This Mathematics unit covers a range of concepts relating to fractions and decimals.
It consists of 11 lessons of approximately 60 minutes duration.
The sequence of lessons and suggested time frames should be regarded as a guide only; teachers should pace lessons in accordance with the individual learning needs of their class.
An assessment task for monitoring student understanding of the unit objectives is included and will require an additional lesson.
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Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to ...
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/...
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line;
Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number;
Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models.
Relate decimals to fractions that name tenths and hundredths; and
Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations;
Determine if two given fractions are equivalent using a variety of methods;
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