What does it mean to "convince" in mathematics?

To provide clear reasons or evidence to support an idea

Which of these is an example of a mathematical conjecture?

If you add 1 to any even number, the result will always be a prime number

What is a counter example?

An example that shows a conjecture is not always true

How can you test if your conjecture is true for all cases?

Look for a pattern and try to prove it works for all numbers

Which statement is a conjecture that needs more investigation?

The difference between any two odd numbers is always even

If you notice that 1+3=4, 3+5=8, and 5+7=12, what might you conjecture?

The sum of two consecutive odd numbers is always even

What is a conjecture in mathematics?

A guess or prediction based on observations

If someone says "All multiples of 4 are even numbers," how could you convince them this is true?

Explain that any number multiplied by an even number is always even

What's the best first step when you want to make a mathematical conjecture?

Observe patterns and gather information

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WEEK 4 NUMERACY SUMMER ONLINE CLASS

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Answers

1
What does it mean to "convince" in mathematics?
To argue loudly
To provide clear reasons or evidence to support an idea
To guess randomly
To memorize formulas
2
Which of these is an example of a mathematical conjecture?
2+2=4
All even numbers are divisible by 2
The sum of the angles in a triangle is always 180°
If you add 1 to any even number, the result will always be a prime number
3
What is a counter example?
A way to solve word problems
An example that proves a conjecture is always true
An example that shows a conjecture is not always true
A type of mathematical equation
4
How can you test if your conjecture is true for all cases?
Look for a pattern and try to prove it works for all numbers
Try it with one more example
Assume it's always true without checking
Ask your teacher
5
Which statement is a conjecture that needs more investigation?
A rectangle has four right angles
Squares have four equal sides
The difference between any two odd numbers is always even
10−7=3
6
If you notice that 1+3=4, 3+5=8, and 5+7=12, what might you conjecture?
Odd numbers are always less than even numbers
The sum of two consecutive odd numbers is always even
Adding any two numbers always results in a larger number
All odd numbers add up to even numbers
7
Which of these is NOT a good way to support a mathematical conjecture?
Providing multiple examples
Saying "because I said so"
Explaining your reasoning step by step
Using a diagram
8
What is a conjecture in mathematics?
A mathematical formula
A type of geometric shape
A guess or prediction based on observations
A proven fact
9
If someone says "All multiples of 4 are even numbers," how could you convince them this is true?
Draw a picture of the number 4
Explain that any number multiplied by an even number is always even
Show them 44, 88, and 1212 are even
Tell them to just believe you
10
What's the best first step when you want to make a mathematical conjecture?
Ask someone else to do it for you
Write down the answer immediately
Memorize all the math facts you know
Observe patterns and gather information

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