© 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

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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)


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)


1 kg = 1,000 g 1 hg = 100 g 1 dag = 10 g 1 g = 10 dg 100 cg 1,000 mg

1 gram

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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°

÷ ¾ ˃ ˂ +


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

÷ ¾ ˃ ˂ +


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.


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.

© Rachel Brown 2015 - Lawrence's...

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