problem solving strategies. estimate fractions: fractions: estimate to 0, ½, 1 estimate to 0, ½, 1...
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ProblemProblemSolvingSolvingStrategiesStrategies
EstimateEstimate
• Fractions:Fractions:
Estimate to 0, ½ , 1Estimate to 0, ½ , 1
• Decimals:Decimals: Estimate Estimate
• + - × ÷: + - × ÷: EstimateEstimate
Draw a pictureDraw a picture• prime factor treeprime factor tree• fractionsfractions• area, perimeter, area, perimeter, volume, surface areavolume, surface area
Make a ChartMake a Chart
factorsfactors multiplesmultiples equivalent fractionsequivalent fractions ratiosratios
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
Look BackLook Back
Does the answer make Does the answer make sense?sense?
Is it reasonable?Is it reasonable?
CRCT ReviewCRCT Review
Numbers and Numbers and Operations UnitOperations Unit
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
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
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
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
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
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
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)
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!
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)
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)
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.
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)
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
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)
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%
CRCT ReviewCRCT Review
Measurement Measurement UnitUnit
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
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)
Customary VolumeCustomary Volume
Customary UnitsCustomary Units
1gal = 4 qt1gal = 4 qt
1gal = 8 pints1gal = 8 pints
1gal = 16 cups1gal = 16 cups
Metric UnitsMetric Units
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)
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)
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)
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
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!
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.
CRCT ReviewCRCT Review
GeometryGeometry
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.
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.
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
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
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.
a regular pentagon has 5 internal a regular pentagon has 5 internal angles and 5 lines of symmetry.angles and 5 lines of symmetry.
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°
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
CRCT ReviewCRCT Review
AlgebraAlgebra
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
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
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
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.
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
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
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
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)
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)
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
CRCT ReviewCRCT Review
Data AnalysisData Analysis
andand
ProbabilityProbability
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
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