Patterns and Algebra II Stage 3 Alice Vigors 2017

Teaching and Learning Sessions Session One: We are learning to identify a rule for number patterns Session Two: We are learning to create a number pattern based on a rule Session Three: We are learning to write rules from number patterns Indicators Addressed: complete a table of values for number patterns involving one operation (including patterns that decrease) and describe the pattern in words, eg  describe the pattern in a variety of ways and record descriptions in words, eg 'It goes up by ones, starting from four' determine a rule to describe the pattern from the table, eg 'To get the value of the term, you add three to the position in the pattern' use the rule to calculate the value of the term for a large position number, eg 'What is the 55th term of the pattern?' explain why it is useful to describe the rule for a pattern by describing the connection between the 'position in the pattern' and the 'value of the term' (Communicating, Reasoning)  interpret explanations written by peers and teachers that accurately describe geometric and number patterns (Communicating)  make generalisations about numbers and number relationships, eg 'If you add a number and then subtract the same number, the result is the number you started with'  Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM Selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM Gives a valid reason for supporting one possible solution over another MA3-3WM Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane MA3-8NA Alice Vigors 2017

Session One We are learning to identify a rule for a number pattern Alice Vigors 2017

We are learning to identify a rule for a number pattern Activating Prior Knowledge We are learning to identify a rule for a number pattern 5 10 15 20 25 30 What do you see, observe or notice about this pattern? What rule might this pattern be following? Is there more than one? Explain. If we apply this rule, what would the next number in the sequence be? How do you know?  Alice Vigors 2017

Building Explanations & Reasoning with Evidence We are learning to identify a rule for a number pattern Independent Investigation: What do you see, observe or notice about each of these patterns? What operation is being used to generate the next term, e.g. the rule may be add 4 each time or multiply by two each time. Pattern Number Pattern Rule One 0 2 4 6 8 10 12 14 16 18 20 Two 0 3 6 9 12 15 18 21 24 27 30 Three 18 16 14 12 10 8 6 4 2 0 Four 2 4 8 16 32 64 Five 24 12 6 3 Six 6 11 16 21 26 31 36 41 Seven 32 29 26 23 20 17 14 11 8 Eight 2 6 18 54 162 Nine 270 90 30 10 Ten 52 47 42 37 32 27 22 Alice Vigors 2017

Reflecting on Learning We are learning to identify a rule for a number pattern Exit Ticket: Choose two of these sentence starters to answer about today’s lesson. Today I learnt… This connected to what I already knew because… This extended what I knew by… One thing that still puzzles me is… Alice Vigors 2017

Session Two We are learning to create a number pattern based on a rule. Alice Vigors 2017

Activating Prior Knowledge We are learning to create a number pattern based on a rule. Add 10 If this is the rule, what might the pattern look like? Pairs: create a pattern that follows this rule.  Alice Vigors 2017

Building Explanations & Reasoning with Evidence Assessment MA3-8NA We are learning to identify a rule for a number pattern Independent Investigation: Create 3 different number patterns based on each one of these rules. Rule One: Add 4 Rule Two: Subtract 2 Rule Three: Multiply by 2 Rule Four: Divide by 2 Alice Vigors 2017

Building Explanations & Reasoning with Evidence Assessment MA3-8NA We are learning to identify a rule for a number pattern Independent Investigation: Work out what rule is being used in each pattern below and create your own pattern using this rule. Rule Five? 3 11 19 27 35 43 51 59 Rule Six? 6 24 96 384 1536 Rule Seven? 6400 1600 400 100 25 Rule Eight? 59 53 47 41 35 29 23 A pattern was made using the following rule: Subtract 3. If the last number in the pattern was 14: What were the previous 3 numbers? What would the next 2 numbers be? Alice Vigors 2017

Reflecting on Learning We are learning to identify a rule for a number pattern Exit Ticket: Choose two of these sentence starters to answer about today’s lesson. Today I learnt… This connected to what I already knew because… This extended what I knew by… One thing that still puzzles me is… Alice Vigors 2017

Session Three We are learning to write rules from number patterns Alice Vigors 2017

Activating Prior Knowledge We are learning to write rules from number patterns Tickets to the movies cost $12 for adults. What do you see, observe or notice about this pattern? How could you describe this rule? Explain the pattern: How much would it cost for 5 adults or 10 adults? Number of Adults 1 2 3 Cost per ticket $12 $24 $36  Alice Vigors 2017

Building Explanations & Reasoning with Evidence Assessment MA3-8NA We are learning to write rules from number patterns Independent Investigation: Jenny earned $4 each hour she worked. Hours Worked 1 2 3 4 5 Money Earned $4 $8 $12 $16 $20 What do you see, observe or notice about this pattern? How could you describe the rule being used? How would you record the rule? Explain the pattern: How much money would Jenny earn after 6 hours? How much money would Jenny earn after 10 hours? Alice Vigors 2017

Building Explanations & Reasoning with Evidence Assessment MA3-8NA We are learning to write rules from number patterns Independent Investigation: Michael was five years older than Sam. Sam’s Age 1 2 3 4 5 Michael’s Age 6 7 8 9 10 What do you see, observe or notice about this pattern? How could you describe the rule being used? How would you record the rule? Explain the pattern: How old will Michael be when Sam is 6? How old will Michael be when Sam is 10? Alice Vigors 2017

Building Explanations & Reasoning with Evidence Assessment MA3-8NA We are learning to write rules from number patterns Independent Investigation: Michelle always had 3 times more lollies than Tyler. Tyler’s Lollies 1 2 3 4 5 Michelle’s Lollies 6 9 12 15 What do you see, observe or notice about this pattern? How could you describe the rule being used? How would you record the rule? Explain the pattern: How many lollies would Michelle have if Tyler had 6? How many lollies would Michelle have if Tyler had 10? Create your own pattern and have a partner determine the rule Alice Vigors 2017

Reflecting on Learning We are learning to write rules from number patterns Exit Ticket: Choose two of these sentence starters to answer about today’s lesson. Today I learnt… This connected to what I already knew because… This extended what I knew by… One thing that still puzzles me is… Alice Vigors 2017