Grades 3–5NumberPlanned
Fractions and decimals
Fractions as numbers on the number line, equivalent fractions, comparing and adding fractions, and decimals as fractions whose denominators are powers of ten.
math.number.fractions
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 4
You will learn to
- Place fractions on a number line and explain a/b as a copies of 1/b.
- Generate equivalent fractions and use them to compare, add and subtract fractions.
- Convert between decimals with up to three places and fractions with denominators 10, 100 and 1000.
- Multiply a fraction by a whole number.
Definition
- For a whole number b > 0, 1/b is the length of each part when the unit interval is cut into b equal parts, and a/b is the length of a such parts.
- a/b and c/d are equivalent (equal as numbers) when ad = bc.
- A decimal such as 0.37 means 37/100.
Theorem
- a/b = (na)/(nb) for every whole number n > 0.
- a/b + c/d = (ad + bc)/(bd).
- A fraction in lowest terms has a terminating decimal expansion exactly when its denominator has no prime factors other than 2 and 5.
Common misconceptions
- Adding numerators and denominators: 1/2 + 1/3 is not 2/5.
- Thinking a larger denominator means a larger fraction.
- Believing 0.25 > 0.3 because 25 > 3.
- Thinking fractions are only parts of shapes rather than numbers.
Leads to
Optional discoveries
- Real numbers and irrationality Some numbers, such as √2, cannot be written as fractions at all.
- ← Measuring length and time
Learning pathways
Further reading
- Hung-Hsi Wu, Understanding Numbers in Elementary School Mathematics (2011)