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Problem Problem Solving Solving Strategies Strategies

Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

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Page 1: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

ProblemProblemSolvingSolvingStrategiesStrategies

Page 2: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

EstimateEstimate

• Fractions:Fractions:

Estimate to 0, ½ , 1Estimate to 0, ½ , 1

• Decimals:Decimals: Estimate Estimate

• + - × ÷: + - × ÷: EstimateEstimate

Page 3: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Draw a pictureDraw a picture• prime factor treeprime factor tree• fractionsfractions• area, perimeter, area, perimeter, volume, surface areavolume, surface area

Page 4: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Make a ChartMake a Chart

factorsfactors multiplesmultiples equivalent fractionsequivalent fractions ratiosratios

Page 5: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Guess and CheckGuess and Check• AlgebraAlgebra

““n” – 15 = 35n” – 15 = 35

a. 20 b. 50 c. 45 d. 10a. 20 b. 50 c. 45 d. 10

Page 6: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Look BackLook Back

Does the answer make Does the answer make sense?sense?

Is it reasonable?Is it reasonable?

Page 7: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

CRCT ReviewCRCT Review

Numbers and Numbers and Operations UnitOperations Unit

Page 8: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Greatest Common FactorGreatest Common Factor

Find the GCF of 4 and 12Find the GCF of 4 and 12

Factors of 4: 1,2,Factors of 4: 1,2,44

Factors of 12: 1,2,3,Factors of 12: 1,2,3,44,6,12,6,12

The GCF of 4 and 12 is The GCF of 4 and 12 is 44

Page 9: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Least Common MultipleLeast Common Multiple

Find the LCM of 3 and 12Find the LCM of 3 and 12

Multiples of 3: 3,6,9,Multiples of 3: 3,6,9,1212,…,…

Multiples of 12: Multiples of 12: 1212, 24, 36,…, 24, 36,…

The LCM of 3 and 12 is The LCM of 3 and 12 is 1212

Page 10: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Prime FactorizationPrime Factorization

Factor TreeFactor Tree (Student Video)(Student Video)

100100

25 x 425 x 4

5x 5 2 x 2 = 5x5x2x25x 5 2 x 2 = 5x5x2x2

Page 11: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

FractionsFractions

Estimate..Estimate.. Estimate..Estimate.. Estimate..Estimate..

Is the fraction closer to 0 ½ or 1?Is the fraction closer to 0 ½ or 1?

Draw a picture if you have a doubtDraw a picture if you have a doubt

Page 12: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Equivalent FractionsEquivalent Fractions

The fractions 2/3, 4/6, and 6/9 The fractions 2/3, 4/6, and 6/9 are are equivalent fractionsequivalent fractions. They . They name the same basic fraction name the same basic fraction 2/3. 2/3.

You can re-name fractions by You can re-name fractions by multiplying by the GIANT 1 multiplying by the GIANT 1 methodmethod

Page 13: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Comparing FractionsComparing Fractions

Fractions can be compared using Fractions can be compared using cross multiplication.cross multiplication.

Which fraction is larger 5/9 or Which fraction is larger 5/9 or 4/5? Of course, 4/54/5? Of course, 4/5!!

5

9

4

5

Page 14: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Fraction BasicsFraction BasicsAdd and Subtract: Add and Subtract:

Denominators Denominators must bemust be the same! the same! (Video)(Video) (Student Video)(Student Video)

Multiply:Multiply: Top, Bottom, Simplify Top, Bottom, Simplify (Student Video)(Student Video)

Divide:Divide: Just flip the second and Just flip the second and

MultiplyMultiply (Student Video)(Student Video)

Page 15: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Decimals Decimals Estimate… Estimate.. EstimateEstimate… Estimate.. Estimate

When placing decimal numbers in When placing decimal numbers in order, order, annex zerosannex zeros (if needed) (if needed)

Which is larger 11.19 or 11.9?Which is larger 11.19 or 11.9?

Annex zeros to give both decimals Annex zeros to give both decimals the same number of places after the same number of places after the decimal. 11.19 / 11.9the decimal. 11.19 / 11.900. .

You can see that 11.90 is the larger!You can see that 11.90 is the larger!

Page 16: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Decimals – Add / SubtractDecimals – Add / Subtract

This one is easy!This one is easy!

Just line up the decimals!Just line up the decimals! (Student Video)(Student Video)

Page 17: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Decimals - MultiplyDecimals - Multiply Just Just multiply as usualmultiply as usual. Then, count . Then, count

the number of places to the right of the number of places to the right of both decimal numbers. Move the both decimal numbers. Move the decimal this number of places to the decimal this number of places to the left in your answer!left in your answer!

What is 3.2 x 0.1?What is 3.2 x 0.1?32 x 1 = 32. Move the decimal 2 32 x 1 = 32. Move the decimal 2

places to the left to equal 0.32places to the left to equal 0.32(Student Video)(Student Video)

Page 18: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Decimals - DivideDecimals - Divide

Remember, Remember, the divisor must become a the divisor must become a whole number before dividing!whole number before dividing!

0.50.5Move the decimal in the divisor Move the decimal in the divisor

and the dividend 1 place to and the dividend 1 place to the right the right (Student Video)(Student Video)

18 45.

Page 19: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Percent (%) of a NumberPercent (%) of a NumberChange the % to a fraction & Change the % to a fraction &

multiplymultiplyoror

Change the % to a decimal & Change the % to a decimal & multiply.multiply.

What is 10% of 200?What is 10% of 200?1/10 x 200/1 = 20 1/10 x 200/1 = 20 or or .10 x 200 = 20.10 x 200 = 20

(Student Video)(Student Video)

Page 20: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Fractions to DecimalsFractions to Decimals

To change a fraction to a decimal, just To change a fraction to a decimal, just divide as usual. Annex zeros and divide as usual. Annex zeros and remember the decimal point in the remember the decimal point in the answer!answer!

Change 3/5 to a decimal Change 3/5 to a decimal

0.60.6

55

(Student Video)(Student Video) (Student Video)(Student Video)3

Page 21: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Percents to FractionsPercents to Fractions

Remember, percent means Remember, percent means “per hundred”“per hundred”

What is 33% as a fraction?What is 33% as a fraction?33/10033/100

It’s that easy!It’s that easy!

(Student Video)(Student Video)

Page 22: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Fractions-Decimals-PercentsFractions-Decimals-Percents

1 1.0 100%1 1.0 100%

½ .50 50%½ .50 50%

1/3 .333 33.3%1/3 .333 33.3%

¼ .25 25%¼ .25 25%

1/5 .20 20%1/5 .20 20%

1/10 .10 10%1/10 .10 10%

Page 23: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

CRCT ReviewCRCT Review

Measurement Measurement UnitUnit

Page 24: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

LengthLength

Standard UnitsStandard Units

1 yd = 3 ft1 yd = 3 ft

1 ft = 12 in1 ft = 12 in

1 mi= 5,280 ft1 mi= 5,280 ft

Metric UnitsMetric Units

1km = 1000 m1km = 1000 m

1m = 100 cm1m = 100 cm

1cm = 10 mm1cm = 10 mm

Page 25: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Metric LengthMetric Length

Units of Measure:Units of Measure:

Millimeter (mm)Millimeter (mm)Centimeter (cm)Centimeter (cm)Meter (m) about 1 yardMeter (m) about 1 yardKilometer (km) about ½ mileKilometer (km) about ½ mile

(Student Video)(Student Video)

Page 26: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Customary VolumeCustomary Volume

Customary UnitsCustomary Units

1gal = 4 qt1gal = 4 qt

1gal = 8 pints1gal = 8 pints

1gal = 16 cups1gal = 16 cups

Metric UnitsMetric Units

Page 27: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

PerimeterPerimeter

The distance around any The distance around any closed figure.closed figure.

A border is put around a A border is put around a rectangular room that is 12ft wide rectangular room that is 12ft wide and 10 ft. long. How much border and 10 ft. long. How much border material is needed?material is needed?

Answer: 44 ft.Answer: 44 ft.

(Student Video)(Student Video)

Page 28: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Area of Rectangular PrismsArea of Rectangular Prisms The number of square units needed to The number of square units needed to

cover a surface enclosed by a cover a surface enclosed by a geometric figure.geometric figure.

Surface Area of a Rectangular Prism Surface Area of a Rectangular Prism Length x Width Length x Width oror Base x Height Base x Height

How many 1-inch tiles are needed to How many 1-inch tiles are needed to cover a square table with a sidecover a square table with a side measure of 20 inches?measure of 20 inches?

Answer: 400 square inchesAnswer: 400 square inches (Student Video)(Student Video)

Page 29: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Surface Area of Rectangular PrismsSurface Area of Rectangular Prisms

““Panther Method” times 2Panther Method” times 2

What is the total surface area of a What is the total surface area of a cereal box that measures 8in. by cereal box that measures 8in. by 2in. by 11in?2in. by 11in?

Answer: 254 square inchesAnswer: 254 square inches

(Student Video)(Student Video)

Page 30: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Volume of Rectangular PrismsVolume of Rectangular Prismsin 3D!in 3D!

Length x Width x HeightLength x Width x Height

What is the volume of a container What is the volume of a container with length 10cm, width 2cm, and with length 10cm, width 2cm, and height 6cm?height 6cm?

Answer: 10cm x 2cm x 6cm = 120 cubic cmAnswer: 10cm x 2cm x 6cm = 120 cubic cm

Page 31: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Circumference of CirclesCircumference of Circles

∏∏dd or or 22∏∏rr

What is the circumference of a tire What is the circumference of a tire with a diameter of with a diameter of 2020 inches? inches?

Answer:Answer:

Since pi = 3.14 and the diameter is 20 inches, then the circumference is 3.14 x 20 Since pi = 3.14 and the diameter is 20 inches, then the circumference is 3.14 x 20 inches or 62.8 square inches!inches or 62.8 square inches!

Page 32: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Area of Circles Area of Circles

(∏(∏r r squaredsquared))

What is the area of a pizza with a What is the area of a pizza with a radius of radius of 6 6 inches?inches?

Answer: Since pi = 3.14 and the radius is 3cm, the area of this circle is Answer: Since pi = 3.14 and the radius is 3cm, the area of this circle is 3.14 x 36 inches or 113.04 square cm. 3.14 x 36 inches or 113.04 square cm.

Page 33: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

CRCT ReviewCRCT Review

GeometryGeometry

Page 34: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Congruent FiguresCongruent Figures

2 figures are 2 figures are congruent congruent when they when they are the are the same shapesame shape and the and the same same size.size.

2in. X 4in. 2in. X 4in.

Page 35: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Similar FiguresSimilar Figures

2 figures are 2 figures are similar similar when they are when they are the same shape but the same shape but notnot the same the same size.size.

Page 36: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

These triangles are These triangles are similarsimilar. What . What is the length of the base of is the length of the base of triangle 2?triangle 2? 11 22

6 10 5 3 6 10 5 3

4 ??4 ?? Answer: 2Answer: 2

Page 37: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Geometry:Geometry:Textbook SitesTextbook Sites

Chapter 7: Proportional RelationshipsChapter 7: Proportional Relationships7-4 Similar Figures7-4 Similar Figures7-6  Scale Drawings and Maps7-6  Scale Drawings and Maps

   Chapter 8: Geometric RelationshipsChapter 8: Geometric Relationships8-9  Congruence8-9  Congruence8-11 Line Symmetry8-11 Line Symmetry

Page 38: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Line SymmetryLine Symmetry

A figure has A figure has line symmetryline symmetry if a if a single line or fold splits the shape single line or fold splits the shape into congruent halves.into congruent halves.

Page 39: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

    a regular pentagon has 5 internal a regular pentagon has 5 internal angles and 5 lines of symmetry.angles and 5 lines of symmetry.

  

Page 40: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Rotational SymmetryRotational SymmetryA figure has A figure has rotational symmetryrotational symmetry if it can be rotated and have the if it can be rotated and have the

figure match the original positionfigure match the original position

Order of Rotation: 5Order of Rotation: 5

Angle of Rotation:Angle of Rotation:

360360° ÷ 5 = 72°° ÷ 5 = 72°

Order of Rotation: 7Order of Rotation: 7

Angle of Rotation:Angle of Rotation:

360360° ÷ 7 = 51.4°° ÷ 7 = 51.4°

Page 41: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Geometric NetsGeometric Nets

A flat pattern that can be folded to A flat pattern that can be folded to make a solid figure.make a solid figure.

Cylinder Square Pyramid CubeCylinder Square Pyramid Cube

Page 42: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

CRCT ReviewCRCT Review

AlgebraAlgebra

Page 43: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

PatternsPatternsFill in the missing numbers in this table Fill in the missing numbers in this table

if if yy=6=6xx

Holt Work TextHolt Work Text

XX yy11 ??

33 ??

?? 3636

Page 44: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

RatiosRatios

A A ratio ratio compares 2 numbers. compares 2 numbers. Ratios can be written in the Ratios can be written in the following ways:following ways:

1 to 4 1:4 ¼1 to 4 1:4 ¼

Holt Work TextHolt Work Text

Page 45: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

RatiosRatios

CameronCameron used 12 red beads and 60 used 12 red beads and 60 white beads to make a necklace. white beads to make a necklace. What was the ratio of red to white What was the ratio of red to white beads to total beads?beads to total beads?

a.a.1:5 1:5 b.b. 1:6 1:6 c.c. 1:12 1:12 d.d. 1:4 1:4

Answer: There are 72 total beads and 12 are red. The ratio is 12/72, which Answer: There are 72 total beads and 12 are red. The ratio is 12/72, which can be simplified as 1/6 – a 1:6 ratiocan be simplified as 1/6 – a 1:6 ratio

Page 46: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

ProportionsProportions

A A proportionproportion compares 2 different compares 2 different ratios and shows that they are ratios and shows that they are equal.equal.

We can determine if 8/12 = 2/3 is a We can determine if 8/12 = 2/3 is a proportion by cross multiplication. proportion by cross multiplication. The two ratios make a proportion The two ratios make a proportion when the cross products are equal.when the cross products are equal.

Page 47: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Proportions: “Z Method”Proportions: “Z Method”2/8 = x/242/8 = x/24 1/8 = 7/x1/8 = 7/x

Holt Work TextHolt Work Text

3 out of every 5 parents vote in an 3 out of every 5 parents vote in an election. If there are 450 parents, election. If there are 450 parents, how many can be expected to how many can be expected to vote?vote?

Answer: 270 parents can be expected to voteAnswer: 270 parents can be expected to vote

Page 48: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Proportions in the Form Proportions in the Form y = kxy = kx

JenniferJennifer earns $20 for every 2 hours earns $20 for every 2 hours that she baby-sits. On Saturday that she baby-sits. On Saturday night, she babysat for 3 hours. How night, she babysat for 3 hours. How much money does she earn?much money does she earn?

Answer: $30Answer: $30

Page 49: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Proportions in the Form Proportions in the Form y = kxy = kx

If you graph each equation below, all of If you graph each equation below, all of the graphs will be straight lines. The the graphs will be straight lines. The steepest line would represent which steepest line would represent which equation?equation?

a. y=1/9a. y=1/9xx b. y=2/9 b. y=2/9xx c. y=1/3 c. y=1/3xx d. y=2/3 d. y=2/3xx

Graphing CalculatorGraphing Calculator

Page 50: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Evaluating Algebraic EquationsEvaluating Algebraic Equations

When a letter is shown beside a When a letter is shown beside a number with no sign, it means tonumber with no sign, it means to multiply!multiply!

4a 4 x a 4·a4a 4 x a 4·a

(Student Video)(Student Video)

Page 51: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Solving One Step EquationsSolving One Step Equations

if 4if 4aa = 36, = 36, aa = ? = ? (9)(9)

if if nn – 19 = 28, – 19 = 28, nn = ? = ? (47)(47)

if if zz + 10 = 12, + 10 = 12, zz = ? = ? (2)(2)

if if xx2 2 –1 = 24, –1 = 24, xx= ? = ? (5)(5)

if 36/if 36/mm = 6, = 6, mm = ? = ? (6)(6)

Page 52: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

Evaluating Algebraic EquationsEvaluating Algebraic Equations

What is the value of this What is the value of this expression when expression when dd = 3? = 3?

dd22 + 14 + 14

a. 20 b. 23 c. 25 d. 47a. 20 b. 23 c. 25 d. 47

Answer: bAnswer: b

Page 53: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

CRCT ReviewCRCT Review

Data AnalysisData Analysis

andand

ProbabilityProbability

Page 54: Problem Solving Strategies. Estimate Fractions: Fractions: Estimate to 0, ½, 1 Estimate to 0, ½, 1 Decimals: Estimate Decimals: Estimate + - × ÷: Estimate

ProbabilityProbability……the chance than an eventthe chance than an event will happen. will happen.

Experimental probability approaches approaches theoretical probabilitytheoretical probability as the number of as the number of events is large.events is large.

00 : : cannot occurcannot occur

½½ : : 50-50 chance50-50 chance

11 : : certaincertain