SE2 Math FIT Project Sign in and take a name tag. Help yourself to refreshments! We’ll begin at 12:45!

The Plan Sharing of Experience with ONAP Consolidation of Data Data Driven Decisions BREAK Patterns and Relationships Homework for Next Session

Small Group Sharing Part A Activities (optional) Part B Something that went well… Something that surprised me was…. Lessons learned….. Now I know…. Always have to do this whenever a new group forms Write a sentence to describe each prompt. Need cue cards for this.

Consolidation of Data What does your school data tell you about your students?

The Assessment Cycle Review Plan For Improvement Analyze Collect Information Implement

Assessment For Learning What are the needs of my students? What are my plans to address those needs? How will I know my students have learned what I set out to teach them? How can I use my current resources? What other supports do I need? what we’re interested in is the conversation around:

Patterns and Relationships Expressions and Equality The Patterning and Algebra Strand Algebraic Thinking Patterns and Relationships Expressions and Equality

Growing and Shrinking Patterns Continuum of Learning Grade 3 Grade 4 Grade 5 Repeating patterns Identify, describe, create (two attributes) Extend (number) Extend, describe, create (number) Make predictions (geometric, number) Extend, create (reflections) Extend, create (translations) Growing and Shrinking Patterns Identify, describe (+- x) Create (+., -) extend, describe, create (number) Create (+., -, x) extend, describe, create (geometric, numeric Make predictions (geometric, numeric) Relationships Geometric to number, number line, bar graph Action, transformation, operation, attribute etc. Term to term number Make a table of values Build a model (table of values, term, term number) what we’re interested in is the conversation around:

Describe The Border Papers Border Paper B Border Paper A Border Paper A

What exactly is a pattern? The main reason we focus upon pattern is that patterns enable us to predict, expect and plan!

More Complex Repeating Patterns Attributes Colour: red, green, yellow, red (ABCA) Size: big, big, small (AAB) Shape: star, triangle (AB)

Two Attribute Patterns Colour and Shape are DEPENDENT attributes. When you change to a square you change colours automatically, The colour and shape change automatically, In pattern two, the colour of the object is not dependent on the shape of the object. Colour and Shape are INDEPENDENT attributes.

Pattern Puzzles Grade 2 And Up

Repeating Pattern Notation At some point, students need to learn the notation (…) to indicate a pattern continues. When we write 2, 4, 6, 8 we are talking about a four-element set of numbers, but when we write 2, 4, 6, 8 . . . We mean a pattern continues forever.

Break Time

Growth Patterns Patterns are the basis of how our number system is structured. For many children mathematics seems to be learning the rules and steps to follow in order to get the right answer. They do not look for the underlying order and logic of the mathematics. If children do not use looking for patterns as a basic approach to understanding learning mathematics becomes much more difficult. Patterns make it possible to predict what is supposed to happen in mathematics, rather than seeing the teacher’s answer book as the only source of verification Young children develop their algebraic thinking by studying patterns through activities that involve physical motion, designs made from concrete materials and conjectures. In Growth patterns the terms in the pattern don’t repeat. Instead they continue on in an orderly way that makes it possible to predict what comes next.

What Comes Next? 1, 2, 3 . . . 1, 2, 3, 4, 5, 6, 7 1, 2, 3, 5, 8, 13, 21 1, 2, 3, 1, 2, 3, 1, 2, 3

Growing and Shrinking Patterns Growing means you keep adding, (multiplying), Shrinking means you keep subtracting, (dividing). Arithmetic sequences, where each number is a fixed amount greater or less than the preceding one e.g. 3, 5, 7, 9 . . . or 12, 10, 8, 6 . . . Geometric sequences, where each number is a fixed multiple e.g. 2, 4, 8, 16 . . . or 100, 20, 4 . . . Other sequences where the growth is not constant e.g. 3, 4, 6, 9, 13 (increase by 1 more each time)

Number Patterns Place value Basic Facts Addition and subtraction Multiplication and Division

Types Pattern Rules 5, 8, 11, 14 . . . When stating a recursive pattern rule it is important to state the beginning term and then state the change. For the sequence, 5, 8, 11, 14,… Start at 5 and then add 3 to each successive term. The explicit pattern rule or general rule tells us the value of any number of the pattern. For the sequence, 5, 8, 11, 14,... (3n+2) OR (2 + 3n) . Term Value 1 2 3 4 5 8 11 14

Make the next 2 rockets in this pattern. Stage 1 Stage 2 Stage 3 Make the next 2 rockets in this pattern. What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3

“Begin with 4 and add one each time” Rockets Stage 1 Stage 2 Stage 3 Stage # 1 2 3 Total Blocks 4 5 6 What is a rule for the total number of blocks? Recursive Rule “Begin with 4 and add one each time” What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3

Rockets Stage 1 Stage 2 Stage 3 4 5 6 1 2 3 3 + 1 3 + 2 3 + 3 Total Blocks 4 5 6 Stage # 1 2 3 Constant + Variable 3 + 1 3 + 2 3 + 3 Recursive Rule “Begin with 4 and add one each time” What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3 How many blocks are needed for the 10th rocket?

“Begin with 4 and add one each time” Rockets Stage 1 Stage 2 Stage 3 Total Blocks 4 5 6 Stage # 1 2 3 Constant + Variable 3 + 1 3 + 2 3 + 3 Recursive Rule “Begin with 4 and add one each time” What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3 Explicit Rule n + 3 What is the explicit pattern rule for finding any stage of rocket?

Constants and Variables Use colour tiles to build the next two stages What is the recursive pattern rule? Stage 1 Stage 2 Stage 3 What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3

Constants and Variables Use different colours to show the composition of the pattern Ask Yourself: -What stays constant? -What changes? What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3 Term 1 Term 2 Term 3

Explicit Pattern Rules The explicit pattern rule or general rule tells us the value of any number of the pattern. To find the generalized pattern rule you must see the relationship between the term number and the value. So for the pattern 3, 4, 5, 6, 7, …. Value Term Constant + Variable 1 2 3 4 2 yellows + 1 red 2 yellows + 2 reds 2 yellows + 3 reds 2 yellows + 4 reds So a rule for the final pattern is 2 plus the term number which can be written as 2 + n or n+2.

Constants and Variables Use different colours to show the composition of the pattern Ask Yourself: -What stays constant? -What changes? What is constant ? 3 What changes +1 break down the initial value in terms of the change 4= 1+3 = n+3 belongs to the stage constant to what is added. Break initial value in terms of the change 4= 1+3 5= 1+1 +3 6= 1+1+1+3 Term 1 Term 2 Term 3

Explicit Pattern Rules The explicit pattern rule or general rule tells us the value of any number of the pattern. To find the generalized pattern rule you must see the relationship between the term number and the value. So for the pattern 3, 4, 5, 6, 7, …. 1 yellows + 2 red Term Value 1 2 3 4 Constant + Variable 1 yellows + 3 reds 1 yellows + 4 reds 1 yellows + 5 reds So a rule for the final pattern is 1 plus one MORE than the term number which can be written as 1 + (n+1) or n + 2.

Discovering Patterns and Relationships

Representations of the Same Pattern

Using Graphing to Make Predictions

Table of values Linear equation if the constant difference is the same. A rule for the final pattern is two times the term number which can be written as 2n

Average score was 58% at the board and provincial level.

Consolidating Concepts Growing Patterns Rule: Start at 3 and add 3. 3, 6, 9, 12, 15 . . . 3 x Skip Counting

8 + 4 = + 5 Next Session: Expressions and Equality 8 + 4 = + 5 What goes in the box?

Homework Continue the conversations with your grade team or division. 2. Try the equality question with your students (bring samples, if possible to the next session) 3. Visit the Math Lab folder on Tel for patterning activities across the grades. Bring any interesting samples to the next session to share.