Graphing Numerical Patterns
Students will form ordered pairs from corresponding terms of two numerical patterns and graph them on a coordinate plane.
Key Questions
- Construct ordered pairs from two related numerical patterns.
- Analyze how the relationship between two patterns is reflected on a coordinate graph.
- Differentiate between independent and dependent variables in a pattern relationship.
Common Core State Standards
About This Topic
Colonial government was a blend of English tradition and new American adaptations. Students examine early steps toward democracy, such as the Mayflower Compact, which established the idea of a social contract, and the Virginia House of Burgesses, the first representative assembly in the colonies. The topic also covers the limitations of these early systems, including who was allowed to vote and hold office, and the role of the colonial governor appointed by the King.
This topic lays the groundwork for understanding the American Revolution and the U.S. Constitution. It aligns with standards regarding the development of political institutions. Students grasp this concept faster through structured discussion and peer explanation as they compare different colonial charters and laws.
Active Learning Ideas
Simulation Game: The House of Burgesses
Students act as 'burgesses' (representatives) and must debate a law regarding tobacco prices or land use. They experience the process of representative government and the challenges of reaching a compromise.
Inquiry Circle: Who Can Vote?
In small groups, students look at the voting requirements for different colonies. They create a 'voter profile' for 1750 and discuss who was excluded from the democratic process and why.
Think-Pair-Share: The Social Contract
Pairs discuss what it means to 'agree to follow the rules' for the good of the group. They relate this to the Mayflower Compact and then to their own classroom rules.
Watch Out for These Misconceptions
Common MisconceptionColonial government was a full democracy.
What to Teach Instead
Only a small group of people (usually white, land-owning men) could vote. A collaborative investigation into voting laws helps students see the limited nature of early American democracy.
Common MisconceptionThe King had total control over every daily law.
What to Teach Instead
Because of the distance from England, colonies had a lot of 'salutary neglect' and made many of their own laws. A simulation of the House of Burgesses helps students see how much local power the colonists actually had.
Suggested Methodologies
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Frequently Asked Questions
What was the Virginia House of Burgesses?
What is a 'social contract'?
Who was allowed to participate in colonial government?
How can active learning help students understand colonial government?
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
unit plannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
rubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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