Problem Solving Strategies

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ProblemSolvingStrategies

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Estimate

• Fractions
• Estimate to 0, ½ , 1
• Decimals Estimate
• - Estimate

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Draw a picture

• prime factor tree
• fractions
• area, perimeter, volume, surface area

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Make a Chart

• factors
• multiples
• equivalent fractions
• ratios

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Guess and Check

• Algebra
• n 15 35
• a. 20 b. 50 c. 45 d. 10

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Look Back

• Does the answer make sense?
• Is it reasonable?

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CRCT Review

• Numbers and Operations Unit

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Factors and Multiples

• Factors are limited
• (10 1x10,2x5)
• Multiples are unlimited
• (2 2,4,6,8,10)

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Greatest Common Factor

• Find the GCF of 4 and 12Factors of 4 1,2,4
• Factors of 12 1,2,3,4,6,12
• The GCF of 4 and 12 is 4

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Least Common Multiple

• Find 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

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Prime Factorization

• Factor Tree (Student Video)
• 100
• 25 x 4
• 5x 5 2 x 2 5x5x2x2

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• Fractions

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Fractions

• Estimate.. Estimate.. Estimate..
• Is the fraction closer to 0 ½ or 1?
• Draw a picture if you have a doubt

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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

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Comparing Fractions

• Fractions can be compared using cross
  multiplication.
• Which fraction is larger 5/9 or 4/5? Of course,
  4/5!

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Fraction Basics

• Add 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)

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• Decimals

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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!

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Decimals Add / Subtract

• This one is easy!
• Just line up the decimals!
• (Student Video)

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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)

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Decimals - Divide

• Remember, the divisor must become a whole number
  before dividing!
• 0.5
• Move the decimal in the divisor and the dividend
  1 place to the right (Student Video)

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Percent () of a Number

• Change the to a fraction multiply
• or
• Change the to a decimal multiply.
• What is 10 of 200?
• 1/10 x 200/1 20 or .10 x 200 20
• (Student Video)

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Fractions to Decimals

• To 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
• 0.6
• 5
• (Student Video) (Student Video)

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Percents to Fractions

• Remember, percent means per hundred
• What is 33 as a fraction?
• 33/100
• Its that easy!
• (Student Video)

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Fractions-Decimals-Percents

• 1 1.0 100
• ½ .50 50
• 1/3 .333 33.3
• ¼ .25 25
• 1/5 .20 20
• 1/10 .10 10

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Now

• Numbers and Operations
• Lets Practice

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CRCT Review

• Measurement Unit

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Length

• Standard Units
• 1 yd 3 ft
• 1 ft 12 in
• 1 mi 5,280 ft

• Metric Units
• 1km 1000 m
• 1m 100 cm
• 1cm 10 mm

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Customary Length

• Measure to the nearest half, fourth, eighth, and
  sixteenth of an inch
• (Student Video)

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Metric Length

• Units of Measure
• Millimeter (mm)
• Centimeter (cm)
• Meter (m) about 1 yard
• Kilometer (km) about ½ mile
• (Student Video)

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Customary Volume

• Customary Units
• 1gal 4 qt
• 1gal 8 pints
• 1gal 16 cups

• Metric Units

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Perimeter

• The 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.
• (Student Video)

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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)

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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
• (Student Video)

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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

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Circumference of Circles

• ?d or 2?r
• 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!

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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.

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Geometric Nets

• A flat pattern that can be folded to make a
  solid figure.
• Cylinder Square Pyramid Cube

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Now

• Measurement
• Lets Practice

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CRCT Review

• Geometry

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Line Symmetry

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

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• This photograph shows 2 lines of symmetry-
  vertical and horizontal
• (Notice how the prayer towers, called minarets,
  are reflected in the water and side to side).

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Rotational Symmetry

• A figure has rotational symmetry if it can be
  rotated and have the figure match the original
  position

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Rotational Symmetry

• Degree of Rotation 5
• Angle of Rotation
• 360 5 72

• Degree of Rotation 7
• Angle of Rotation
• 360 7 51.4

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Congruent Figures

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

2in. X 4in.
2in. X 4in.
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Similar Figures

• 2 figures are similar when they are the same
  shape but not the same size.

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These triangles are similar. What is the length
of the base of triangle 2?

• 1 2
• 6 10 5 3
  
• 4 ??
• Answer 2

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Simple Scale Drawings

• A key shows the distance represented by a unit
  of length.
• 1 in. 10 miles
• 2 in. __ miles
• 3 ½ in. __ miles

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Simple Scale Drawings

• Nick is making a scale model of a planet that
  is 50,000 mi. in diameter. If the scale is 1cm
  1,000 mi. , what is the diameter (in cm) on the
  scale model?
• Answer 50cm

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Prisms and Pyramids

• Faces-Edges-Vertices
• Rectangular Prism 6 12 8
• Triangular Prism ___ ___ ___
• Square Pyramid ___ ___ ___
• Triangular Pyramid ___ ___ ___
• Cone ___ ___ ___
• Cylinder ___ ___ ___

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Now

• Geometry
• Lets Practice

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CRCT Review

• Algebra

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Ratios

• A ratio is a fraction that shows the
  relationship of one amount to another amount.
• ¼ 14 ratio

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Ratios

• Tasha 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.15 b. 16 c. 112 d. 14
• Answer There are 72 total beads and 12 are
  red. The ratio is 12/72, which can be simplified
  as 1/6 a 16 ratio

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Patterns

• Patterns show relationships between numbers.
• ex. 2,5,8,___
• What is the pattern?

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Patterns
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Proportions

• When 1 variable is increased, the other
  variable must be increased by the same amount.
  Ratios work just like fractions!
• 15 210 315

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Proportions

• To make a juice recipe, mix a ratio of 2
  parts juice to 5 parts water. Which shows the
  correct mixture?
• 2 qt. juice to 5 gal. water
• 4 qt. Juice to 10 qt. water
• 6 oz. juice to 9 oz. water
• 1 qt. juice to 3 qt. water

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Proportions the Big Z

• 2/8 x/24 1/8 7/x
• Ralph types 45 words per minute. How many
  minutes will it take to type 3 pages if there are
  300 words on each page? 20,75,90 or100?
• Answer 20 minutes

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Proportions

• If 2 eggs are needed to make 5 waffles, how
  many waffles can Julio make from 2 dozen eggs?
• a. 20 b. 30 c. 50 d. 60
• Answer d

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One Step Equations

• When a letter is shown beside a number with no
  sign, it means to multiply!
• 4a 4 x a 4a
• (Student Video)

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One Step Equations

• if 4a 36, a ?
  (9)
• if n 19 28, n ?
  (47)
• if z 10 12, z ?
  (2)
• if x(squared)124, x ? (5)
• if 36/m 6, m ? (9)

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Now

• Algebra
• Lets Practice

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CRCT Review

• Data Analysis
• and
• Probability

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Probability

• the chance than an event will happen.
  Experimental probability approaches theoretical
  probability as the number of events is large.
• 0 cannot occur
• ½ 50-50 chance
• 1 certain

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What is the probability of pulling a red card?
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Theoretical Probability

• (Student Video)
• Student Video

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What is the probability of spinning a color other
than purple?
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Thursday

• Math CRCT
• Lets Just Do It in 2007!