1. Region 8 Math Collaborative 2015 Additive and Multiplicative Relationships

2. Collecting, Generating, & Representing Data for Additive & Multiplicative Relationships  3 rd Grade: Represent real-world relationships using number pairs in a table and verbal descriptions. Readiness Standard.  4 th Grade: 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.  5 th Grade: Generate a numerical pattern when given a rule in the form y=ax or y=x + a and graph. Readiness Standard. (Using whole numbers, decimals and fractions with equal and unequal denominators)  5 th Grade: Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table. Readiness Standard.

3. Number Patterns & Sequences  Sequence-an ordered list of numbers, usually set apart by commas, such as 2, 4, 6, 8, 10, 12, …  Building a connection between input-output tables and sequences:  A doggy daycare charges $110 for two full days of daycare, $165 for three full days of daycare, $440 for eight full days of daycare, and $330 for six full days of daycare. Using the rule, d x 55, where d represents the number of full days of daycare, determine the cost of 11 full days of daycare at the doggy daycare and justify your solution with a sequence representing the relationship between the input and output values. Rule (numerical expression) d x 55 11 x 55 605 Verbal: For 11 full days of daycare at the doggy daycare, it will cost $605.

4. Input1234567891011 Process1x552X553X554X555X556X557X558X559X5510X5511X55 Output55110165220275330385440495550605 Sequence : 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, 605, … The INPUT represents the Position in sequence The OUTPUT represents the sequence value Using the data collected from problem scenarios on Day Two, add the representation of sequence to your results for each problem.

5. Summer Job  Sara makes $20 for every lawn she mows.  Use an input-output table to generate the numerical pattern.  Identify the relationship between the input and output with an expression and with a rule.  Graph the relationship on a coordinate grid.

6. Bead-Dazzled  Sally is making beaded necklaces to sell during the annual Spring Craft Show. She created a table to keep track of the number of beads she used for making her necklaces. If the pattern continues, how many beads will Sally have used to make 7 necklaces?

8. Day Two Graphical Representations Revisited  Limited to Quadrant I of the coordinate plane  Horizontal axis represents an input value, x  Vertical axis represents an output value, y  Multiplicative numerical pattern –  a pattern that occurs when a constant non-zero value is multiplied by an input value to determine the output value (y=ax)  Multiplicative patterns from the rule y = ax create a graph of points that lie in a straight line and pass through the origin (0, 0).  Multiplicative numerical patterns exist in a table when a constant non-zero value is multiplied by each input value to result in a respective output value.  Additive numerical pattern –  a pattern that occurs when a constant non-zero value is added to an input value to determine the output value ( y = x + a )  Additive patterns from the rule y = x + a create a graph of points that lie in a straight line and do not pass through the origin (0, 0).  Additive numerical patterns exist in a table when a constant non-zero value is added to each input value to result in a respective output value.

11. What type of relationship?

14. Generate a set of ordered pairs from a rule using an input-output table  Y = 2x  Y = 1.2x  Y = x + 2  Y = x + 1.25

16. Processes and Characteristics