# NA3-5: Know fractions and percentages in everyday use.

This means students will understand the meaning of the digits in a fraction, how the fraction can be written in numerals and words, or said, and the relative order and size of fractions with common denominators (bottom numbers) or common numerators (top numbers). Fundamental concepts are that fractions are iterations (repeats) of a unit fraction, for example 3/5 = 1/5 + 1/5 + 1/5 and 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3. This means the numerator (top number) is a count and the denominator tells the size of the parts, for example in 5/3 there are five parts. The parts are thirds created by splitting one into three equal parts. This means that fractions can be greater than one, for example 4/3 = 1 1/3, and that fractions have a counting order if the denominators are the same, for example 1/3, 2/3, 3/3, 4/3,... The size of the denominator also affects the size of the parts being counted in a fraction. For example, thirds of the same whole are smaller than halves of the same whole. So fractions with common numerators have an order of size based on the size of the parts, for example 2/7 < 2/5 < 2/3 (< means “less than”). Students at Level Three should know simple common fraction-percentage relationships, including 1/2 = 50%, 1/4 = 25%, 1/10 = 10%, 1/5 = 20%, and use this knowledge to work out non-unit fractions as percentages, for example 3/4 = 75%.

- Add and subtract fractions with like denominators.
- Explore and record equivalent fractions for simple fractions in everyday use.
- Recognise that equivalent fractions occupy the same place on the number line.
- Recognise and apply the multiplicative relationship between simple equivalent fractions300

Students will:

- gather and record category data and investigate features of the data
- interpret data displays and draw conclusions from graphs.

Students should discover that:

- there is only a weak relationship between volume, mass, or product type and how it is packaged.

use addition and subtraction to solve money problems

- Know common percentages as proportions of a whole amount.
- Express common percentages as fractions and vice versa.
- Express simple ratios as part-whole decimals.
- Calculate simple percentages of amounts.

This unit introduces the fact that fractions come from equi-partitioning of one whole. So the size of a given length can only be determined with reference to one. When the size of the referent whole varies then so does the name given to a given length.

- Name the fraction for a given Cuisenaire rod with reference to one (whole).
- Find the one (whole) when given a Cuisenaire rod and its fraction name.
- Create a number line showing fractions related to a given one (whole).
- Identify equivalent fractions

use addition and subtraction to solve money problems

- Apply the understanding that fractions can be quotients (or the result of division), e.g. 3 ÷ 5 = 3/5.
- Model and represent division problems with fractions, that involve a measurement or sharing interpretation of division.
- Write and solve division problems that involve fractions.

- Understanding improper fractions and mixed numerals.
- Understanding the importance of a common denominator when adding and subtracting fractions.
- Adding and subtracting fractions with the same denominator.

- Understanding improper fractions and mixed numerals.
- Understanding the importance of a common denominator when adding and subtracting fractions.
- Adding and subtracting fractions with the same denominator.

- State which of two fractions is larger.
- Explain why a fraction is close to 0, 1/2 or 1.

Ordering unit fractions (exercises 1 and 2)

Ordering non-unit fractions (exercises 3 to 5)

order fractions

find equivalent fractions

- Apply the understanding that fractions can be quotients (or the result of division), for example, 3 ÷ 5 = 3/5.
- Represent sharing division using diagrams, words, and symbols.
- Anticipate the results of a sharing situation using knowledge of the dividend and divisor, that is, a ÷ b = a/b (the idea300

Rename improper fractions as mixed numbers and position improper fractions on a number line.

- Identify that multiples of the denominator indicate that a fraction can be renamed as a whole number
- Convert improper fractions to mixed numbers

use addition and subtraction to solve money problems

- Record in words, the actions and results of finding a fraction of a fraction.
- Record and respond to written multiplication equations.
- Use arrays to model and solve multiplication equations that involve subdividing the unit.
- Notice, explain and generalise what is happening to the numbers in a300

use addition and subtraction to solve money problems

find fractions using paper folding

find 1/3 of a money amount

use addition and subtraction to solve money problems

use multiplication to solve money problems

find 1/3 of money amounts

use addition to solve money problems