Julie Anderson Dunedin College of Education Secondary Numeracy Project Auckland Feb 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 recap Fraction 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 Oranges There are 3 oranges to every one apple in the bowl How many apples and how may oranges, 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 ratios Apples 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 Fruit Apples, 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.

Imaging Transfer 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?