patterns in mathematics unit 3 notes.notebook Unit 3: Patterns in Mathematics

Transcription

1 Unit 3: Patterns in Mathematics Entrance Activity (10 minutes!) 1

2 Topic 1: Understanding the relationships within a tables of values to solve problems. Lesson 1: Creating Representations of Relationships in a Table of Values With a partner, create a model using toothpicks or a drawing on your whiteboard to represent the information provided in this table. Number of Squares Number of Toothpicks What patterns do you see in each column? Start at 1, increases by 1 each time Start at 1, increases by 3 each time 2

3 Toothpick Model: 3

4 Number of Squares Number of Toothpicks What are the next two covered values in this extended table? Can you spot the error in this table? How do you know it is an error? 4

5 Exit Activity Sam has a weekly paper route. He gets paid $30 a week. The following table of values shows his earnings over a 5 week period. Identify the error in this table and explain how you know it is an error. Weeks Earnings ($)

6 Lesson 2: Describing the pattern within each column of a table of values. The table below shows changes in the height of a plant over time: Week Plant Height (cm) How can we describe patterns in each column of this table of values? 6

7 Weeks start at 1 and increase by 1 each time. Height starts at 6 and increases by 4 each time. 7

8 Let's practice describing patterns in a table of values: 8

9 Now... try this! Exit activity Describe the pattern in each column of this table of values describing amount of snowfall cm per hour: Hour Snowfall (cm)

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15 Exit Activity Choose two of the following questions. Create a table of values to show the value of x. 15

16 Rewriting Phrases as Algebraic Expressions a Subtract 7 from c b 30 divided by d c The product of 5 and e d The sum of 8 and f 16

17 Rewriting Phrases as Algebraic Expressions Exit Card (a) Subtract 18 from a number (b) Add 4 to double a number (c) Three times a number divided by 2 17

18 Algebra Word Problems 18

19 Think Pair Share Judy pays $10 for her cell phone. Each time she uses the Internet, it costs $2. This relationship can be represented by the pattern rule: 2n + 10 n represents the number of times she may use the Internet, which could be many possibilities Use this pattern rule to complete the table shown here. Number of Internet Visits (n) Cost per Month

20 Exit Card: Find the Missing Value (Paintball) - Worksheet 10 minutes 20

21 Input/Output Tables Click here for an introductory video! 21

22 Input / Output Machine #1 What rule could have been used to get an output of 12 from an input of 4? 22

23 Input / Output Machine #2 What rule could have been used to get an output of 12 from an input of 4? 23

24 Exit Card: Input/Output Tables 1. Use the What s my Rule? box to model the input and output for each row in the tables above. 2. Come up with a pattern rule expression that can be used to describe the relationship between all the input/output combinations in the table. Remember: The pattern rule expression has to apply to all the input/output combinations in the table, not just the first one! 24

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