Grade 2: "Patterning: Extending and Predicting"
(From: Mathology)
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(From: Mathology)
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This Mathology lesson plan can be accessed in both English and French by logging into your Mathology.ca/Mathologie.ca account and searching for “Patterning Activity Card 2: Repeating Patterns: Extending and Predicting”
Content
Content
Big Idea:
Big Idea:
Extending and predicting elements in repeating patterns
Expectations:
Expectations:
C1. Patterns and Relationships: identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real‐life contexts
• Patterns: C1.3 determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns represented with shapes and numbers
C4. Mathematical Modelling: apply the process of mathematical modelling to:
• represent, analyse, make predictions, and provide insight into real‐life situations
Learning Goals
Learning Goals
We want students to understand...
We want students to understand...
Regularity and repetition form patterns that can be generalized and predicted mathematically.
Success Criteria
Success Criteria
I can...
I can...
Extend a pattern by repeating its core over and over
Use the core of a pattern to help me make predictions
Materials
Materials
Counters (for Before)
String, pipe cleaners, or heavy thread
At least 3–5 colours and different sizes of beads
Coloured pencils
Master 4: Bracelet Cores
Master 5: My Bracelet Plan
Master 6: Assessment
(All Line Masters can be accessed by logging into your Mathology / Mathologie account)
Vocabulary
Vocabulary
Repeating patterns
Attribute
Pattern core
Predict
Element
Extend
circle
teacher background
teacher background
Students may benefit from prior experience with:
identifying and extending repeating patterns
representing repeating patterns with letters
Key concepts
Patterns can be extended because they are repetitive by nature.
Pattern rules are generalizations about a pattern, and they can be described in words.
Patterns can be extended in multiple directions, such as up, down, right, and left.
To make a near prediction about a pattern is to state or show what a pattern will look like just beyond the given representation of that pattern. The prediction can be verified by extending the pattern.
To make a far prediction about a pattern is to state or show what a pattern will look like well beyond the given representation of that pattern. Often calculations are needed to make an informed prediction or to verify a prediction.
To identify missing elements of patterns is to complete a representation for a given pattern by filling in the missing parts.
Note
In order to extend, predict, or determine missing elements, students need to generalize patterns, using pattern rules.
Rules should be used to verify predictions and to critically analyse extensions and solutions for missing elements.
Pedagogy
Pedagogy
Minds On
Minds On
Show students a repeating pattern with counters (e.g., red, blue, green, red, blue, green, red, blue, green).
Ask: “What is the core of this pattern? How can we represent it using letters?”
Arrange the counters in the same order to form a circle. Ask, “What is the core of this pattern?”
Help students see that, depending on the starting point and the direction, several cores are possible.
Action!
Action!
Give each pair a core (Master 4a), two plans (Master 5a), two lengths of string, and an assortment of beads. Have coloured pencils available.
You are each going to make a repeating bracelet using the core I gave you. Plan your bracelet. Colour circles to represent beads.
Put beads on string to model the core. Trade strings with your partner.
Predict the 15th bead. Talk about how you know.
Repeat the core six more times to finish each other’s bracelet. Tie the ends.
Check the bracelets against the plans. Were your predictions correct? Are the bracelets correct?
Teacher Moves
Probing Questions:
How did you use the core to plan your bracelet?
How would you describe your bracelet to a friend?
How did you predict the 15th bead? Were you correct?
How did you extend the pattern to finish the bracelet?
LOOK-FORS:
LOOK-FORS:
Are students able to use the core to accurately plan their bracelets?
Are students able to extend their partner’s pattern?
Are students able to accurately predict the colour of the 15th bead?
Are students able to check that the bracelets are correct, or does the circular pattern confuse them?
Consolidation Of Learning
Consolidation Of Learning
Bring students back together to share and discuss how they extended the patterns and made their predictions (e.g., guessing, extending the pattern mentally, using skip-counting, repeating the core). Display a bracelet. Have volunteers identify as many different cores in the bracelet as they can. Help students see that when a repeating pattern forms a circle, there are many different ways of looking at the pattern.
Highlight for Students
We can extend a pattern by repeating its core over and over.
We can use the core of a pattern to help us make predictions.
Supports for student learning
Supports for student learning
Accommodations: Use a core from Master 4b and the plan with fewer beads (Master 5b). Partners repeat the core four more times.
Extension: Use a core from Master 4c and the plan with more beads (Master 5c).
Combined Grades Extension: Students create a bracelet involving two attributes (e.g., size and colour).
Assessment
Assessment
All assessments, in the moment feedback/prompts, and independent tasks can be accessed by logging into your Mathology/Mathologie account.
SEL Self-Assessments (English) and Teacher Rubric
Extension
Extension
Log in to your Mathology.ca / Mathologie.ca account to access Intervention and Extension activities, Professional Learning Videos and Assessment tools.
Technology
Technology
If you require support logging into your Mathology/Mathologie account, please contact Kerry Stack or Erica Doucet.
Use the Counters Tool (or Mathies Colour Tiles) in front of the class to explore circular repeating patterns. Drag counters to the workspace to create a circular pattern with one attribute changing. To change the colour of a counter, click the Paint Brush button, choose a colour, then click on a counter. Have students identify as many different cores in the pattern as they can.
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