- Model and solve problems involving the intersection of two straight lines.
- Solve problems using analytic geometric involving properties of lines and line segments. Verify geometric properties of triangles and quadrilaterals using analytic geometry.
- Determine the basic properties of quadratic relations. Relations transformations of the graph of y = x2 to the algebraic representation of y = a(x - h)2 + k.
- Solve quadratic equations and interpret the solutions with respect to the corresponding relations. Solve problems involving quadratic relations.
- Use knowledge or ratio and proportion to investigate similar triangles and solve problems related to similarity. Solve problems involving right triangles, using the primary trigonometric rations and the Pythagorean Theorem. Solve problems involving acute triangles, using the sine law and the cosine law.
There are also the mathematical processes to consider:
The mathematical processes that support effective learning in mathematics are as follows:
• Problem solving
• Reasoning and proving
• Selecting tools and computational strategies
I decided that my first cycle would be all about relationships. Students will do activities that allow them to collect and work with data and they will look at patterns to help establish important relationships right away. As always, time is flexible with any of these activities and things never go according to plan! But I have a plan anyway.
Day 0: The Crow and the Pitcher
I stole this from Pam Wilson who blogged about it here.
I bought some great, tall cylindrical glasses (pictures will be in Tuesday's post) and more marbles and created this handout (update: the handout now includes homework). I have different sized marbles so if a group finishes early they can experiment with larger marbles or combinations of different sizes. By the end of the class, I will put some water in my glass and have each group determine the number of marbles needed to fill it. Then we will see which group came closest by actually adding marbles until the water reaches the very top of the glass. It should be fun.
I love doing activities on the first day, not only because it is a great way for the semester to begin for the students, but also because I get the opportunity to observe my students. I did not teach any grade 9s last year, so I won't know any of them. I will learn their names as I circulate and also learn who the extroverts are, who is quiet, who thinks they can sit back and let the others do the work, who is enthusiastic, who is a perfectionist...
Day 2 & 3: Visual Patterns
I have often professed my love for visual patterns and particularly for Fawn Nguyen's site: visualpatterns.org. I decided to spend at least two days working through linear and quadratic patterns. I made this handout (made = stole pictures and formatted stuff). The first three pages are the patterns students will work on in class and the last two will be their homework. This will help set up the mindset of seeing more than one way to solve a problem and will hopefully challenge some of the high flyers that are used to not having to do too much thinking.
Day 4: Solve Me (Balance Benders)
No handout on this one yet, but we will be spending time here, having fun while solving equations.
That's the plan for my first week. After that we will do ropes, frogs, Desmos, some 26 squares and more. Stay tuned!