Level 5: Proportional Reasoning
Materials:
Instructions:
Place the CD Card in front of the student and say, “How much is this CD now? … Ask student to explain his/her reasoning and note response.
If dealt with reasonably confidently, place the Plant Growth Card in front of the student, then say, “What can you say about how much the plant has grown in one week?” … If not offered, ask, “How might this be written as a percentage?” Ask student to explain his/her reasoning and note response.
If both problems answered relatively easily, place the Skate Board Card in front of the student and ask:“What was the price of the skate board before the sale?” … Explore and note student’s thinking. If the student appears to be experiencing some difficulty, point to the paper and pen and say “You can work it out on paper if you like.” Retain student working and/or note response as appropriate.
If this answered correctly, place the Sales Tax Card in front of the student and say, “In some countries, sales tax is added to the cost of an item at the cash register. How would you estimate how much you would have to pay for the Harry Potter book?” … Explore and note student’s thinking.
5.8 Advice Rubric
While most students are able to recognise and use common percents such as 50%, 25 % and 33⅓ %, many experience difficulty using percent to describe growth (or decay) and/or rely on inefficient, rulebased solution strategies (eg, to find 7.5% multiply by 7.5 then divide by 100).
This task examines the extent to which students are able to use percent to solve problems and justify solutions. It assumes some prior experience with percent and some capacity for mental computation.
Observed response 
Interpretation/Suggested teaching response 
Halves to solve CD problem, may give additive response to Plant Growth problem, little/no response to remaining problems 
Suggests limited understanding of percent, may not understand relationship to decimal fractions and/or have access to appropriate recording strategies  Use halving and fifthing strategies to construct diagrams and line representations for tenths and hundredths (see Partitioning (PDF  215Kb) (pdf  199.51kb) paper). Use to locate given decimal fractions on an open number line
 Review meaning of percent and relationship to hundredths
 Review recording strategies for solving simple percent problems, extend to a wider range of percent problems such as the ones included here

Finds 50%, recognises % growth but may not be able to describe this accurately (eg, says 50% more), may make a start on remaining problems but experiences difficulty (eg, may find ¾ of $84) 
Some understanding of percent and how it can be applied to describe change, needs to consolidate solution strategies  Review solution strategies. Introduce/review more formal, generalisable recording strategies for solving percent problems, particularly ones involving percents larger than 1.
 Invite students to create similar problems. Use to focus on identifying what needs to be done and why. Discuss advantages of using questions like, Will the answer be more or less? Why?” Review solution strategies

Able to solve all problems relatively efficiently 
Suggests sound understanding of percent as an operator and how it can be used to describe growth, may need to refine solution strategies  Introduce more complex problems, particularly ones involving less familiar rational numbers and more ambiguous situations
 Explore and discuss strategies for solving an expanded range of proportional reasoning problems, particularly ones involving the use of nonintegral values
 Consider relating ratios to work on transformations, scale diagrams, variation, inverse proportion, and more complex missing value problems
