Figure This! Math Challenges Fun Math Lessons Index of EARAT Manuals: The Apprenticeship Network Interactive Mathematics Intermath Online Mathematics Dictionary Math Central Math in Daily Life Math is Fun Math TV Math Worksheets Mudd Math Fun Facts National Library of Virtual Manipulatives The Math Forum @ Drexel University Trades Math Workbook Virtual Math Your Financial Toolkit Planning Traditionally, teachers start unit planning with interesting activities and textbooks in mind, rather than starting with the big ideas or concepts they want the students to master. If learning is to be effective for the students, the teacher must begin with the final destination in mind. Teachers should be clear about what learning outcome(s) and goal(s) will be set for the students and what assessments will be used to provide evidence that the students have mastered the learning outcome(s) and goal(s) (Wiggins, G. and McTighe, J. (1998). Understanding by Design). A concern with teaching any mathematics course is the time it takes to cover the content. Employing a conceptual approach allows the teacher to become a facilitator or guide to coach learners in building on what they already know. This constructivist approach allows learners to: build on their prior knowledge place less emphasis on memorization and rote learning see mathematical skills as useful tools and processes build a depth of knowledge develop an understanding of the connections in mathematics build self-confidence and a positive disposition towards mathematics. (ABE Level Three: Mathematics Curriculum Guide, pp. 128) When a teacher uses a conceptual approach, instruction framed around context focuses on concepts rather than content. According to the National Council of Teachers of Mathematics (2000):
Appendix A.8 Investment Options Resource: The CITY A Financial Life Skills Resource Prior Knowledge: List some of your short-term goals and long-term goals. How much money will you need for each of the goals? What is your plan for making these goals a reality? How could you save for a large purchase? What are savings? What do you know about investments? Activity: Have students work through the following information using a strategy (e.g. think-pair-share, jigsaw, concept circle, etc.) Instruction: People can choose from a wide variety of investments. This chart shows you some things to consider about some of the main types of investments. Type Expected Return Risk Liquidity Savings accounts, Guaranteed Investment Certificates (GICs), term deposits: Money deposited with banks, trust companies and credit unions • usually a fixed annual rate • GICs sometimes tied to performance of an index or other standard • low to moderate • principal amount is usually insured, but interest rates can be fixed or variable • savings may be withdrawn at any time • some GICs and term deposits must be held to maturity, but many allow for early redemption or cashing out at a cost Treasury bills: Short-term (less than 1 year) debt securities issued by government • determined by difference between purchase price and value at maturity • very low • not redeemable, but can usually be sold quickly through investment dealers Equities: Shares in ownership of a company (also called stocks) • may pay regular dividends to share holders • potential return may depend entirely on changes in share • moderate to high • depends on size and stability of company, management, competition, etc. • shares traded on stock exchanges are usually quite easy to sell • shares that aren't listed on an exchange may be
price difficult or impossible to sell Fixed income investments: Government and corporate bonds and debentures • interest rate is usually fixed • bonds with longer terms will usually pay higher interest rates • high risk "junk" bonds offer even higher rates • risk of borrower defaulting is very low for government bonds but can be low to high for corporate bonds • bond values go up and down with changing market interest rates • most bonds can be bought and sold quickly through investment dealers • some bonds are traded on stock exchanges Mutual funds: Units in a pool of money that's managed for a large number of investors by a professional money manager • may include interest, dividends and capital gains (or losses) • return will depend on manager's investment decisions and on the management fees charged • low to very high, depending on what the fund invests in and on the skill of the fund manager • most mutual funds allow investors to cash in (redeem) their holdings on short notice Real estate: Property such as land or houses • depends on price, location, real estate market, etc. • may include rent or increase in value • low to high • depends on price, location, real estate market, etc. • takes more time to sell than many other investments • hard to sell small portions • depends on market Direct investment: Investing your money to finance a private business • low to very high • success depends on the business concept, the manager and on economic • medium to very high • depends on type of business, competition, skill of the business manager, and the economy • low • may be very hard to sell
Appendix B.14 Landscape Design Resource: Landscape Design. MathLinks 9 (2009). p. 253, 281 Introduction: Gardeners and landscapers are often required to calculate areas when designing a landscape for a backyard, commercial property, or park. When determining how much soil, gravel, mulch, and seed they need for a project, landscape designers also calculate volumes. Here is a landscape design created for a property. Practice and Questions: Landscape Design. MathLinks 9 (2009). p. 253 Project: You have been hired to create a landscape design for a park. The park is rectangular and covers an area of 500 000 m2. The park includes the following features: A play area covered with bark mulch A sand area for playing beach volleyball A wading pool The features in your design include the following shapes: A circular area A rectangular area A parallelogram-shaped area with the base three times the height Include the following in your design: A scale drawing showing the layout of each of the required features A list showing the area of each feature and the volume of each material (mulch, sand, and water) required to complete the park. Extension: Research the cost of the items in your home community and determine a budget for your new park.
Non-example #1 <1 and <14 Non-example #2 <1 and <6 Non-example #3 <5 and <14 Non-example #4 <1 and <10 Non-example #5 <2 and >14 Non-example #6 <2 and <13
Angle Pair Set #1 <1 and <6 <2 and <5 <3 and <8 <4 and <7 <9 and <14 <10 and <13 <11 and <16 <12 and <15 Angle Pair Set #2 <1 and <2 <9 and <10 <1 and <5 <9 and <13 <2 and <6 <10 and <14 <5 and <6 <13 and <14 <3 and <4 <11 and <12 <3 and <7 <11 and <15 <4 and <8 <12 and <16 <7 and <8 <15 and <16 Angle Pair Set #3 <5 and <10 <6 and <9 <7 and <12 <8 and < 11 Angle Pair Set #4 <1 and <9 <2 and <10 <3 and <11 <4 and <12 <5 and <13 <6 and <14 <7 and <15 <8 and <16 Angle Pair Set #5 <1 and <14 <2 and <13 <3 and <16 <4 and <15 Angle Pair #6 < 5 and <9 <6 and <10 <7 and <11 <8 and <12
Non-example #1 <1 and <14 Non-example #2 <3 and <8 Non-example #3 < 6 and <11 Non-example #4 <1 and <10 Non-example #5 <2 and <14 Non-example #6 <5 and <11