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# Chapter 7 Week 7 Notes Sped 482

Clarion

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This 5 page Class Notes was uploaded by Morrissette32 on Friday March 18, 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 8 views. For similar materials see Direct instruction in Mathematics in Special Education at Clarion University of Pennsylvania.

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Date Created: 03/18/16

Chapter 7 Addition Vocabulary 1. Addition - (a) the process of combining smaller sets to form a larger set and then determining the total number of the larger set, or (b) the union of two disjoint sets. Disjoint sets have no members in common. 2. Addend- the numbers of the smaller set in an addition statement. (Example: in 4+3=7, the addends are 4 and 3) 3. Missing Addend- a problem type in which students solve for an addend. (Example: 6+ ___ = 9) 4. Sum- the number of the new set formed by combining the smaller sets. (Example: in 4+3=7, the sum is 7) 5. Commutative Law of Addition - the sum is the same, regardless of the order in which the numbers are added. (Example: 4+3=7 and 3+4=7) 6. Associative Law of Addition – any method of grouping may be used to obtain the sum of several addends. {Example: (1+2)+3=6 or 1+(2+3)=6] 7. Identity Element for Addition – when any whole number and zero are added, the result is a whole number. 8. Renaming - converting a sum of 10 or more to the number of tens groups and the number of ones; e.g. 17 is renamed as 10 and 7. In 19+28, the sum in the ones column (17) is renamed as 10 and 7 so that the 10 can be written in the tens column. This process had previously been called carrying. When used in addition renaming is quite similar to expanded notation. In subtraction, a tens number is usually renamed as one 10 and the number of remaining tens, e.g. 70 is renamed 10 and 60. In a problem such as 74-16, the 70 is renamed so that a 10 and the 4 can be combined, allowing a student to subtract 6 from 14. Six tens remain in the tens column. 9. Regrouping – the same process as renaming, except it is carried out with objects or counters rather than numerals, just as 8+4 can be renamed 10+2, so llllllllllll can be regrouped as llllllllll ll. NOTES Two stages of teaching addition. 1. Beginning Stage – Students are taught to solve simple addition problems with concrete or semi-concrete objects representing each addend. Introduced in Kindergarten or First Grade, 2. Second Stage – Addresses teaching students to work problems that require them to rely on mental computation rather tstn on representations of concrete objects. Introduced in the later part of 1 grade and continues into intermediate grades. Three Basic Types of Addition Problems 1. First type of Column Problem introduced involves adding multi-digit numbers in which the sum in each column is less than 10; thus, renaming is not required. (36+13) 2. the next major type of problem involves adding two or more multi-digit numbers in which the sum of one or more columns is greater than 10 and requires renaming. (36+15) 3. The third major type of problem involves addition of three or more multi-digit numbers. Complex Addition Facts – problems in which a student must mentally add a single- digit number to a two-digit number. Introduced early to mid second grade. Having Students draw lines has several advantages: • Drawing lines graphically demonstrates equality. • Teachers can more readily monitor student performance with groups of students. • The lines provide a written record of student performance, which makes diagnosis of skill deficits easier. Beginning Stage Teaches Two Strategies 1. Addition the Slow Way 2. Missing Addend Strategy Missing Addend Strategy in Beginning Stage The strategy is based on the equality rule. Equality Rule – you must end with the same number on both sides of the equal sign. To solve the simple form of missing addend problems, the students first find the side of the equal sign that tells how many they end with. The teacher then points out that the sides are not equal until the students end with the same number on both sides. The teacher directs the students to draw lines on the side of the box so that the sides will be equal and to fill in the missing numeral. Pre-skills needed prior to introducing addition the slow way 1. Identifying and writing the numeral 0-10 and the symbols +, , - , and = . 2. Equality rule 3. Reading an equation. 4. Drawing the appropriate number of lines to represent a numeral. 5. Counting the lines in two groups 6. Writing the numeral that represents a set of objects. Student Makes an Error in a structured board presentation. The teacher should repeat the question, model the correct answer, then repeat the question again, and ask the students to respond, Addition the Fast Way Introduced when students are able to work a mixture of addition and missing addend problems with 80-90% accuracy. Taught as a transitional step between the strategy in which students draw lines for each member of sets represented by each addend and later exercises in which students memorize addition facts. Pre-skill integrated in the addition the fast way strategy – rote counting beginning at a number other than 1. Four Basic Steps in Diagnosing and Remedying Errors 1. The teacher analyzes worksheet errors and hypothesizes about the cause of each error. 2. The teacher interviews the student to determine the cause of the error if it is not obvious. 3. The teacher provides re-teaching through board and/or worksheet presentations. 4. The teacher tests the student on a set of problems similar to the ones on which the original errors were made. Two Categories Worksheet Errors Fall 1. Component Skill Error- skills errors indicating a deficit on one or more of the component skills that makes up the strategy. 2.Strategy Error- indicating problems with the application of the strategy (strategy errors often are the result of a student’s forgetting certain steps in a procedure. Pre-skill needed to be taught before addition problems with renaming are introduced – adding three single-digit numbers When students are asked to identify the next two numbers to be added, students often reply with the second and third numbers instead of the sum of the first two numbers and the third number. 2 3 + 4 They say 3+4 instead of 5+4 ------- Why and How renaming is done Explained by pointing out that a tens number may not appear in the ones column and therefore must be carried to the tens column. “We have a problem. Twelve equals 1 ten and 2 ones. We can’t have a ten in the ones column. So we put the 1 ten at the top of the tens column” Structured – Board and worksheet, the teacher should use only examples of the type being introduced. Less Structured – The teacher should give the students a cumulative review worksheet. Two Types of Complex Addition Facts 1. a single-digit number is added to a teen number and the total does not exceed 19. 2. a single digit number is added to a teen number and the sum totals 20 or more. First Type of Complex Addition The students learn to transform a complex fact into two simple facts. Ex. 16+3 into 10+6+3, add 6+3 then 10+9. Three Most Common Component Errors Made in Addition Problems 1. Renaming 2. The wrong number involves not renaming the ten at all Ex. 48 + 36 74 3. Failure to attend to the sign. Ex. 342 304 + 131 - 201 211 505

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