Mental Math: Bridging and Compensation
Developing flexible strategies like bridging through ten and using near doubles.
Key Questions
- Explain how changing a number to a nearby multiple of ten can make mental addition easier.
- Analyze why different people use different mental paths to reach the same sum.
- Assess when it is faster to calculate mentally than to write it down.
NCCA Curriculum Specifications
About This Topic
Abstract Expressionism encourages 3rd Year students to break free from the 'rules' of representation and focus on the raw power of paint. This topic supports the NCCA's emphasis on personal expression and the creative process. Students learn that art doesn't always have to look like something recognizable; it can be a record of an emotion, a movement, or a reaction to music. They explore the work of artists like Jackson Pollock or the Irish artist Mary Swanzy to see how energy can be captured on canvas.
This topic is particularly liberating for students who feel restricted by a lack of 'drawing skill'. It focuses on brushwork, texture, and the physical act of painting. By experimenting with different ways of applying paint, dripping, splashing, or thick impasto, students discover their own artistic voice. This topic benefits from hands-on, student-centered approaches where the classroom becomes a laboratory for movement and sound.
Active Learning Ideas
Inquiry Circle: The Rhythm of Paint
The class works on a large communal canvas spread on the floor. As different genres of music play, students use various tools (brushes, sponges, even cardboard) to mark the paper in time with the beat, responding to the energy of the sound.
Think-Pair-Share: Decoding Abstraction
Students look at an abstract painting and write down three 'feeling' words it evokes. They share these with a partner to see if the artist's use of color and line communicated the same emotion to both of them.
Stations Rotation: Tool Experimentation
Set up stations with non-traditional painting tools: spray bottles, old credit cards for scraping, and sponges. Students spend five minutes at each station, creating a 'texture library' in their sketchbooks.
Watch Out for These Misconceptions
Common MisconceptionAbstract art is just 'messing around' and takes no skill.
What to Teach Instead
Students often think anyone can do it. By having them try to replicate a specific 'mood' using only three colors and one type of brushstroke, they realize that abstract art requires careful choices about balance and composition.
Common MisconceptionAn abstract painting is 'unfinished' if it doesn't have a subject.
What to Teach Instead
Students may look for hidden shapes. Peer discussion helps them shift their focus to the 'formal elements', color, line, and texture, as the actual subject of the work.
Suggested Methodologies
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Frequently Asked Questions
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Planning templates for Mathematical Foundations and Real World Reasoning
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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