Workplace and Apprenticeship 10
Aside from integrating QR codes and cellphones into lessons for all of the indicators, the following Outcomes and Indicators exemplify easy and specific uses for QR codes and cellphones.

WA10.2

Analyze puzzles and games that involve spatial reasoning using problem solving strategies.

Here, you can use QR codes as hint cards for the games and puzzles to aid students in problem solving. You can also download a number of Apps for SmartPhones that use problem solving skills for games and puzzles.

WA 10.3 e, 10.3 f, 10.4 e, and 10.5 f

Provide an approximate measurement in SI units for a measure given in Imperial units (e.g., 1 inch is approximately 2.5 cm, 1 kg is a little more than 2 lbs)

Develop (using proportional reasoning), generalize, explain, and apply strategies (including formulas) to convert measurements from:
• SI to Imperial units (e.g., Celsius to Fahrenheit, centimetres to inches, kilograms to pounds, litres to quarts)
• Imperial to SI units (e.g., Fahrenheit to Celsius, inches to centimetres, pounds to kilograms, quarts to litres).

Develop, generalize, explain, and apply strategies to convert units of linear measurements within the same system (e.g., feet to yards, or metres to millimetres).

Develop, generalize, explain, and apply strategies to convert, within the same system of measurement, area measurements expressed in:
• an SI unit squared to another SI unit squared
• an Imperial unit squared to another Imperial unit squared.

There's an app for that. You can have students use a conversion app to assist them in finding the relationships between the two measuring systems.

WA 10.4 i

Critique the statement “the distance between Regina and Saskatoon is 2 hours”.

Students can scan a QR code that links to a variety of pages that help them to reason that distance and time are related through speed, but not replaceable for one another.

WA 10.5 a

Describe situations relevant to self, family, or community in which SI and/or Imperial units for area measurement are used.

Many manufacturers are now placing QR codes on their products. Students can scan these QR codes on the products to read about the product, its origin, and the measurements used.

WA 10.6 a

Model, including the use of drawing, concrete materials, and technology, the meaning, role, and use of the Pythagorean Theorem, using examples and non-examples.

This one was almost too obvious. Use a QR code to link to a variety of sources. Alternatively, link to website that sketches out Pythagorean triangles. Also, I'm pretty sure there's an app for that!

WA 10.6 b

Observe and analyze a set of triangles to judge if the Pythagorean Theorem could be used to determine an unknown side length and explain the reasoning.

Post these triangles either online or on the wall in your classroom and have a QR code with each of them that links to an explanation of whether they can or cannot use the Pythagorean Theorem.

WA 10.6 h

Create , solve, and verify the reasonableness of solutions to problems relevant to self, family, or community, for which the Pythagorean Theorem can be used.

Each student can scan a QR code to link to a online flashcard creator/website and submit a problem they created, as well as try to solve problems their classmates create.

WA 10.7 c

Verify whether two or more given polygons are similar.

Similar to the suggestion for 10.6b, post a set of varying polygon sets with accompanying QR codes that explain why two polygons are similar or are not similar.

WA 10.8 c

Develop, generalize, explain, and apply formulae for the primary trigonometric ratios (cosine, tangent, and sine).

There's an app for that. However, students can also scan a QR code that links to any number of online resources, simple explanations, hints, diagrams, examples, etc. to help them in developing, generalizing, explaining, and/or applying the primary trig ratios.

WA 10.9 h

Observe and sort a set of pairs of lines as perpendicular, parallel, or neither, and justify.

Here, you can play QR code Memory. Divide students in to groups of two or three. Each player gets to flip over two cards per turn. Have a line on one side of the card (make sure to label the side that is the top), and on the reverse have a QR code. If the two QR codes both link to the same site, which links to a justification. If that player can correctly justify why he or she made a match, that player gets a point and can try to find another pair. If not, the next player gets to take a turn. This game can work for a variety of mathematical concepts as well.

WA 10.9 m

Describe and apply strategies for determining if lines or planes are perpendicular or parallel in situations relevant to self, family, or community (e.g., are the walls perpendicular to the floor? Are the corners square? Are the seams on the duvet parallel? Are the joists parallel?).

Here, have students look at a QR code and find parallel/perpendicular situations with in the QR code. The code can also link to online games where students have to identify all the parallel/perpendicular cases in a given situation.

WA 10.9 r

Analyze and describe the role of angles, parallel lines, perpendicular lines, and transversals in games and sports (e.g., chess, curling, pool, hockey, soccer, and basketball).

Guess what! There's an app for that (i.e. there are apps with all these games and more)!

WA 10.10 a

Create and solve problems relevant to self, family, and community that involve best buy, and explain the solution in terms of the cost as well as other factors, such as quality and quantity.

Again, scan the QR codes on different items and learn about the products. Also, there is an app that lets you scan the item and it will automatically bring up the prices of that item at different stores in your area.

WA 10.10 b

Describe and analyze, using relevant examples taken from print and other media, different sales promotion techniques (e.g., deli meat at $2 per 100g seems less expensive than $20 per kilogram).

In lieu of wasting paper and bringing in a ton of old flyers, have students scan the QR codes that many companies are now starting to put on their flyers (or soon should!), which will link them directly to that store's flyer on their phone.

WA 10.10 d

Develop (using proportional reasoning), explain, and apply strategies for:
• comparing the unit price of two or more items
• solving situational problems involving currency exchange
• determining percent increase or decrease for a given situation.

There's an app for that! Students can either scan the QR codes of times, look at the flyers (see above), or use a currency converter on their phone to help them find the information necessary for solving these types of problems.

WA 10.10 e

Develop using proportional reasoning and mental mathematics strategies, explain, and apply strategies for estimating the cost of items or services in Canadian currency while in a foreign country or when making purchases via the Internet, and explain why this may be important.

Because of the rush of online shopping, which cellphone users can now do on their phone, it is important that students become aware of just how much they could be spending. Students should pretend to buy several items using their cellphone and get a total (must be in a currency other than Canadian dollars) without actually buying the items. Once they have their total, they should estimate their cost in Canadian dollars, then calculate their actual cost.

WA 10.11 k

Critique the statement “When planning for a budget, it is important to calculate net pay rather than rely only on gross pay”.

There's an app for that. Students can use budgeting apps to look at the difference between gross and net pay, as well as the impact that has on their budget. This can work for most of the indicators for 10.11 as well.

Foundations and Pre-Calculus 10

FP. 10.1f

Investigate and report about the numbers 0 and 1 with respect to factors, multiples, square roots, and cube roots.

Students could scan a QR code that leads them to a variety of pages and youtube videos that talk about the numbers 0 and 1.

FP. 10.2b

Create and explain a pattern that describes the decimal form of an irrational number (e.g., write the digits from 0 to 9 in order, then put two of each digit – 0011223344 … – followed by three of each digit and so on).

This would be a great place to use the flashcards. They could write the irrational number and the decimal form on one side and the justification on the other. A quick way to see if they can do this.

FP 10.2g, 10.5g,j, 10.10b,c,d

Explain, using examples, how changing the value of the index of a radical impacts the value of the radical.

Explain why evaluating at a value for the variable in a product of polynomials in factored form should give the same solution as evaluating the expanded and simplified form of the polynomial product at the same value (e.g., explain why x^2+5x+6 should have the same value as (x+3)(x+2) when evaluated at x = -4).

Explain, using concrete or visual models, how the processes of factoring and multiplication are related

Sketch, describe, provide and explain situational examples of the different ways that the graphs of two linear equations (two variables) can intersect and explain the meaning of the points of intersection.

Develop, generalize, explain, and apply strategies for solving systems of equations graphically, with and without the use of technology and verify the solutions.

Develop, generalize, explain, and apply strategies, including verification of solutions

Again both of these could have videos or podcasts made on their phone. That could be directed to from QR codes.

You could have students explain this in a podcast from their cellphone. A QR code could be used to direct them to the site to do this on.

They could also be asked to post youtube videos they make with their phone directly to a website.

FP. 10.2i,j

Analyze patterns to generalize why (a^-n)=(1/(a^n)), adoes not equal 0

Analyze patterns to generalize why 1/(a^n)=the nth root of a, ndoes not equal 0, n is an element of I and a>0 when n is an even integer.

These could all be done using QR codes to send a student to different examples of this from which they can make the generalization.

FP 10.2i

Analyze simplifications of expressions involving radicals and/or powers for errors.

Hello youtube. I'm sure that you could find a number of videos where these are used incorrectly and the QR code could be used to direct students to them.

FP 10.2n

Create a representation that conveys the relationship between powers, rational numbers, and irrational numbers.

Students could use cell phones in a number of ways here. They could make a youtube video. post an image to a blog or wiki, make a blog or wiki post

Because FP 10.3 is extremely similar to outcomes in Workplace and Apprenticeship 10 regarding measurements I will not repost them here.

FP 10.4 is the same as WA 10.8 c (Develop, generalize, explain, and apply formulae for the primary trigonometric ratios (cosine, tangent, and sine).) Thus the same ideas exist.

FP 10.5 e

Analyze the multiplication of two polynomials for errors and explain the strategy used.

This would be another good place for blog posts and podcasts from their phone. Cue cards could be used to give them questions that they need to analyze.

FP 10.5 i, 10.10e

Critique the statement "any trinomial can be factored into two binomial factors".'

Critique the statement "two lines always intersect at exactly one point".

QR codes could be used to direct students to places where they could find information on the topics and develop a response from what they learn.

FP 10.6 a

Provide and discuss examples of different types of relations relevant to one’s life, family, or community (e.g., person A is the mother of person B, or person A is a brother of person B.).

Students could be directed to a discussion board to express their views and give examples.

Graph, with or without technology, a set of data, and determine the restrictions on the domain and range.

The data could come from a site that a QR code directs students too. They could also use QR codes to gain access to a graphing calculator for their phone.

FP 10.6 f

Provide and explain examples of situations that could be represented by a given graph.

Students could be sent to sites with images of graphs (perhaps one could be found in the viewing information of a youtube video) and then explain their response in a podcast from their phone. They could also be given the first half of a flashcard (linked to by a QR code) and have to respond on the back of the flashcard.

FP 10.7 a,b

Provide examples, relevant to self, family, or community, to explain the importance of slope

Illustrate and explain, using examples relevant to self, family, or community, how slope is rate of change

Students could make QR codes to link you to images of their answers and include their explanations of why it is an example either on the link or on the page with the QR code.

FP 10.8 d,e,f,g,j

Analyze situations, graphs, tables of values, equations, or sets of ordered pairs to determine if the relationship described is linear

e. Match corresponding types of representations of linear relations (e.g., situations, graphs, tables of values, equations, and sets of ordered pairs).

Develop, generalize, explain, and apply strategies for determining the intercepts (as values and ordered pairs) of a linear relation from its graph.

Determine the slope, domain, and range of the graph of a linear relation.

Solve a situational question that involves the intercepts, slope, domain, or range of a linear relation.

QR codes could link students to real graphs, tables of values and equations that people use everyday.

FP 10.9 d

Graph and write equations for linear data generated within an experiment or collected from a situation.

Students could be linked to experiments done by professionals and then be asked to graph and write the equations from the experiment.

## Direct Curriculum Ties

Workplace and Apprenticeship 10Aside from integrating QR codes and cellphones into lessons for all of the indicators, the following Outcomes and Indicators exemplify easy and specific uses for QR codes and cellphones.

• SI to Imperial units (e.g., Celsius to Fahrenheit, centimetres to inches, kilograms to pounds, litres to quarts)

• Imperial to SI units (e.g., Fahrenheit to Celsius, inches to centimetres, pounds to kilograms, quarts to litres).

• an SI unit squared to another SI unit squared

• an Imperial unit squared to another Imperial unit squared.

lookat a QR code and find parallel/perpendicular situations with in the QR code. The code can also link to online games where students have to identify all the parallel/perpendicular cases in a given situation.• comparing the unit price of two or more items

• solving situational problems involving currency exchange

• determining percent increase or decrease for a given situation.

Foundations and Pre-Calculus 10Explain why evaluating at a value for the variable in a product of polynomials in factored form should give the same solution as evaluating the expanded and simplified form of the polynomial product at the same value (e.g., explain why x^2+5x+6 should have the same value as (x+3)(x+2) when evaluated at x = -4).