In this activity students are each given one card. The card will either have a fraction, percent or decimal. Their job is to find the two other students who have the same value but a different representation. This shouldn't take too long and could be repeated every couple of days just to solidify conversion between fraction, decimal and percent.
If you wish you can also have students do this individually with this Desmos cardsort.
Gr7 - determine, through investigation, the relationships among fractions, decimals, percents, and ratios
Gr8 - translate between equivalent forms of a number (i.e., decimals, fractions, percents)
MPM1D, MFM1P - As review
Download the cards and cut them out (you may want to put them on cardstock and laminate)
Shuffle the cards and distribute one per student. Note that there are 12 sets of 3 cards so you may want to remove sets to more closely match your student population.
Instruct students to find the two other people that have the same value but a different representation.
Once students find their partners they will be in groups of three,
Group Fractions, Decimals, Percent Cards (Googledoc) (pdf)
In Ontario our grade 7 students are introduced to solving simple equations in the form ax + b = c where the values of a, b and c are whole numbers. We think it's a good idea for them to start by having some sort of visual representation of each equation. In this activity, students are given 16 cards that correspond to 16 equations represented as strips (the top and bottom of the strips represent the left and right sides of the equations). They are more commonly called bar models but we have always used the name equation strips. Students solve for x given the strips and then rewrite the algebraic form equation. We originally got this idea from the 2011 Solving Equations Gap Closing resource (pg14).
[Updated Mar 6, 2018 - now both the printable cards and the dynamic websketch have equations in the form 2x - 5 = 19. This puts it beyond the grade 7 expectation but could be an extension or just used for grade 8]
[Updated Dec 19, 2019 - now including a single dynamic Desmos version where you can switch all the versions using sliders as well as a Desmos Activity where students first do some static practice problems and then it finishes with a Challenge Creator where students make their own question for the others to solve]
[Updated May 9th, 2022 - I added a card sort to the Desmos Activity and included a pdf version]
Grade 7 Patterning & Algebra - solve linear equations of the form ax = c or c = ax and ax + b = c or variations such as b + ax = c and c = bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator
Grade 8 Patterning & Algebra - as review
Each group gets a set of 16 cards (24 if you use the cards with minuses)
Make several copies of the cards on card stock and laminate them so they last longer. You may wish to copy each set onto a different colour so that if they get mixed up you know each set by their colour.
Cut out the cards so that each group gets a set of 16.
Each group of 2-3 students gets one full set of 16 cards.
Students are to determine the value of x for each card.
Once determining x then they should then determine the algebraic expression for each card
You can circulate with the solution card to check answers.
Once finished you can create your own cards using this web sketch or this Desmos sketch. This allows you to change the coefficients of a, b & c and it generates all four possible configurations. This web sketch assumes that a, b & c will be whole numbers and will not allow any solutions that have x as negative. Once you put your coefficients in then take a screenshot, use the screen capture software of your choice to copy and paste the version you want to use (For Windows use the Snipping Tool, for Chromebooks use Shift CTRL F5, for Macs use Command Shift 4, or iPad use the Home and Sleep buttons together. You can then paste into the word processor of your choice.
If using the Desmos Activity, pair students so that they can have conversations about the
strips. Be sure to explain how when they create their challenge, they will first have to solve it before they can submit it for the rest of the class to do. When using the Desmos activity, note that the "x's" are missing to make the connections to explicit equations less visible. This is so that students are free from the stigma of actual equations while still solving them. You might want to start with this.
Note that if you want to modify the Desmos activity, you might want to watch this video on how to do it:
[Added July 2024] And here is @Howie_Hua doing some explainer videos of how to use Equation Strips (Bar Models)
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)
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.
Instruct students to
find the two other people that have different representations for the same
quadratic relation.
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.
In this activity students are each given one card. The card will either have a fraction, percent or decimal. Their job is to find the two other students who have the same value but a different representation. This shouldn't take too long and could be repeated every couple of days just to solidify conversion between fraction, decimal and percent.
