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Reading Dimensions Using a Standard Ruler Todd Andrus TEE 4400 Landon Ashcroft Dr. Gary Stewardson Zac Hirschi Fall 2011 Brad Parker Jared Thomas Joseph Woodard Objectives • Terminal Objective – read dimensions using a standard ruler • Performance Objective – given a diagram of a standard ruler with extension and dimension lines, read dimensions to a 16th of an inch, using proper or mixed fractions in their lowest terms, with a minimum score of 90% correct. Objectives • Enabling Objectives – define the following terms: whole numbers, proper fractions, improper fractions, mixed fractions, numerator, and denominator – identify extension lines, dimension lines, arrowheads, and dimensions – explain how to identify units on a standard ruler – reduce fractions to their lowest terms – change improper fractions to proper fractions Fractions 3 4 Fractions Numerator 3 4 Fractions Numerator 3 4 Denominator Types of Numbers & Fractions Whole Numbers: Types of Numbers & Fractions Whole Numbers: 0 1 2 3 4 5… Types of Numbers & Fractions Whole Numbers: 0 1 2 3 4 5… Mixed Fractions: Types of Numbers & Fractions Whole Numbers: 0 1 2 3 4 5… 3 1 1 Mixed Fractions: 3 1 9 ... 16 8 4 Types of Fractions Proper Fractions: Types of Fractions 5 1 9 Proper Fractions: ... 8 4 16 Types of Fractions 5 1 9 Proper Fractions: ... 8 4 16 Improper Fractions: Types of Fractions 5 1 9 Proper Fractions: ... 8 4 16 18 9 6 Improper Fractions: ... 16 8 4 Reducing Fractions 8 ? 16 Reducing Fractions 8 ? What is the largest 16 whole number that will divide into both the numerator and denominator? Reducing Fractions 8 1 8 8 16 2 16 8 Reducing Fractions 8 1 16 2 Reducing Fractions If you are unable to identify the largest whole number that will divide into both the numerator and denominator, dividing both numbers by 2 will reduce the fraction using multiple steps. 8 ? 16 This only works with fractions that have an even denominator. Reducing Fractions 8 ? 16 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 8 4 16 8 Reducing Fractions 8 4 ? 16 8 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 8 4 2 16 8 4 Reducing Fractions 8 4 2 ? 16 8 4 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 8 4 2 1 16 8 4 2 Reducing Fractions 8 4 2 1 16 8 4 2 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 8 1 16 2 Reducing Fractions 12 ? 16 Reducing Fractions 12 ? 16 What is the largest whole number that will divide into both the numerator and denominator? Reducing Fractions 12 312 4 16 4 16 4 Reducing Fractions 12 3 16 4 Reducing Fractions If you are unable to identify the largest whole number that will divide into both the numerator and denominator, dividing both numbers by 2 will reduce the fraction using multiple steps. 12 ? 16 Remember, this only works with fractions that have an even denominator. Reducing Fractions 12 ? 16 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 12 6 16 8 Reducing Fractions 12 6 ? 16 8 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 12 6 3 16 8 4 Reducing Fractions 12 6 3 ? 16 8 4 Can both numerator and denominator be divided evenly by 2? Reducing Fractions 12 3 16 4 Practice Fraction Lowest Terms 10 ? 16 Practice Fraction Lowest Terms 10 5 16 8 Practice Fraction Lowest Terms 36 ? 64 Practice Fraction Lowest Terms 36 9 64 16 Reducing Fractions Improper Fractions Mixed Fractions 11 ? 4 Reducing Fractions Improper Fractions Mixed Fractions 11 ? 4 How many times will 4 go into 11, and what is the remainder? Reducing Fractions Improper Fractions Mixed Fractions 11 2 4 4 goes into 11 two times. Reducing Fractions Improper Fractions Mixed Fractions 11 3 3 is the remainder and goes in the numerator 2 4 Reducing Fractions Improper Fractions Mixed Fractions 11 3 2 4 4 4 stays in the denominator Reducing Fractions Improper Fractions Mixed Fractions 19 ? 16 Reducing Fractions Improper Fractions Mixed Fractions 19 ? 16 How many times will 16 go into 19, and what is the remainder? Reducing Fractions Improper Fractions Mixed Fractions 19 1 16 16 goes into 19 one time. Reducing Fractions Improper Fractions Mixed Fractions 19 3 3 is the remainder and goes in the numerator 1 16 Reducing Fractions Improper Fractions Mixed Fractions 19 3 1 16 16 16 stays in the denominator Practice Improper Fractions Mixed Fractions 9 ? 2 Practice Improper Fractions Mixed Fractions 9 1 4 2 2 Practice Improper Fractions Mixed Fractions 11 ? 4 Practice Improper Fractions Mixed Fractions 11 3 2 4 4 Lines on Drawings The physical shape of an object is shown • object lines • hidden lines • center lines Measurements are not specified with these lines. Lines on Drawings Measurements are specified on the drawing by utilizing: • extension lines • dimension lines • arrowheads • dimensions Extension Lines Extension lines are fine, solid, straight lines that align with the features on the object to be specified. Dimension Lines and Arrowheads Dimension lines are fine, solid, straight lines with arrowheads. They point to extension lines, and indicate the feature on the object that is being measured. Arrowheads are placed at the end of dimension lines to identify the referenced extension line. Dimensions Dimensions are numerical measurements of a part; written in conjunction with dimension lines. 14 3 31 2 51 8 9 15 16 Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? a) extension line b) object line c) dimension line d) arrowhead Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? a) extension line Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? a) extension line b) object line c) dimension line d) arrowhead Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? d) arrowhead Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? a) extension line b) object line c) dimension line d) arrowhead Practice 14 3 31 2 51 8 9 15 16 What type of dimension element is identified with the red oval? c) dimension line Reading a ruler Rulers are typically divided by 8ths, 16ths, 32nds, and 64ths of an inch. For this lesson we will use rulers with 8th and 16th increments. Reading a ruler The 8 at the beginning of the ruler indicates it is divided into 1 8 inch increments. If the ruler does not indicate units, you will have to count the number of lines in one inch to determine the increments. of the ruler. Reading a ruler On the other edge of the ruler the inches are divided into 1 16 inch increments. The 16 at the beginning of the ruler indicates the smallest units represented. Reading a ruler When reading a ruler divided in 1 inch increments, the 8 8 represents the denominator and the number of units counted represents the numerator. Reading a ruler When reading a ruler divided in 16 inch increments, the 1 16 represents the denominator and the number of units counted represents the numerator. 1 inch lines Red lines represent whole inch increments. They are the longest lines on the ruler. 1 2 inch lines Red lines represent 1 2 inch increments. They are the second longest lines. 1 4 inch lines Red lines represent 1 4 inch increments. They are slightly shorter than the 1 2 inch lines 1 8 inch lines Red lines represent 1 8 inch increments. Notice how the lines get shorter as the fractions get smaller. 1 16 inch lines Red lines represent 1 16 inch increments. Reading a ruler X What is the dimension represented by X above? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? Dimension X is on the 8 8 side of the ruler, therefore 8 is in the denominator Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 8 Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? Dimension X is past the 2 inch mark, but before the 2 8 3 inch mark Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 2 3. How many increments are past the 2 inch mark? 8 Reading a ruler X What is the dimension represented by X above? 1 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 2 3. How many increments are past the 2 inch mark? Dimension X is 1 8 increment past the whole number 2 Reading a ruler X What is the dimension represented by X above? 1 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 2 3. How many increments are past the 2 inch mark? 4. Is dimension X in lowest terms? 8 Reading a ruler X What is the dimension represented by X above? 1 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 2 3. How many increments are past the 2 inch mark? 4. Is dimension X in lowest terms? 8 Dimension X is in lowest terms. Reading a ruler X What is the dimension represented by X above? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 8 Dimension X is on the 8 side of the ruler, therefore 8 is in the denominator Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 8 Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? Dimension X is past the 1 inch mark but before the 1 8 2 inch mark Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 1 3. How many increments are past the 1 inch mark? 8 Reading a ruler X What is the dimension represented by X above? 4 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 1 3. How many increments are past the 1 inch mark? Dimension X is 4 8 increments past the whole number 1 Reading a ruler X What is the dimension represented by X above? 4 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 1 3. How many increments are past the 1 inch mark? 4. Is dimension X in lowest terms? 8 Reading a ruler X What is the dimension represented by X above? 1 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 1 3. How many increments are past the 1 inch mark? 4. Is dimension X in lowest terms? No, 4 8 reduces to 1 2 2 Reading a ruler X What is the dimension represented by X above? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 16 Dimension X is on the 16 side of the ruler, therefore 16 is in the denominator Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 16 Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? Dimension X is past the 2 2 16 inch mark, but before the 3 inch mark Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 2 inch mark? 2 16 Reading a ruler X What is the dimension represented by X above? 13 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 2 inch mark? Dimension X is 13 2 16 increments past the whole number 2 Reading a ruler X What is the dimension represented by X above? 13 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 2 inch mark? 4. Is dimension X in lowest terms? 2 16 Reading a ruler X What is the dimension represented by X above? 13 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 2 inch mark? 4. Is dimension X in lowest terms? 2 16 Dimension X is in lowest terms Reading a ruler X What is the dimension represented by X above? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 16 Dimension X is on the 16 side of the ruler, therefore 16 is in the denominator Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 16 Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? Dimension X is past the 3 3 16 inch mark, but before the 4 inch mark Reading a ruler X What is the dimension represented by X above? 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 3 inch mark? 3 16 Reading a ruler X What is the dimension represented by X above? 12 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 3 inch mark? 3 16 Dimension X is 12 increments past the whole number 2 Reading a ruler X What is the dimension represented by X above? 12 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 3 inch mark? 4. Is dimension X in lowest terms? 3 16 Reading a ruler X What is the dimension represented by X above? 3 1. What is the smallest ruler increment represented for dimension X? 2. How many whole numbers are represented in dimension X? 3. How many increments are past the 3 inch mark? 4. Is dimension X in lowest terms? 3 No, 12 16 reduces to 3 4 4 Practice A. _______ D. _______ B. _______ E. _______ C. _______ F. _______ Practice 3 8 A. _______ D. _______ B. _______ E. _______ C. _______ F. _______ Practice 3 A. 8 _______ D. _______ 414 B. _______ E. _______ C. _______ F. _______ Practice 3 8 A. _______ D. _______ 414 B. _______ E. _______ 214 C. _______ F. _______ Practice 3 8 A. _______ 1 9 16 D. _______ 414 B. _______ E. _______ 214 C. _______ F. _______ Practice 3 8 A. _______ 1 16 9 D. _______ 414 B. _______ 212 E. _______ 214 C. _______ F. _______ Practice 3 8 A. _______ 1 9 16 D. _______ 414 B. _______ 212 E. _______ 214 C. _______ 15 16 F. _______