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Shareables

Grades k–2
Grades 3–5
Grades 6–8
Grades K–2
Grades 3–5
Grades 6–8

Grades K–2

Getting Groceries

What You’ll Need:
Scissors
Paper
Grocery receipts with different numbers of items on them (but not 20 items)

Cut a piece of paper so that it looks like the same length as a receipt from a grocery store if you buy about 20 things.

Sample Answer:

Put ‘em Together

What You’ll Need:
Put ‘em Together printout

Print and cut out the cards from the Put ‘em Together printout. Shuffle and put them face down in a pile. Then give students these instructions:
Play in pairs or threes. Each player chooses 3 cards. If two of the numbers added together equal the third number, the player gets 2 points. If two of the numbers added together are 1 or 2 away from the third number, the player gets 1 point. If two of the numbers added together are 3 or more away from the third number, the player gets 0 points.

Return the cards to the pile and shuffle them before playing again.

The first player to get 12 points wins.

Sample Answer:
Jaspreet chooses 4, 8, and 10. 4 + 8 = 12, which is 2 away from 10. Jaspreet gets 1 point.
Adam chooses 5, 6, and 11. 5 + 6 = 11, so Adam gets 2 points.
Rose chooses 1, 9, and 13. Since 1 + 9 is 3 away from 13, Rose gets 0 points.

In a Row

What You’ll Need:
In a Row printout

Print and cut out the cards from the In a Row printout. Shuffle and put them face down in a pile Then give students these instructions:

Play in pairs. Each player picks up 4 cards and arranges them to create 2 different two-digit numbers. They then subtract the 2 numbers.

If there are consecutive (in a row) digits in the two numbers created and the answer after subtracting, the player gets a point.

Return the cards to the pile and shuffle them before playing again.

The first player to get 10 points wins.

Sample Answer:
Carter chooses 3, 9, 1, and 4. He creates the numbers 49 and 31. He subtracts his numbers to get 18. There is an 8 in 18 and a 9 in 49, but no 7 in 31 to get 7, 8, 9. There is a 3 in 31 and a 4 in 49, but no 2 or 5 in 18 to get 2, 3, 4 or 3, 4, 5. The three numbers (49, 31, and 18) do not have any digits in a row, so Carter gets no points.
Brianne chooses 1, 4, 5, and 9. She creates the numbers 94 and 51, and the difference is 43. There is a 3 in 43, a 4 in 94, and a 5 in 51; since 3, 4, and 5 are consecutive numbers, Brianne gets a point.

Paw Prints

What You’ll Need:
Paw Prints printout

You might read a book to students about animal footprints (e.g., Whose Track is That? By Stan Takiela, or Big Tracks, Little Tracks: Following Animal Prints by Millicent E. Selsam).

Share the Paw Prints printout with students and talk about how they’re alike and different.

Let them choose a favourite and either create a pattern or a path with their animal footprint.

Alternatively, students could create two of each of six of the prints drawn on cards and create a matching game.

Example:

I picked the bear paw prints and the tiger paw prints. I noticed that they both have claws and a big paw print at the bottom. I also noticed that the bear has one extra toe.

Grades 3–5

Make a Difference

What You’ll Need:
Make a Difference printout

Print and cut out the cards from the Make a Difference printout. Shuffle and put them face down in a pile. Then give students these instructions:
Play in pairs. Each player chooses five cards and makes a three-digit number and a two-digit number to subtract.
The player with the greater difference gets a point.

Return the cards to the pile and shuffle them before playing again. The first player to get 10 points wins.

Sample Answer:
Jasmine picks 3, 4, 9, 2, 5 and makes the numbers 954 and 23. The difference is 931.
Aki picks 1, 1, 8, 2, 4 and makes the numbers 842 and 11. The difference is 731.
Jasmine gets a point because her difference is greater than Aki’s.

Fraction Action

What You’ll Need:
Fraction Action printout

Print and cut out the cards from the Fraction Action printout. Shuffle the cards and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player chooses two cards and creates a fraction less than 1.

Compare the fractions. The player with the greater fraction gets a point.

Return the cards to the pile and shuffle them before playing again. The first player to get 10 points wins.

Sample Answer:
Sammie chooses 8 and 20.
Derek chooses 4 and 6.
8/20 is the same as 2/5 and 4/6 is the same as 2/3.
2/3 is greater, so Derek gets a point. 

All About Tens

What You’ll Need:
All About Tens printout

Print and cut out the cards from the All About Tens printout. Shuffle the cards and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up three cards and arranges them to make a two-digit number and a one-digit number to multiply. The player with the greater tens digits in the product gets a point.

Return the cards to the pile and shuffle them before playing again. The first player to get 10 points wins.

Sample Answer:

Elleanor chooses 4, 5, and 8, and multiplies 48×5 to get 240. The tens digit is 4.
Devi chooses 3, 7, and 9, and multiplies 39×7 to get 273. The tens digit is 7.
Devi gets a point because she has the greater tens digit.

Six Apart

What You’ll Need:

No materials necessary

Two regular shapes (all sides equal) have the same perimeter and the side lengths of the two shapes are 6 cm apart.

What could the shapes be and how long are the sides?

Sample Answers:
It could be a square with side lengths of 18 cm and a hexagon with side lengths of 12 cm. They both have a perimeter of 72 cm.
OR
It could be a square with side lengths of 12 cm and an octagon with side lengths of 6 cm. They both have a perimeter of 48 cm.
OR
It could be a hexagon with side lengths of 15 cm and a decagon with side lengths of 9 cm. They both have a perimeter of 90 cm.

Grades 6–8

Plus or Minus

What You’ll Need:
Plus or Minus printout

Print and cut out the cards from the Plus or Minus printout. Shuffle and put them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up 2 cards and can either add them or subtract them. The player with the greater result gets a point. 

Return the cards to the pile and shuffle them before playing again. The first player to get 10 points wins.

Sample Answer:
Zaki chooses 4 and –12. He chooses to subtract: 4 – (–12) = 16.
Ameena chooses 10 and 2. She chooses to add: 10 + 2 = 12.
Zaki has the greater result, so he gets a point.

How Fast?

What You’ll Need:
Calculator

Provide this information about animals’ speeds.

Antelope 88 km/h
Hare 1333 m/min
Cheetah 33 m/sec
Ostrich 17 km/15 min
Wildebeest 243 km/3 h

Then pose the following to the students:
• Which animal is fastest?
• Which is slowest?
• Create a problem using the data where the solution to the problem is less than 3.

Sample Answer:
To figure out the fastest animal, I converted all the measurements to km/h.
1333 m/min is almost 80 km/h.
33 m/sec is about 119 km/h.
17 km/15 min is 68 km/h.
243 km/3 h is 81 km/h.

The fastest is the cheetah.
The slowest is the ostrich.

My problem is this one:
How many more kilometres per hour does a wildebeest go than a hare?
Answer: 81 km/h – 80 km/h = 1 km/h

Algebra Away!

What You’ll Need:
Algebra tiles (virtual or physical)

Provide students with algebra tiles. Then give students these instructions:
Model an equation with a total of 12 algebra tiles.
Solve the equation.
Repeat with three other equations.
Use some positive and some negative tiles in at least two of the equations.

Sample Answer:

4x = 3x − 5

Frazzled Fractions

What You’ll Need:
Random number generator

Give students these instructions:

Play in pairs. Each player uses the random number generator to get four random numbers between 1 and 100. Each player then creates two fractions with the four numbers and subtracts the two fractions.
The player with the greater difference wins a point.

Repeat the process. The first player to get 10 points wins.

Sample Answer:
Roberto’s random choices were 12, 26, 14, and 82.

The fractions he chose to create were 82/12 and 14/26.

The difference was 82/12 minus; 14/26, which is about 7 minus; 1/2 = 6 1/2.

Julia’s random choices were 6, 10, 23, and 48.
The fractions she chose to create were 48/6 and 10/23.
The difference of 48/6 minus; 10/23 was about 8 minus; 1/2 = 7 1/2.

You can see Julia’s answer is greater from the estimate; there was no need, this time, to actually do the calculation. So Julia gets a point. 

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Grades K–2

Pond Pairs
Pond Pairs

What You’ll Need:
Counters

Pose this problem for students:
A pond has frogs, swans, and ducks. There are 10 animals altogether. How many of each could there be if 2 of the numbers are the same?

Sample answers:
There could be 2 frogs, 4 swans, and 4 ducks.
There could be 3 frogs, 3 swans, and 4 ducks.
There could be 1 frog, 1 swan, and 8 ducks.

Bunches of Bananas

What You’ll Need:
Pictures of bunches of bananas

Pose this problem to students:
How many bananas do you think are usually in a bunch?

Example:
I think there are usually about 6 bananas in a bunch.

Pond Pairs
Pet Pictures

What You’ll Need:
Two sheets of blank paper
Pencil, pen, or markers

Give students these instructions:
On one sheet of paper, draw a picture of a big dog. On another sheet of paper, draw a tiny mouse and a cat that isn’t too big. Make sure the cat in your second picture is about half the size of the dog in your first picture.

Tricked You!

What You’ll Need:
Cups of different sizes
Water

Give students these instructions:
Fill two different cups with water. Set up your cups so that the cup that holds more does not look like it does. See if you can “trick” a grown-up by asking which holds more. Then show them which really holds more.

Example:
I filled a thin but tall glass all the way to the top and a wide glass a bit over half. The wide glass had more water than the thin glass but looked like it had less. I asked my dad which glass had more water. He guessed that the thin glass had more water.
I poured the water into two glasses of the same size to show my dad that the wide glass had more water in it. I tricked him.

Pond Pairs
Double-Digit Draw

What You’ll Need:
Double-Digit Draw printout

Print and cut out the number cards from the Double-Digit Draw printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up four cards and makes two numbers greater than 10. If the sum of the two numbers is more than 60, the player gets a point. Return the cards to the pile, shuffle, and repeat. The first person with 10 points wins.

Example:
Alem picks up the numbers 1, 1, 4, and 1. He makes the numbers 11 and 41. The sum is not more than 60, so Alem does not get a point.
Kendra picks up the numbers 2, 3, 3, and 5. She makes the numbers 32 and 53. The sum is more than 60, so Kendra gets a point.

Card Continuation

What You’ll Need:
Card Continuation printout

Print and cut out the number cards from the Card Continuation printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Place two cards face up in a row, making sure that the smaller number is first. If the two numbers come in a row when you count (such as 3 and 4, or 8 and 9), the first player gets a point. If the two numbers are not in a row (such as 2 and 5, or 7 and 4), the second player gets a point. Return the cards to the pile, shuffle, and repeat. Take turns. The first player with 10 points wins.
With your partner, decide if you think the game is fair. Why or why not? How long does it usually take to win?

Example:
Serena picked up a 4 and a 5. She gets a point because her numbers are in a row.
Luca picked up a 5 and a 9. He does not get a point because his numbers are not in a row.
The game is not fair because there are not as many combinations in a row as combinations not in a row. It took 12 turns for someone to win.

Pond Pairs
Geometric Giraffe
What You’ll Need:
Pattern blocks

Give students these instructions:
Use pattern blocks to make a giraffe. How many pattern blocks did you use?

Example:
I used 17 pattern blocks to make my giraffe.

Bar Barriers

What You’ll Need:
Bar Barrier printout
Pencil or pen

Print and cut out the bar models from the Bar Barrier printout. Give each student a bar model. Then give students these instructions:
Put numbers in the bars so that the bottom numbers add up to the top number and the sizes of the two bottom sections seem right.

Example:

Grades 3–5

Pond Pairs
Six-Sided Selection

What You’ll Need:
Six-Sided Selection printout
Pencil

Give students these instructions:
Using the centimetre grid paper on the Six-Sided Selection printout, make a variety of different-looking hexagons that have an area of 60 square units.

Example:

Destination Directions

What You’ll Need:
Destination Directions printout
Pencil or pen

Print and cut out the instruction cards and grid paper from the Destination Directions printout. Shuffle the cards, and place them face down in a pile. Give each student grid paper. Then give students these instructions:
Draw a dot on your grid. Imagine your dot is facing north. Pick up an instruction card and make the appropriate moves on the grid. Continue until all the cards have been used. If a card says to move back, do not change the way you are facing. Note where your dot ends and which direction it is facing.
Shuffle your cards, and play two more times. Do you usually end up in the same spot?

Example:
On my first try, I picked up cards in this order:

I ended up 5 to the right of where I started, facing left.

On my second try, I picked up cards in this order:

I ended up 7 to the right and 2 down from where I started, facing left.

On my last try, I picked up cards in this order:

I ended up 1 above where I started, facing left.
Every time I play, I end up in different spots, but always facing left.

Pond Pairs
Line Leaper

What You’ll Need:
Line Leaper printout

Pose this problem for students:
Using one of the number lines on the Line Leaper printout, make three jumps of one size and two jumps of another size, starting at 0 and doing one jump after the other. You end up at 75. What are the sizes of the jumps?

Sample answer:
It could be 3 jumps of 5 and 2 jumps of 30.
It could be 3 jumps of 7 and 2 jumps of 27.
It could be 3 jumps of 11 and 2 jumps of 21.

20s and 2

What You’ll Need:
No materials necessary

Pose this problem to students:
You want to figure out what numbers you can divide so that the quotient is in the 20s, and there is a remainder of 2. Think of at least four possibilities.

Sample answers:
65 ÷ 3 = 21 R2
90 ÷ 4 = 22 R2
102 ÷ 5 = 20 R2
178 ÷ 8 = 22 R2

Pond Pairs
Lowest Leftover

What You’ll Need:
Lowest Leftover printout

Print and cut out the number cards from the Lowest Leftover printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up three cards and creates a two-digit number and a one-digit number and creates a division expression. Divide and figure out the remainder. The person with the lower remainder gets a point. Return the cards to the pile, shuffle, and repeat. The first player to get 10 points wins.

Example:
Elora picks up a 9, 2, and 3. Elora creates the division expression 23 ÷ 9. Her remainder is 5.
Zahn picks up a 4, 1, and 6. Zahn creates the division expression 61 ÷ 4. His remainder is 1.
Zahn gets a point because he has the lower remainder.

Pattern Plan

What You’ll Need:
Pattern blocks (concrete or virtual)

Provide students with concrete pattern blocks or with access to digital blocks. Then give students these instructions:
Create a design with your pattern blocks so that (frac{2}{3}) of the area is yellow, but only (frac{1}{2}) of your pattern blocks are yellow.

Examples:

Pond Pairs
Perimeter Predicament

What You’ll Need:
No materials necessary

Pose this problem for students:
A rectangle has a perimeter that is exactly five times its width. What could the dimensions be?

Sample answer:
Since the perimeter is 2 lengths plus 2 widths, each length must be (1frac{1}{2}) widths. So, the rectangle could have the dimensions of 3 by 2, 30 by 20, 9 by 6, and so on.

Fortune 4-5-6

What You’ll Need:
Fortune 4-5-6 printout

Print and cut out the cards from the Fortune 4-5-6 printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up four cards and then chooses three of their cards to create a two-digit number and a one-digit number. Multiply your two-digit number by your one-digit number. If the tens digit of the product is 4, 5, or 6, the player gets a point. If the tens digit is not a 4, 5, or 6, the player does not get a point. Return the cards to the pile, shuffle, and repeat. The first player with 5 points wins.

Example:
Ray picks up the numbers 2, 2, 9, and 4. He makes the numbers 29 and 4. The product is 116, which does not have a 4, 5, or 6 in the tens digit. He does not get a point.
Benton picks up the numbers 2, 3, 6, and 7. He makes the numbers 76 and 2. The product is 152, which has a 5 in the tens digit. He gets a point.

Grades 6–8

Pond Pairs
Possibility Prediction

What You’ll Need:
Two number cubes

Give students these instructions:
Roll two number cubes 20 times. Predict which of the possibilities below is most likely. Test your prediction.
A: I will roll at least one 6 six times.
B: My rolls will add up to 7 six times.
C: I will roll doubles at least once.

Example:
Elva predicts that the most likely possibility is rolling at least one 6 six times. Elva experimented by rolling her number cubes 20 times.
1, 1 1, 3 2, 4 2, 6 1, 4 2, 2 1, 5 5, 4 4, 6 5, 5 5, 4 1, 2 5, 4 6, 3 6, 5 1, 4 5, 6 6, 2 1, 3 6, 2
Elva rolled a 6 seven times. Her rolls never added up to 7. She rolled three doubles. Elva’s prediction was correct.

Juice Can Conundrum

What You’ll Need:
No materials necessary

Pose this problem to students:
Choose the prices of cans of juice so that if 5 cans from Store A cost _____, they cost a little less per can than 3 cans from Store B that cost _____.

Example:
I decided that a can of juice from Store A might cost $3.99, so 5 cans would cost $19.95. But they have to cost a little less than each of the 3 cans from Store B. I made the 3 cans cost $4 each, so that 3 cost $12. My numbers were $19.95 and $12.

Pond Pairs
Circle Circumstance
What You’ll Need:
Calculator (optional)

Pose this problem for students:
A circle has an area of ____ square centimetres and a circumference of ____ centimetres. If the first number is about 100 more than the second, what is the radius of the circle?

Example:
I decided to try a radius of 8 centimetres with an area of 64π square centimetres and a circumference of 16π centimetres. The first number is 48π greater, which is more than 100. I need a smaller radius.
I tried a radius of 5 centimetres with an area of 25π square centimetres and a circumference of 10π centimetres. The first number is 15π greater, which is only about 50. I need a bigger radius.
I tried a radius of 7 centimetres with an area of 49π square centimetres and a circumference of 14π centimetres. The first number is 35π greater, which is about 100.

Percent Precision

What You’ll Need:
Percent Precision printout
Calculator (optional)

Print and cut out the number cards from the Percent Precision printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up four cards and makes a two-digit percent and a two-digit number. Players choose a number so that their percent of that number is close to the two-digit number they created. If their number is between 20 and 40 and their percent of that number is within 2 of their two-digit number, they get a point. Return the cards to the pile, shuffle, and repeat. The first player with 10 points wins.

Example:
Dominique picks up the numbers 3, 2, 4, and 7. She creates 74% and the number 23. She figured that if you took 74% of 31, she’d get about 23. She got a point because she got close to her number.
Jeffrey picks up the numbers 1, 8, 9, and 4. He creates 49% and the number 18. He figured that if he took 49% of 36.7, he’d get about 18. He also gets a point.

Pond Pairs
Better Half
What You’ll Need:
Better Half printout
Calculator (optional)

Print and cut out the number cards from the Better Half printout. Shuffle the cards, and place them face down in a pile. Then give students these instructions:
Play in pairs. Each player picks up four cards and creates two fractions to multiply. The player with a product closer to (frac{1}{2}) gets a point. Return the cards to the pile, shuffle, and repeat. The first player to get 10 points wins.

Example:
Cameron picks up the numbers 1, 1, 7, and 9. He multiplies (frac{1}{7}) × (frac{9}{1}) = (frac{9}{7}).
Lauren picks up the numbers 2, 6, 8, and 3. She multiplies (frac{2}{6}) × (frac{8}{3}) = (frac{16}{18}).
Lauren gets a point because her number is closer to (frac{1}{2}).

Patchwork Polygons

What You’ll Need:
Drawing materials (online or actual)

Give students these instructions:
Create an interesting tessellation based on a polygon of your choice.

Examples:

Pond Pairs
Quadrant Quest

What You’ll Need:
Quadrant Quest printout

Give students these instructions:
Choose four points on the coordinate grid from the Quadrant Quest printout to make a trapezoid so that two points are 3 apart, two points are 5 apart, and two points are 13 apart. The points must be in different quadrants.

Example:
I chose (4, −2) and (4, 1). They are 3 apart.
I chose (−9, 1) since it is 13 away from (4, 1).
I chose (−1, −2) since it is 5 away from (4, −2).
Therefore, the four points are (4, −2), (4, 1), (−9, 1), and (−1, −2).

Dimension Deductions

What You’ll Need:
Calculator

Pose this problem for students:
Determine the dimensions of either a prism or a cylinder with a surface area of about 100 cm2.

Example:
I decided to use a square prism with a base that was 2 cm × 2 cm. That means that the 2 bases together have an area of 8 cm2. That leaves 92 cm2 for the area of the 4 rectangles. I divided 92 by 4 to get 23, so I know that each rectangle has an area of 23 cm2. Since one side of each rectangle is 2 cm, I divided 23 by 2 to get 11.5. My prism’s height is 11.5 cm.