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1 4 STUDENT S TEACHER S STUDENT S EDITION SAMPLE EDITION Fourth FourthGrade GradeMathematics Reading STA STA AR AR Practice and Reinforce Diagnose and Remediate Evaluate and Pass Your Source For STAAR Tutorial Materials 2012 TripleNterprises Publishing This program is protected by copyright law and international treaties. Unauthorized reproduction of any portion of it may result in severe and criminal penalties and will be prosecuted to the maximum extent possible.

2 Texas STAAR Exam Lesson 16, 4.5(B) Reporting Category 2: Computations and Algebraic Relationships (4.5) Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to (B) represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Readiness Standard Today we are going to learn what an input/output table is and how to follow the rules of the table. Put lesson slide 1 on white board / overhead. Read lesson slide 1 Now that we have an understanding of how patterns of paired numbers work, let's try to fill in an input-output table. Put lesson slide 2 on white board / overhead. Read lesson slide 2 Answers for example 1: Answers for example 2: Do STAAR practice 4.5(B) and logic/manipulative 4.5(B) 2014 TripleNterprises Educational Publishing 1

3 Lesson 16 LESSON SLIDE 1 Input-Output Tables An input-output table contains pairs of numbers that are related to one another based on a rule. Look at the description of the table below: The input is the position in the sequence Input value Output value The output is the value of the position The output value is based on the rule associated with the table. In this case, the output value is 5 times In the table above, the rule for the table is input value 5 As we can see, the output value in each position is five times the value in the input column. For example, input position 3 has an output value of 15, because: 3 5 = 15. What would the value be for the 10 th position in the input value? What about an x value of 15? 10 5 = = 75 Sometimes we are given the output value and have to determine the input value. For example, what would the input value be for the output value of 60? In this case we do the opposite operation, division, to find the answer: 60 5 = 12 So for the output value of 60, the input value is TripleNterprises Educational Publishing 2

4 Lesson 16 LESSON SLIDE 2 Input-Output Tables Example 1 Using the pattern y = x + 4, fill in the blanks in the table below: Solution Strategy: Our last table was a multiplicative table, meaning each input value was multiplied by some factor to get the output value. This table is an additive table, which means each input value is added to a given number to get the output value. In this case, each input value needs to be added to 4 in order to get the output value. As a class, work together to fill in the missing table values. Example 2 Using the pattern y = x 11, fill in the blanks in the table below: Solution Strategy: When determining the y value in the chart, we multiply the x value by 11. When determining the x value in the chart, we divide the y value by 11. As a class, fill in the chart TripleNterprises Educational Publishing 3

5 STAAR Practice 4.5(B) 1 Each bag of marbles at the toy store comes with a certain number of marbles and a certain number of stickers. This relationship is represented by the equation: Total items (T) = marbles (m) + 3 Based on this rule, fill in the missing number in the table below: Marbles (m) Total Items ? 2 The grocery store sells juice boxes in cartons of 12. This is represented by the equation: Number of cartons (C) = Juice Boxes (j) x 12 Based on this rule, fill in the missing numbers in the table below: Cartons (C) Juice boxes (j) Which expression below correctly states the relationship of the ordered pairs of numbers in this table: A x + 9 = y B x 9 = y C x = y D x = y X y TripleNterprises Educational Publishing 4