2003 MATHEMATICS NCSCOS Grade 5 Indicators

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2003 MATHEMATICS NCSCOS Grade 5 Indicators. Math Vocabulary by Goal. Goal 1. 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.

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### 2003 MATHEMATICS NCSCOSGrade 5 Indicators

Math Vocabulary by Goal

Goal 1

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

Expandednotation form

Picture Form

300+20+6

Forms of Numbers

1,111

326

Three hundred twenty-six

Word Form

Standard form

ten- thousands

ones

hundreds

hundredths

Hundred- thousands

thousands

tens

tenths

thousandths

The position of a single digit in a whole number or decimal number containing one or more digits.

145,305.791

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

366

370

400

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

.5 = .50

.30 = .300

? < .5

? =.1,.2,.3,.4,or .5

.5 =.05

.3 = .003

equal to

less than or equal to

not equal to

Symbols used to determine relationships of equalities.

Equal to/not equal to

http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm

3 -Numerator

7 -Denominator

Equal parts of a whole or group written with a numerator and a denominator.

Fraction

http://math.rice.edu/~lanius/fractions/

3

4

Numerator: number of each part

Denominator: number of parts

1

2

fraction

2

Whole number

Fractions

7

3

Improper fraction

mixed number

http://www.visualfractions.com/MixtoFrCircle.html

1/2 = 3/6

Fractions that are the same or equal

Equivalent Fractions

http://www.learningplanet.com/sam/ff/index.asp

http://www.shodor.org/interactivate/activities/fracsorter/index.html

.1

.01

.001

Numbers written in standard form to show a value less than 1.

one-tenth

one-hundredth

one-thousandth

Decimal

http://www.321know.com/cmp42bx2.htm

Problem Solving Strategies

http://www.mathstories.com/strategies.htm

Problem Solving Method

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

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?

Make a diagram/ picture

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?

Jill/Makayla

Jill/Tanya

Makayla/Tanya

3 ways

Organized list

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/problem_solving.php

Using objects, models, representations

http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html

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

Goal 2

The learner will recognize and use

standard units of metric and customary

measurement.

1000 ml = 1 L

1 L

1 ml

Units of capacity in the metric system.

liter

http://www.metricamerica.com/litre.htm

G

Q

Q

PP

2 c = 1 pt

2 pt = 1 qt

4 qt = 1 gal

PP

cc

cc

cc

cc

Q

Q

PP

cc

cc

PP

cc

cc

Units of capacity in the customary system.

cup, pint, quart, gallon

http://www.edhelper.com/math/capacity_fg1943.htm

Benchmark/landmark

http://www.mathcats.com/explore/convert.html

100cm = 1m

1000 m = 1 km

Units of length, width and distance in the metric system.

centimeter, meter, kilometer

http://www.metricamerica.com/centimetre.htm

12in = 1 ft

3 ft = 1 yd

5280 ft = 1 mi

Units of length, width and distance in the customary system.

Inches, Feet, Yards, Miles

http://www.funbrain.com/measure/

Benchmark/landmark

http://www.aaamath.com/B/mea69_x2.htm

1000g = 1kg

Units of weight (or mass) in the metric system.

gram and kilogram

http://www.studyzone.org/testprep/math4/d/metgraml.cfm

16 oz = 1lb

2000 lbs = 1 ton

Units of weight (or mass) in the customary system.

ounce, pound, and ton

http://www.edhelper.com/math/length_weight_fg2255.htm

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

1100

350

350

An angle with a measure of more than 90 degrees, but less than 180 degrees.

Obtuse Angle

http://www.manatee.k12.fl.us/sites/elementary/palmasola/mathlabtutan1b.htm

http://www.toonuniversity.com/6m_angle_d.html

600

600

600

An angle less than 90 degrees

Acute Angle

http://www.mathsnet.net/shape/category2.html

130

50

Two angles that share a common side

130

50

Two adjacent angles whose sum is 180 degrees

Supplementary Angles

http://www.mathsisfun.com/geometry/supplementary-angles.html

http://www.mathopenref.com/anglesupplementary.html

45

45

Two adjacent angles whose sum is 90 degrees

Complementary Angles

http://www.mathwarehouse.com/geometry/angle/complementary-angles.php

http://www.mathopenref.com/anglecomplementary.html

45

45

Angles that have the same measure.

Congruent Angles

Goal 3

The learner will understand and use

properties and relationships of plane

figures.

These markings indicate congruent sides.

When sides of a shape are equal in length

Congruent Sides

4 in

4 in

4 in

All three sides of this triangle are congruent.

Equilateral Triangle

http://www.factmonster.com/ipka/A0876325.html

http://library.thinkquest.org/20991/textonly/quizzes/geo/q4/p1.html

4 in

4 in

3 in

This triangle has two congruent sides.

Isosceles Triangle

http://www.homeschoolmath.net/gy/equilateral_isosceles.php

4 in

3 in

5 in

This triangle has no congruent sides

Scalene Triangle

http://www.mathsisfun.com/triangle.html

Regular Polygon

Irregular Polygon

Any four sided figure

A

B

A line with two endpoints

Midpoint

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

Two rays that meet at a vertex

Angle

Sides or angles immediately next to each other.

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

Hexagon

Trapezoid

Four sided figure. opposite sides equal lengths and parallel, opposite angles equal

An eight sided figure

An five sided figure

Octagon

Rhombus

Pentagon

http://www.aplusmath.com/cgi-bin/games/geopicture

9 diagonals/ sum of interior angles - 720º

2 intersecting diagonals/ sum of interior angles 360º

2 intersecting diagonals/ sum of interior angles 360º

Parallelogram

Hexagon

Trapezoid

5 diagonals/ Sum of interior angles - 540º

2 intersecting perpendicular diagonals/ sum of interior angles 360º

20 diagonals/ sum of interior angles - 1080º

Octagon

Rhombus

Pentagon

Number of diagonals in a polygon:

+3 +4 +5 +6

Sum of interior angles in a polygon:

+180 +180 +180 +180 +180

two types of trapezoids

Two right angles

No right angles

Two congruent sides

Right Trapezoid

Isosceles Trapezoid

Line of symmetry

When a straight line is drawn through a shape so that the two halves are congruent.

Symmetry

http://library.thinkquest.org/J002441F/symmetry.htm

Rotational Symmetry

http://www.learner.org/channel/courses/learningmath/geometry/session7/part_b/index.html

Half turn - 180 degrees

Point of rotation

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.

Goal 4

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

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

The middle number in a set of data; must put numbers in order from least to greatest first.

Median

http://regentsprep.org/Regents/math/mean/Pmeasure.htm

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

The number that occurs most in a set of data.

Mode

89,  73,  84,  91,  87,  77,  94

73, 77, 84, 87, 89, 91, 94

94 – 73 = 21

21

Subtract the smallest number from the largest number in a set of data.

Range

http://www.mathgoodies.com/lessons/vol8/range.html

http://www.quizville.com/range.php

1

2

3

4

5

6

7

3, 3, 7

2, 9, 9, 9

1

3, 9

1, 4, 6

2

5, 7, 7, 8

A way to arrange data with the tens on the left and the ones listed on the right.

Stem and Leaf Plot

http://regentsprep.org/Regents/math/data/stemleaf.htm

http://www.shodor.org/interactivate/activities/stemleaf/index.html

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

l

A graph that uses pictures to represent data.

Key

Pictograph

http://www.studyzone.org/testprep/math4/d/graphdatal.cfm

label

scale

interval

title

http://www.mcwdn.org/Graphs/LineGraph.html

Shows change over time; will have months, days or other time words in the problem.

Line Graph

title

labels

scale

Is used to compare facts about groups and numbers that can be counted

Bar Graph

http://www.mcwdn.org/Graphs/BarGraph.html

title

key

labels

Compares parts to the whole; decimals and fractions may be used on this graph

Circle Graph

http://www.mcwdn.org/Graphs/CirclePieQuiz.html

IIII IIII IIII

The number of times an event occurs; may use tally marks to record

tallies

Frequency

http://www.studyzone.org/testprep/math4/d/tablestallyl.cfm

Goal 5

The learner will demonstrate an

understanding of patterns, relationships,

and elementary algebraic representation.

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.

10

16

20

5

20

100

Algebraic Expression

http://mathsnet.net/algebra/l2_equation.html

l

Equation

http://www.studyzone.org/testprep/math4/d/numericalp.cfm

Function Machine

A chart that shows a consistent rate of change.

T-chart

Input/Output chart

http://www.shodor.org/interactivate/activities/NumberCruncher/

X + 3 = 7

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

.5 = .50

.30 = .300

? < .5

? =.1,.2,.3,.4,or .5

.5 =.05

.3 = .003

equal to

less than or equal to

not equal to

Symbols used to determine relationships of equalities.

Equal to/not equal to

http://www.studyzone.org/testprep/math4/k/greaterlessthanl.cfm

3

5

Red chips

Blue chips

The quotient of two numbers used to compare two quantities.

Ratio

http://www.studyzone.org/mtestprep/math8/c/ratiol.cfm

Resources
• Web resources are listed at the bottom of each slide.