Alice Vigors 2017 PATTERNS AND ALGEBRA Stage 3

TEACHING AND LEARNING SESSIONS 1. Can we continue and create number patterns and describe how they are created? 2. Can we create simple geometric patterns? 3. Can we identify the rule to describe the pattern and calculate the corresponding value for a larger number? Ali ce V 2017 igors ü Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA 3 -1 WM ü Selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA 3 -2 WM ü Gives a valid reason for supporting one possible solution over another MA 33 WM ü Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane MA 38 NA

SESSION ONE Alice Vigors 2017 Can we continue and create number patterns and describe how they are created?

CAN WE CONTINUE AND CREATE NUMBER PATTERNS AND DESCRIBE HOW THEY ARE CREATED? 1 1. 6 3 10 What do you see, observe or notice? 2. What does this make you think, in terms of how the pattern is created? How it is repeated? 3. What questions or puzzles do you still have about these numbers? Alice Vigors 2017

CAN WE CONTINUE AND CREATE NUMBER PATTERNS AND DESCRIBE HOW THEY ARE CREATED? Independent Investigation: q. Can you use this number pattern to determine the missing terms? q. What strategies can we use to determine a term in a number pattern? Can you show your thinking in a number of ways? Group One 2 Group Two Group Three 7 5¼ 6 17 25 ½ 10 27 45 ¾ Alice Vigors 2017 5 th, 8 th and 10 th terms 14 37 65 ¼ 5 th, 10 th, 15 th and 25 th terms 5 th, 10 th, 31 st, 64 th and 112 th terms

CAN WE CONTINUE AND CREATE NUMBER PATTERNS AND DESCRIBE HOW THEY ARE CREATED? Independent Investigation: q. Can you create your own number pattern and describe how it was created? q. Turn over ONE number card from a deck of playing cards. q. Use this number to create a number pattern. q. Describe the pattern that has been created Alice Vigors 2017

SESSION TWO Alice Vigors 2017 Can we create simple geometric patterns?

CAN WE CREATE SIMPLE GEOMETRIC PATTERNS? 1. What do you see, observe or notice? 2. What does this make you think, in terms of how the pattern is created? How it is repeated? 3. What questions or puzzles do you still have about these numbers? Pairs: Determine the next term in this pattern. Alice Vigors 2017

CAN WE CREATE SIMPLE GEOMETRIC PATTERNS? How can we use this visual representation to create a table of values to show the pattern? Term in the pattern (T) Blocks needed (B) Alice Vigors 2017

CAN WE CREATE SIMPLE GEOMETRIC PATTERNS? Independent Investigation: Group One Group Two Group Three § Create this geometric pattern using blocks: § Create this geometric pattern using counters: § § Create a table of values about your geometric pattern. Create this geometric pattern using matchsticks: § Repeat your pattern 3 more times. § Challenge: What would the 10 th term be? § Challenge: What would the 15 th and 32 nd terms be? § Challenge: What would the 10 th and 15 th terms be? Alice Vigors 2017

SESSION THREE Alice Vigors 2017 Can we identify the rule to describe the pattern and calculate the corresponding value for a larger number?

CAN WE IDENTIFY THE RULE TO DESCRIBE THE PATTERN AND CALCULATE THE CORRESPONDING VALUE FOR A LARGER NUMBER? 1. What do you notice about how the pattern changes from the 1 st term to the 2 nd term? 2. What do you notice about how the pattern is arranged? 3. What do you think is happening here? 4. What questions or puzzles do you have about this pattern? 5. How might we work out what the 3 rd term would look like? Alice Vigors 2017

CAN WE CONTINUE AND CREATE NUMBER PATTERNS AND DESCRIBE HOW THEY ARE CREATED? Independent Investigation: q. Draw the visual representation of your pattern. q. Use a table of values to describe the pattern you have created. What is the rule for this pattern? q. Repeat the pattern two more times using this rule. q. What would the 5 th, 10 th, 25 th, 50 th and 100 th terms be for this pattern? Term in the pattern (T) Matchsticks needed (M) Alice Vigors 2017 Assessment – MA 3 -8 NA q. Use matchsticks/ popsicle sticks to create a geometric pattern with two terms.