Julie AndersonDunedin College of EducationSecondary Numeracy ProjectAuckland Feb 23-24 2005

Advanced Proportional: Stage 8

Teaching sequence using the teaching model Knowledge Materials Imaging Number Properties-abstraction

Advanced Proportional Language

Proportion - Fraction Ratio – Comparison (same measure) Rate (different measures-80km per hour

40 slaters per square metre) Multiplicative relationships with rates and

ratios Proportional relationships between measures

Quantities co-vary (change together) To understand a ratio or a rate you must

distinguish a relationship that remains constant when two linked quantities are changing together

The constant relationship is not directly observable

AP Strategy learning outcomes Find proportional relationships between measures 12 headbands are made with 15 metres of ribbon.

How many headbands can you make from 25 metres of ribbon?

Convert from ratios to proportions and visa versa Find amounts in given ratios Four grey garden tiles are used too every three red

ones. If you use 210 tiles altogether how many are grey and how many are yellow.

Ratio using Fruit Cards Knowledge recap Materials Imaging Number Properties

Knowledge recapFraction versus a Ratio What fraction of the group is the pear? the orange? What fraction of the group are bananas?, apples? How many bananas compared to the apples in the

group? What is the ratio of lemons to pears?, lemons to

bananas?

Fruit Bowl Problems

Apples and OrangesThere are 3 oranges to every one apple in the bowlHow many apples and how mayoranges, if there are 40 pieces of fruit in the bowl?

24 in the bowl?16 in the bowl?52 in the bowl?

What fraction (proportion) are apples?What fraction (proportion) are oranges?

What is the ratio of oranges to apples?

Fruit Bowl Problems

Harder ratiosApples and Bananas

3 apples to every 2 bananas in the fruit bowl

How many apples and how many bananas if 40 in the bowl? 25 in the bowl? 60 in the bowl?

More FruitApples, bananas and oranges

For every 4 apples in a box

there are 3 bananas and 2 oranges

How many of each fruit if 45 in the box? 180 in the box? 72 in the box?

Make up Own Problems Make up a problem that someone else can

work out using three types of fruit, in a given ratio.

Challenge them to find a range of different amounts in the box.

Make up a problem using a different context that they can choose.

ImagingTransfer the model to other situations In a school of 360 pupils there are 5 boys to

every 4 girls. How many girls are there?

Joe works 3 days and Sam works 4 days painting a roof. Altogether they get paid $150. How much should each get?

Multilock block models Colour mixes 18 yellow with 6 blue in a mix to make a

green What mix might go into smaller pots to make

the same colour?

Proportional relationships-rate It takes 20 bales of hay a day to feed 300

sheep. How many bales would you need each day to feed 120 sheep.

How did you work it out?

Dog Biscuits The amount of dog biscuits to be feed to a

dog depends on the weight of the dog. If the packet recommends that an 18kg dog

needs 12 biscuits, how many biscuits should you feed a 30kg dog, a 10kg dog?

How did you work it out?