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.

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.

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.