problem solving strategies. estimate fractions: fractions: estimate to 0, ½, 1 estimate to 0, ½, 1...
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Fractions: Estimate to 0, , 1
+ - : Estimate
Draw a picture
prime factor treefractionsarea, perimeter, volume, surface area
Make a Chart
Guess and CheckAlgebra
n 15 = 35
a. 20 b. 50 c. 45 d. 10
Does the answer make sense?
Is it reasonable?
CRCT ReviewNumbers and Operations Unit
Greatest Common Factor Find the GCF of 4 and 12 Factors of 4: 1,2,4 Factors of 12: 1,2,3,4,6,12 The GCF of 4 and 12 is 4
Least Common MultipleFind the LCM of 3 and 12
Multiples of 3: 3,6,9,12,Multiples of 12: 12, 24, 36,
The LCM of 3 and 12 is 12
Prime FactorizationFactor Tree (Student Video)
25 x 4
5x 5 2 x 2 = 5x5x2x2
FractionsEstimate.. Estimate.. Estimate..
Is the fraction closer to 0 or 1?
Draw a picture if you have a doubt
Equivalent Fractions The fractions 2/3, 4/6, and 6/9 are equivalent fractions. They name the same basic fraction 2/3.
You can re-name fractions by multiplying by the GIANT 1 method
Comparing Fractions Fractions can be compared using cross multiplication.
Which fraction is larger 5/9 or 4/5? Of course, 4/5!
Fraction BasicsAdd and Subtract: Denominators must be the same! (Video) (Student Video)Multiply: Top, Bottom, Simplify (Student Video) Divide: Just flip the second and Multiply (Student Video)
Decimals Estimate Estimate.. Estimate When placing decimal numbers in order, annex zeros (if needed)
Which is larger 11.19 or 11.9?
Annex zeros to give both decimals the same number of places after the decimal. 11.19 / 11.90. You can see that 11.90 is the larger!
Decimals Add / Subtract This one is easy!
Just line up the decimals! (Student Video)
Decimals - Multiply Just multiply as usual. Then, count the number of places to the right of both decimal numbers. Move the decimal this number of places to the left in your answer!
What is 3.2 x 0.1?32 x 1 = 32. Move the decimal 2 places to the left to equal 0.32(Student Video)
Decimals - DivideRemember, the divisor must become a whole number before dividing!
0.5Move the decimal in the divisor and the dividend 1 place to the right (Student Video)
Percent (%) of a NumberChange the % to a fraction & multiplyorChange the % to a decimal & multiply.
What is 10% of 200?1/10 x 200/1 = 20 or .10 x 200 = 20(Student Video)
Fractions to DecimalsTo change a fraction to a decimal, just divide as usual. Annex zeros and remember the decimal point in the answer!
Change 3/5 to a decimal 0.65(Student Video) (Student Video)
Percents to Fractions Remember, percent means per hundred
What is 33% as a fraction?33/100
Its that easy!
Fractions-Decimals-Percents1 1.0 100% .50 50%1/3 .333 33.3% .25 25%1/5 .20 20%1/10 .10 10%
CRCT ReviewMeasurement Unit
LengthStandard Units1 yd = 3 ft1 ft = 12 in1 mi= 5,280 ftMetric Units1km = 1000 m1m = 100 cm1cm = 10 mm
Metric LengthUnits of Measure:
Millimeter (mm)Centimeter (cm)Meter (m) about 1 yardKilometer (km) about mile
Customary VolumeCustomary Units1gal = 4 qt1gal = 8 pints1gal = 16 cupsMetric Units
PerimeterThe distance around any closed figure. A border is put around a rectangular room that is 12ft wide and 10 ft. long. How much border material is needed?
Answer: 44 ft.
Area of Rectangular Prisms The number of square units needed to cover a surface enclosed by a geometric figure.
Surface Area of a Rectangular Prism Length x Width or Base x Height How many 1-inch tiles are needed to cover a square table with a side measure of 20 inches?
Answer: 400 square inches (Student Video)
Surface Area of Rectangular Prisms
Panther Method times 2
What is the total surface area of a cereal box that measures 8in. by 2in. by 11in?
Answer: 254 square inches
Volume of Rectangular Prismsin 3D!
Length x Width x Height
What is the volume of a container with length 10cm, width 2cm, and height 6cm?
Answer: 10cm x 2cm x 6cm = 120 cubic cm
Circumference of Circles
d or 2r What is the circumference of a tire with a diameter of 20 inches? Answer: Since pi = 3.14 and the diameter is 20 inches, then the circumference is 3.14 x 20 inches or 62.8 square inches!
Area of Circles (r squared)
What is the area of a pizza with a radius of 6 inches?
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.
Congruent Figures 2 figures are congruent when they are the same shape and the same size.
2in. X 4in.2in. X 4in.
Similar Figures 2 figures are similar when they are the same shape but not the same size.
These triangles are similar. What is the length of the base of triangle 2?
6 10 5 3
4 ?? Answer: 2
Chapter 7: Proportional Relationships 7-4 Similar Figures 7-6 Scale Drawings and Maps Chapter 8: Geometric Relationships 8-9 Congruence 8-11 Line Symmetry
Line Symmetry A figure has line symmetry if a single line or fold splits the shape into congruent halves.
a regular pentagon has 5 internal angles and 5 lines of symmetry.
Rotational SymmetryA figure has rotational symmetry if it can be rotated and have the figure match the original position
Order of Rotation: 5
Angle of Rotation:360 5 = 72
Order of Rotation: 7
Angle of Rotation:360 7 = 51.4
Geometric Nets A flat pattern that can be folded to make a solid figure.
Cylinder Square Pyramid Cube
PatternsFill in the missing numbers in this table if y=6x
Holt Work Text
Ratios A ratio compares 2 numbers. Ratios can be written in the following ways:1 to 4 1:4
Holt Work Text
Ratios Cameron used 12 red beads and 60 white beads to make a necklace. What was the ratio of red to white beads to total beads?a.1:5 b. 1:6 c. 1:12 d. 1:4
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 ratio
Proportions A proportion compares 2 different ratios and shows that they are equal.
We can determine if 8/12 = 2/3 is a proportion by cross multiplication. The two ratios make a proportion when the cross products are equal.
Proportions: Z Method2/8 = x/24 1/8 = 7/x Holt Work Text 3 out of every 5 parents vote in an election. If there are 450 parents, how many can be expected to vote?
Answer: 270 parents can be expected to vote
Proportions in the Form y = kx Jennifer earns $20 for every 2 hours that she baby-sits. On Saturday night, she babysat for 3 hours. How much money does she earn?
Proportions in the Form y = kx If you graph each equation below, all of the graphs will be straight lines. The steepest line would represent which equation? a. y=1/9x b. y=2/9x c. y=1/3x d. y=2/3x
Evaluating Algebraic Equations When a letter is shown beside a number with no sign, it means to multiply!4a 4 x a 4a
Solving One Step Equationsif 4a = 36, a = ? (9)
if n 19 = 28, n = ? (47)
if z + 10 = 12, z = ? (2)
if x2 1 = 24, x= ? (5)
if 36/m = 6, m = ? (6)
Evaluating Algebraic Equations What is the value of this expression when d = 3? d2 + 14 a. 20 b. 23 c. 25 d. 47 Answer: b
Data Analysis and Probability
Probabilitythe chance than an event will happen. Experimental probability approaches theoretical probability as the number of events is large. 0 : cannot occur : 50-50 chance 1 : certain