Chapter 9 Week 9 Notes
Chapter 9 Week 9 Notes Sped 482
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SPED 245 - C02
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This 3 page Class Notes was uploaded by Morrissette32 on Sunday April 3, 2016. The Class Notes belongs to Sped 482 at Clarion University of Pennsylvania taught by Mrs. Mohney in Spring 2016. Since its upload, it has received 10 views. For similar materials see Direct instruction in Mathematics in Special Education at Clarion University of Pennsylvania.
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Date Created: 04/03/16
Chapter 9 Multiplication Vocabulary Multiplication - the process of combining a specific number of sets, each including an equal number of elements into a single larger set. Multiplicand - the number of sets in the multiplication process. Factors - the multiplicand and the multiplier in a multiplication process. Product – the answer in a multiplication problem, the number designating elements in the combined set of multiplication problem; i.e. the sum of all the equal sets. Commutative Property - The commutative property for multiplication states that changing the order of two numbers in a multiplication equation does not change the answer Associative Property - the associative property for multiplication states that if a, b, and c are whole numbers, then (a x b) x c = a x (b x c). Identity Element - the identity element for multiplication is 1. Any number times 1 equals that number. Distributive Property - the distributive property of multiplication over addition says that if a, b, and c are whole numbers, then a x (b x c) = (a x b) + (a x c). Notes During the beginning stage of multiplication, students are taught to solve a problem such as 3 times 4 by holding up 4 fingers and skip counting them by 3. During the second stage of multiplication students no longer use skip counting on their fingers. They do only mental computations. Two Basic Types of Advanced Multiplication Problems 1. Single-digit factor and a multi-digit factor. 2. Multiplying two-digit numbers. Single-digit multiplication is introduced when students have mastered three count by series (twos, fives, nines) and can read and write all numerals between 1 and 99. Usually around mid-second grade. Steps taking during the beginning stage when solving problems like 5x=20 Students must determine the number of times they count by 5 to get to 20. Students extend fingers every time they skip count; they extend one finger when they say 5, a second when they say 10 and so on till they reach 20 (4 extended fingers). Two algorithms for solving problems with a multi-digit factor 1. long form or low stress algorithm 2. short form Advantages of Long form It does not alternate between multiplication and addition. It seldom requires renaming. It clearly shows the distributive property of multiplication. Disadvantage Problems involving multi-digit factors many numerals must be written as partial products. Advantages of Short form Relative efficiency in solving problems with multi-digit factors Wide spread usage Disadvantage Understanding the process when he alternates between addition and multiplication. With the inclusion of complex addition facts, Three pre-skills needed to work multiplication problems involving a single digit and multi-digit factor. 1. multiplication facts 2. place value skills, including expanded notation and placing a comma in the proper position when writing an answer in the thousands. 3. Complex addition facts in which a single-digit number is added to a two-digit number. Initial multiplication problems Problems should be limited so that they include only basic facts the teacher is sure students have memorized as students learn more basic facts these should be integrated into multiplication problems. Advanced Addition Facts are complex addition facts which involve adding a single- digit number to a two-digit number mentally. Utilized during short form multiplication algorithm when the student adds the carried units to the product of a column. Place Value Grid - purpose to initially prompt the students to place numerals from the product in the proper column. Horizontal Multi-digit Multiplication Problems are introduced after students can correctly work vertically aligned problems. The teacher presents a strategy in which the students rewrite the problem vertically, writing one-digit factor under the multi- digit factor. Two rules that govern example selection for multiplication 1. basic facts included in problems should be those that the student has already mastered. 2. Less structured, supervised practice and independent worksheets should include a mixture of problems. ½ problems of the most currently introduced, ½ problems of previously introduced (10% of that is addition). New pre-skill required to work multiplication problems with two-digit factors Column addition with renaming.