Resource Info
Continued support for high school mathematics implementation is provided in this resource. You will find:
- engaging lessons and resources for Math 10C, 20-1, 20-2, 30-1, 30-2, and 30-3
- a focus on understanding and applying the Seven Mathematical Processes (as aligned with the Ministerial Order on Student Learning #001/2013)
- formative and summative assessment materials and strategies
The Seven Mathematical Processes
The Front Matter of Alberta’s 10-12 Mathematics curriculum provides valuable information. Emphasis is placed on not only understanding curricular outcomes but also on the Seven Mathematical Processes. The links below focus on ideas on how to implement these seven processes in high school math.
MathCaching
http://mathbits.com/caching/MathCacheDirectionsOpen.html
In the spirit of geocaching, they have created activities called “MathCaching” which use the internet to find hidden boxes to reveal clues to the continuation of the games. Your success at “MathCaching” is dependent upon your skills at solving mathematical problems.
The MathCaching games are subject area dependent. There are free versions of MathCaching for Basic Math Skills (“BasicCaching”), Algebra (“AlgeCaching”), Geometry (“GeoCaching”), Algebra2 (Alge2Caching), Trig (“TrigCaching”), PreCalculus (“PreCalcuCaching”), Calculus (“CalcuCaching”) and TI-84+ Caching.
Assessment
Formative Assessment and Strategies in Secondary Mathematics
How can you help your students in becoming engaged thinkers? One key is Formative Assessments.
The Formative Assessment and Strategies in Secondary Mathematics resource will highlight and provide examples of useful formative assessment strategies.
Communication
Developing Relationships
Being able to develop relationships and create a good classroom environment may promote and assist communication during classroom activities. The following link on Developing Relationships presents strategies that may assist with promoting good relationships with students and a positive classroom atmosphere that is conducive to communication. Strategies include a “Who I Am” sheet that may be used as a tool to begin conversations with students and another strategy is a fun get to know you activity called “Five Things in a Bag”
Discuss Mathematics / Teach Each Other
Student learning is increased when students are able to discuss mathematical concepts and teach each other. The following teaching strategies may be used to promote student discussion.
Communication in Assignments
Students can create products that may help them practice a variety of forms of communication (written, audio, video, etc). The following are some possible products that students may create:
Show Me You Know Assignment
A “Show Me You Know…” Assignment involves the students providing evidence that they understand a particular concept. This evidence can come in various forms (written, audio, video, etc.). This type of assignment works well for procedural concepts and students demonstrate a “recipe” explaining the mathematical steps involved.
The following link contains two examples of student solutions to a “Show Me You Know… Substitution” Assignment:
Applying Assignments
Students are presented with a number of problems that require them to apply their skills in a new context. Students will select a question and write a complete solution to the problem including all explanations of their thinking. Marking will be done according to this rubric that breaks up the mark into half for the solution and half for justification / communication. M10-C Polynomials Example: Algebra & Number Applying Assignment
Below is an example that may be used to help explain expectations.
Susan is making a rectangular area rug with a similar design to a square rug she made earlier. (MHR pg. 212)
a) What are the dimensions if the new rug is 2 ft longer and 1 ft narrower than the square rug?
b) Write an expression for the area of the new rug.
c) If the square rug is 3 ft by 3 ft, which rug has the greater area?
- Poor Solution – the solution is correct but limited justification and communication
- Good Solution – correct solution and clearly explained
Connections
Connections consists of two main parts:
- Connections between mathematical ideas. (Mathematical Flow)
- Connections to real world applications. (Authentic Tasks)
Connections Between Mathematical Ideas
The following examples show attempts at connecting mathematical ideas…
- Adding & Subtracting Polynomials (use other concepts to show the idea of adding items of similar size / combining like terms)
- Area Model for Multiplication (Connect Basic Numerical Multiplication to Polynomial Multiplication)
Connections to Real World Applications
- M30-3 Purchase a Vehicle Project
- M30-3/M20-2 Probability & Games (Dice Games: Settlers of Catan or Pig)
– Play games to collect experimental probability for the sum of two dice and then compare to theoretical probability.
– Discuss how understanding probabilities can help when making decisions.
Mental Mathematics and Estimation
No Calculators
One attempt to improve mental mathematics is to not allow students the use of calculators for the Algebra & Number unit in Math 10C. The General Outcome for Algebra & Number is “develop algebraic reasoning and number sense” and eliminating the use of calculators prevents students from using the calculators unnecessarily and forces them to improve their number sense.
A great example of estimation is asking students to place a variety of powers, radicals, fractions, etc. onto a number line. This really shows a student’s number sense and understanding of the numerical value of powers and radicals.
Estimate First
In a PD Session I went to with Dan Meyer, he really emphasized getting students to make a guess before attempting to solve a problem. You can ask students to make three guesses: one they know is too low, one they know is too high, and one they think is correct.
One benefit from estimating first is that it helps with student “buy-in”. Students often want to know who made the best guess and how close they were to the correct answer.
Problem Solving
Investigations
The following examples ask students to look for patterns and then make conclusions.
- M10C Investigate Integer Exponents
- M10C Function Notation
- M10C Investigate Slope Intercept Form
- M20-2 Operations on Radicals (Addition & Subtraction, Multiplication, Division)
Lesson Flow
In the flow of my lessons I often present a problem first and then debrief with the students afterwards. It is often amazing what the students can come up with when presented with a problem and then their work can be a basis for discussion during the debrief. The debrief time also provides a time to formalize their work and I find the class is usually more interested in what you have to say since they are invested in the problem. The following are some example problems I’ve used:
Dan Meyer has also proposed a method called 3 Acts to help engage students in problems. Find a description of 3 Acts here and examples here.
Reasoning
The following are examples where inductive and deductive reasoning may be used throughout the mathematics curriculum:
M30-1 Matching Activity
Technology
Technology assists in exploring patterns and viewing multiple representations. Technology gives students the opportunity to be engaged learners.
The following are examples where technology may be used to assist teaching:
M20-2 Angles in Polygons
Distance-Time Gizmo from LearnAlberta.ca (Search within Learn Alberta for Distance-Time Gizmo)
Sine Law – Geogebra Animation by Glen Reesor
Other Useful Technologies
Explore Learning
ExploreLearning Gizmos are accessable through Alberta Education. The web site also allows a five minute trial of the activity. The Gizmos are online simulations that power inquiry and understanding.
xMind
A free, easy to use mind mapping program.
Prezi
A free (for educators) zooming presentation program.
YouTube
YouTube contains many educational videos. Have students upload their own video creations to your own YouTube channel.
Geogebra
A free dynamic math software program. Visit Glen Reesor’s site for some excellent Geogebra Creations!
Graph Sketch
A simple easy to use online graph sketching program.
Geometers Sketchpad
The Geometer’s Sketchpad requires a purchased license. There are many free activities available to download. The is an app for the iPad.
Learn Alberta
A website with many interactive learning programs for students & teachers.
Graph
A graphing program with many features.
Wolfram Alpha
A powerful computational knowledge engine.
Visualization
Concrete Materials
The following are examples where manipulatives may assist in visualizing abstract concepts.
- M10C Polynomial Algebra Tiles – Algebra tiles are a life-saver for students who struggle with abstract concepts.
- M10C Nets for Surface Area – Allowing students to derive the surface area formulas from nets assists in their understanding of the formulas and how to use them.
- Volume of Pyramids vs. Prisms Investigation – Use giant geo-solids and water or sand to show how many pyramids will fit into the corresponding prism with the same base and height. Get students to guess first!
- M30-3 Transformations in Art -Students loved this lesson where we identified as many transformations that we could find in various pieces of geometric art. They then created their own pieces! (Activity Files)
Technology
The use of images, animations and video can assist students in their visualization of concepts.
Variety of Visual Representations
Graphic organizers are a great way to assist students in visualization as well as making connections.