© Rachel Brown 2015 - Lawrence's...
Transcript of © Rachel Brown 2015 - Lawrence's...
© Rachel Brown 2015
© Rachel Brown 2015
Place Value:Hundred Ten Hundred TenMillions Millions Millions Thousands Thousands Thousands Hundreds Tens Ones
100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
3 5 2, 8 0 4, 1 9 7
Standard Form: 352,804,197
Word Form: Three hundred fifty two million, eight hundred four thousand, one hundred ninety seven
Expanded form: 300,000,000 + 50,000,000 + 2,000,000 + 800,000 + 4,000 + 100 + 90 + 7
Value:
the value of the 8 is 800,000 because it is in the 100,000’s place The value increases by x10 as you move to the left and ÷10 as you move to the right
Comparing: less than (<), greater than (>), or equal to (=)
Begin in the highest place value and compare each digit until you find a place value where the digits
are different, the higher digit indicates the higher overall number
Ex. 186, 295 ___186, 925 the place values are equal until the 100’s place, the 100’s place is higher
in the second number so choose the < symbol, 186, 295 < 186, 925
Rounding:
1. Read the directions to find which place value to round to
2. Underline this digit
3. Look to the right of the underlined digit
4. If the number to the right is 0-4, the underlined numbers stays the same
5. If the number to the right is 5-9, the underlined number is rounded up one
6. All numbers to the left of the underlined digit stay the same
7. All numbers to the right of the underlined digit become zero
Ex. Round 386,973 to the nearest ten thousands place
386,973 underline the 8 because it is in the ten thousands place
9 the 8 rounds up to a 9 because the number to the right (6) is 5-9
390,000 keep the numbers to the left the same, change the numbers to the right of the under
lined number to zeros
Ex. Round 1,495,376 to the nearest millions place
1,495,376 underline the 1 because it is in the millions place
1 the 1 stays the same because the number to the right (4) is 0-4
1,000,000 change the numbers to the right of the underlined number to zeros
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© Rachel Brown 2015
1 1 1 1
Operations:
Multi-Digit Addition and Subtraction:
235,897 16,495,378 16,495,378156,348
392,245 11,958,564
Multi-Digit Multiplication:
Area Model Method 1,645x93=
Algebraic Notation Method 1,645x93= Shortcut Method 1,645x93=
1,645 93= (1,000+600+40+5) (90+3)=
1,000x90= 90,000
600x90= 54,000
40x90= 3,600
5x90= 450
1,000x3= 3,000
600x3= 1,800
40x3= 120
5x3= 15
+
If the sum of a place
value is greater than 9,
regroup one ten to the
le�
4,536,814-
If the top number is
smaller, regroup 10
from the place value
to the le�
4,536,814-
14 4 135 814
90x1,000
90,000
90x600=
54,000
90x40=
3,600
90x5=
450
3x1,000=
3,000
3x600=
1,800
3x40=
120
3x5=
15
93=
90
3
+
+ + +1,645= 1,000 600 40 5
90,00054,0003,6003,0001,800
45012015+
152,985
152,985+
Don’t forget to add
the subtotals in each
box
Step 1: 1,645
x 93
4,935
Step 2: 1,645
x 93
4,935
148,050
152,985+
1 1 1
5 4 4
Don’t forget to
add the zero
when mul� plying
by a ten
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© Rachel Brown 2015
Division:
Area Model Method 2,968 ÷ 7= 8,541 ÷ 4=
Digit By Digit Method Expanded Notation Method
2,968 ÷ 7= 8,541 ÷ 4= 2,968 ÷ 7= 8,541 ÷ 4=
-2 800
168
140
28
0
7
4
2,968
-
-
28
20400
=424
2,9682,800
168
16814028
282807
400 20 4+ + = 424
Operations:
- - -8,5418,000
541
541400141
14112021
2120
14
2,000 100 30+ + = 2,135R 1
+ 5
- - - -
7
424
2,9682 8
16
14
28
0
-
-
-
28
2,135 R1
-12
4 8,5418
0 5
4
14
21
20
1
-
-
-
4 8,5418,000
541
400
141
120
21
20
1
-
-
-
2,000100
305
=2,135 R1
-
Interpreting the Remainder:
1. Report it: Report the whole number and the remainder as your full answer
-As the remainder Ex. 2,135 r1
-As a fraction Ex. 2,135 ¼
2. Ignore It: Drop the remainder and report only the whole number
Ex. 2,135
3. Round Up: The remainder causes you to round the whole number up one
Ex. 2,136
4. It is the Answer: Give only the remainder as your answer
Ex. 1 left over
In each problem
with a remainder,
consider what to
do with it
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© Rachel Brown 2015
Algebra:
Expressions: Made up of terms with operations in between. Some expressions include variables– letters that rep-
resent an unknown number
Ex. 3y + 5 (there are two terms: 3y and 5, and one operation: + )
Given y = 4, the expression can be evaluated by plugging in 4 for y. 3 x 4 + 5 = 17
Equations: Made up of terms on either side of an equal sign. Equations are often written to solve word problems.
The inverse operation can sometimes be used to solve the equation for the variable.
4 + p = 10 25 - n = 10 7 x 8 = k 100 x b = 300 64 ÷ 8 = r 24 ÷ 4 = f 3y + 2y = 10
10 - 4 = p 25 -10 = n 7 x 8 = 56 300 ÷ 100 = b 64 ÷ 8 = 8 24 ÷ 4 = 6 5y = 10
P= 6 n = 15 k = 56 b = 3 r = 8 f = 6 y = 2
Factors: Terms that are multiplied to create a given product. All numbers have one and themselves as factors.
Factor Pairs: Two numbers that multiply to make a given product
- The factor pairs of 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6
Prime Number: a number with only one factor pair, one and itself
- 2 is the first prime number, and it is the only even prime
- Primes to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Composite Number: a number with more than one factor pair
- All even numbers except for 2 are composite
- Composites: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38
- To prove a number is composite, find another factor pair other than one and itself ex. 3 x 3 = 9
Multiples: A whole number is a multiple of all of its factors.
The first ten multiples of eight are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Multiples can be found by skip counting by the given number
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© Rachel Brown 2015
Data and Patterns:
Patterns: You can generate a number or shape pattern by following a given rule.
Ex. Rule: + 8 Ex. You can find the rule by looking at the data
Ex.
____________
The next term in the pattern is heart because every other term is a heart.
Data: Numbers in a data set can be shown in a line plot
Ex. 2/8, 3/8, 3/8, 3/8, 3/8, 1/2, 1/2, 5/8, 5/8, 5/8, 1, 1,1
4 12
5 13
8 16
10 18
20 28
1 3
2 6
3 9
4 12
5 15
The data is increasing, so the rule is
either add or mul� ply.
Row one: the rule is either add 2 or x 3
Row two: the rule is either add 4 or x 3
Look for the common pa� ern
So, the rule is x 3
18
28
38
48
58
68
78
1
X XXXX
XX
X
XX
XX
X
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© Rachel Brown 2015
Measurement:
Metric:
Meters – measures length using a meter stick
Liters – measures capacity using a measuring cup
or dropper
Grams – measures weight or mass using a scale
Kilometers
(km)
Hectometers
(hm)
Decameters
(dam)
Meters Decimeters
(dm)
Centimeters
(cm)
Millimeters
(mm)
10x larger 10x larger 10x larger Base unit 10x smaller 10x smaller 10x smaller
1 km = 1,000 m 1 hm = 100 m 1 dam = 10 m 1 m = 10 dm 100 cm 1,000 mm
1 decimeter
1 centimeter
1 millimeter
Kiloliters
(kL)
Hectoliters
(hL)
Decaliters
(daL)
Liters Deciliters
(dL)
Centiliters
(cL)
Milliliters
(mL)
10x larger 10x larger 10x larger Base unit 10x smaller 10x smaller 10x smaller
1 kL = 1,000 L 1 hL = 100 L 1 daL = 10 L 1 L = 10 dL 100 cL 1,000 mL
Kilograms
(kg)
Hectograms
(hg)
Decagrams
(dag)
Grams Decigrams
(dg)
Centigrams
(cg)
Milligrams
(mg)
10x larger 10x larger 10x larger Base unit 10x smaller 10x smaller 10x smaller
1 kg = 1,000 g 1 hg = 100 g 1 dag = 10 g 1 g = 10 dg 100 cg 1,000 mg
1 gram
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© Rachel Brown 2015
Measurement:
Customary:
Length – measured using a ruler or measuring tape
Capacity – measured using a measuring
cup or dropper
Mass – measures weight using a scale
Time –
12 inches = 1 foot 3 feet = 1 yard 63,360 Inches = 1 mile
36 inches = 1 yard 5,280 Feet = 1 mile 1,760 Yards = 1 mile
8 fluid ounces = 1 cup 2 cups = 1 pint 2 pints = 1 quart
4 quarts = 1 gallon 16 cups = 1 gallon 4 cups = 1 quart
16 ounces = 1 pound
2,000 pounds = 1 ton
60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day
7 days = 1 week 52 weeks = 1 year 365 days = 1 year
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© Rachel Brown 2015
Fractions:
Parts of a Fraction:
A fraction is a part of one whole divided into equal parts. The top number
is the numerator and shows how many parts you have. The bottom num-
ber is the denominator and shows how many equal parts the whole is
divided into.
Unit Fractions:
Unit fractions have a numerator of one. A whole can be made by adding
unit fractions the number of times of the denominator.
Operations with Fractions:
Addition Subtraction Multiplication by a
2
4
=24
=+ +33
13
13
13
13
13
+ =23
57
17
- =47
3 x17
= 37
Equivalent Fractions: Represent the same amount of the whole even though the number and size of the parts
differ. Find equivalent fractions by multiplying or dividing the same number with the top and bottom of the fraction.
Comparing Fractions: Small denominators mean larger fractions. Find common denominators or compare to
benchmark fractions like 1/4, 1/2, or 3/4 to see which is larger.
Fractions to Decimals: Decimals places . 10ths, 100ths
= 0.4 = 0.04 = 0.75 0.5 > 0.1 because >
0.58 < 0.73 because <
Whole Number
Multiply the whole number by the numerator,
keep the denominator the same
1 x 32 x 3
=36
5 ÷ 510 ÷ 5
=12
1 13 5
˃4
1034
1004 x 10 = 40
10 x 10 = 10034
10040
100˃
410
75100
4100
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© Rachel Brown 2015
Geometry:
Figures:
Point A Line BC Ray EF Line Segment GH Angle IJK
Acute Angle Right Angle Obtuse Angle Perpendicular Parallel
<90° =90° 90°< angle <180° Lines Lines
Acute Right Obtuse Isosceles Equilateral Scalene
Triangle Triangle Triangle Triangle Triangle Triangle(all angles <90°) (one right angle) (one obtuse angle) (two equivalent sides) (all sides equivalent) (no equivalent sides)
Quadrilateral Trapezoid Parallelogram Rhombus Rectangle(4 sides, 4 angles) (4 sides, 4 angles) (4 sides, 4 angles) (4 sides, 4 angles) (4 sides, 4 right angles)
(1 pair II sides) (2 pairs II sides) (4 = sides, 2 pairs II sides) (2 pairs II sides)
Protractor: Square Pentagon(4 sides, 4 right angles) (5 sides, 5 angles)
(2 pairs II sides, 4 = sides)
Hexagon Octagon(6 sides, 6 angles) (8 sides, 8 angles)
Center the protractor at the vertex of the angle
Line the bottom ray up with 0° on the protractor
Find where the second ray intersects the protractor
B C E F G HI
JK
The middle
le� er is
the vertex
A
40°
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© Rachel Brown 2015
Geometry:
Angle Measure is Additive:
Two adjacent (next to each other, sharing one ray) angles can be added together to form a larger angle measure
Angle BCG = angle ACB + angle ACG
If angle ACB = 45°
angle ACG = 45°
then ACB + ACG = 90°
Therefore BCG = 90°
To find x°
Solve the equation x + 30° = 90°
x = 90°- 30°
x = 60°
Perimeter: The distance around the outside of a figure Area: The number of square units inside a figure
Formula for the perimeter of a rectangle- Formula for the area of a rectangle-
P=(L+W) x 2 or P=S + S + S + S A = L x W A= 5 in. x 8 in.
A= 40 square inches
Symmetry: A line of symmetry divides a figure into two equal parts. One part is the mirror image of the other so that
the figure can be folded across the line into matching parts.
A
B C
D
E
F
G
45°
45°X°
30°
90°
Length (L)
Wid
th(W
)Side (S)
S
S
S
Length (L)
Wid
th(W
)
5 inches
8in
ches
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© Rachel Brown 2015
Obtuse Triangle Isosceles Triangle Acute Triangle
Quadrilateral Trapezoid Rhombus
Parallelogram Rectangle Square
Pentagon Hexagon Octagon
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Prac� ce drawing and labeling each figure, then write the name of the figure in the blank below the grid.
© Rachel Brown 2015
Point Line Ray
Line Segment Perpendicular Lines Intersecting Lines
Parallel Lines Right Angle Acute Angle
Obtuse Angle Right Triangle Equilateral Triangle
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Prac� ce drawing and labeling each figure, then write the name of the figure in the blank below the grid.