# YEAR 5 MATHS FOCUS

## NUMBERS AND ALGEBRA

Fractions & Decimals

Learning Experiences

Fractions & Decimals

## FRACTIONS & DECIMALS

OUTCOME

A student:

MA3-7NA:

compares, orders and calculates with fractions, decimals and percentages

TEACHING POINTS | In Stage 3 Fractions and Decimals, students study fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. A unit fraction is any proper fraction in which the numerator is 1, eg 12, 13, 14, 15, … |

Students need to interpret a variety of word problems and translate them into mathematical diagrams and/or fraction notation. Fractions have different meanings depending on the context, eg show on a diagram three-quarters (3/4) of a pizza, draw a diagram to show how much each child receives when four children share three pizzas. | |

Fractions may be interpreted in different ways depending on the context, eg two-quarters (2/4) may be thought of as two equal parts of one whole that has been divided into four equal parts. The image shows 1 square divided into quarters. Two-quarters are shaded. | |

Alternatively, two-quarters (2/4) may be thought of as two equal parts of two wholes that have each been divided into quarters. 2 squares, each divided into quarters, 2 of which are shaded: ‘one-quarter + one-quarter = two-quarters’. |

LANGUAGE | Students should be able to communicate using the following language: whole, equal parts, half, quarter, eighth, third, sixth, twelfth, fifth, tenth, hundredth, thousandth, one-thousandth, fraction, numerator, denominator, mixed numeral, whole number, number line, proper fraction, improper fraction, decimal, decimal point, digit, place value, decimal places. |

The decimal 1.12 is read as ‘one point one two’ and not ‘one point twelve’. | |

When expressing fractions in English, the numerator is said first, followed by the denominator. However, in many Asian languages (e.g. Chinese, Japanese), the opposite is the case: the denominator is said before the numerator. |

## Expectations of Attainment

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) | place fractions with denominators of 2, 3, 4, 5, 6, 8, 10 and 12 on a number line between 0 and 1, e.g. |

compare and order unit fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100 {Critical and creative thinking} | |

– compare the relative value of unit fractions by placing them on a number line between 0 and 1 {Communicating, Reasoning} | |

– investigate and explain the relationship between the value of a unit fraction and its denominator {Communicating, Reasoning, Critical and creative thinking} |

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) | identify and describe ‘proper fractions’ as fractions in which the numerator is less than the denominator {Literacy} |

identify and describe ‘improper fractions’ as fractions in which the numerator is greater than the denominator {Literacy} | |

express mixed numerals as improper fractions and vice versa, through the use of diagrams and number lines, leading to a mental strategy, e.g. {Literacy} | |

model and represent strategies, including using diagrams, to add proper fractions with the same denominator, where the result may be a mixed numeral, e.g. | |

model and represent a whole number added to a proper fraction, e.g. 2+3/4=2 3/4 | |

subtract a proper fraction from another proper fraction with the same denominator, e.g. 7/8−2/8=5/8 | |

model and represent strategies, including using diagrams, to add mixed numerals with the same denominator, e.g. | |

use diagrams, and mental and written strategies, to subtract a unit fraction from any whole number including 1, e.g. | |

solve word problems that involve addition and subtraction of fractions with the same denominator, eg ‘I eat 1/5 of a block of chocolate and you eat 3/5 of the same block. How much of the block of chocolate has been eaten?’ {Critical and creative thinking} | |

– use estimation to verify that an answer is reasonable {Problem Solving, Reasoning, Critical and creative thinking} |

Recognise that the place value system can be extended beyond hundredths (ACMNA104) | express thousandths as decimals |

interpret decimal notation for thousandths, e.g. 0.123=123/1000 | |

state the place value of digits in decimal numbers of up to three decimal places |

Compare, order and represent decimals (ACMNA105) | compare and order decimal numbers of up to three decimal places, eg 0.5, 0.125, 0.25 {Literacy} |

interpret zero digit(s) at the end of a decimal, eg 0.170 has the same value as 0.17 | |

place decimal numbers of up to three decimal places on a number line between 0 and 1 |

Learning Experiences

To be added