## This page contains lessons and activities we have taught/co-taught in GSSD math classrooms.

Ideas and resources for exploring fractions with manipulatives

**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.

Quadratic graph equation DR entrance match

Collaborative matching and word wall activity

fraction matching groups of three

**Teaching a Problem Solving Strategy**

Click here for link to the notebook file

**Understanding Fractions using fraction strips N5.5, 6.7, 7.5, 8.4**

## –Notebook lesson (saved as ppt for slideshare)

Click here for a link to the notebook file

Fraction matching activity to find partners (word doc). You can cut out these fractions and put them on cards for a reusable activity

fraction matching groups of three

Ideas and resources for exploring fractions with manipulatives

Adding fractions with fraction pieces handout

**Teaching the importance of communication and a thorough answer**

**Generating Criteria for Assessement**

Click here for a link to the notebook file

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

Math Benchmarking Rubric – 2012

**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

Braden and Jill were asked the following question

Collaborative matching and word wall activity

Math 6 Measuring Angles Word definitions

Math 6 Measuring Angles Photos, Practice Sheets

**P6.2 and 6.3 Modeling Equalities with Algebra Tiles and Equation Mats**

P6.3 Associative and Commutative Properties Matching Game

P6.3 Model the Following Equations on an Equation Mat

Click here for a downloadable Equation Mat

**N 6.2 Factors**

Lesson Plan N 6.2 Factors exit slip

**P7.1 Writing an expression for a Linear Relation**

Can I write the expression for a linear relation

Math 7 N7.1 Patterns and Relations hand out

**N 8.1 Estimating Square Roots**

Click here for a link to the notebook file

N 8.1 f estimating square roots entrance slip

N 8.1 f estimating square roots

**N 8.3 Ratios**

Click here for a link to the notebook file

Ratio-AppleJuiceProblem-Entrance Slip

Ratio-SkittlesProblem-Exit Slip

**N 8.3 Ratio and Proportion Inquiry Lesson**

## Lisa Johnson, Canora Comp

Lesson Plan Lisa Similar Figures

Similar Activity (Barbies) Lesson plan

Similar Activity (Barbies) Similar

Journal Entry – Barbie and Ken

**N 8.5 Fraction Pod Review Activity **

Lisa Johnson, Canora Comp

Recipes to Riches – symbolic-1

Student worksheet Tell me What you Know oh oh – teacher lead conference

Till Math do us Part – pictoral

When student’s can’t do the pods…(1)