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

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

3. 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.

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

5. The Assessment Cycle Review Plan For Improvement Analyze
Collect Information
Implement

6. 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:

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

8. 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:

9. Describe The Border Papers
Border Paper B
Border Paper A
Border Paper A

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

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

12. 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.

13. Pattern Puzzles
Grade 2 And Up

14. 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, We mean a pattern continues forever.

15. Break Time

16. 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.

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

18. 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, or 12, 10, 8,
Geometric sequences, where each number is a fixed multiple
e.g. 2, 4, 8, or 100, 20,
Other sequences where the growth is not constant
e.g. 3, 4, 6, 9, 13 (increase by 1 more each time)

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

20. Types Pattern Rules
5, 8, 11,
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

21. 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= 6=

22. “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= 6=

23. 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
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= 6=
How many blocks are needed for the 10th rocket?

24. “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
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= 6=
Explicit Rule
n + 3
What is the explicit pattern rule for finding any stage of rocket?

25. 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= 6=

26. 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= 6=
Term 1
Term 2
Term 3

27. 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.

28. 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= 6=
Term 1
Term 2
Term 3

29. 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.

30. Discovering Patterns and Relationships

31. Representations of the Same Pattern

32. Using Graphing to Make Predictions

33. 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

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

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

36. 8 + 4 = + 5 Next Session: Expressions and Equality
8 + 4 =
What goes in the box?

37. 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.