This page contains lessons and activities we have taught/co-taught in GSSD math classrooms.
Matching Activity–any grade or topic
This idea comes from one of my favourite resources, Cooperative Learning and Mathematics, Dina Kushnir, Kagan Publishing
There are various ways to use the matching activity. In general, meet kids at the door and hand each one a card. Then tell them to find their partner. The less you explain about how partners are determined, the better. Students need to communicate and explain to one another how to find partners. I’ve used this with fractions (mixed and improper), geometry definitions and diagrams (which can then become part of the word wall), matching equations to graphs (linear, polynomial, rational), simplifying radicals, and many other topics.
This activity can be a way to randomly pair or group your students. You can expand on the communication opportunities by having partners explain to another pair or to the class how they knew they were partners. It is also a formative assessment opportunity and peer teaching opportunity. You can keep it short or elaborate on it in many ways.
Teaching a Problem Solving Strategy
Understanding Fractions using fraction strips N5.5, 6.7, 7.5, 8.4
–Notebook lesson (saved as ppt for slideshare)
Fraction matching activity to find partners (word doc). You can cut out these fractions and put them on cards for a reusable activity
Teaching the importance of communication and a thorough answer
Generating Criteria for Assessement
Slide 1: Have a discussion about what math really is: A way to describe the world, relationships that govern matter and life, a way of modeling,predicting, determining, etc.
Slide 2: Some examples of math in life: Population models, DNA, equations that govern traffic flow and help design cities, etc
Slide 3: Video. Preload this.
Slide 4: Canada is one of the only countries where people would say “I teach Math”. In most countries they say “Maths”, short for Mathematics, plural because there are so many disciplines: Statistics, probability, geometry, discreet math, algebra, calculus, logic. Many kinds of thinking are mathematical thinking. I usually discuss with students that solving puzzles, doing art and many other things are really forms of mathematical thinking. Many students that think they are “not good at math” will often excel at and enjoy many of these other types of mathematical thinking. This is empowering. I also often discuss how Abraham Lincoln, the young lawyer, read Euclid’s “The Elements”, because mathematical proof is the basis of logical argument. I expand on this by discussing what its like to argue a court case, and have evidence. Also Lincoln is an example of a very successful person who struggled with school mathematics.
Slide 5: Students think math is old, boring, dry, but I like to present it as a living, vibrant, current study. We are still discovering and learning. I know 0/0 is a poor example because a calculus teacher will argue that it is an indeterminate case and demonstrate it on a graph, but really, what is an indeterminate case? And for the purpose of middle years math this can generate good discussion, because kids will argue that you can’t have zero in a denominator–this is undefined. But zero in a numerator gives us zero. On the other hand, and number over itself equals one.
I follow this up with the example of famous mathematical conundrums, such as Fermat’s last theorem, solved by Andrew Wiles in the 1980s. There is a great 9 minute youtube clip of the documentary–a real engaging example of proof and its pursuit. Vi harts videos are great here too. Also the Clay Institutes “Millennium Problems”, a million dollar prize for anyone who can solve these. One was solved fairly recently, and the mathematician turned down the million dollars, saying “My proof is reward enough” (you can google this).
All these examples help students think about math beyond the text. Real math is not solving problems who’s answers are in the back of the book anyway! Real math is exciting, collaborative, and surprising–and essential to sciences, construction, design, biology, etc. You can augment this with many examples: Golden ration (phi) in nature, Pascals triangle and combinatorics and the wierd powers of 11, the grade 6 students who created a triangle like Pascal’s triangle, probability like the Monty Hall problem, and so on.
Slide 6: A discussion of proof. You can use the diagram to prove that vertically opposite angles are congruent. The casino is there as a visual for an anecdote about mathematicians in casinos who sometimes have to calculate games and give-aways associated with slots. They would calculate, for example, how many times a slot machine would be played before a car-giveaway would be won, ensuring the take covered the cost of the car. But if luck causes the car to be won before its paid for, they may be asked by management to explain their calculations. ( I include this because I’ve heard of this happening!) The point here is that proof is as important as the answer.
Slide 7: The example on left is the plane that crash landed over Gimli Manitoba because someone calculated the fuel wrong. The correct answer is important!!! On the right side is a question that has more than one correct answer–it depends (this is from Dan Meyers three act maths).
Slide 8: Hopefully students have now had a bit of insight into why a thorough answer is more than a number. We need to explain and make our reasoning visible, and provide proof. Now students can brainstorm what a thorough answer looks like, and generate some criteria. They can do some “peer assessment” on benchmarking summative assessement tasks (use anchor papers) or on the GSSD anchor papers saved on this site under GSSD Benchmarking. After students create their criteria and use it to self and peer assess some answers to math problems, you can introduce the exemplars rubrics or create your own
SS 6.1 Measuring Angles
To make this lesson relative and provide applications, we took photos of the school yard and nearby community, printed them in grayscale and lightened the saturation a bit so students could write on them, and printed as pdf’s. Students measured as many angles as they could and then discussed the purpose of the angle in the structure, such as design, support, drainage, etc.
For the full set click the link: Math 6 Measuring Angles Photos, Practice Sheets
Math 6 Measuring Angles Photos, Practice Sheets
P6.2 and 6.3 Modeling Equalities with Algebra Tiles and Equation Mats
Click here for a downloadable Equation Mat
N 6.2 Factors
P7.1 Writing an expression for a Linear Relation
N 8.1 Estimating Square Roots
N 8.3 Ratios
N 8.3 Ratio and Proportion Inquiry Lesson
Lisa Johnson, Canora Comp
N 8.5 Fraction Pod Review Activity
Lisa Johnson, Canora Comp