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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

Making 10

What You’ll Need:
10-Frames
Paper bag

Cut out pieces of the filled 10-frames to show 1, 2, 3, 4, 5, 6, 7, 8, and 9. Put two copies of each number in a bag. Also, have a blank 10-frame available for students who want to use one.

Give students these instructions:
Draw pieces from the bag until you have a total of 10.

Sample answer:

Solve the Riddle

What You’ll Need:
Coloured counters

Give students these instructions:
Show counters to make this true and solve each problem.
There are 2 more REDS than BLUES.
There are 3 more GREENS than REDS.

1. There are 2 blues.

Sample answer:

2. There are 6 reds.

Sample answer:

3. There are 10 greens.

Sample answer:

Toothpick Pictures

What You’ll Need:

30 or 40 toothpicks

Give students these instructions:
Choose a number of toothpicks. Use them to make a picture.
How many toothpicks did you use?
Make another picture, but this time use more toothpicks. How many toothpicks did you use? How do you know it’s more?

Sample answer:

I used 10 toothpicks for the houses and 8 for the sidewalks in the first picture. That’s 18 toothpicks.

I used 22 toothpicks the second time. I know it was 4 more than 18 since I added 2 toothpicks to each path.

My Lunch

What You’ll Need:

Play money

Display a food list like the following:
Food
Samosa 55¢
Sandwich 75¢
Pasta 50¢
Vegetables & dip 35¢

Drink
Milk 30¢
Juice 40¢
Pop 20¢

Give students these instructions:
Choose one food and one drink. What is the total cost?
Choose a different drink. How much more or less does this drink cost than the first one you chose? What is the new total?

Sample answer:
Pasta and milk is 80 cents.

If I get juice instead, it is 10 cents more, so the new total is 90 cents.

Grades 3–5

Feeling Punchy

What You’ll Need:

No materials necessary

Show students a picture with labels like the following:

1. How many millilitres of punch are there in total?

2. How many more millilitres are in the bowl that holds most than the bowl that holds least?

3. Create three different capacities for the bowls where your answers to Questions 1 and 2 would be the same.

Sample answer:
1. 1 L = 1000 mL
That means 0.1 L = 100 mL.
That means the bowls hold 4000 + 5100 + 3800 mL, which is 12 900 mL (almost 13 L).

2. Since 5100 – 3800 = 1300, there are 1300 more millilitres in the bowl that holds most compared to the bowl that holds least.

3. I have to make up values so that the total stays the same and the difference between the most and least stays the same.
I decided to add 1 L to the 5.1 and 3.8, so the difference would stay the same, but then that changes which bowl held the least.
So, I decided to subtract 0.1 L from 5.1 and 3.8 and then add 0.2 L to 4.
I get 4.2 L, 5 L, and 3.7 L and it all still works.

More or Less

What You’ll Need:
Fraction

materials (optional)
Hundredths grid (optional)

The fraction 3/[//] is more than 5/*.
What could the numbers [//] and * be?
Think of at least six possible answers.

Sample answer:
¾ is more than 5/10, so the numbers are 4 and 10.
3/2 is more than 5/6, so the numbers are 2 and 6.
3/3 is more than 5/9, so the numbers are 3 and 9.
3/8 is more than 5/100, so the numbers are 8 and 100.
3/12 is more than 5/25, so the numbers are 12 and 25.

Amazing Angles

What You’ll Need:
Paper
Protractors

Draw an angle for each description:
• between 20° and 25°
• a little less than 45°
• a little more than 125°
• two angles that add to 90°

Sample response:

Up and Down

What You’ll Need:

No materials necessary

Create a pattern that follows a pattern rule that involves both increases and decreases.
The pattern must include the numbers 88 and 115.

Sample answer:
The pattern might be 8, 150, 18, 149, 28, 148, … .
You start with 8 and 150 and alternate between going up by 10 and down by 1.
88 will be the 17th term and 115 will be the 72nd term.

Grades 6–8

Billionaire Bargains

What You’ll Need:

Calculator

About how many could you buy if you had a billion dollars?
– sports cars
– tickets to a concert
– bars of gold
– palaces

Sample answer:
A Jaguar F-TYPE might cost about $125,000. Since 4 of those would be half a million dollars, I could buy 8 for a million dollars.
A billion is 1000 millions, so I could get about 8000 sports cars.

A ticket to a Taylor Swift concert might cost $1000 and a billion is one million thousands, so I could buy about 1 000 000 tickets.

If a bar of gold costs almost $22,000, 5 bars would be about $100,000.
100 000 times 10 000 is 1 billion. So, I could buy about 5 × 10 000, or about 50 000 bars.

Palaces can be a lot of different sizes. I found a castle in France that has 40 rooms and costs 16.8 million euros. That’s about $24 million Canadian dollars. I could buy about 42 palaces.

Lowest Tenths

What You’ll Need:
Calculators
Number Cards <RM>

Students may play in groups of two to four. Provide these instructions:
• Shuffle the cards, and turn them over.
• Each player chooses six cards to form two numbers, one of the form [].[] and another of the form [][].[][].
• Each player divides the greater number by the smaller one. The player with the lowest tenths digit scores 1 point.
• The first player with 10 points wins.

Sample answer:
Parker arranged her cards to divide 52.14 by 6.1 and got 8.547…, so her tenths digit was 5.
Sage arranged her cards to divide 39.25 by 6.8 and got 5.772…, so her tenths digit was 7.
Parker scored 1 point.

Six Toothpicks

What You’ll Need:

Six toothpicks

Show students an equilateral triangle formed with three toothpicks.

Challenge students to add three more toothpicks to make a figure with four equilateral triangles that are all the same size.

Response:

Probability Predictor

What You’ll Need:
No materials necessary

Present this situation to students:
You have some coins in your pocket.
What coins and how many of each might you have if the probability of choosing a nickel, not putting it back, and then choosing a dime is very close to 1/10?

Sample answer:
You could have 5 nickels, 4 dimes, and 6 quarters; the probability would be 5/15 × 4/14 = 2/21, which is pretty close to 1/10.
OR
There could be 1 nickel, 1 dime, and 2 quarters, the probability would be 1/4 × 1/3 = 1/12, which is pretty close to 1/10.

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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.

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.

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.

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.

Grades 3–6

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:

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.

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.

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 \(1\frac{1}{2}\) widths. So, the rectangle could have the dimensions of 3 by 2, 30 by 20, 9 by 6, and so on.

Grades 6–8

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.

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.

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 \(\frac{1}{2}\).

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).