Why do we do this math? Why do we have a numerator and a denominator? Why do we need to learn how to multiply?
Basically, any question you ask about math that begins with why is a purpose question. So, any answer you find gives you a purpose to your math.
Questions
When you are stumped by a problem, try to figure out what you actually need to understand by asking questions.
DON'T SAY "I Don't Get It!" Instead say "What part don't I get?" and "What questions do I have about this problem?"
Some examples might be: How do I divide such a large amount into so few groups?
How do I multiply by numbers bigger than 12 when I don't know those facts?
Can I make this problem into two smaller problems?
Can I draw a model to help me understand this?
Is this problem about groups of items or about just a bunch of items?
What would this fraction look like if I had fraction circles?
Are there any clues I missed in the question or word problem?
Is there another way to approach this problem?
What are the authors of this math problem trying to tell me?
Patterns
Write about one of the methods you have been learning about.
Tell about what patterns you have noticed when you multiply. You should use the following sentence frames to help you write your patterns:
Every time I multiply by (tell the number or type of number), I notice
When I (do this), (this) seems to happen.
If I (do this), Then (this) is the result.
Whenever the problem says (this), I know to (do this).
I noticed that (this) happens whenever I (do this).
Conjectures
These are what happen when you believe you have found a pattern that might work all the time.
That means, you might believe it is a rule, but you haven't checked it to see.
To check a conjecture, make a model with manipulatives or the number pieces app. If you can prove that it works with manipulatives, it should be a rule.
Do three different problems that you think should follow the rule to see if it is truly a rule.
Rules
Once you have proven a conjecture, it becomes a rule.
This is how we have properties, like distributive and associative properties. Mathematicians, pros at math, spend their time finding patterns, making conjectures, testing them, and creating the words to describe the rules.
If you find a rule someone has already made, I want you to copy their words for the rule and try to put it in your own words.
If you find a rule through your own testing, I want you to try to create good words to describe the rule and share it with others. Mr. E may help you with these words.
Mathematical Thinking Page
Why do we do this math? Why do we have a numerator and a denominator? Why do we need to learn how to multiply?
Basically, any question you ask about math that begins with why is a purpose question. So, any answer you find gives you a purpose to your math.
When you are stumped by a problem, try to figure out what you actually need to understand by asking questions.
DON'T SAY "I Don't Get It!" Instead say "What part don't I get?" and "What questions do I have about this problem?"
Some examples might be: How do I divide such a large amount into so few groups?
How do I multiply by numbers bigger than 12 when I don't know those facts?
Can I make this problem into two smaller problems?
Can I draw a model to help me understand this?
Is this problem about groups of items or about just a bunch of items?
What would this fraction look like if I had fraction circles?
Are there any clues I missed in the question or word problem?
Is there another way to approach this problem?
What are the authors of this math problem trying to tell me?
Write about one of the methods you have been learning about.
Tell about what patterns you have noticed when you multiply. You should use the following sentence frames to help you write your patterns:
Every time I multiply by (tell the number or type of number), I notice
When I (do this), (this) seems to happen.
If I (do this), Then (this) is the result.
Whenever the problem says (this), I know to (do this).
I noticed that (this) happens whenever I (do this).
These are what happen when you believe you have found a pattern that might work all the time.
That means, you might believe it is a rule, but you haven't checked it to see.
To check a conjecture, make a model with manipulatives or the number pieces app. If you can prove that it works with manipulatives, it should be a rule.
Do three different problems that you think should follow the rule to see if it is truly a rule.
This is how we have properties, like distributive and associative properties. Mathematicians, pros at math, spend their time finding patterns, making conjectures, testing them, and creating the words to describe the rules.
If you find a rule someone has already made, I want you to copy their words for the rule and try to put it in your own words.
If you find a rule through your own testing, I want you to try to create good words to describe the rule and share it with others. Mr. E may help you with these words.