Tarsia Puzzle Squares and Square Roots

We came across these puzzles a few years ago. The premise is that you have a bunch of questions and matching answers. Students have cards that have either an answer or question on the edge. They then have to match up the edges that have the pairs of questions and answers and eventually it will make a shape. In this case the activity is matching up perfect squares and square roots.
We found these puzzles originally on the Mr Barton Maths site under the Tarsia Jigsaw Page. The nice thing here is the Tarsia software can be downloaded here (click the green button to download - unfortunately it is Windows only) and you can edit or create your own puzzles. So this puzzle was one of our creations. There are even banks of hundreds of already created puzzles on the site (just scroll down on the Tarsia page and look for the smiley faces for zipped files). These are great puzzles to pull out when you want to break up a long class or have 10 min at the beginning or end of a class to fill.

• Gr7NS - represent perfect squares and square roots, using a variety of tools 
• Gr8NS - estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not 

Tarsia Card Prep work: There are two downloads (three if you include the actual Tarsia file). The actual cards for the puzzle and the answer card. The cards for the puzzle come on 2-4 sheets (there are different styles of puzzles) and each triangle needs to be cut out (see image tot the right). We have found that if you have several sets of the same puzzle (say if students do it in groups of 3) then it is best to copy each set in a different colour. That way it is harder to get the sets mixed up and easier for clean up after (ie you only need to check if there are 18 cards of each colour). We find that the cards last longer if you laminate them first then cut them.

1. This activity can be done in groups or individually and can take about 5-10 min depending on the student.
2. Hand students the entire set and ask them to match up the numbers written as a square root and its answer.
3. In this case the finished puzzle looks like a diamond.

• Note: this puzzle is a little tricky since all the numbers on the outside edge are not perfect squares and thus have no match. Also there are numbers that appear twice like 16 since it is the root of 256 and has a root of 4

• Square Root Tarsia Cards (pdf)
• Square Root Tarsia Solution (pdf)
• Square Root Tarsia Editable (xjsw)

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

Data Management Scavenger Hunt

This is an activity that we adapted from a TIPS activity (Grade 8 Unit 11, Day1, Pg 3). In this activity student are given a set of data (with no labels) and asked to find their matching graph and title (which are randomly placed around the room). Once finding their cards they are given a question card to use with their graph and data. It's actually a surprisingly difficult activity but it helps bring out conversations about types of data and what they should look like.

• Gr7DM - select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph; read, interpret, and draw conclusions from primary data and from secondary data presented in charts, tables, and graphs (including relative frequency tables and circle graphs);
• Gr8DM - select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph; read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);
• MBF3C - D1.5 identify different types of one-variable data, and represent the data, with and without technology, in appropriate graphical forms (e.g.,histograms, bar graphs, circle graphs, pictographs)
• MAP4C - D1.4 create a graphical summary of two-variable data using a scatter plot , with and without technology
• MDM4U - D1.5 interpret statistical summaries to describe the characteristics of a one-variable data set (note that this certainly can be used as review of all types of data)

Data Management Cards Prep work: Print, laminate (optional) and cut the cards out. Separated out the sets of data from the graphs and Titles. Each page contains one set of data, graph and title (note that one set has two possible matching graphs). Also included in the set are a page with extra questions and a page with the answer key on it.

1. Prep the classroom by randomly sticking the graphs and the titles around the room for students to find. Note that this activity was originally made for grade 8 but if you wanted to do it for grade 7 you should probably consider taking out any graphs with scatter plots.
2. Put students into groups of 2 or three (there are 17 different sets of cards)
3. Each group gets a set of data and are told to wander the room looking for their matching graph and title. Some of these are not easy so students should work together to decipher the information. You should probably circulated to give hints (with your answer key).
4. Once a group finds their matching cards, they are given a question card to answer regarding their graph.
5. If they finish early give them another set of data to try.

Data Management Scavenger Hunt (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 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

Sort Students into Groups using Equivalent Fractions

If you want a quick activity that you can use to randomly put students into groups of four, look no further. This activity uses fractions with common denominators and then equivalent fractions to sort students into groups. This could be used with any class where students can add fractions and compare equivalent factions.
In each row are two sets of fractions with common denominators. When you add each pair (with the same denominator) they will simplify to the same fraction

• Grade 7 Number Sense & Numeration
• Grade 8 Number Sense & Numeration (review)
• MPM1D
• MFM1P

• Fraction Cards Prep work: Cut the cards out. Note that there are 8 rows of fractions. Remove sets according to how many students you have.
• Bag or Bin to put cards in

1. Choose a fraction and find your partner (the person who has the same common denominator). Introduce yourself. He or she is your team member. 
2. Add your fractions and simplify the answer. 
3. Find the other team with the same simplified fraction. Introduce yourselves. This is your group of four

• None yet

• Choosing Groups with Fractions 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

Quadrilateral Heads Up

Made popular on The Ellen Show, Heads Up is a game where one person holds a card on their forehead (facing their opponent) and the second person has to give hints about what is on the card (without using any of the words on the card). The first person uses the clues to try to guess what is on their forehead.
In grade 8 we have an expectation that requires students to classify quadrilaterals based on characteristics of the diagonals. This activity does a good job of consolidating that knowledge in a fun game.

• Grade 8 Geometry and Spatial Sense - sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation using a variety of tools. Can also relate to : investigate and describe applications of geometric properties in the real world.
• MPM1D (for review of polygon properties)

• One set of Quadrilateral Picture cards per pair of students
• One Quadrilateral Prompt card per pair of students

1. Give each pair of students one set of cards (18 picture cards and one prompt card)
2. One student is the "guesser" and the other gives the clues.
3. The guesser randomly selects a picture card, without looking at it, and places it on their forehead.
4. The other person gives clues about the properties of the quadrilaterals seen on the picture card. They should use clues relating to the diagonals (to hit the expectation) and may use the prompt card to help remind them of possible clues they can give. Note that by focussing the clues on the diagonals, this requires both the guesser and clue giver to know about their properties relating to quads. Note that we have included an image on each card to connect to the real world. However, we want the clues to be about the diagonals not about the pictures (ie we don't want students to say "its a football field" as a clue)
5. Once the guesser guesses correctly, they can choose another card and play again or the two students can switch roles.

 

None yet but here is a clip of it happening on The Ellen Show

• Quadrilateral Heads Up Picture Cards (doc) (pdf) 
• Quadrilateral Heads Up Prompt Card (doc) (pdf) There are 6 cards on this sheet but only one is needed per group.

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