Geography of a # Line
What is the midpoint of 0 and 10 on the number line?
5
Find the area of a rectangle with a width of 4 and a length of 6.
24 square units
What comes next in this pattern: 2, 4, 6, 8, __?
10
What is the result of this number trick: Start with 5, multiply by 2, subtract 3, and divide by 7?
1
What is the formula for the area of a rectangle?
Area = length × width
Place these numbers in order on a number line: -5, 3, 0, -2.
-5, -2, 0, 3
Which is larger: the area of a rectangle with dimensions 3x5 or 4x4?
4x4 (16 square units vs. 15 square units)
If a bucket represents an unknown value, how do you write the total value of 3 buckets and 5 marbles?
3b+5
Why do we use variables in number tricks?
To represent unknown or changing values and make the trick work for any number.
A rectangle has a length of 7 and a width of 3. What is its area?
21 square units
If a point is halfway between -6 and 4, what is its location?
-1
True or False: The area of a square with side length 5 is 20.
False (it’s 5×5=255 \times 5 = 255×5=25)
If a number trick starts with adding 7 to your number and ends with subtracting 3, what is the simplified rule?
Add 4 to your starting number.
If the rule of a number trick is 3x+2, what happens when you start with 4?
3(4)+2=12+2=14
True or False: The area of a rectangle is always larger than its perimeter.
False (e.g., for a 1 × 10 rectangle, the area is 10, and the perimeter is 22.)
True or False: The number 0 is always to the left of positive numbers on the number line.
True
Using the distributive property, simplify: 3(4+2).
3⋅4+3⋅2=12+6=18
Solve this puzzle: I’m thinking of a number. When you multiply it by 2 and subtract 4, you get 10. What is the number?
7
Describe the habit of "thinking about structure" and give an example from the number line.
"Thinking about structure" means identifying patterns or properties, such as noticing that numbers are evenly spaced on the number line. Example: The midpoint between -2 and 6 is 2 because it’s equidistant from both ends.
How can you use the distributive property to find the area of a rectangle with length 12 and width 8?
Split the length or width into smaller parts, such as (10 + 2):
12 x 8 = (10 + 2) x 8 = 10 x 8 + 2 x 8 = 80 + 16 = 96
How would you represent the distance between -7 and 3 using absolute value?
∣−7−3∣=10
If the area of a rectangle is 36 and the length is 9, what is the width?
4
True or False: Every pattern has a repeating sequence.
False
Create a number trick where the final answer is always 8, no matter the starting number.
Multiply your number by 0, add 8.
The area of a rectangle is 56 square units, and the width is 8 units. What is the length?
7 units