B6 Mathematics · Term 2 Week 5: Fractions

Lesson notes

Learning Objectives

Indicator: B6.1.3.1.3 - Use models to explain the result of multiplying a fraction by whole number, a whole number by a fraction and a fraction by fraction

By the end of the lesson, learners can:

Use area models and number lines to show what it means to multiply a fraction by a whole number (e.g., 2/3 × 5).
Use rectangular models to explain multiplying a whole number by a fraction (e.g., 3 × 2/3) and interpret the result as “of”.
Use grid or area models to demonstrate the product of a fraction by a fraction (e.g., 2/3 × 3/4).
Draw a model to justify the answer to any given fraction multiplication problem among the three cases.
Solve simple word problems involving fraction multiplication and explain their reasoning using their drawn models.

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Curriculum details

Strand: Number (Strand 1)
Sub-strand: Fractions (1.3)
Content standard: B6.1.3.1 - Demonstrate an understanding of strategies for comparing, adding, subtracting, multiplying and dividing common, decimal and percent fractions
Indicator: B6.1.3.1.3 - Use models to explain the result of multiplying a fraction by whole number, a whole number by a fraction and a fraction by fraction
Suggested placement: Term 2, Week 5 (Week 17 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.
Curriculum reference: Mathematics Curriculum for Primary Schools (Basic 4-6), 2019, p. 133
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g. 1. To multiply a whole number by a mixed fraction (e.g. 3 × 2 2/3) one can multiply the whole number by the whole number and then whole number by the fraction and add the products or change the mixed fraction to improper fraction and multiply; i.e. 3 × 2 2/3 = (3×2) + 3× 2/3) = 6 + 2/3+2/3+2/3 = 66/3 = 8 or 3 × 2 2/3 = 2 2/3+2 2/3+2 2/3 = 6 (2+2+2)/3 = 66/3 = 8
E.g. 2. To multiply a fraction by a whole number the multiplication is interpreted as "of"; e.g. 2/3 ×5 means shade 2/3 of 5 ; i.e. finding two-thirds of each of five objects; i.e. 2/3 ×5 is 2/3 of 5 quantities, which leads 10 thirds, i.e. 2/3 ×5 = 10(1/3) = 10/3 = 31/3
E.g. 3. To multiply a fraction (i.e. common or mixed) by a whole number (e.g. 4 2/5 × 5 ) first change all into common fractions, then multiply the numerators separately and multiply the denominators separately and simplify, i.e. 4 4/5 × 5 = 24/5 × 5 / ( 1 ) == (24×5)/5 = 120/5 = 24/1 = 24. [Note, the product can be simplified before multiplying the numerators separately and multiplying the denominators separately].