Numeracy Task Details

As seen in the quote on the previous page – numeracy is not about abstraction, but rather the use of mathematics in life’s contexts and situations. That is, numeracy is about getting the job done with the mathematics that is already in place. As such, the tasks on the previous page have been designed to require a lot of mathematical thinking without relying on a lot of mathematical knowledge. This may seem like a bit of an oxymoron, but when you start to play with these tasks you will see that it isn’t. These tasks really do allow for a great deal of mathematical activity and discussion without relying to heavily on specific pre-requisite knowledge.

As a result, these tasks are a great resource for many aspects of teaching and learning that you may wish to focus on in your classroom. From formative assessment to group work, from persistence to writing, from estimation to reasoning these tasks provide a context within which you can invite learners into the discourse of mathematics in general, and foster numeracy proficiencies in particular.

In what follows I outline the characteristics and qualities of these numeracy tasks that allow for these affordances.


Four Types of Numeracy Tasks

[EXPAND click to read more]

The Numeracy tasks I have been involved in developing tend to fall into one of four categories:

  • Fair Share Tasks – These are tasks that involve a scenario in which something needs to be shared. How this is to be best accomplished is always problematic as the notion of fairness is not well defined. Goody Bags, Sharing Cookies, and Giving out Bonuses are some examples of Fair Share Tasks.
  • Planning Tasks – These are tasks that involve a situation in which some sort of planning must take place. They could be budget type problems or they could be spatial problems. Going Bowling, Trip to the Waterslides, and Playland Adventure are some examples of Planning Tasks.
  • Estimation Across a Large Number of Variables Tasks – These are tasks that require the solver(s) to make several estimations in order to arrive at a possible solution. Although often being restrained to one unit of measure (like time) the estimates range across a wide spectrum of contexts. The Concert in Toronto is an excellent example of this kind of task.
  • Modelling Tasks – These tasks require the solver to develop a strategy for action based on one set of data or information. They are then required to apply this strategy to another set of data and then make adjustments as necessary. The 2004 Summer Olympics Results task is an example of this type of task.

Of course, many tasks are actually a blending of these types requiring students to plan and estimate, or estimate and share, etc.

There is a 5th type of task that I am just now beginning to experiment with. This type of task will be structured around the concept of subjective probability – a skill that is vitally important in a numerate society. Stay tuned!

[/EXPAND]


Qualities of a Good Numeracy Task

[EXPAND click to read more]

Each of the numeracy tasks on the previous page have all been developed to have the same five qualities:

  • Low Floor – There is something in each of these tasks that every student in the intended grade range can engage in. By necessity, this means that careful consideration is given to the prerequisite knowledge that is needed to begin a task.
  • High Ceiling – There is room at the top to go beyond the trivial. That is, the task can be interpreted or extended in such a way so as to allow some students to incorporate high degrees of mathematical thinking.
  • Huge Degrees of Freedom – There are lots of opportunity to make decisions as to how to proceed. Although this always pertains to chosen strategies, these tasks are designed more specifically to allow students many options to choose from.
  • Fixed Constraints – When faced with huge degrees of freedom students can become paralyzed by the overwhelming number of possibilities available to them. Constraints are therefore used to give them something to organize their thinking around – thus liberating them to begin.
  • Inherent Ambiguity – Deliberate ambiguity is used not only to create situations where the students must MAKE decisions but also to create situations where they become AWARE that they are making decisions. These places of decision then become excellent points of discussion and prompts for writing about their thinking.

Attention to each of these five qualities allows us to create tasks that become effective vehicles for a number of different teaching and learning outcomes. What it does NOT do, nor should it, is allow for the creation of tasks that encourage students to work towards ONE best answer. These are open-ended tasks that allow for many interpretations and many different solutions.

[/EXPAND]


Designing Numeracy Tasks

[EXPAND click to read more]

The numeracy tasks that are available on this website have all been designed following the same set protocol.

  • Engaging Context – The design of each task starts with the identification of a context that may be of interest to the target age group. I say may because the interest inherent in the task is sometimes difficult to gauge.
  • Locate the Problematic Situation – This begins with deciding which of the four types of numeracy tasks this is going to be most closely alligned with. Once this has been determined the problematic nature of the task can begin to take form – how can we make planning or sharing or estimation more complicated here? Often the answer is through the use of ambiguity.
  • Finalize the Pilot Task – The first draft of the task is finalized through a process of attending to each of the aforementioned five qualities of a good task.
  • Pilot Test – The task is tested on a class of students and evaluated according to its potential to engage students in thinking, discussion, and written output. It is important NOT to judge the task on its ability to drive the students towards a normative single answer.
  • Refine – Based on the pilot test the task is refined for more general use.

Once the task is complete it is important to resist the urge to think of it as perfect. The task needs always to be thought of as open to further refinement and development. This is why the tasks are offered as word documents rather than PDF’s.

[/EXPAND]


WordPress Themes

cheep generic viagra
buy cialis now
cialis br
30mg cialis
cialis canadian pharmacy
cialis brand verses generic cialis
voagra online without prescription
buy buy free viagra viagra viagra
cheapest viagra in uk
buy cheap online uk viagra
cialis brand name
rx levitra 100mg
Buy viagra Buffalo
order generic cialis softtabs online
viagra buy now pay later
5mg cialis generic
discount viagra uk
cheapest generic viagra sent overnight
discount viagra sales
Buy viagra Tacoma
order cheap cialis
buy cheap purchase uk viagra
buy discount levitra
cialis by fedex
cheapest generic viagra and canada
cialis black reviews
order 50mg cialis
viagra canada generic
viagra canadian prescriptions
overnight delivery cialis
36 hour levitra
Buy viagra Memphis
viagra buy in uk online
Buy viagra Minneapolis
buy cheap viagra online
canada pharmacy discounted viagra 100
cialis black 800mg
levitra 125 mg
buy cialis wighout prescription
cheapest price for viagra
cialis cheapest
buy viagra no prescription
over the counter drug to viagra
viagra by mail order
viagra canadian price shipped
patanol cialis nexium
cialis 2005
viagra canada pharmacy
buy buy cheap viagra
discount viagra or xanax
cheapest viagra
levitra online prescription
buy buy sale viagra viagra
Buy viagra Pittsburgh
cialis cialis drug generic flomax
cheapest viagra homepage
discount viagra brand drug
cialis 5mg
Buy viagra El Paso
discount viagra wholesale stores discount pharmacy
buy buy cheap viagra
buy free viagra viagra
discount viagra canada
discount viagra pharmacy online
buy deal viagra
cheapsest viagra online
cheapest viagra anywhere
buy form generic viagra
viagra buy australia
cialis no prescription
cialis 36 hours
levitra 10mg 20mg
cialis canadian generic
Buy viagra Rome
buy cheap viagra
buy cheap cheap kamagra uk viagra
cialis online prescription
Buy viagra Nashville
over the counter viice for generic viagra
viagra canadian
buy buy discount viagra viagra viagra
cialis buy cialis online
Buy viagra Modesto
cheapest viagra on the internet
cialis cheap online
buy discount viagra viagra viagra
buy cialis internet
cheapest place to buy viagra
cialis 50 mg
buy levitra wighout prescription
cheapest generic substitute viagra
buy viagra wighout prescription
overnight express delivery generic cialis
Buy viagra Detroit
buy cost low viagra
cheapest price for viagra
cheapest viagra anywhere
cialis best cialis price
cheap cialis canada
buy cialis no prescription
cheapest viagra in the uk
cheapest regalis viagra
buy levitra no prescription
buy cheap deal pill viagra
buy viagra cheap prices
cialis 100mg price
cialis dosage 20mg
order cialis on-line
discount viagra overseas
viagra and eye damage
buy and purchase viagra online
cialis buy generic flomax
over the counter viagra london
discount viagra canada
cheapest viagra generic substitute
generic levitra wholesale 100mg
40 grams of cialis
overnight delivery of cialis
discount viagra viagra
order generic cialis c o d
viagra buy general
cheap levitra canada
cheapest brand viagra
cialis buy
viagra 125 mg
cheapest viagra prices us licensed pharmacies
buy buy medved viagra viagra
order cialis tampa florida
buy cheap cheap kamagra uk viagra
buy canada viagra
cialis 50mg
viagra cailis
viagra buying
Buy viagra Albuquerque
viagra 100mg
buy discount viagra online
buy viagra and cilas
paypal cialis po box
cheep viagra from inda
buy buy cheap medved viagra
20 mg cialis
generic viagra wholesale 100mg
cialis cialis forum pharmacy
100 mg viagra us pharmacy
cheapest viagra on the net
Buy viagra Tulsa
viagra 50mg online
cialis black reviews
cialis britain
viagra buy uk
canada pharmacy discounted levitra 100
buy discount viagra online a href
buy cheap viagra 32
cialis canada
cialis causes muscle ache because
cialis 10
order cialis pills
20mg cialis
viagra canada generic
discount drugs levitra 100mg
cheapest uk supplier viagra
cheap cialis canada
levitra 50mg
redtube viagra
cheapest generic viagra
buy cheap viagra
viagra canadian price shipped
cialis cheap no prescription
cialis cialus
viagra by money order
viagra buy generic
viagra express
Buy viagra Louisville
cheapest place to buy viagra online
50mg cialis
cheapest generic viagra and xanax pills
cialis certified online pharmacy
Buy viagra Newark
cialis cheap prices
buy canada in viagra
buy buy online viagra viagra
cialis 20mg reviews
buy deal herbal viagra viagra
cialis cialis
250 mg levitra
cialis without prescription
buy viagra 100mg
cialis buy online
buy buy sale viagra viagra
cheapest price for generic viagra
order generic cialis
cheapest uk viagra
cheapest prices for viagra online
over the counter viagra substitute
viagra canadian
cialis buzzmachine by jeff jarvis
cialis buy cialis generic cialis
generic viagra 20mg pills erections
Buy viagra Omaha
order cialis online from dreampharmaceuticals
buy australian viagra
cheapest viagra online pharmacy
cialis britan
cialis black 800mg
viagra by mail canada
50 mg levitra
discount viagra cialis
discount viagra drug
cialis buy cheap cialis online index
cheapest price on viagra
cheapest price for viagra and xanax
cheapest site viagra
buy cheap generic online viagra
buy cheap viagra uk
buy discount online viagra
cheapest viagra prices uk
viagra 50mg
buy australian viagra
cialis buy online cheap tadalafil
cheapest prices for viagra online
buy viagra cheap india pharmacy
buy discount viagra
over sea generic viagra
viagra by overnight delivery
order generic cialis softtabs
cialis by phone
cheapest cialis
levitra no prescription
cheapest prices on generic viagra
cialis cheap online direct
cheapest price viagra us licensed pharmacies
Buy viagra Long Beach
buy cheap deal online viagra viagra
buy cheap cialis
buy cheap viagra prescription online
cheap cialis canada
cialis best effect
Buy viagra Tucson
cialis buy on line
50 mg levitra retail price
generic levitra 20mg pills erections
viagra canada prescription
cheapest viagra prices
buy buy free viagra viagra viagra
buy cheapest viagra
cheap 25mg cialis
cialis canadian geneic
Buy viagra Oakland
order cialis now
order cialis online
cialis 10mg 20mg
Buy viagra New Orleans
100mg levitra
levitra 50mg online
buy viagra cialis levitra online prescription
cheapest generic silagra viagra
cheapest viagra on line
buy buying sale viagra
buy viagra 50mg
buy discount viagra
ordering information of cialis from canada
Buy viagra Baltimore
buy cheap viagra on the net
buy viagra cheaply
cialis buy cialis online order cialis
cheapest viagra in uk
cheapest in uk viagra
buy viagra canada
cheapest price viagra
cialis cheapest online prices
generic cialis wholesale 100mg
viagra buying online
cheapest generic viagra 99 cents
Buy viagra Houston
10mg levitra
buy viagra alternative
buy viagra cialis
discount viagra sale online
cheapest uk supplier viagra
cialis black
cheapest viagra us pharmacy
levitra 25 mg
cialis bestseller
cheap viagra without prescription
cialis black
buy diet viagra online
cheapest viagra in the uk
buy cialis viagra
order cialis on line
cialis cialis viagra viagra
viagra no prescription
buy viagra cheapest best prices online
levitra 100mg
levitra 20 mg
discount viagra generic
cialis blindness
cialis cheap visa
100mg cialis
buy cheap sale viagra
Buy viagra Charlotte
cialis calis
cialis brand cialis 100mg
Buy viagra Philadelphia
Buy viagra Fresno
cheapest viagra world
Buy viagra Mesa
cialis canadian drugs
viagra by the pill
viagra buy it online now
buy viagra cheap online
viagra brand viagra 100mg
buy discounted viagra
viagra buy contest
100mg viagra
buy cialis online now
100 mg levitra us pharmacy
cialis cialis cialis genuinerx net viagra
cheapest generic viagra and xanax
order cialis uk
discount drugs cialis 100mg
cialis cheap overseas
cialis 5m tablets
buy cheap viagra in uk
viagra canadaian prices
cheep viagra from indea
Buy viagra Indianapolis
buy cheap uk viagra
viagra buy viagra online
buy cheap viagra online u
cialis cancdian dugs
buy cheap viagra online now
buy cialis 50mg
cialis reviews
cialis causes high blood pressure
cialis cialis uk
50 mg cialis
buy viagra
order viagra cialis flomax pharmacy
buy cheap online prescription viagra
buy cheap online viagra viagra
viagra 20 mg
buy buy online sale viagra viagra
cialis cheap online pharmacy
cialis canada online pharmacy viagra
cialis cialis online online
viagra canada
levitra brand levitra 100mg
cialis best price
cheapest prices on generic viagra
overnight shipping cialis
viagra online prescription
cheapest viagra homepage
cialis brands
buy viagra ebay
cialis 800mg
cialis buy generic ed
order cialis
cheapest uk viagra
cheapest viagra tablets
cheapest prescription viagra
cialis 20 mg
cialis cialis tadalafil
cheapest viagra online in the uk
levitra 100mg price
viagra and eye sight
cialis cialis generic viagra
cheap viagra canada
order cialis and viagra
viagra canada online pharmacy
cheapest generic price viagra
cheapest viagra online
discount viagra pills
discount viagra sale
buy viagra by pill
cheap websites for viagra
Buy viagra Arlington
cheapest viagra in uk che
cheapest viagra uk
cialis cialis information
order cialis overnight delivery
buy buying sale viagra
Buy viagra Fort Worth
buy cheap deal viagra viagra viagra
viagra canadian prescriptions
cheapest viagra
check generic order pay viagra
generic viagra 100mg
cialis cialis genuinerx net viagra
viagra buy it
cheap viagra without a prescription
viagra canada online
buy cheap online viagra
cialis canadian
viagra buy viagra
cialis black
cialis 10 mg
buy cialis online viagra
buy levitra online 50mg
Buy viagra Riverside
viagra buy ionline