Lecture 11 Powerpoint
Homework Debrief
Conduct a review of homework completed by students. Discuss common errors and misconceptions that arose during the assignments. Encourage students to share their thoughts on which problems they found most challenging and why. Provide clarifications on problems that were difficult for the group.
Subtraction Strategy Review
Engage students in a thorough analysis of various subtraction strategies employed during lessons. Discuss the most difficult subtraction strategies students encountered and explore reasons for these challenges. Additionally, share which strategies were found easiest, fostering discussions on why some methods work better than others.
Addition and Subtraction Story Situation Types
Introduce various story situation types related to addition and subtraction. Detail each situation type with examples, focusing on how they apply in real-world contexts. Have students create their own problems based on these types, such as Result Unknown, Total Unknown, and Change Unknown situations.
Addition and Subtraction Learning Trajectory
Analyze how different story situation types align with the levels in the learning trajectory of addition and subtraction. Discuss the progression students typically make as they deepen their understanding of these concepts and how this translates into their mathematical growth.
WI State Standards for Adding and Subtracting with Larger Numbers
Review the Wisconsin State Standards that guide instruction in addition and subtraction, particularly with larger numbers. Discuss expectations for different grade levels and how those educational standards prepare students for more complex mathematical operations as they advance through grades.
Addition and Subtraction with Larger Numbers
Explore strategies and techniques for performing addition and subtraction calculations with larger numbers. Include discussions on barrier numbers and how to decompose numbers into manageable parts to simplify operations. Provide practice problems that target these skills.
Equality and the Equal Sign
Examine the concept of equality and the significance of the equal sign in mathematical equations. Address common misconceptions that children may have about the equal sign merely representing the outcome of a calculation, emphasizing its role in indicating balance in equations.
Learning Intentions
We are learning to:
Understand Problem Story Situations.
Explore WI State Standards for addition and subtraction with larger numbers to ensure alignment with educational expectations.
Improve skills in addition and subtraction with larger numbers to enhance computational fluency and confidence.
Examine students’ understanding of equality and its significance in mathematical development, preparing them for future algebraic concepts.
Subtraction Strategy Check-in
Conduct a check-in discussion focused on subtraction strategies. Reflect on the most challenging subtraction strategies and allow students to express their thoughts articulately, ensuring they grasp both the strategies and the reasoning behind their effectiveness.
Problem Situations
Addition and Subtraction Problem Situations
Result Unknown:
Example: "Eight frogs sat on the grass. Three frogs jumped out of the pond and joined them. How many frogs are on the grass now?"
Equation: 8 + 3 = ?
Total Unknown:
Example: "The vase held three red flowers and eight yellow flowers. How many flowers were together in the vase?"
Equation: 3 + 8 = ?
Change Unknown:
Example: "Eight frogs were sitting on the grass. Some other frogs jumped over, and then there were eleven frogs. How many frogs jumped over?"
Equation: 8 + ? = 11
Comparison Problems:
Variations include inquiries such as "How many more?" and "How many fewer?" focusing on comparing quantities based on given figures.
Problem Type Sorting
Facilitate an activity where students sort provided story problems based on the situation types:
Join
Separate
Part-Part-Whole
Comparison
Encourage class discussion about the sorting choices and reasoning.
Addition and Subtraction Learning Trajectory
Analyze how different story situation types map to levels in the learning trajectory, illustrating the growth in understanding addition and subtraction. Review how educators can recognize and support each level of understanding in students.
Standards for Addition and Subtraction with Larger Numbers
1st Grade Standards (Operations and Algebraic Thinking)
Extend counting sequences and understand place value for improved number sense.
Perform addition and subtraction within 100, reinforcing strategies through practice.
Use properties of operations based on place value effectively.
2nd Grade Standards (Operations and Algebraic Thinking)
Solve word problems involving addition and subtraction, making connections to real-life scenarios.
Utilize mental strategies for calculations within 20, fostering quick recall and flexibility.
3rd Grade Standards (Operations and Algebraic Thinking)
Represent and solve problems using properties of multiplication and division, connecting these concepts with addition and subtraction.
Solve two-step word problems, enhancing critical thinking and problem-solving skills.
Strategies for Addition and Subtraction
Breaking Numbers by Place Value:
Example: Calculating 116 + 118 by adding hundreds, tens, and units separately, promoting a clear understanding of place value.
Making Friendly Numbers:
Adjusting numbers to make calculations easier through rounding, illustrated by the example: 116 + 118 adjusted to 116 + 120 - 2, facilitating simpler mental math.
Chunking:
Keeping numbers whole while adding components by place value, aiding in clarity during computations.
Understanding Equality
Importance of Equality and the Equal Sign
Review the critical role of the equal sign as a symbol that signifies a relationship of equivalence in mathematics. Highlight how children often misunderstand it as merely indicating the result of a calculation, which can lead to misconceptions in later math understanding.
Levels of Understanding
Rigid Operational Understanding:
Students treat equals as merely asking to "find the answer" without recognizing the balance.
Flexible Operational Understanding:
Students can solve equations but may not comprehend the equivalency on both sides of the equation.
Basic Relational Understanding:
Students recognize the equality relationship and can express generalizations about equality in different contexts.
Comparative Relational Understanding:
Students fully understand the equal sign, applying logical shortcuts to determine truth without computation.
Closing Reflection
Facilitate a closing reflection session to discuss strategies that promote the development of computational fluency. Review shifting expectations across grades related to performing addition and subtraction, particularly with larger numbers, ensuring preparedness for future educational challenges.