STILLWATER CROSSING · THE COURSE NOTES · BRIDGE MATH 5/6

Week 1 · Place Value and the Four Operations

This week

Lessons 1, 2, 3, 4, & 5

Papers

Class as usual

Method

No calculators, ever · show every step

Note-Taking Tip: Notice how these notes are organized with a heading for each topic and key vocabulary. When you take notes, always start with a clear heading!

Instructional notes

Each digit in a number has both a place and a value . Digits are separated into groups of 3 by commas to form periods . h t b h t m h t t h t o u e i u e i u e h u e n n n l n n l n n o n n e d b l d m l d t u d s s r i i r i i r h s r e l o e l o e o a e d l n d l n d u n d b i s m i s t s d s i o i o h a s l n l n o n l s l s u d i i s s o o a n n n s s d s

2 3 4 , 5 6 7 , 8 9 0 , 1 2 3

billions millions thousands units

We can write numbers in 3 ways. • Standard Form: 34,657 • Word Form: thirty-four thousand, six hundred fifty-seven • Expanded Form: 30,000 + 4,000 + 600 + 50 + 7

BILLIONS			MILLIONS			THOUSANDS			UNITS
hundred billions	ten billions	billions	hundred millions	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

Example

Write the following number in standard and expanded form, then identify the place and value of the 7. 4 billion, 705 million, 210

Standard Form: ________________4,705,000,210____________________

Place: ____hundred millions___ Value: __700,000,000____

Practice

Identify the place and the value of the 6 in the number. 340,506,201,978 Place: __millions _______ Value: __6,000,000 _ ___ Write 840,305,769,210 in word form and expanded form. Word Form: __eight hundred forty billion, three hundred five million, seven hundred sixty-nine thousand, two hundred ten____________________________________________ Expanded Form: 800,000,000,000 + 40,000,000,000 +

Instructional notes

Addition is combining numbers called addends together. The answer to an addition problem is the sum . In addition, the order of will not the addends change the answer. This is called the commutative property.

Subtraction is the process of taking one number, the subtrahend , away from another, called the minuend . The answer is the difference. The order of the numbers matters. Helpful Hint: Turn addition and subtraction problems vertically to solve.

Example

Solve. Label each number as the addend, minuend, subtrahend, sum or difference. Addend_ _Addend__ __Sum__ 345 Minuend 135 + 59 = 194 -214 Subtrahend_ 131 _Difference__

Practice

Solve and label each number as the addend (A), minuend (M), subtrahend (Sub), sum or difference (D). A A Sum A A Sum 467 + 258 = 725 1,234 + 892 = 2,126

M Sub D M Sub D 789 - 567 = 222 512 - 311 = 201

Instructional notes

Finding the Unknown Addend Addition and subtraction are __inverse_____ or opposite operations. We can use subtraction to find an unknown ___addend_ ___.

Example

Use subtraction to solve for the unknown addend. Then check your answers.

Practice

Use subtraction to solve for the unknown addend. Then check your answers.

X + 26 = 35 S + 59 = 108

X=9 S = 49

Instructional notes

Multiplication & Division

Multiplication is the process of combining equal groups of numbers. Like addition the commutative property tells us that __order_ does not matter. The numbers being multiplied are called factors. The answer is the product . In a long multiplication problem, the numbers in the middle are called partial products .

Division is breaking a larger number into smaller equal parts. Leftovers are called the remainder . The number being divided is the dividend____ ____. The number doing the dividing is the divisor_________. The answer is the quotient .

Division Steps Hint: ÷ X - c ↓r

Example

Solve. Label the factors, divisor, dividend, partial products, product and quotient.

246 factor 90r5 quotient X35 _factor__ divisor 6 545 dividend 1230 _partial product +7380 _partial product 8,610 _product_____

Practice

Solve. Label the factors, divisor, dividend, partial products, product and quotient.

73 quotient 947 quotient

158 × 26 = 4,108 703 × 58 = 40,774

158 factor 703 factor X 26 factor X 58 factor 948 partial product 5624 partial product + 3160 partial product + 35150 partial product 4,108 product 40,774 product

Instructional notes

Roman Numerals

Symbol I V X L C D M Value 1 5 10 50 100 500 1,000

• Add repeated symbols: XX = 10 + 10 = 20 • A symbol may not be repeated more than 3 times • V, L, and D are never repeated or subtracted • Lesser value after a greater value means we __add __ • Lesser value before a greater value means we subtract

Example

Write each Roman or Arabic numeral. 1,100 = MC CMLII = __952___

Practice

Write each Roman or Arabic numeral.

13 = __XIII___ CXX = _ 120_ 1,000 = M 699 = _DCXCIX___ CDLXXXIX = 489 50 = _L____

Homework this week

Work-text	Lesson 1	Lesson 2	Lesson 3	Lesson 4	Lesson 5
Speed drill	2	3	5

Terms on the record

Term	Meaning
commas	are separated into groups of 3 by commas to form periods .
periods	are separated into groups of 3 by commas to form periods .
addition	Addition is combining numbers called addends together.
addends	Addition is combining numbers called addends together.
sum	The answer to an addition problem is the sum . In addition, the order of
subtraction	Subtraction is the process of taking one number, the
subtrahend	subtrahend , away from another, called the minuend .
minuend	subtrahend , away from another, called the minuend .

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