Number and Algebraic Patterns

Lesson notes

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Number and Algebraic Patterns (1.1)

Content standard

1.1.1.CS.2 - Demonstrate knowledge and understanding of numbers in relation to Surds, Indices and Logarithms. 1.1.1.LO.1 Solve problems involving properties of binary operations. 1.1.1.LO.2 Model and solve real life problems on sets. 1.1.1.LO.3 Expand binomials with positive integral indices and simplify coefficients of the terms. 1.1.1.LO.4 Perform basic operations on surds as well as solve simple indicial and logarithmic equations.

Indicator

1.1.1.LI.2 - Rationalise surds with binomial denominators. Collaborative Learning: Learners will be working in convenient groups (e.g., ability, mixed-ability, mixed gender, or pairs etc.) to solve problems involving rationalisation.

Suggested placement

Semester 1, Week 5 (Week 5 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

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• exemplars - p.56: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
• exemplars - p.57: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 56

Exemplars (from the NaCCA curriculum)

Talk for Learning Approaches: Learners will brainstorm using participatory activities such as think-pair-share/square and debate to discuss when and how to rationalise surds.
Experiential Learning: Learners will work with others in groups and pairs to create surds problems involving basic operations, properties and types of surds.
Activity 1: Use Talk for Learning Approaches (building on what others say, managing Talk for Learning, structuring Talk for Learning), collaborative learning approaches and experiential learning approaches to investigate conjugates and rationalisation of surds.
- In groups, discuss the rationalisation of surds to discover that rationalising surds involves changing the surd denominator to a rational number. That is: & & √' = × √' √' √' &√' = ' Example: ! ! √. = × √. √. √. √. = .
- Learners in groups discuss the rationalisation of surds with binomial denominators. Learners discover that to rationalise this type of surds, multiply the fraction by the conjugate of the denominator. That is: 𝑎 𝑎 1 − √𝑏 = × 1 + √𝑏 1 + √𝑏 1 − √𝑏
! Example: Rationalise "*√.
! "$√. Solution = "*√. × "$√.
"$√. ,
. ) Example: Simplify "$√) − "*√)
2 Expected Solution: 7 − √2
Activity 2: Learners in groups create and solve problems in surds.
Example:
Express y15 i√27 − √) j in the form 𝑝w𝑞 where 𝑝 and 𝑞 ∈ 𝑅 √"
Expected Solution: 7√5 7√5
Teaching and Learning Resources:
- Textbooks
- Curriculum
- Cardboards
- Reading resource
- Colour pens
- Notebook
- Technological tools
Assessment (1.1.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.
1 Simplify × !$)√" 1 !*)√" !*.√. Express in "$ √. the form 𝑚 + 𝑛√5; 𝑚, 𝑛 ∈ ℤ