Notes for the 3 rd Grading Period Mrs. Neal 6 th Advanced & 7 th Average.

Notes for the 3rd Grading Period

Mrs. Neal

6th Advanced & 7th Average

Section 5.4 Section 5.4 Fractions and DecimalsFractions and Decimals

ObjectiveObjective– To write fractions as terminating or repeating To write fractions as terminating or repeating

decimals and to write decimals as fractionsdecimals and to write decimals as fractions

VocabularyVocabulary– 1. 1. Terminating decimalsTerminating decimals – decimals that stop- they – decimals that stop- they

have an end – have a remainder of zerohave an end – have a remainder of zero

Ex. ¼ = .25Ex. ¼ = .25 3/8 = .3753/8 = .375– 2. 2. Repeating decimalsRepeating decimals – decimals that go on without – decimals that go on without

end repeating the same number or series of numbers.end repeating the same number or series of numbers.Ex. 1/3 = .333333…Ex. 1/3 = .333333… 6/11 = .54545454…6/11 = .54545454…


– 3. 3. Bar NotationBar Notation – a way of writing an – a way of writing an abbreviation of a repeating decimal – draw a abbreviation of a repeating decimal – draw a bar over the first number or set of numbers bar over the first number or set of numbers that repeat.that repeat.

Ex. .333333… = .3Ex. .333333… = .3 .54545454… = .54.54545454… = .54


How to:How to:– Fraction changed to a DecimalFraction changed to a Decimal

Divide the numerator of the fraction by the Divide the numerator of the fraction by the denominatordenominator

– Ex numeratorEx numerator numerator numerator ÷ denominator÷ denominator

denominatordenominator

33 3 3 ÷ 5 = 0.6 or .6÷ 5 = 0.6 or .6

55

66 6 6 ÷8 = 0.75 or .75÷8 = 0.75 or .75

88


How toHow to– Decimal changed into a FractionDecimal changed into a Fraction

Terminating decimalTerminating decimal– The place value of the last digit becomes the value of the The place value of the last digit becomes the value of the

denominator of the fraction. The numbers following the denominator of the fraction. The numbers following the decimal point become the numerator. Then simplify to decimal point become the numerator. Then simplify to lowest terms.lowest terms.

– Ex .56 – the last number is six and it is in the hundredths Ex .56 – the last number is six and it is in the hundredths place so 100 is the denominator and 56 is the numeratorplace so 100 is the denominator and 56 is the numerator

.56.56 56 56 ÷ 2 = 28÷ 2 = 28 ÷ 2 = 14 ÷ 2 = 14

100 100 ÷ 2 = 50 ÷ 2 = ÷ 2 = 50 ÷ 2 = 2525


How to How to – Decimal changed into a FractionDecimal changed into a Fraction

Repeating decimalRepeating decimal– Count the amount of numbers in the set of repeating Count the amount of numbers in the set of repeating

numbers – that is how many nines (9) are to be used for numbers – that is how many nines (9) are to be used for the denominator.the denominator.

– EX .12121212… = .12 – two numbers are repeating so two EX .12121212… = .12 – two numbers are repeating so two nines are used for the denominator the numerator is the nines are used for the denominator the numerator is the numbers that repeat.numbers that repeat.

1212 .3333. = .3 = 3 = 1.3333. = .3 = 3 = 1

9999 9 9 3 3

Section 5.5 Section 5.5 Fractions and PercentsFractions and Percents

ObjectiveObjective– To write fractions as percents and percents as To write fractions as percents and percents as

fractionsfractions VocabularyVocabulary

– 1. 1. RatioRatio – a comparison of two numbers by division – a comparison of two numbers by division – comparison of the numerator to the denominator– comparison of the numerator to the denominator Ways to write a ratio – 3 out of 5 people prefer rainy daysWays to write a ratio – 3 out of 5 people prefer rainy days

– 3 out of 5 or 3:5 or 33 out of 5 or 3:5 or 3 55

– 2. 2. PercentPercent – A ratio in which the numerator is – A ratio in which the numerator is compared to 100 ( 100 is the denominator). Any compared to 100 ( 100 is the denominator). Any number over 100 is a percent!number over 100 is a percent!


How toHow to– Fraction changed to a PercentFraction changed to a Percent

18 = ?18 = ? Make an equivalent fraction with aMake an equivalent fraction with a3030 100 100 denominator of 100denominator of 100

18 ?18 ? Cross multiply then divide by theCross multiply then divide by the 30 10030 100 remaining numberremaining number

18 x 100 18 x 100 ÷30 = 60 so 18 = 60 which is 60%÷30 = 60 so 18 = 60 which is 60% 30 10030 100

22 = 2 = ? = 2 = ? = 2 x 100 ÷5 = 40 so 2 = 40%= 2 x 100 ÷5 = 40 so 2 = 40%55 5 100 5 100 5 5

1.

2.


How toHow to– Percents changed to FractionsPercents changed to Fractions

Put the percentage over 100 in a fraction Put the percentage over 100 in a fraction then simplify.then simplify.

– 40% = 40 40% = 40 ÷ 20 = 2÷ 20 = 2

100 100 5 5– 6% = 6 6% = 6 ÷ 2 = 3÷ 2 = 3

100 50100 50– 24% = 24 24% = 24 ÷ 4 = 6÷ 4 = 6

100 25100 25

Sections 5.6Percents and Decimals

Objectives To write percents as decimals and to write decimals as percents.

How toChange a decimal to a percent – 2 ways

1. multiply the decimal by 100Ex .45 = .45x 100 = 45 so .45 = 45%

2. move the decimal point two places to the right

Ex .45 = .45 = 45 = 45%

Sections 5.6Percents and Decimals

How to Change percents into decimals – 2 ways

1. divide the percent by 100Ex 7% = 7 ÷ 100 = .07 so 7% = .07

2. move the decimal point two places to the left

Ex 7% = 7 = (fill in empty space with zero) = .07

Section 5.8 Comparing and Ordering Rational Numbers Objective – To compare and order fractions,

decimals, and percents Vocabulary

1. Common denominator – a common multiple of the denominators Ex: 2 3 three common denominators

3 4 of 3 and 4 are 12, 24, 36 2. Least Common Denominator – the lowest of the

common multiples So 12 would be the LCD of 12, 24, and 36

Section 5.8 Comparing and Ordering Rational Numbers 3. Rational Numbers – numbers that can be

written as a fraction – made up of whole numbers, integers, terminating and repeating decimals, fractions and percents

Remember in order to compare or order rational numbers, they must be in the same form – percent form, decimal form, or fraction form.

Section 5.8 Comparing and Ordering Rational Numbers Ways to compare

1. Put in decimal for and compare the decimal values Ex: Compare 8/9 to 5/6

8/9 = .888… and 5/6 = .8333… So 8/9 > 5/6

2. Find the common denominator, make equivalent fractions and compare the numerators Ex: Compare 3/5 to 5/8

3/5 = 24/40 and 5/8 = 25/40 So 5/8 > 3/5

Section 7.5 Fractions, Decimals, and Percents

ObjectiveTo write percents as fractions and vice

versaPercents fractions and decimal are all different

names that represent the same number.80% Percent

fraction 4 0.8 Decimal

5

Section 7.5 Fractions, Decimals, and Percents

How to 1. Change the fraction into a decimal by

dividing the numerator by the denominator 2. Change the decimal to a percent by

multiplying the decimal by 100 and add the % sign

Fraction Decimal Percent Percent Decimal Fraction

Section 6.3Section 6.3Adding and SubtractingAdding and Subtracting

Mixed NumbersMixed Numbers Objective Objective

– To add and subtract mixed numbersTo add and subtract mixed numbers 2 Ways2 Ways

– 1. Turn the mixed number into an improper 1. Turn the mixed number into an improper fraction – find a common denom.- then add or fraction – find a common denom.- then add or subtract the numerators- then reduce and subtract the numerators- then reduce and simplify if necessarysimplify if necessary

Example 1 4Example 1 4 1919 3131 1919 6363 9 39 3 99 33 99 99

19+63 = 8219+63 = 82 1 1 99 99 9 9

+ =

Change to improper Find common denom. and rename

=

Add and reduce change back to mixed #

=

2 7

9

+ +

Section 6.4Section 6.4Multiplying Fractions and Mixed Multiplying Fractions and Mixed

NumbersNumbers ObjectiveObjective

• To multiply fractions and mixed numbersTo multiply fractions and mixed numbers Review VocabularyReview Vocabulary

• GCF – greatest common factor – the greatest of GCF – greatest common factor – the greatest of the common factors for two or more numbersthe common factors for two or more numbers

Multiplying Fractions – to multiply fractions, Multiplying Fractions – to multiply fractions, multiply the numerators and multiply the multiply the numerators and multiply the denominatorsdenominators

aa cc a x ca x c ac ac 3 6 3x6 18 3 6 3x6 18 22

bb dd b x db x d bd bd 5 9 5x9 45 5 9 5x9 45 55

x = = x = = =

Section 6.4Section 6.4Multiplying Fractions and Mixed Multiplying Fractions and Mixed

NumbersNumbers Multiplying Mixed NumbersMultiplying Mixed Numbers

Change the mixed number into an improper Change the mixed number into an improper fraction then multiply straight across like before fraction then multiply straight across like before and reduce or change back to a mixed numberand reduce or change back to a mixed number

ExampleExample

2 42 4 14 414 4 5656 8 8 22

3 73 7 3 7 3 7 2121 3 3 33x4 = = = = 2

Section 6.6Section 6.6Dividing Fractions and Mixed Dividing Fractions and Mixed NumbersNumbers• ObjectiveObjective

– Divide fractions and mixed numbersDivide fractions and mixed numbers

• To divide by a fraction, multiply by its To divide by a fraction, multiply by its multiplicative inversemultiplicative inverse

a c a d a x d ada c a d a x d ad 7 3 7 4 7x4 7 3 7 4 7x4 28 128 1

b d b c b x c bcb d b c b x c bc 8 4 8 3 8x3 8 4 8 3 8x3 24 624 6

1÷ = x = = ÷ = x = = =

Section 10.1 AnglesSection 10.1 Angles

• Objective – To classify and draw angles

• Vocabulary– 1. Angle – two rays with a common endpoint– 2. Degrees – unit used to measured angles– 3. Vertex – the point where two rays meet –

an endpoint– 4. Acute angle – an angle that measures less

than 90 degrees

Section 10.1 AnglesSection 10.1 Angles

– 5. Right Angle – an angle that measures exactly 90 degrees

– 6. Obtuse angle – an angle that measures more than 90 degrees but less than 180 degrees

– 7. Straight angle – an angle that measures exactly 180 degrees – a straight line

– 8. Adjacent angles – two angles that share a common side

• Symbols– 1. - symbol for angle

10.3 Angle Relationships

Objective To identify and apply angle relationships

Vocabulary 1. Vertical angles – opposite angles formed by two

intersecting lines – they have the same measure 2. Congruent angles – angles with the same

measure 3. Supplementary angles – two angles whose

measures sum to 180 degrees

4. Complementary angles – two angles whose measures sum to be 90 degrees

Symbol = is congruent to

1 angle 1 and angle 4 are vertical angles

3 2 they are congruent to each other

4 angles 2 and 3 are vertical angles and are congruent

140 40 angles 1 and 2 equal 180 so they are supplementary angles



Complementary anglesthe angles sum is 90 55

35

10.4 Triangles10.4 Triangles

Objective Objective To identify and classify trianglesTo identify and classify triangles

VocabularyVocabulary1. 1. TriangleTriangle – a figure with three sides and – a figure with three sides and

three angles whose sum measures 180 three angles whose sum measures 180 degreesdegrees

2. 2. Acute triangleAcute triangle – a triangle with all acute – a triangle with all acute angles angles

(all less than 90 degrees)(all less than 90 degrees)

10.4 Triangles10.4 Triangles

3. 3. Right TriangleRight Triangle – a triangle with one right angle – a triangle with one right angle4. 4. Obtuse TriangleObtuse Triangle – a triangle with one obtuse – a triangle with one obtuse

angleangle5. 5. Scalene TriangleScalene Triangle – a triangle with no congruent – a triangle with no congruent

sides – all are different lengthssides – all are different lengths6. 6. Isosceles triangleIsosceles triangle – a triangle with 2 congruent – a triangle with 2 congruent

sidessides7. 7. Equilateral triangleEquilateral triangle – a triangle with all 3 sides – a triangle with all 3 sides

congruentcongruent SymbolSymbol

m 1 - measure of angle 1m 1 - measure of angle 1

Section 10.5 Section 10.5 QuadrilateralsQuadrilaterals

• Objective Objective – To identify and classify quadrilateralsTo identify and classify quadrilaterals

• VocabularyVocabulary– 1. 1. QuadrilateralQuadrilateral – a closed figure with four – a closed figure with four

sides and four angles that equal 360 degreessides and four angles that equal 360 degrees– 2. 2. ParallelogramParallelogram – quadrilateral with opposite – quadrilateral with opposite

sides parallel and opposite sides congruentsides parallel and opposite sides congruent– 3. 3. TrapezoidTrapezoid – quadrilateral with one pair of – quadrilateral with one pair of

parallel sidesparallel sides


– 4. 4. RhombusRhombus – parallelogram with 4 – parallelogram with 4 congruent sidescongruent sides

– 5. 5. RectangleRectangle – parallelogram with 4 right – parallelogram with 4 right anglesangles

– 6. 6. SquareSquare – parallelogram with 4 right – parallelogram with 4 right angles and 4 congruent sidesangles and 4 congruent sides


• SymbolsSymbols– > - arrows on the sides means they are > - arrows on the sides means they are

parallelparallel– / - slashes on the sides means they are / - slashes on the sides means they are

congruentcongruent

10.7 Polygons and 10.7 Polygons and TessellationsTessellations

Objective Objective To classify polygons and determine which To classify polygons and determine which

polygons can form a tessellationpolygons can form a tessellation

VocabularyVocabulary 1. 1. PolygonPolygon – a simple closed figure formed by – a simple closed figure formed by

three or more straight lines that do not cross.three or more straight lines that do not cross. 2. 2. PentagonPentagon -- 5 sided polygon 5 sided polygon

3. 3. HexagonHexagon- - 6 sided polygon6 sided polygon


4. 4. HeptagonHeptagon - 7 sided polygon - 7 sided polygon 5. 5. Octagon Octagon - - 8 sided figure8 sided figure

6. 6. NonagonNonagon - 9 sided polygon - 9 sided polygon 7. 7. DecagonDecagon - 10 sided polygon - 10 sided polygon 8. 8. Regular PolygonRegular Polygon - a polygon that has - a polygon that has

sides congruent and all angles congruent sides congruent and all angles congruent (the same) – equilateral triangles and (the same) – equilateral triangles and squares are examples.squares are examples.


9. 9. Tessellation Tessellation – a repetitive pattern of polygons that – a repetitive pattern of polygons that fit together with no overlaps or holesfit together with no overlaps or holes

Polygons that tessellate have side numbers or degrees that Polygons that tessellate have side numbers or degrees that go evenly into 360 degreesgo evenly into 360 degrees

Divide 360 by the number of sides or the number of degrees Divide 360 by the number of sides or the number of degrees to see if a figure can tessellateto see if a figure can tessellate

Only regular polygons can tessellateOnly regular polygons can tessellate Example soccer ball, checkerboard blanketExample soccer ball, checkerboard blanket Formula for finding each angle measure in a Formula for finding each angle measure in a

polygon 180(n-2) n = number of sidespolygon 180(n-2) n = number of sides nn

Section 10.8 TranslationsSection 10.8 Translations

ObjectiveObjective To graph translations of polygons on a coordinate To graph translations of polygons on a coordinate

planeplane

VocabularyVocabulary 1. 1. TransformationTransformation – a movement of a figure on a – a movement of a figure on a

coordinate planecoordinate plane3 types 1.) reflection – flip over an axis3 types 1.) reflection – flip over an axis

2.) rotation – turn of the figure on the 2.) rotation – turn of the figure on the graphgraph

3.) translation – slide of the figure on the graph3.) translation – slide of the figure on the graph

Transformations can occur alone or as a combinationTransformations can occur alone or as a combination

Section 10.8 TranslationsSection 10.8 Translations

2. 2. TranslationTranslation – Sliding motion – Sliding motionIf slides up or down – the Y coordinate changesIf slides up or down – the Y coordinate changes

If slides left or right – The X coordinate changesIf slides left or right – The X coordinate changes

Translations to the right or up – addition occursTranslations to the right or up – addition occurs

Translations to the left or down – subtraction occursTranslations to the left or down – subtraction occurs

Ex.Ex. The coordinates of ABC are A =(2,2) B=(5,2)C=(4,6) The coordinates of ABC are A =(2,2) B=(5,2)C=(4,6)

Translate the figure 3 units left and 2 units upTranslate the figure 3 units left and 2 units up

A=(2-3,2+2)=(-1,4) B=(5-3,2+2)=(2,4) C=(4-3,6+2)=(1,8)A=(2-3,2+2)=(-1,4) B=(5-3,2+2)=(2,4) C=(4-3,6+2)=(1,8)

Section 10.9 Reflections

• Objective • To identify figures with lines of symmetry and graph

reflections on a coordinate plane

• Vocabulary• 1. Line symmetry –a figure that when folded the

halves are identical• 2. Line of symmetry – a line that divides a figure into

two halves that are reflections of each other• 3. Reflection – a transformation in which a figure is

reflected (flipped) over a line of symmetry – the X or the Y axis


• The reflections are mirror images across the x or y axis. The points should be equally spaced on either side of the axis.

• If the figure is reflected over the y axis, the x-coordinate changes to positive or negative


• If the figure is reflected over the x-axis the y-coordinate changes to either positive or negative

Ex. Quadrilateral ABCD has verticesA(1,2) B(3,5) C(6,5) D(6,2) reflect over y axis ( x coordinate changes)A’(-1,2) B’(-3,5) C’ (-6,5) D’(-6,2)

Section 6.8 Section 6.8 Geometry: Perimeter and AreaGeometry: Perimeter and Area

ObjectiveObjective To find the perimeters and areas of figuresTo find the perimeters and areas of figures

VocabularyVocabulary 1. 1. PerimeterPerimeter – the distance around a geometric – the distance around a geometric

figure – add al the side lengths together.figure – add al the side lengths together. Perimeter of a rectanglePerimeter of a rectangle

P= l + l + w + w or P = 2l + 2wP= l + l + w + w or P = 2l + 2w formulaformulal = lengthl = length w = widthw = width shows the shows the

relationshiprelationshipamong among

quantitiesquantitiesP= 3+3+5+5 = 16 unitsP= 3+3+5+5 = 16 units

33

5

Section 6.8 Section 6.8 Geometry: Perimeter and Geometry: Perimeter and AreaArea

2. 2. AreaArea – the number of square units of space – the number of square units of space inside of a geometric figure. Uses two inside of a geometric figure. Uses two dimensions to calculate – EXPRESSED IN dimensions to calculate – EXPRESSED IN SQUARE UNITSSQUARE UNITS Area of a rectangle Area of a rectangle

A = l A = l xx w w Formula - length Formula - length xx width width

Area of a squareArea of a square

A = S A = S 2 2 Formula – s= side- so side x side Formula – s= side- so side x side

A = 4 A = 4 2 2 or 4 x 4 = 16 units or 4 x 4 = 16 units 22

4

Section 11.4Section 11.4Area of ParallelogramsArea of Parallelograms

Objective Objective – To find the area of parallelogramsTo find the area of parallelograms

VocabularyVocabulary– 1. 1. BaseBase – any side parallelogram = b – any side parallelogram = b– 2. 2. HeightHeight – the length of a segment= h perpendicular – the length of a segment= h perpendicular

to the base with endpoints on opposite sidesto the base with endpoints on opposite sides

Area = b x hArea = b x h

Also expressed in square Also expressed in square

unitsunits

base

height

Section 11.5 Section 11.5 Area of Triangles and TrapezoidsArea of Triangles and Trapezoids

Objective Objective To find the areas of triangles and trapezoidsTo find the areas of triangles and trapezoids

VocabularyVocabulary1. 1. TrapezoidTrapezoid - quadrilateral with one pair of - quadrilateral with one pair of

parallel sides.parallel sides. Area of a triangle = A = 1 x b x h or b x hArea of a triangle = A = 1 x b x h or b x h

area = .5 x base x height area = .5 x base x height 22 22

A = .5x3x7A = .5x3x7

A = 10.5 cm sqA = 10.5 cm sq

base

height

7 cm

3cm

Section 11.5 Section 11.5 Area of Triangles and TrapezoidsArea of Triangles and Trapezoids

Area of a trapezoid Area of a trapezoid

expressed in square unitsexpressed in square unitsA = .5h(bA = .5h(b 1 1 + b + b 22))

or h (bor h (b11 + b + b22))

22

A = .5 x 5 (8 + 12 )A = .5 x 5 (8 + 12 )

A = .5 x 5 ( 20 )A = .5 x 5 ( 20 )

A = .5 x 100A = .5 x 100

A = 50 in squaredA = 50 in squared

h=height

Base 1

Base 2

8in

12in

5 in

Section 6.9 Circumference of Circles

Objective – To find the circumference of circles

Vocabulary 1. Circle – a set of points in the same plane that

are all equal distance from the center. 2. Diameter – distance across a circle through

the center = d 3. Radius – the distance from the center to the

side of the circle – half the distance across the circle – half the diameter = r

Section 6.9 Circumference of Circles

4. Circumference – the distance around the circle = 2 x 3.14 x r or 3.14 x d

C = 3.14 x 8 = 25.12 cm

C = 2 x 3.14 x 3 = 18.84 in

8cm

3in

Section 11.6Section 11.6Area of CirclesArea of Circles

ObjectiveObjective To find the area of circlesTo find the area of circles

VocabularyVocabulary 1. 1. PiPi – the Greek letter that represents an – the Greek letter that represents an

irrational number – approximately = 3.14irrational number – approximately = 3.14

r= radius – half the r= radius – half the distance distance of a circleof a circle

r

Section 11.6Section 11.6Area of CirclesArea of Circles

Area of a circle = A = 3.14rArea of a circle = A = 3.14r22

d = d = diameter =2rdiameter =2r

A = 3.14 x 2A = 3.14 x 22 2 = 3.14 x 4 = = 3.14 x 4 = 12.56 ft sq12.56 ft sq

11/2 = 5.5 A= 3.14 x 5.5 11/2 = 5.5 A= 3.14 x 5.5 22 = 3.14 x 30.25 = 95 = 3.14 x 30.25 = 95 mmmm22

d

2 ft

11mm

Section 5.7 Least Common Multiple

• Objective• To find the least common multiple of

two or more numbers

• Vocabulary• 1. Multiple – the product of a number

and any whole number• 2. Least Common Multiple (LCM) – the

lowest of the common multiples of two or more numbers excluding zero.


• How to – 2 methods• 1. List the multiples of the numbers

until a common one is found• Ex Find the LCM of 6 and 10

− 6 - 6,12,18,24,30 30 is the LCM − 10 – 10,20,30 of 6 and 10

• Ex Find the LCM of 3 and 7− 3 – 3,6,9,12,15,18,21 21 is the LCM

of 3− 7 – 7,14,21 and 7


• 2. Write the prime factorization• Ex Find the LCM of 12 and 18

12 186 2 3 6

3 2 3 2

So 12 = 3 x2 x 2 and 18 = 3 x 3 x 2 use the multiples that occur the most

2x2 and 3x3 = 2 x 2 x 3 x 3 = 36 so the LCM of 12 and 18 is 36

10.6 Similar Figures

• Objective • To determine whether figures are similar and find

the missing length in a pair of similar figures.

• Vocabulary• 1. Similar Figures – figures that have the same

shape but not necessarily the same size. The sizes are proportional. The angles are congruent.~ = similar

10 = 8 = 6 - proportional 5 4 3 sidesCongruent angles

A

B

C

10 6

8

E

DF

53

4

10.6 Similar Figures

• 2. Indirect Measure – using the length, width or height of figures that are too difficult to measure directly• Ex Paul is 5 ft tall, his shadow is 4 ft long. The

flagpole’s shadow is 36 ft long, how tall is the flagpole.

5 = x 4 x 9 = 36 so 5 x 9 = x =45 4 36 the flagpole is 45 ft tall

6 = 5 = 4 ? = 12 18 15 ?

18 15

?

6 5

4

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Notes for the 3 rd Grading Period Mrs. Neal 6 th Advanced & 7 th Average.

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