Download Sum of interior angles

2003 MATHEMATICS NCSCOS
Grade 5 Indicators
The learner will understand and compute
with nonnegative rational numbers.
A real number that can be written as
the ratio of two integers (positive or
negative whole number, fraction, or
decimal)
Rational Number
Expanded
notation form
Picture Form
300+20+6
Forms of
Numbers
Three hundred twenty-six
Word Form
1,111
326
Standard form
http://www.aaamath.com/plc31d-placevalue-add.html
The position of a single digit in a
whole number or decimal number
containing one or more digits.
tenthousands
hundreds
ones
hundredths
145,305.791
Hundredthousands
thousands
tens
tenths
thousandths
Place Value
http://mrsbogucki.com/aemes/resource/apps/placeval/placeval.htm
Arranged from smallest to largest
Ascending Order
http://www.studyzone.org/testprep/math4/e/decorderl.cfm
Arranged from largest to smallest
Descending Order
An answer close to the exact
answer. Usually found by rounding.
366
370
400
Approximately/About
http://www.myschoolhouse.com/courses/O/1/16.asp
Numbers that divide exactly into
another number.
12 – 1,2,3,4,6,12
36 – 1,2,3,4,6,9,12,18,36
48 – 1,2,3,4,6,8,12,16,24,48
Factors
http://illuminations.nctm.org/tools/tool_detail.aspx?id=12
Number that results from multiplying
a given number by a set of whole
numbers.
4 – 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
6 – 6, 12, 18, 24, 36, 42, 48, 54
8 – 8,16, 24, 32, 40, 48, 56
Multiples
http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html
Having the same amount or value;
the state of being equal.
Equivalence
http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html
Symbol used to compare relationships
of inequalities.
Symbol used to compare numbers
Symbol used to compare numbers
Less Than/Greater Than
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
Symbols used to determine
relationships of equalities.
.5 = .50
? < .5
.30 = .300
equal to
.5 =.05
.3 = .003
? =.1,.2,.3,.4,or .5
less than or
equal to
not equal to
Equal to/not equal to
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
Equal parts of a whole or group
written with a numerator and a
denominator.
3
-Numerator
7
-Denominator
Fraction
http://math.rice.edu/~lanius/fractions/
Denominator:
number of
parts
3
4
Numerator:
number of
each part
Fractions
7
3
Improper fraction
Whole
number
1
2
2
fraction
mixed number
http://www.visualfractions.com/MixtoFrCircle.html
Fractions that are the same or equal
1/2
=
3/6
Equivalent Fractions
http://www.learningplanet.com/sam/ff/index.asp
http://www.shodor.org/interactivate/activities/fracsorter/index.ht
Numbers written in standard form to
show a value less than 1.
.1
one-tenth
.01
one-hundredth
.001
one-thousandth
Decimal
http://www.321know.com/cmp42bx2.htm
Problem Solving
Strategies
http://www.mathstories.com/strategies.htm
Problem Solving Method
Look Back
Justify, prove, evaluate or explain the
reasonableness of your answer.
Using a table/chart
X
X
X
http://www.studyzone.org/testprep/math4/k/chartprobl.cfm
http://www.mathstories.com/strategies_makeatable.htm
Guess and Check
Prince Carl divided 15 stone
games into two piles: games
he owns and games his
brother owns. He owns 3 more
games than his brother. How
many games does his brother
own?
Answer: Prince Carl – 9 Brother - 6
http://www.mathstories.com/strategies_guesscheck.htm
Make a diagram/ picture
Question: Laura has 3 green chips,
4 blue chips and
1 red chip in her bag.
What fractional part
of the bag of chips is green?
http://www.mathstories.com/strategies_drawpicture.htm
Make an organized list
Question: Jill, Makayla and Tanya
don’t want to ride the Ferris-wheel
alone. How many ways can they ride
if the ride will only fit two at a time?
Organized
list
Answer
Jill/Makayla
Jill/Tanya
Makayla/Tanya
3 ways
http://www.mathstories.com/strategies_makealist.htm
Work Backwards
The castle kitchen waiters
brought in 4 pies left over from
the feast. Twelve pies were
eaten at the feast. Queen Mab
took 2 home with her. How
many pies did the waiters
bring into the feast at the
beginning?
2
12
4=
2 + 12 + 4 =
18
http://www.mathstories.com/strategies_working_backward.htm
Using a calculator
Calculator
Riddles
From
DPI
http://community.learnnc.org/dpi/math/archives/2005/06/proble
m_solving.php
Using objects, models,
representations
http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html
Information in a problem that does NOT help
you solve the problem.
The peasants had to dig
a trench 3 feet side to
side and 10 times as
long. It took them 4 days
to dig it. There were 7 of
them digging. How long
was the trench?
Extra Information
Putting numbers together to make
them easier to work with
1 + 4 + 3 +7 + 6 + 8 + 9 + 2 = ?
10 + 10 + 10 + 10 = 40
Compose
http://www.studyzone.org/testprep/math4/d/commutativep.cfm
Breaking a number apart to make it
easier to work with.
30 X 14
(30 X 10) + (30 X 4)
300 + 120 = 420
Decompose
http://www.studyzone.org/testprep/math4/d/commutativep.cfm
Mathematical sentence where the
left side of the equals sign has the
same value as the right side.
Equation
http://www.aplusmath.com/Games/PlanetBlast/index.html
The learner will recognize and use
standard units of metric and customary
measurement.
Units of capacity in the metric
system.
1000 ml = 1 L
liter
http://www.metricamerica.com/litre.htm
Units of capacity in the customary system.
QQ
PP
PP
QQ
PP PP
cc cc
cc cc
cc cc
2 c = 1 pt
2 pt = 1 qt
4 qt = 1 gal
cc cc
cup, pint, quart, gallon
http://www.edhelper.com/math/capacity_fg1943.htm
Benchmark/landmark
Benchmark Comparisons for
Metric and Customary Measurements
Greater Than/
Less Than
Metric Units
Customary Units
2.54 cm (about 2.5)
1 in
cm < in
0.9 m (about 1)
1 yd
m > yd
1.6 km (about 1.5)
1 mi
km <mi
.45 kg (about .5)
1 lb
kg > lb
.95 L (about 1)
1 qt
L > qt
http://www.mathcats.com/explore/convert.html
Units of length, width and distance
in the metric system.
100cm = 1m
1000 m = 1 km
centimeter, meter, kilometer
http://www.metricamerica.com/centimetre.htm
Units of length, width and distance
in the customary system.
12in = 1 ft
3 ft = 1 yd
5280 ft = 1 mi
Inches, Feet, Yards, Miles
http://www.funbrain.com/measure/
Benchmark/landmark
Benchmark Comparisons for
Metric and Customary Measurements
Metric Units
Customary Units
2.54 cm (about 2.5)
1 in
0.9 m (about 1)
1 yd
1.6 km (about 1.5)
1 mi
.45 kg (about .5)
1 lb
.95 L (about 1)
1 qt
http://www.aaamath.com/B/mea69_x2.htm
Greater Than/
Less Than
cm < in
m > yd
km <mi
kg > lb
L >qt
Units of weight (or mass) in the
metric system.
1000g = 1kg
gram and kilogram
http://www.studyzone.org/testprep/math4/d/metgraml.cfm
Units of weight (or mass) in the
customary system.
16 oz = 1lb
2000 lbs = 1 ton
ounce, pound, and ton
http://www.edhelper.com/math/length_weight_fg2255.htm
Benchmark/landmark
Benchmark Comparisons for
Metric and Customary Measurements
Greater Than/
Less Than
Metric Units
Customary Units
2.54 cm (about 2.5)
1 in
cm < in
0.9 m (about 1)
1 yd
m > yd
1.6 km (about 1.5)
1 mi
km <mi
.45 kg (about .5)
1 lb
kg > lb
.95 L (about 1)
1 qt
L >qt
Tool used to measure angles
Protractor
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html
http://www.enchantedlearning.com/math/label/protractor/
Two segments that meet to form a
90 degree angle.
Right Angle
http://www.icteachers.co.uk/children/sats/triangles.htm
http://www.mathsnet.net/shape/category1.html
An angle with a measure of more than
90 degrees, but less than 180 degrees.
1100
350
350
Obtuse Angle
http://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htm
http://www.toonuniversity.com/6m_angle_d.html
An angle less than 90 degrees
600
600
600
Acute Angle
http://www.mathsnet.net/shape/category2.html
Two angles that share a common
side
130
50
Adjacent Angles
http://www.mathwords.com/a/adjacent_angles.htm
Symbol used to identify an
angle
A
=
ABC
C
B
Angle Notation
Two adjacent angles whose sum is
180 degrees
130
50
Supplementary Angles
http://www.mathsisfun.com/geometry/supplementary-angles.html
http://www.mathopenref.com/anglesupplementary.html
Two adjacent angles whose sum is
90 degrees
45
45
Complementary Angles
http://www.mathwarehouse.com/geometry/angle/complementary-angles.php
http://www.mathopenref.com/anglecomplementary.html
Angles that have the same measure.
45
45
Congruent Angles
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
The learner will understand and use
properties and relationships of plane
figures.
When sides of a shape are equal in
length
These markings indicate
congruent sides.
Congruent Sides
All three sides of this triangle are
congruent.
4 in
4 in
4 in
Equilateral Triangle
http://www.factmonster.com/ipka/A0876325.html
http://www.amblesideprimary.com/ambleweb/sketchpad/equilateral.htm
http://library.thinkquest.org/20991/textonly/quizzes/geo/q4/p1.html
This triangle has two congruent
sides.
4 in
4 in
3 in
Isosceles Triangle
http://www.homeschoolmath.net/gy/equilateral_isosceles.php
http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm
This triangle has no congruent sides
4 in
3 in
5 in
Scalene Triangle
http://www.amblesideprimary.com/ambleweb/sketchpad/scalene.htm
http://www.mathsisfun.com/triangle.html
A polygon for which all sides are
congruent and all angles are congruent.
Regular Polygon
A polygon for which all sides and all
angles are not congruent.
Irregular Polygon
Any four sided figure
Quadrilateral
http://regentsprep.org/Regents/math/quad/LQuad.htm
A line with two endpoints
Midpoint
A
B
Line Segment
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/g0101201.asp
A line with one endpoint
Ray
http://www.mathleague.com/help/geometry/basicterms.htm#rays
The point at which two rays meet.
Vertex
Two rays that meet at a vertex
Angle
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
Sides or angles immediately next to
each other.
Adjacent
http://www.kidport.com/Grade5/Math/MeasureGeo/MeasuringAngles.htm
To divide into two equal sections;
to cut in half.
Bisect
Two lines that will never touch or
intersect because they are the same
distance apart.
Parallel Lines
http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php
Lines that intersect at right angles to
each other.
Perpendicular Lines
http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php
Making an estimate or best guess
by appearance or with little
evidence.
Is this a right triangle?
How do you know?
What is your evidence? Can
you tell without measuring?
Conjecture
A line joining two non-adjacent
vertices of a polygon.
Diagonal
http://www.math.fau.edu/Richman/Liberal/polydiag.htm
Four sided figure; all sides equal;
opposite sides parallel; all right
angles
Sum of interior
angles - 360º
2 intersecting,
bisecting,
perpendicular
diagonals
Square
http://www.mathleague.com/help/geometry/polygons.htm#righttriangle
Four sided figure; opposite sides
equal lengths and parallel; all right
angles
Rectangle
Four sided figure; opposite sides
equal lengths and parallel; all right
angles
Sum of interior
angles - 360º
2 intersecting
diagonals.
Rectangle
http://encyclopedia.laborlawtalk.com/Rectangle
http://www.standards.dfes.gov.uk/primary/publications/mathematics/12874/nns_useict026000carroll.swf
A four-sided figure in which the
two pairs of adjacent sides have
the same length.
Sum of interior
angles - 360º
2 intersecting,
perpendicular
diagonals
Kite
Four sided figure. Opposite sides
equal lengths and parallel
An six sided figure
Four sided figure. Top and
bottom sides parallel
Parallelogram
Four sided figure. opposite sides equal
lengths and parallel, opposite angles
equal
Hexagon
Trapezoid
An eight sided figure
An five sided figure
Octagon
Rhombus
Pentagon
http://ejad.best.vwh.net/java/patterns/patterns_j.shtml
http://www.aplusmath.com/cgi-bin/games/geopicture
2 intersecting diagonals/ sum of
interior angles 360º
2 intersecting diagonals/ sum of
interior angles 360º
Parallelogram
2 intersecting perpendicular
diagonals/ sum of interior
angles 360º
Rhombus
Trapezoid
5 diagonals/
Sum of interior
angles - 540º
Pentagon
9 diagonals/ sum of
interior angles - 720º
Hexagon
20 diagonals/ sum of
interior angles - 1080º
Octagon
Number of diagonals in a polygon:
#of sides
4
5
6
7
8
# of
diagonals
2
5
9
14
20
+3
+4
+5
+6
Sum of interior angles in a polygon:
#of sides
3
4
5
Sum of
int.
angles
180º
360º
540º 720º
+180
+180
+180
6
+180
7
8
900º
1080º
+180
two types of trapezoids
Two right angles
No right angles
Two congruent sides
Right Trapezoid
Isosceles Trapezoid
A ten sided polygon
Decagon
When a straight line is drawn through a
shape so that the two halves are
congruent.
Line of symmetry
Symmetry
http://library.thinkquest.org/J002441F/symmetry.htm
When an outline of a turning figure matches
its original shape
.
Rotational Symmetry
http://www.adrianbruce.com/Symmetry/10.htm
http://www.learner.org/channel/courses/learningmath/geometry/session7/part_b/index.html
To turn an object, usually 90 degrees,
180 degrees, or 270 degrees.
Point of
rotation
Half turn 180 degrees
Quarter
turn - 90
degrees
3 Quarter
turn -270
degrees
Rotations
http://regentsprep.org/Regents/Math/rotate/PracRot.htm
http://www.studyzone.org/mtestprep/math8/f/symturns5p.cfm
The same direction as the way
hands on the clock go.
Clockwise
Counter Clockwise
The opposite direction of the way
the hands on the clock go.
The learner will understand and use
graphs and data analysis.
Collection of information often organized
on graphs or charts for analysis.
Data
http://www.studyzone.org/testprep/math4/d/graphdatal.cfm
The middle number in a set of data; must put
numbers in order from least to greatest first.
93, 84, 97, 98, 100, 78, 86, 100, 85, 92
78, 84, 85, 86, 92, 93, 97, 98, 100, 100
78, 84, 85, 86, 92, 93, 97, 98, 100, 100
92 + 93 = 185
185 / 2 = 92.5
92.5
Median
http://regentsprep.org/Regents/math/mean/Pmeasure.htm
The number that occurs most in a set of data.
56, 66, 68, 73, 44, 62, 73, 44, 89, 55, 41, 73
41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89
41, 44, 44, 55, 56, 62, 66, 68, 73, 73, 73, 89
73
Mode
Subtract the smallest number from the largest
number in a set of data.
89, 73, 84, 91, 87, 77, 94
73, 77, 84, 87, 89, 91, 94
94 – 73 = 21
21
Range
http://www.mathgoodies.com/lessons/vol8/range.html
http://www.quizville.com/range.php
A way to arrange data with the tens on the left and
the ones listed on the right.
1
3, 3, 7
2
2, 9, 9, 9
3
1
4
3, 9
5
1, 4, 6
6
2
7
5, 7, 7, 8
Stem and Leaf Plot
http://regentsprep.org/Regents/math/data/stemleaf.htm
http://www.shodor.org/interactivate/activities/stemleaf/index.html
Used to find coordinates for ordered
pairs for the X and Y axis.
Coordinate Grid/ X-Y Chart
http://www.shodor.org/interactivate/activities/pcoords/index.html
http://www.shodor.org/interactivate/activities/coords2/index.html
A horizontal number line on which each
value of a set is denoted by an “x” over
a value.
The number of x’s
indicates how many
times each score
occurred.
Line Plot
http://www.studyzone.org/testprep/math4/d/rangel.cfm
A graph that uses pictures to represent
data.
Key
Pictograph
http://www.studyzone.org/testprep/math4/d/graphdatal.cfm
Shows change over time; will have months, days or
other time words in the problem.
label
scale
interval
title
Line Graph
http://www.mcwdn.org/Graphs/LineGraph.html
Is used to compare facts about groups and numbers
that can be counted
title
labels
scale
Bar Graph
http://www.mcwdn.org/Graphs/BarGraph.html
Compares parts to the whole; decimals and
fractions may be used on this graph
title
key
labels
Circle Graph
http://www.mcwdn.org/Graphs/CirclePieQuiz.html
The number of times an event occurs;
may use tally marks to record
tallies
IIII IIII IIII
Frequency
http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm
The learner will demonstrate an
understanding of patterns, relationships,
and elementary algebraic representation.
A letter or symbol that represents a
number in an algebraic expression.
Each side of
the =
symbol
must
balance
Variable
http://www.aplusmath.com/Games/PlanetBlast/index.html
http://www.vectorkids.com/vkvariable.htm
Contains at least one variable as well
as other numbers and/or operations.
16
10
20
5
20
100
Algebraic Expression
http://mathsnet.net/algebra/l2_equation.html
A mathematical sentence where the
left side equals the right side.
Equation
http://www.studyzone.org/testprep/math4/d/numericalp.cfm
A chart that shows a consistent rate of
change.
Function
Machine
T-chart
Input/Output chart
http://www.studyzone.org/testprep/math4/k/addpatternsl.cfm
http://www.shodor.org/interactivate/activities/NumberCruncher/
The variable represents the number
you are solving to find, termed as the…
Unknown
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
An ordered set of numbers, shapes, or other
mathematical objects, arranged according to
a rule.
Pattern
http://www.studyzone.org/testprep/math4/i/dpatternsl.cfm
http://www.studyzone.org/testprep/math4/k/patternsl.cfm
http://www.studyzone.org/testprep/math4/k/patternsp.cfm
Pattern Changes
Constant Change
2,4,6,8,10….
Varying Change
3,7,4,8,5,9,6,10,7…
Proportional Change
3 4 5 6 7 8 9…
20
5 6 7 8 9 10 11….
22
Pattern Types
Geometric Pattern
Patterns using shapes
Numeric Pattern
4, 8,16,32,….
Patterns using numbers
Any number in the pattern can be
found by finding the relationship or rule
of the pattern.
3,6,9,12,15,18…… Nth term = 3n
10th term = 3(10) = 30
Nth Term
Symbols used to determine
relationships of equalities.
.5 = .50
? < .5
.30 = .300
equal to
.5 =.05
.3 = .003
? =.1,.2,.3,.4,or .5
less than or
equal to
not equal to
Equal to/not equal to
http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm
The quotient of two numbers used to compare
two quantities.
3
5
Red chips
Blue chips
Ratio
http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm
Resources
• Web resources are listed at the bottom of
each slide.
• Additional resources:
– NCDPI Math Glossary
• http://community.learnnc.org/dpi/math/archives/Glo
ssarySP.pdf
– Houghton Mifflin Math
• http://www.eduplace.com/kids/hmm/g_5.html