## Level 4a

# Number and Algebra

## Chapter 3 - FRACTIONS

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## Overview of the chapter

**Rich tasks**

- These are problem solving open-ended questions that require students to investigate the history of fractions, teach how to share when the answer is a fraction and to investigate equivalent fractions. These tasks can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place, or given as homework or extension.

- Sharing
- History of Fractions
- Tangram fractions

> More on "Rich tasks for this Chapter"...

**1. Sharing**

**Students should already know points 1, 3, 5 and 6.**

- Being able to teach something is the true test of whether you understand it.
- Encourage students to prepare their lesson well with accompanying posters, computer presentations, using the internet, using materials, etc.

**2. History of fractions**

- Students research the history of fractions.

**3. Tangram fractions**

**Students should already know points 1, 3 and 4.**

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**Tangram pieces** | **Fraction of the whole** |

Large triangle | |

Small triangle | |

Medium triangle | |

Parallelogram | |

Square | |

Use the fractional values above to complete the chart.

Tangram pieces | Expression | Fraction of the whole 7-piece square |

1. Both large triangles | | |

2. Small triangle and square | | |

3. Medium triangle and square | | |

4. Large triangle minus medium triangle | | |

5. Parallelogram minus small triangle | | |

6. 4 large triangles | | |

7. 12 small triangles | | |

8. Half of a large triangle | | |

9. One quarter of a large triangle | | |

10. All 7 pieces | | |

**Fractions greater than 1**

- Convert between improper fractions and mixed fractions.

> More on "Fractions greater than 1"...

**Students should already know points 1, 3 and 4.**

**Teaching ideas**

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**Teacher notes**

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- Encourage students to understand how to change a mixed fraction into an improper fraction and vice versa before they learn the algorithm.

**Equivalent fractions**

- Understand, identify and create equivalent fractions.
- Simplify fractions to their simplest form.

> More on "Equivalent fractions"...

**Students should already know points 1, 3 and 4.**

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**Teaching ideas**

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** Fraction walls (Teacher resource sheet 11)**

This link displays fractions walls for 1/2s, 1/4s, 1/8s, 1/15s and 1/20s.

Put students into groups and assign a wall to a group.

Ask students to write as many equivalent fractions as they can in one minute.

Ask each group to explain to the rest of the class why two of their fractions are equivalent.

**Teacher notes**

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Use materials such as fraction walls, fraction pieces, folding of paper, fraction circles to help students understand this.

A common error is for students to add rather than multiply to find equivalent fractions. You could show using an example that this doesn’t work.

Another common error is for students only to multiply or divide either the numerator or denominator but not both.

- Encourage understanding of why multiplying or dividing both the numerator and denominator by the SAME number gives an equivalent fraction. Use diagrams or paper folding to illustrate. Doubling the number of parts the whole has been divided into doubles the number of the original (shaded) selected parts.

If you triple the number of parts then the parts selected also triples and so on.

**Adding and subtracting fractions**

- Draw diagrams to show addition of fractions with the same denominator.
- Add and subtract fractions with the same denominator, giving answers as fractions and mixed fractions in their simplest from.

> More on "Adding and subtracting fractions"...

**Students should already know points 1, 3 and 4.**

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**Teaching ideas**

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2 3/4 + 3/4 (Colour 2 3/4 on strips and then colour another 3/4 to get answer 3 2/4 or 3 1/2)

4/5 + 3/5

1 2/3 + 2/3

1 7/8 + 5/8

1 3/4 + 1/2 (Colour 1 3/4 then 2/4 for the half to get 2 1/4)

1 3/5 + 7/10 (Colour 1 6/10 then another 7/10 to get 2 3/10)

**Teacher notes**

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- A common error is for students to add both the numerators and the denominators when adding fractions. Show using diagrams why this is incorrect. Encourage students to use materials to show fractions and then add them together.

**Comparing and ordering fractions using number lines and benchmarks**

- Using estimation and comparison with 1/2.
- Estimating using number knowledge and deciding if fractions are greater or less than 1/2 and whether they are closer to 0, 1/2 or 1.
- Using a number line.
- By creating equivalent fractions (related denominators).

> More on "Comparing and ordering fractions using number lines and benchmarks"...

**Teaching ideas**

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1/3, 2/3, 5/6 and 7/12

3/5, 2/3, 7/12 and 5/8

1/2, 2/5, 1/3, 1/4 and 3/8

Which of these is greater than 1/2?

2/3, 5/8, 3/8, 7/12, 5/12, 7/16

**Teacher notes**

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- Encourage the use of a range of strategies and thinking to work these out.
- Students must call on their number knowledge to work out the answers.
- An extension is to ask students by how much the fraction is ….. (less than/more than 0, 1/2 or 1).
- This nzmaths unit is related to this concept: https://nzmaths.co.nz/resource/fraction-benchmarks?parent_node=
- Ordering fractions can be done in several ways depending on the fractions given.
- You could hand out a copy of the some number lines to help.

Printable Master "Empty Number Lines"

Printable Master "Empty Number Lines - Tenths"

Printable Master "Empty Number Lines - Hundredths"

**Finding fraction of**

- Finding a fraction of a whole by finding a unit fraction first.

> More on "Finding fractions of"...

**Students should already know points 5 and 6.**

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**Teaching ideas**

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Make the cube using the net given.

A die (numbered 1-6)

You will need to have 24 of something – squares, chairs, counters, jelly beans, squares of chocolate ….

Divide the class into groups.

The groups take turns to roll the die.

They then either cover to take that fraction of whatever you have 24 of.

Example If they roll 1/4 they would take or cover 6 of the 24 ….

The group with the most once all 24 items or pieces have all gone is the winner.

**Teacher notes**

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- It is important that students understand why to find, for example, 1/5 we divide by 5. To make fifths we divide something into five equal parts.
- Encourage students to put units with their answers where necessary.

for example 1/5 of 20 cm = 4 cm.