Sort students into groups using Quadratic Representations

In this activity students are each given one card. The card will either have a graph, table of values or equation of a quadratic relation. Their job is to find the two other students who have the other two representations of the same quadratic relationship. This shouldn't take too long and could be repeated every couple of days to solidify conversion between representations.
New: Alternatively, you could have students just work individually on this Desmos card sort 

• MPM2D - A3.3 determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y = a(x – r)(x – s);
• MBF3C - A1.8 determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation
• MCF3M - A1.5 determine, through investigation, and describe the connection between the factors used in solving a quadratic equation and the x-intercepts of the graph of the corresponding quadratic relation
• MCR3U - As review

• Download the cards and cut them out (you may want to laminate them)
• If you are doing the Desmos Cardsort instead, students should have devices to do the sort on (note that phones have screens that are too small)

1. Shuffle the cards and distribute one per student. Note that there are 11 sets of 3 cards so you may want to remove sets to more closely match your student population.
2. Instruct students to find the two other people that have different representations for the same quadratic relation. 
3. Once students find their partners they will be in groups of three

If doing the Desmos Cardsort instead, have students (or pairs of students) complete each page of the cardsort. You may wish to consolidate on the last page of the card sort.

• GroupQuadratics (Googledoc) (pdf)
• Desmos CardSort 

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Sort Students into Groups using Linear Representations

In this activities students are each given one card. The card will either have a graph, table of values or equation of a linear relation. Their job is to find the two other students who have the other two representations of the same linear relationship. This shouldn't take too long and could be repeated every couple of days to solidify conversion between representations

MPM1D, MFM2P  - 

• graph lines by hand, using a variety of techniques
• identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b

• Download the cards and cut them out (you may want to laminate them)

1. Shuffle the cards and distribute one per student. Note that there are 11 sets of 3 cards so you may want to remove sets to more closely match your student population.
2. Students will find the other people who have the same linear relationship

• GraphTableLineMatch (doc) (pdf)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

An Open Sort dealing with Similarity and Congruence

In this activity students are given a card that has some sort of image on it. This is an open sort. That is students are then asked to sort themselves with no other instructions. Teachers are often leery of this type activity (with so few instructions) because they are worried that it might not go the way they want. Sometimes that is true but most times kids will do alright. And they need opportunities to think freely about math without the burden of assessment. This is a great way to do it.
New: Alternatively, you could have students just work individually on this Desmos card sort

• Gr7GS - distinguish between and compare similar shapes and congruent shapes, using a variety of tools
• Gr8GS - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes.

Set of Open Sort cards. There are 21 all together so you may need two sets if you have a bigger class. Print them on card stock, cut them out and laminate (optional)

1. Each student is given a card 
2. Ask students to sort themselves out using any criteria they wish
3. If sorting isn't happening in the way you wish, you may want to take some of the openness away and give them a bit more instruction.

The videos, below, are only visible in the WECDSB domain. That is, only teachers in our school board can see the video if they are logged into their MyTools2Go accounts.

• Open Sort Similarity Cards (pdf) (doc)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Sort Students into Groups Using Integers

If you want a quick activity that you can use to randomly put students into groups of two or four, look no further. This activity uses integers represented in words and with tiles to sort students into groups. This could be used with any class where students can add integers (subtraction is not needed) and represent them with tiles.
In each row is a set of integer cards that represent the same number. The next row will have a set of cards that has the opposite number. 

• Grade 7 Number Sense & Numeration 
• Grade 8 Number Sense & Numeration (review)

• Integer Cards Prep work: Cut the cards out. Note that every two rows of cards make up a set of four. Remove sets according to how many students you have.
• Bag or Bin to put cards in

1. Each person chooses a card and finds their partner. The person with a card that represents the same integer. Stop here if you only want students in pairs.
2. Next this pair of students looks for the other pair of students who has a number that will add together with theirs to equal zero

• Choosing Groups with Integer Cards (doc) (pdf)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Sort Graphs into Types of Data

This is a simple and quick sorting activity for graphs to help introduce the idea of types of data. And although that is the intended purpose it is done as an open sort so that students can (hopefully) start to see that there are different types of data without being formally introduced to them. This is not intended to be a long activity but just a short Minds On type to begin a class. Keep in mind that if students don't sort them by data type then you may have to ask some leading questions to help move them that way. Though this was originally developed for the MDM4U class, by removing some of the graphs, it could be used for grades as low as 7 (for example, grade 7 students will likely not have seen histograms).
[Updtae - Now a Desmos Card Sort version exists]

• Gr7DM, Gr8DM - collect and organize categorical, discrete, or continuous primary data and secondary data
• MBF3C - identify different types of one-variable data (i.e., categorical, discrete, continuous)
• MDM4U - distinguish different types of statistical data (i.e., discrete from continuous, qualitative from quantitative, categorical from numerical, nominal from ordinal, primary from secondary, experimental from observational, microdata from aggregate data)

• One set of graph cards per group

1. put students in groups
2. distribute cards with graphs 
3. ask them to sort in any way they see fit. Use the results to steer towards types of data. Students should focus on both the look of the graph and the characteristics of the data being shown.
4. possible leading questions: "Can you arrange these so that there are only two groups? If so can you arrange each of those two groups into sub groups?" 
5. As an extension or alternate activity, students could sort by types of graph.

Note that the graph of the number of friends is a histogram which might lead some to think it is continuous data. This could be a good talking point as the number of friends a person can have can only be a discrete amount. 

Types of Data cards (doc) (pdf)
Desmos Card Sort (with self checking feature for numerical and categorical)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks