Download Course: 6th grade Math 3rd Nine Weeks Instructional Guide Unit 1

Course: 6th grade Math
3rd Nine Weeks
Unit 1: Fractions, Decimals, Percents, Ratios, and Rates
Instructional Guide
Estimated Time: 2 Weeks
GLE 0606.2.3 Understand and use ratios, rates and percents.
GLE 0606.2.4 Understand and convert between fraction, decimal, and percent forms of rational numbers.
GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0606.1.6 Read and interpret the language of mathematics and use written/oral communication to express mathematical
ideas precisely.
GLE 0606.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and
reasonableness of the solution.
Pre-requisite Skills:
1. Recognize equivalent representations of the same number.
2. Write terminating decimals in the form of fractions or mixed numbers.
3. Compare whole numbers, decimals and fractions using the symbols <, > and =.
Essential Questions:
 How do operations with decimals/fractions compare to operations with whole numbers?
 How are whole numbers, fractions, decimals and percents related to one another?
 When and why do I use proportional comparisons?
 How does comparing quantities describe the relationship between them?
Unit Vocabulary:
percent, rate, ratio, repeating decimal, terminating decimal, equivalency, proportions
Scaffolded Ideas:
1. A ratio is a comparison between two or more quantities.
2. The quantities can be either numbers or measures.
3. Ratios are classified based on the type of comparison:
Measures of the same type: part-to-whole comparisons or
part-to-part comparisons
Measures of different types: rates
4. When two different types of measures are being compared, the ratio is usually called a rate.
5. Ratios can be written in the following ways: a:b, a/b, and a to b.
Checks for
State
I Can
Instructional Resources/
Connections
Understanding Performance
Statements
Strategies
Indicators
0606.2.4
I Can...
Chapter 8 Sec 1 pg 392
 www.portaportal.com Guest Access box password:
SPI 0606.2.6
Understand ratio as Solve
Chapter 8 Sec 2 pg 398
courseoutlines
a fraction used to
*apply the ratio forms a:b,
Chapter 8 Sec 3 pg 402
problems
compare two
a/b, and a to b in problem  6th Grade MNPS Curriculum Guides
Chapter 8 Sec 6 pg 412
involving
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
quantities by
division.
0606.2.5 Recognize
a:b, a/b, and “a to
b” as notations for
ratios.
0606.2.6 Recognize
common
percentages as
ratios based on
fractions whose
denominators are 2,
3, 4, 5, or 10.
0606.2.7 Connect
ratio and rate to
multiplication and
division.
ratios, rates
and percents.
(power, 3rd 9
weeks)
Power SPIs: bold and italicized
solving.
*understand the
relationship between
ratios and fraction forms.
* recognize common
percentages as ratios
based on fractions.
http://mnps2010.wikispaces.com/

Ratios, Rates, and Proportions Activities
http://math.pppst.com/ratio-proportion-percent.html

Navigating through Measurement in Grades 6-8
“Ratios – Perimeters and Areas”

SpringBoard: “Penny Stacking” (Measurement
Conversions)

Literature:
“Measuring Penny” by Loreen Leedy
“If the World Were a Village” (Percent – Marilyn Burns
Math and Nonfiction grades 3-5)
“Cut Down to Size at High Noon” (Length &
Proportional Reasoning)
“ If you Hopped Like a Frog” (length, proportional
reasoning - Marilyn Burns Math and Nonfiction grades
3-5)
“Jim and the Beanstalk (length, proportional reasoning
- Marilyn Burns Math & Literature grades 4-6))

BBC: Number Math Percentages
http://www.bbc.co.uk/schools/ks2bitesize/maths/activiti
es/percentages.shtml

AAA Math: Ratios
http://www.321know.com/g62a_rx1.htm#section2

Mathline:
Is It Really News?” (6-8)
http://www.pbs.org/teachers/mathline/lessonplans/pdf/
msmp/news.pdf

NCTM Illuminations Activities:
“Fractions Model I”
http://illuminations.nctm.org/ActivityDetail.aspx?ID=11
“Fractions Model II”
http://illuminations.nctm.org/ActivityDetail.aspx?ID=44
Fractions Model III”
http://illuminations.nctm.org/ActivityDetail.aspx?ID=45

“In Your Shadow” Indirect Measurement Activity
Lesson from
*understand and explain
the connection between
ratio and rate as it relates
to multiplication and
division.
Nested SPIs: italicized
Other SPIs: normal type
http://illuminations.nctm.org/LessonDetail.aspx?ID=L51
5
0606.2.1 Efficiently
compare and order
fractions, decimals
and percents;
determine their
approximate
locations on a
number line.
0606.2.8 Recognize
that a terminating
decimal equals a
fraction with a
denominator that is
a power of ten.
0606.2.9 Recognize
that the decimal
form of a rational
number either
terminates or
repeats.
SPI 0606.2.5
Transform
numbers from
one form to
another
(fractions,
decimals,
percents, and
mixed
numbers).
(nested, to
Power std. in
2nd 9 weeks)

I Can...
*convert equivalent
representations of
numbers ( fractions,
decimals, percents, and
mixed numbers.
*compare and order
fractions, decimals and
percents.
*place fractions, decimals,
and percents on their
approximate locations on a
number line.
SpringBoard: “Cooking with Andre’” (Fractions to
decimals to whole numbers)
Chapter 8 Sec 7 pg 418
Chapter 8 Sec 8 pg 422

SpringBoard: “Batter Up! First Inning” (Percentages)

SpringBoard: “Nutrition Fun” (Fractions, Decimals, and
Percents)

Literature:
“Ed Emberley’s Picture Pie” (Fractions & percents as
part of a whole – Marilyn Burns Math & Nonfiction
grades 3-5)
“Fraction Fun” by David Adler
“Fraction Action” by Loreen Leedy

Mrs. Glosser's Math Goodies:
Changing Fractions. to Percents
http://www.mathgoodies.com/lessons/vol4/fractions_to
_percents.html
*explain the concept of
terminating and repeating
decimals
Chapter 8 Sec 9 pg 426
Chapter 8 Sec 10 pg
432
Test Item Examples for SPI060.2.6: Solve problems involving ratios, rates and percents.
Joey solves math problems at a rate of about 3 problems every 7 minutes. He continues to work at the same rate. How many minutes should Joey
take to solve 45 math problems?
A. 15 minutes
B. 21 minutes
C. 105 minutes
D. 135 minutes
The area of the floor in Rogelio’s family room is 400 square feet. A rug covers 80 square feet of the floor. What percent of the family room floor is
covered by the rug?
A. 5%
B. 20%
Power SPIs: bold and italicized
C. 50%
Nested SPIs: italicized
D. 80%
Other SPIs: normal type
The floor area of Ms. Hernandez’s classroom is 900 square feet. A reading center uses 108 square feet of the classroom floor area. What percent of
the classroom floor area is used as the reading center?
A. 8%
B. 12%
C. 80%
D. 90%
A store sold 255 DVDs in 5 days. If sales continue at the same rate, which is the best prediction of the number of DVDs the store could expect to sell
in 30 days?
A. 7,650
B. 6,000
C. 1,500
D. 1,000
Paola is making batches of spaghetti sauce for a dinner at school. Her recipe uses 1 2/3 pounds of ground meat for each batch of sauce. She started
with 27 pounds of ground meat and has already made 3 batches of the sauce. How many more batches of sauce should she be able to make?
A. 13
B. 16
C. 22
D. 24
There are 20 students in 4 plays in Mr. Stewart’s class, and there are 24 students in 3 plays in Mrs. Rodriguez’s class. Based on this information,
which statement is true?
A. The ratio of students in Mr. Stewart’s class in plays to students in Mrs. Rodriguez’s class in plays is 6:5.
B. The ratio of students to plays is 5:1 in Mr. Stewart’s class and 8:1 in Mrs. Rodriguez’s class.
C. The ratio of students to plays is 1:5 in Mr. Stewart’s class and 1:8 in Mrs. Rodriguez’s class.
D. The ratio of plays in Mr. Stewart’s class to plays in Mrs. Rodriguez’s class is 3:4.
Test Item Examples for SPI0606.2.5: Transform numbers from one form to another (fractions, decimals, percents, and mixed numbers).
Mr. Kincaid has a piece of pipe that is 3.08 meters long. Which length is equivalent to 3.08 meters?
A. 3 2/25 meters
B. 3 4/25 meters
C. 3 1/5 meters
D. 3 4/5 meters
Which percent is equivalent to 8/10 ?
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
A. 125%
B. 80%
C. 45%
D. 20%
Pilar had 6 rows in her garden for planting flowers. She planted daisies in 4 3/5 of the rows. Which improper fraction is equivalent to 4 3/5 ?
A. 17/3
B. 17/5
Power SPIs: bold and italicized
C. 23/3
Nested SPIs: italicized
D. 23/5
Other SPIs: normal type
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Course: 6th grade Math
3rd Nine Weeks
Instructional Guide
Unit 2: Properties of Triangles, Quadrilaterals, and Other
Estimated Time: 2 weeks
Polygons
GLE: 0606.4.1 Understand and use basic properties of triangles, quadrilaterals, and other polygons.
GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0606.1.6 Read and interpret the language of mathematics and use written/oral communication to express mathematical
ideas precisely.
GLE 0606.1.8 Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to
facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Pre-requisite Skills:
1. A polygon is a two-dimensional figure.
2. A prism is a three-dimensional figure.
3. All triangles have three sides and three angles.
4. All quadrilaterals have four sides & four angles.
5. Angles are measured in degrees.
6. Angles are measured using a protractor.
7. A right angle measures 90°.
8. An acute angle measures less than 90°.
9. An obtuse angle measures greater than 90° and less than 180°.
10. Lines are measured using a ruler.
Essential Questions:
 How are angles and shapes related?
 How can you determine the interior angle sum of a triangle? Rectangle?
 How can you determine the measurement of an angle?
 How do line relationships affect angle relationships?
 How are geometric shapes and objects classified?
 How can objects be represented and compared using geometric attributes?
Unit Vocabulary:
degree (angles), equiangular, equilateral, interior/exterior angles, isosceles, protractor, scalene, similarity, triangle, faces, edges,
pyramid, prism, parallel sides, congruent angles, acute angles, obtuse angles, right angles, Triangle Inequality Theorem
Scaffolded Ideas:
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
1. Equivalent triangles have 3 congruent sides and 3 congruent angles.
2. Isosceles triangles have 2 congruent sides and 2 congruent angles.
3. Scalene triangles have no congruent sides or angles.
4. Right triangles
5. Acute triangles
6. Obtuse triangles
7. Any side of a triangle is always shorter than the sum of the other two sides.
8. The sum of the measures of the interior angles of a triangle equals 180°.
9. The sum of the measures of the interior angles of a quadrilateral equals 360°.
10. A straight line equals 180°.
11. Supplementary angles equal 180°.
12. Complementary angles equal 90°.
Checks for
Understanding
0606.4.3 Verify the
basic properties of
triangles and
quadrilaterals using
a protractor and
ruler.
0606.4.4 Classify
triangles by side
lengths (scalene,
isosceles, and
equilateral) and
angle measure
(acute, right,
obtuse, isosceles
and equiangular).
0606.1.10 Use
various methods
(such as dynamic
geometry software)
to explore
properties of
triangles and
quadrilaterals.
State
Performance
Indicators
SPI 0606.4.1
Identify, define
or describe
geometric
shapes given a
visual
representation
or a written
description of
its properties.
(not nested)
Power SPIs: bold and italicized
I Can
Statements
Instructional Resources/
Strategies
Connections
I Can.....
*identify, define, and
describe a
geometric shape
when shown a
visual
representation or
given a written
description of its
properties.
These resources are for SPIs 0606.4.1, 0606.4.2, and 0606.4.3
 “Which nets form a cube” interactive site: “Net Tools”:
Illuminations
http://illuminations.nctm.org/activitydetail.aspx?ID=84
 Navigating through Geometry Grades 6-8
“Indirect Measurement”
 Literature:
“Measuring Penny” (Standard and nonstandard
measurement)
“Grandfather Tang’s Story” (polygons, tangrams, area)
“The Warlords Puzzle” (Tangrams- Marilyn Burns Math
and Literature grades 4-6
“The Greedy Triangle” (polygons)
 Navigating Through Geometry Grades 6-8
Patty Paper “Area Activity” Deriving Area Formulas for
Trapezoids, parallelograms, triangles, and circles.
 Online Area of a Triangle Practice
http://www.mathgoodies.com/lessons/vol1/area_triangle.
html
 Triangle Inequality Activities and Lesson Ideas
http://www.deltastate.edu/docs/math/lp3lclark.pdf
http://mathscience.dadeschools.net/geo/pdf/lessons/Tria
ngle_Inequality.pdf
 SpringBoard: “Play Area” (Geometry)
 SpringBoard: “What’s My Name” (Geometry, figures,
Chapter 7 Sec 1 pg 322
* use a protractor
and a ruler to
check and verify
the properties of
triangles and
quadrilaterals.
* classify triangles
by the side lengths
or the angle
measurements.
Nested SPIs: italicized
Other SPIs: normal type
Chapter 7 Sec 2 pg 326
Chapter 7 Sec 3 pg 332
Chapter 7 Sec 4 pg 336
Chapter 7 Sec 5 pg 344
Chapter 7 Sec 6 pg 348
Chapter 7 Sec 7 pg 352





0606.4.1
Investigate the sum
of the angles in a
triangle and a
quadrilateral using
various methods.
0606.4.2 Relate the
sum of the angles
in a triangle to the
sum of the angles
in polygons.
0606.4.6 Use the
properties of interior
and exterior angles
of polygons to solve
problems.
SPI 0606.4.2
Find a missing
angle measure
in problems
involving
interior/exteri
or angles
and/or their
sums. (not
nested)

I Can...
* demonstrate/
prove that the sum
of the interior
angles of any
triangle equal 180.
angles, lines)
SpringBoard: “Triangle Trivia” (classification of triangles)
IC Teachers: Shapes - Polygons
http://icteachers.co.uk/children/sats/polygons.htm
Literature:
“Shape Up!” By David Adler
“What’s your Angle Pythagoras? :A math adventure” by
Julie Ellis.
Have students draw their own line diagrams including the
notation.
NCTM Illuminations :
“Rectangles & Parallelograms”
http://illuminations.nctm.org/LessonDetail.aspx?id=L350
“Polygon Capture”
http://illuminations.nctm.org/LessonDetail.aspx?id=L270
NCTM Illuminations:
Adding it All Up
http://illuminations.nctm.org/LessonDetail.aspx?id=L765“
* demonstrate/
prove that the sum
of the interior
angles of any
quadrilateral equal
360
* use the properties
of interior and
exterior angles of
polygons to solve
problems.
0606.4.5 Model and
use the Triangle
Inequality Theorem.
I Can...
* model, solve, and
use the Triangle
Inequality
Theorem.
Power SPIs: bold and italicized

NCTM Illuminations –
“Inequalities in Triangles”
(http://illuminations.nctm.org/LessonDDeDetail.aspx?id=L
6816-8)
Nested SPIs: italicized
Other SPIs: normal type
Test Item Examples from SPI 606.4.1: Identify, define or describe geometric shapes given a visual representation or a written description of its
properties.
Which figure has exactly 6 faces and 10 edges?
A. square pyramid
B. pentagonal prism
C. rectangular prism
D. pentagonal pyramid
Aubrey drew a figure with the characteristics listed below.
• exactly 1 pair of parallel sides
• exactly 2 pairs of congruent angles
• exactly 4 sides
Which type of figure did Aubrey draw?
A. rhombus
B. hexagon
C. trapezoid
D. parallelogram
The figure below has 6 congruent faces. Which term best describes the figure?
A. cone
B. cube
C. triangular prism
D. rectangular pyramid
Which characteristic best describes a triangular prism?
A. exactly 5 faces
B. exactly 6 faces
C. exactly 6 edges
D. exactly 12 edges
Test Item Examples from SPI 606.4.2: Find a missing angle measure in problems involving interior/exterior angles and/or their sums.
What is the measure of the missing exterior angle for the figure shown below?
A. 80
Power SPIs: bold and italicized
B. 100
Nested SPIs: italicized
C. 160
D. 260
Other SPIs: normal type
The measures of two of the exterior angles of a triangle are shown below. What is the measure of the third exterior angle?
A. 235
B. 125
C. 75
D. 55
B. 20
C. 100
D. 200
Look at the figure shown below. What is the value of s?
A. 10
Test Item Examples from SPI 606.4.3: Solve problems using the Triangle Inequality Theorem.
The first side of a triangle is 4 centimeters (cm) long, and the second side is 8 centimeters (cm) long. Which of these could be the measure of the
third side of this triangle?
A. 14 cm
B. 12 cm
C. 10 cm
D. 4 cm
A triangle is shown below. Which 3 measures could be the side lengths of this triangle?
A. 4 cm, 10 cm, 13 cm
B. 3 cm, 10 cm, 13 cm
C. 4 cm, 9 cm, 14 cm
D. 3 cm, 9 cm, 14 cm
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Matching Activity: Have the students cut out each of the rectangles and match the term with the correct definition and diagram.
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Course: 6th grade Math
3rd Nine Weeks
Instructional Guide
Unit 3 : Circumference and Surface Area of Circles, Trapezoids, and
Irregular Shapes(2-D and 3-D)
Estimated Time: 3 Weeks
GLE: 0606.4.3 Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and
develop strategies to find the area of composite shapes.
GLE0606.4.4 Develop and use formulas for surface area and volume of 3-dimensional figures.
GLE0606.1.7 Recognize the historical development of mathematics, mathematics in context, and the connections between
mathematics and the real world.
Pre-requisite Skills:
1. A triangle is a three-sided polygon.
2. A rectangle is a four-sided polygon.
3. A pentagon is a five-sided polygon.
4. A hexagon is a six-sided polygon.
5. Linear distance is measured in units.
6. Students should be able to multiply whole numbers, decimals and fractions.
7. Students should be able to show the nets for three-dimensional figures.
Essential Questions:
 How can describing, classifying, and comparing properties of different lines, angles, and certain 2- and 3-dimensional shapes
be useful for solving geometric problems in our 3-D world?
 How can manipulatives and nets increase the ability to visualize, model, and reason about geometric concepts and entities?
 How will applying appropriate and varied models, ratios, and formulas help to estimate or calculate missing
dimensions/distances or measurements of perimeter/circumference, area, and volume?
 How can patterns be used to determine standard formulas for area and perimeter?

How do you find perimeter, area, and volume of geometric figures?
Unit Vocabulary:
circumference, perimeter, polygon, surface area, Pi, diameter, radius, volume, prism, pyramid, cylinder, trapezoid
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Scaffolded Ideas:
1. A polygon is a two-dimensional figure.
2. A prism is a three-dimensional figure that has two bases.
3. A pyramid is a three-dimensional figure that has only one base.
4. Pyramids and prisms are named according to the name of their base.
5. A cylinder is a three-dimensional figure with two identical flat ends that are circular or elliptical and one curved side (a cylinder
looks like a can).
6. A cone is a three-dimensional figure that has a circular base and one vertex.
7. Perimeter is the distance around a polygon.
8. Circumference is the distance around a circle.
9. Pi is the relationship between the circumference of a circle and its diameter.
10. The circumference of a circle is approximately 3.14 times the length of its diameter.
11. Linear distance is measured in units.
12. Area is an expression of how much surface is covered, not a length.
13. Area is measured is square units.
14. Area of regular and irregular shapes can be determined by counting square units or using formulas.
15. Volume is the measure of three-dimensional objects; it tells us about the amount of space something takes up.
16. Area is measured in cubic units.
Checks for
State
I Can
Instructional Resources/
Connections
Understanding Performance
Statements
Strategies
Indicators
 0606.4.11
I Can...
Chapter 10 Sec 1
SPI 0606.4.4
Relate the
*calculate
the
pg 500

Area
of
a
circle
with
Wikki
Stix
Activity
Calculate with
circumference
circumference and area
 Literature:
circumferences of circles.
Chapter 10 Sec 2
of a circle with
“Sir Cumference and the Dragon of Pi” SERIES books
and
areas
of
pg 504
the perimeter of
*discover and apply the
“ Spaghetti and Meatballs for All” (Area & perimeter)
a polygonal
formula
for
Pi.
circles. (nested
http://www.baylor.edu/content/services/document.php/27178.p
Chapter 10 Sec 3
figure.
pt
to 0606.4.5)
pg 508


0606.4.12
Derive the
meaning of Pi
using concrete
models and/or
appropriate
technology.
0606.4.13
Understand the
relationships
among the
Power SPIs: bold and italicized
*demonstrate my
understanding of the
relationships among
radius, diameter,
circumference, and area
of a circle.


Circumference of A Circle
http://www.aaamath.com/geo612-circumferencecircle.html#pgtp
NCTM IlluminationsCircle
String - Circumference
http://illuminations.nctm.org/ActivityDetail.aspx?ID=115
*explain the relationship
between the area of a
trapezoid to that of a
parallelogram.
Nested SPIs: italicized
Other SPIs: normal type
Chapter 10 Sec 4
pg 511
Chapter 10 Sec 5
pg 516

.



radius,
diameter,
circumference
and area of a
circle, and that
the ratio of the
circumference
to the diameter
is the same as
the ratio of the
area to the
square of the
radius, and that
this ratio is
called Pi.
0606.4.14
Relate the area
of a trapezoid
to the area of a
parallelogram.
0606.4.15
Find lengths
given areas or
volumes, and
vice versa.
0606.4.16
Solve
contextual
problems
involving area
and
circumference
of circles,
surface areas
and volumes
of prisms,
pyramids,
cones, and
cylinders.
0606.4.17
Use
manipulatives
to discover
SPI 0606.4.5
Determine
the surface
area and
volume of
prisms,
pyramids and
cylinders.
(power,3rd 9
wks.)
SPI 0606.4.6
Given the
volume of a
cone/pyramid,
find the volume
of the related
cylinder/prism
or vice versa.
(not nested)
Power SPIs: bold and italicized
I Can...
*determine the surface
area and volume of
prisms, pyramids and
cylinders.
*calculate the volume of
a cone when given the
volume of a related
prism and vice versa.
*determine the lengths
of sides of polygons
given the area or
volume.
*use manipulatives to
discover the relationship
between the volume of a
pyramid and a related
prism.






Navigating Through Geometry in Grades 6-8
“Constructing Three-Dimensional Figures”
Navigating through Measurement in Grades 6-8
“Ratios –Surface Areas and Volumes”
Hangman Puzzles on Nets and 3-D Figures
http://www.compasslearningodyssey.com/sample_act/math3_4
/MA3CA05a-package_preloader.swf
Literature:
“Counting on Frank” (Proportional Reasoning, volume - Marilyn
Burns Math & Literature grades 4-6)
Math Central: Irregular Surface Area Exercise
http://mathcentral.uregina.ca/RR/database/RR.09.97/hermsmei
er1.html
Compare Volumes of 3D Shapes
http://www.analyzemath.com/Geometry/compare_volume_3D.h
tml
*use manipulatives to
discover the volume of a
Nested SPIs: italicized
Other SPIs: normal type
Chapter 10 Sec 6
pg 524
Chapter 10 Sec 7
pg 530
Chapter 10 Sec 8
pg 534
Chapter 10 Sec 9
pg 538


the volume of
a pyramid is
one-third the
volume of the
related prism
(the heights
and base
areas are
equal).
0606.4.18
Use
manipulatives
to discover
the volume of
a cone
0606.1.9 Use
age-appropriate
books, stories,
and videos to
convey ideas of
mathematics.
cone.





Incorporating Literature into Math lessons
http://sci.tamucc.edu/%7Eeyoung/middle_school_literature.html
Mathematics in Movies
http://www.math.harvard.edu/~knill/mathmovies/
Literature:
“The I Hate Mathematics Book” (computation, money, shapes,
logical reasoning)
University of St. Andrews: Mathematics History Overview
http://www-history.mcs.stand.ac.uk/history/HistTopics/History_overview.html
Sir Cumference and the Dragon Series for teaching circles.
Test Item Examples for SPI0606.4.4: Calculate with circumferences and areas of circles.
A circle has a diameter of 30 centimeters (cm). Which measurement is closest to the area of the circle?
A. 47.1 cm2
B. 188.4 cm2
C. 706.5 cm2
D. 2,826 cm2
Roberto swung a rope with a ball tied to the end of it in a circle, as shown below. Which is closest to the area of the circle that Roberto made when
he swung the rope?
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
A. 1,519.76 ft2
B. 379.94 ft2
C. 69.08 ft2
D. 34.54 ft2
The circumference of the tire shown below is 72.22 centimeters (cm). Which is closest to the radius of the tire?
A. 4.8 cm
B. 9.6 cm
C. 11.5 cm
The circle below has a diameter of 56 centimeters (cm). Which is closest to the area of the circle?
A. 87.92 cm2
B. 175.84 cm2
Power SPIs: bold and italicized
C. 2,461.76 cm2
D. 9,847.04 cm2
Nested SPIs: italicized
Other SPIs: normal type
D. 23.0 cm
Test Item Examples for SPI0606.4.5: Determine the surface area and volume of prisms, pyramids and cylinders.
The picture below shows the dimensions of a display cabinet shaped like a triangular prism. What is the surface area of the display cabinet?
A. 156 square inches
B. 216 square inches
C. 312 square inches
D. 336 square inches
Raul painted each surface of the cylinder-shaped container shown below. What is the total surface area that Raul painted, in terms of π ?
A. 80π cm2
Power SPIs: bold and italicized
B. 48π cm2
Nested SPIs: italicized
C. 40π cm2
Other SPIs: normal type
D. 32π cm2
The picture below shows a cylinder-shaped basket with a radius of 3 inches and a height of 7 inches. Which is closest to the volume of the basket?
A. 197.82 cubic inches
B. 131.88 cubic inches
C. 65.94 cubic inches
D 28.26 cubic inches
The dimensions of a block of wood shaped like a rectangular prism are shown below. What is the volume of the block of wood?
A. 208 cubic inches
C. 90 cubic inches
Power SPIs: bold and italicized
Nested SPIs: italicized
B. 140 cubic inches
D. 70 cubic inches
Other SPIs: normal type
Test Item Examples for SPI0606.4.6: Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
A cone and a cylinder are shown below. The cone and cylinder have equal heights and bases of equal area. What is the volume of the cylinder, in
cubic centimeters?
A. 110 cubic centimeters
B. 165 cubic centimeters
C. 330 cubic centimeters
D. 990 cubic centimeters
The square pyramid and rectangular prism shown below have the same base area and equal heights. What is the volume of the rectangular prism?
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
A. 8 cubic inches
C. 48 cubic inches
B. 24 cubic inches
D. 72 cubic inches
The two figures shown below have the same base area and equal heights. What is the volume of the cone?
A. 400 in.3
Power SPIs: bold and italicized
Nested SPIs: italicized
B. 600 in.3
C. 1,200 in.3
Other SPIs: normal type
D. 3,600 in.3
Course: 6th grade Math
3rd Nine Weeks
Unit 4: Cartesian Coordinate System
Instructional Guide
Estimated Time: 2 Week
GLE 0606.3.5 Use multiple representations including symbolic algebra to model and/or solve contextual problems that
involve linear relationships
GLE0606.3.6 Understand and use the Cartesian coordinate system.
GLE 0606.3.2 Interpret and represent algebraic relationships with variables in expressions, simple equations and
inequalities
GLE0606.1.7 Recognize the historical development of mathematics, mathematics in context, and the connections between
mathematics and the real world.
Pre-requisite Skills:
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
1. Students should have an understanding of number lines involving positive and negative numbers.
2. Students should have an understanding about tables.
3. Students should have an understanding about reading and interpreting graphs.
Essential Questions:
 How can location maps, charts, grids, and spreadsheets be efficiently indicated by using ordered pairs?
 How can ordered pairs involving negative numbers be used to indicate locations on a coordinate grid?
 How can coordinate graphing aid reasoning to help solve real-world spatial problems?
Unit Vocabulary:
Cartesian coordinate system, x-axis, y-axis, quadrants, ordered pair
Scaffolded Ideas:
1. Ordered pairs are listed (x,y).
2. x tells you to go left or right on the x-axis.
3. A positive x tells you to go right on the x-axis.
4. A negative x tells you to go left on the x-axis.
5. y tells you to go up or down on the y-axis.
6. A positive y tells you to go up on the y-axis.
7. A negative y tells you to go down on the y-axis.
8. The Cartesian coordinate system is composed of 4 quadrants.
9. The 4 quadrants are: quadrant I, quadrant II, quadrant III, and quadrant IV.
10. The intersection of the x-axis and the y-axis is called the point of origin.
11. Algebraic equations and inequalities can be represented verbally, graphically, in a table, numerically, or with manipulatives.
Checks for
State
I Can
Instructional Resources/
Connections
Understanding
Performance
Statements
Strategies
Indicators

0606.3.6
SPI 0606.3.3 Write
I Can…
Use equations
equations that
* interpret and
to describe
correspond to
represent
simple
given situations or
algebraic
relationships
represent a given
relationships
shown in a table mathematical
or graph.
relationship
verbally.

0606.3.7
(Power, 3rd 9
* interpret and
weeks). See also
Move fluently
represent
nested SPIs
between
nd
algebraic
0606.3.4 (2 9wks)
different
nd
relationships
0606.3.5 (2 9wks)
representations
0606.3.8 (1st 9wks);
(such as verbal,
graphically.
0606.3.1(1st 9 wks);
tabular,
* interpret and
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type




numerical,
algebraic, and
graphical) of
equations and
expressions
0606.3.8
Represent
patterns using
words, graphs,
and simple
symbolic
notation.
0606.3.4
Generate data
and graph
relationships
concerning
measurement of
length, area,
volume, weight,
time,
temperature,
money, and
information
0606.3.10
Understand that
in an ordered
pair (x, y), the x
represents
horizontal
location and y
represents
vertical location.
0606.3.11
Identify the
quadrant of the
coordinate
system in which
a point lies.
0606.3.6 (1st 9 wks);
0606.3.2 (1st 9 wks)
SPI 0606.3.9 Graph
ordered pairs of
integers in all four
quadrants of the
Cartesian
coordinate system.
(not nested)
represent
algebraic
relationships in a
table.
* interpret and
represent
algebraic
relationships in
an equation or
inequality.
I Can…
* Plot ordered
pairs in all four
quadrants on the
Cartesian
coordinate plane.
* Identify in which
quadrant an
ordered pair
should be plotted
by whether they
are positive or
negative
numbers.








PortaPortal Resources – “Billy the Bug”
http://www.oswego.org/ocsdweb/games/BillyBug2/bug2.html
Literature:
“The Fly on the Ceiling” (Coordinate graphing)
Battleship game:
http://www.educationworld.com/a_tsl/archives/061/lesson001.shtml
Free printable coordinate and graph paper
1st and 3rd nine weeks
http://www.printfreegraphpaper.com/
Interactive coordinate grid
http://smartboards.typepad.com/smartboard/files/coordina
tes1.swf
University of Vienna: Reading Off Coordinates
http://www.univie.ac.at/future.media/moe/tests/zeich/able
sen.html
InterMath: Coordinates
http://intermath.coe.uga.edu/dictnary/descript.asp?termID
=91
Interactivate:
Maze Game
http://www.shodor.org/interactivate/activities/MazeGame/
Chapter 9 Sec 3 pg
458
Test Item Examples for SPI060.3.3: Write equations that correspond to given situations or represent a given mathematical relationship.
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
The first six terms of a number pattern are shown below.
2, 5, 14, 41, 122, 365, . . .
Which expression can be used to find the value of any number in this pattern when n represents the previous number in the pattern?
A. n+3
B. n−3
C. 3n−1
D. 2n+1
Ben used the expression 3x−2, where x is the previous number, to write a number pattern. Which list of numbers could be part of Ben’s pattern?
A. 1, 5, 17, 53, 161
B. 2, 4, 12, 34, 100
C. 3, 9, 27, 81, 243
D. 4, 10, 28, 82, 244
The table below shows values for x and y. Which expression can be used to find the x-values in the table?
A. 1/4y +3
B. 1/2y
C. 2y
D. 4y +3
The table below shows values for x and y. Which expression can be used to find all the y-values in the table?
A. x +1
B. x +5
C. 2x +1
D. 2x −1
The table below shows values for x and y. Which expression can be used to find y in terms of x?
A. 3x − 6
Power SPIs: bold and italicized
B. x + 4
Nested SPIs: italicized
C. 1/2x
D. 2x
Other SPIs: normal type
Test Examples for SPI 0606.3.9: Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
Which point is located at (−5, 4) on the grid below?
A. Point W
B. Point X
C. Point Y
Which point is located at (1,−5) on the grid below?
A. Point L
Power SPIs: bold and italicized
Nested SPIs: italicized
B. Point M
C. Point N
Other SPIs: normal type
D. Point P
D. Point Z
Which point is located at (6,−4) on the grid below?
A. Point P
Power SPIs: bold and italicized
Nested SPIs: italicized
B. Point Q
C. Point R
Other SPIs: normal type
D. Point S
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type
Power SPIs: bold and italicized
Nested SPIs: italicized
Other SPIs: normal type