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MTH 208 Week 1 Notes

by: Sofia Berkey

MTH 208 Week 1 Notes MATH 208

Marketplace > Elon University > Mathematic > MATH 208 > MTH 208 Week 1 Notes
Sofia Berkey
Elon University
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About this Document

These notes cover 1.1, 1.2, and 1.3
Number And Operations
Class Notes




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This 4 page Class Notes was uploaded by Sofia Berkey on Thursday September 1, 2016. The Class Notes belongs to MATH 208 at Elon University taught by Rosenberg in Fall 2016. Since its upload, it has received 3 views. For similar materials see Number And Operations in Mathematic at Elon University.


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Date Created: 09/01/16
8/30/16 1.1-The Counting Numbers Objectives: 1. Counting numbers 2. Cardinality 3. One to one correspondence 4. Base ten system 5. Place value 6. Expanded form 7. Drawing with base ten blocks 8. Whole Numbers Counting Numbers 1, 2, 3, 4… =infinite Cardinality ● How many objects do you have? ● Ex: ○ What is the cardinality? __4__ One to one correspondence ● Skill needed to be able to determine cardinality ● Assigning a value from one set to exactly one value in another set ● A set is a collection of objects Set 1: 1 2 3 4 Set 2: 1→ 2→ 3→ 4→ -Assigning a number to a circle -That’s how counting occurs Base 10 Number System/Place value ● 10 symbols: 0,1,2,3,4,5,6,7,8,9 ● Using these 10 symbols, also known as digits we can construct any number we want ● Place value: the position of the digit determines its value ○ Ex: 24 vs. 42 ○ Same digits, different quantities ● 3258.24 ○ 3→ thousands ○ 2→ hundreds ○ 5→ tens ○ 8→ ones ○ 2→ tenths place ○ 4→ hundredths place * All these represent powers of 10 2^3 2=base 3=exponent Expanded Form ● Reinforces concepts of place value and base 10 ○ Ex: 3284 ○ Write in expanded form ○ 3(1000) + 2 (100) + 8(10) + 4(1) ○ 3000 + 200 + 80 + 4 Drawing with base 10 blocks > draw pictures of numbers using these three shapes >block, rod, and unit, respectively >10 units=1 block, 100 units=1 block, 10 units=1 rod Number line vs. Number Path ● Number path: helps with counting skills ● Learning to count on a literal path → “chutes and ladders” ● Allows us to upgrade to a number line ○ Allows to see positioning of numbers ○ Allows to see relationship of number to number ○ As you move to the right the numbers get bigger or larger and as you move to the left the numbers get smaller ○ Distance from zero is visible (absolute value) 1.2-Decimals and Negative Numbers Objectives 1. Decimal representation 2. Base 10 blocks 3. Decimals on a number line 4. Integers Decimal Representation Synonyms: decimal number, decimal expansion, decimal notation ● Definition: String of digits that may or may not contain a decimal point Ex 1: express ¾ in decimal notation ➢ .75, 0.75, 0.7500…. ​ Leading zero: placed in the leftmost position of a number ● Does not change the value ​ Trailing zero: use only when a number has a decimal point present ● Go to the very end of the number with a decimal point ● Don’t delete non trailing zeros or non leading zeros Base 10 Blocks blocks=1000 rods=100 units=10 2130 Decimals on the number line 28.3 28.31 28.32 28.34 28.4 Integers …-3, -2, -1, 0, 1, 2, 3, … 2=2/1=4/2 -2+2 -3+3 -10 +10 1.3 Comparing Decimals Objectives 1. Inequality signs 2. Learn to compare with algorithm 3. Learn to compare with a number line 4. $$$ Inequality signs a. a>b → a is greater than b b. a<b → a is less than b c. a≥b → a is greater than or equal to b d. a≤b → a is less than or equal to b Comparing numbers with an algorithm ● algorithm→ step-by-step process ● 271 vs. 275 → which number is bigger? Compare on a number line ● Number farther right is larger ● Number farther left is smaller -3 -2 -1 0 1 2 3 -3 < -1 $ → concept of debt to compare negative numbers 1.4 Rounding Numbers Objectives: 1. Definition of rounding 2. Using number lines to round 3. Rounding with real world quantities Rounding- ​ to lie! ● To round a number in base-ten means to find a nearby number that has fewer (or no more) non-zero digits


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