Proportional Reasoning · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.1.2.LI.2 - Establish additive and multiplicative inverses of fractions using multi-purpose model charts.

By the end of the lesson, learners can:

Use a multi-purpose model chart to locate the additive inverse of a given fraction and explain the pattern they observe.
Use a multi-purpose model chart to locate the multiplicative inverse (reciprocal) of a given fraction and explain the pattern they observe.
State the additive inverse and multiplicative inverse of any given fraction without a chart, and verify by performing the relevant operation.
Apply additive and multiplicative inverses to solve simple equations involving fractions in everyday contexts.

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Curriculum details

Strand: Numbers for Everyday Life (Strand 1)
Sub-strand: Proportional Reasoning (1.2)
Content standard: 1.1.2.CS.1 - Demonstrate an understanding of proportional reasoning involving fractions and its operations and use it to solve real-life problems, including rounding off (decimal places and significant figures). 1.1.2.LO.1 Make connections between fractions and decimals and use them to solve daily problems.
Indicator: 1.1.2.LI.2 - Establish additive and multiplicative inverses of fractions using multi-purpose model charts.
Suggested placement: Semester 1, Week 7 (Week 7 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:

exemplars - p.47: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 47

Exemplars (from the NaCCA curriculum)

Through collaborative group activity, find the multiplicative inverse of a chosen number. Example:

Ten by ten fraction grid with row numerators 1 to 10 and column denominators 1 to 10, equivalent fractions shaded. — A ten by ten grid of fractions. Every cell holds a fraction whose numerator is its row number, 1 to 10 down the page, and whose denominator is its column number, 1 to 10 across, so the leading diagonal is 1/1, 2/2, 3/3 and so on; the equivalent fractions along two diagonals are shaded and joined by arrows.

 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 7 8 9 10 3 3 3 3 3 3 3 3 3 3 1 2 3 4 5 6 7 8 9 10 4 4 4 4 4 4 4 4 4 4 1 2 3 4 5 6 7 8 9 10 5 5 5 5 5 5 5 5 5 5 1 2 3 4 5 6 7 8 9 10 6 6 6 6 6 6 6 6 6 6 1 2 3 4 5 6 7 8 9 10 7 7 7 7 7 7 7 7 7 7 1 2 3 4 5 6 7 8 9 10 8 8 8 8 8 8 8 8 8 8 1 2 3 4 5 6 7 8 9 10 9 9 9 9 9 9 9 9 9 9 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 1 2 3 4 5 6 7 8 9 10 Figure:6
Teaching and Learning Resources:
- fractional boards
- square or grid paper
- multi-base blocks
- algebraic tiles
- video clips
- cardboards
- models
- SHS Mathematics curriculum
Assessment (1.1.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.