
point (2, -1) and label it point H.
y
Quad II
(-,+)
Points in
Quad II
•
•
•
C(-4,3) D(-2,1)
Quad III
(-, -)
Points in
Quad III
Quad I
(+, +)
•
•
Points in
Quad I
•
•
x
•
Origin
(0,0)
E(-4,-3) F(-2,-1)
A(4,3) B(2,1)
•
Quad IV
(+ , -)
Points in
Quad IV
G(4,-3) H(2,-1)
Have students locate point A and point C on their coordinate plane.
Ask students, “What do these two points have in common?” They are both 3 units away from
the x axis and 4 units away from the y-axis. What is different about the two points? Point A is
four units to the right of the y-axis and point C is four units to the left of the y axis. “How is the
difference shown in the ordered pair?” The 4 is negative in point C. Tell students that point C is
the reflection of point A. It is reflected over the y axis. Explain that if they folded their papers in
half at the y-axis, the points A and C would match or touch.
Ask, “Can you identify other points that are reflections of each other over the y-axis?” B and D,
E and G, F and H Are there any points reflected over the x-axis? Yes, A and G, B and H, C and
E, D and F.
Have students plot point (-1, 2). What would be its reflection over the x-axis? (-1, -2) Ask,
“What would be its reflection over the y-axis?” (1, 2) Give students additional points to reflect if
needed.
Distribute the Ordered Pair Cards BLM and the Ordered Pair Record BLM to the students. Have
the students work in groups of two and pair the cards that are reflections and then identify which
axis they reflect over. Discuss answers as a class.
Have students glue their Coordinate Plane graphic organizer into their notebook to use as a study
aid when reviewing the parts of a coordinate plane and graphing points.
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Activity 10: Plotting Shapes (GLEs: 28; CCSS: 6.NS.6b,c; 6.NS.8)
Materials List: Grid Paper BLM, ruler, pencil
Display grid paper. On the grid paper, plot the following points and connect the dots in order.
(2, 7) (2, -5) (-4, -5)
(-4, 7)
Ask students, “What shape was made?” A rectangle “What is the length of each side?” To find
the distance along the x-axis between the points (-4, 7) and (2, 7), a student must recognize that 4 is |-4| or 4 units to the left of 0 and 2 is |2| or 2 units to the right of zero. The two points are 6
units apart on the x-axis. Students should represent this on the coordinate grid and numerically
with the absolute value expression,|-4| + |2|. Along the y-axis, (-4, 7) and (-4, -5) are |7| or 7
units above 0 and |-5| or 5 units below 0. So the two points are 12 units apart. |7| +|-5| = 12.
Ask, “How would you find the area of the rectangle?” Multiply the length by the width. The
length is 12 units and the width is 6 units. “What is the area of the figure?” The rectangle is 6
units × 12 units, so the area is 6 × 12 or 72 square units.
Distribute the Grid Paper BLM and have students draw the x- and y-axis, dividing the grid paper
into 4 quadrants. Ask students to identify in which quadrant each point will lie and to predict
what shape the points will form.
(-6, 3) (3, 3)
(3, -5)
(-6, -5)
Have students plot the points and connect the dots in order. Give students time to individually
answer each question and then discuss as a class.
Ask, “What shape did it form?” A rectangle “What is the length of each side?” To find the
distance along the x-axis between the point (-7, 3) and (3, 3) a student must recognize that -7 is
|-7| or 7 units to the left of 0 and 3 is |3| or 3 units to the right of zero, so the two points are 10
units apart on the x-axis. Students should represent this on the coordinate grid and numerically
with an absolute value expression,|-7| + |3|. Along the y-axis, (-7, 3) and (-7, -5) are |3| or 3
units above 0 and |-5| or 5 units below 0. So the two points are 8 units apart. “What is the area
of the figure?” The rectangle is 12 units × 8 units, so the area is 12 × 8 or 96 square units.
Have students plot other sets of ordered pairs to find the rectangles or squares. Using the
coordinates, students can figure out the length and area. Make sure that the ordered pairs have
the same first coordinates or the same second coordinates in order to find the length and width.
Activity 11: Integer Battleship (GLE: 28; CCSS: 6.NS.6b,c)
Material List: Integer Battleship BLM, folder, tape, pencil
Distribute the Integer Battleship BLM. Have students play in groups of two. Students should be
seated facing each other.
Grade 6 MathematicsUnit 7 Rational Numbers
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2012-13 and 2013-14 Transitional Comprehensive Curriculum
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Tape a folder on the table or desk between the two students to block the view of their
partner’s paper.
Each person selected places 5 points on their coordinate grid to represent the locations for
their ships.
Taking turns, Player 1 calls out a set of coordinates and marks the coordinates on his/her
paper. Player 2 responds – hit or miss. It is a hit if one of player 2’s points is located at
the coordinates called. If the play is a hit, Player 2 removes his/her ship by putting an x
on the point. Player 1 marks an S on their paper to record their hit. If it is a miss, the
player records a point on their paper.
The first one to get all of their opponent’s ships wins.
Sample Assessments
General Assessments
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Have students create portfolios containing samples of his/her work.
Facilitate during small group discussions to determine misconceptions,
understandings, use of correct terminology, and reasoning abilities. Appropriate
questions to ask to promote problem solving might be:
o What do you need to find out?
o What information do you have?
o What strategies are you going to use?
Ask probing questions to help students learn to reason mathematically. Possible
questions to ask may be…
o Is that true for all cases? Explain
o Can you think of a counter example?
o How would you prove that?
o What assumptions are you making?
o How would you convince everyone else that your answer makes sense?
Have students create learning logs (view literacy strategy descriptions) using such
topics as these:
o The most important thing I learned in math this week was…
o The easiest thing about today’s lesson…
Activity-Specific Assessments
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Activity 6: Have students write a real-life situation that can be represented by the
following inequality and give a statement that explains what the inequality means.
-5 < 4
Grade 6 MathematicsUnit 7 Rational Numbers
7-18
2012-13 and 2013-14 Transitional Comprehensive Curriculum
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Activity 9: For each of the following ordered pairs, have students identify in what
quadrant the point lies and what points would be a reflection of it over the x- and y-axes.
1
(-3, 7)
(2, -9.8)
(-5, -8 )
3
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Activity 10: Have students plot the following points, connect the dots in order and answer
the questions.
(-5, 3) (6, 3) (6, -1) (-5, -1)
What shape did it form? What is the length of each side? What is the area of the figure?
Grade 6 MathematicsUnit 7 Rational Numbers
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