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Problem Solving Strategies

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What is the circumference of a tire with a diameter of 20 inches? Answer: ... 2 figures are similar when they are the same shape but not the same size. ... – PowerPoint PPT presentation

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Title: Problem Solving Strategies


1
ProblemSolvingStrategies

2
Estimate
  • Fractions
  • Estimate to 0, ½ , 1
  • Decimals Estimate
  • - Estimate

3
Draw a picture
  • prime factor tree
  • fractions
  • area, perimeter, volume, surface area

4
Make a Chart
  • factors
  • multiples
  • equivalent fractions
  • ratios

5
Guess and Check
  • Algebra
  • n 15 35
  • a. 20 b. 50 c. 45 d. 10

6
Look Back
  • Does the answer make sense?
  • Is it reasonable?

7
CRCT Review
  • Numbers and Operations Unit

8
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

9
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

10
Prime Factorization
  • Factor Tree (Student Video)
  • 100
  • 25 x 4
  • 5x 5 2 x 2 5x5x2x2

11
Fractions
  • Estimate.. Estimate.. Estimate..
  • Is the fraction closer to 0 ½ or 1?
  • Draw a picture if you have a doubt

12
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

13
Comparing Fractions
  • Fractions can be compared using cross
    multiplication.
  • Which fraction is larger 5/9 or 4/5? Of course,
    4/5!

14
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)

15
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!

16
Decimals Add / Subtract
  • This one is easy!
  • Just line up the decimals!
  • (Student Video)

17
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)

18
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)

19
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)

20
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)

21
Percents to Fractions
  • Remember, percent means per
    hundred
  • What is 33 as a fraction?
  • 33/100
  • Its that easy!
  • (Student Video)

22
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

23
CRCT Review
  • Measurement Unit

24
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

25
Metric Length
  • Units of Measure
  • Millimeter (mm)
  • Centimeter (cm)
  • Meter (m) about 1 yard
  • Kilometer (km) about ½ mile
  • (Student Video)

26
Customary Volume
  • Customary Units
  • 1gal 4 qt
  • 1gal 8 pints
  • 1gal 16 cups
  • Metric Units

27
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)

28
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)

29
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)

30
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

31
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!

32
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.

33
CRCT Review
  • Geometry

34
Congruent Figures
  • 2 figures are congruent when they are the same
    shape and the same size.

2in. X 4in.
2in. X 4in.
35
Similar Figures
  • 2 figures are similar when they are the same
    shape but not the same size.

36
These triangles are similar. What is the length
of the base of triangle 2?
  • 1 2
  • 6 10 5 3
  • 4 ??
  • Answer 2

37
GeometryTextbook Sites
  • Chapter 7 Proportional Relationships7-4
    Similar Figures7-6  Scale Drawings and Maps
  •   Chapter 8 Geometric Relationships8-9 
    Congruence8-11 Line Symmetry

38
Line Symmetry
  • A figure has line symmetry if a single line or
    fold splits the shape into congruent halves.

39
  a regular pentagon has 5 internal angles and 5
lines of symmetry. 
40
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

41
Geometric Nets
  • A flat pattern that can be folded to make a
    solid figure.
  • Cylinder Square Pyramid Cube

42
CRCT Review
  • Algebra

43
Patterns
  • Fill in the missing numbers in this table if y6x
  • Holt Work Text

44
Ratios
  • A ratio compares 2 numbers. Ratios can be
    written in the following ways
  • 1 to 4 14 ¼
  • Holt Work Text

45
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.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

46
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.

47
Proportions Z Method
  • 2/8 x/24 1/8 7/xHolt 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

48
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?
  • Answer 30

49
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. y1/9x b.
    y2/9x c. y1/3x d. y2/3x
  • Graphing Calculator

50
Evaluating Algebraic Equations
  • When a letter is shown beside a number with no
    sign, it means to multiply!
  • 4a 4 x a 4a
  • (Student Video)

51
Solving One Step Equations
  • if 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)

52
Evaluating Algebraic Equations
  • What is the value of this expression when d
    3?
  • d2 14 a. 20 b.
    23 c. 25 d. 47Answer b

53
CRCT Review
  • Data Analysis
  • and
  • Probability

54
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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