Happy Monday!
Grade 6s, here is the list I gave you in class today to use as your study guide. If you are comfortable with these concepts, you'll be in great shape for our test on Wednesday.
Make sure you know how to:
- complete a table for an input/output machine with two operations
(e.g., input x4 -2 output)
- write terms of a pattern based on a pattern rule
(e.g., write the first 6 terms using x2, then -5 each time)
- identify a pattern rule when given terms of a pattern
(e.g., 2, 4, 10, 28, 82, …)
- find different patterns when given the same two terms
(e.g., how many different patterns can you find with 5 and 8 as the first 2 terms?)
- explain how you know a number is divisible by 2, 3, 4, 5, 6, 8, 9, and 10 (the Divisibility Rules chart will be provided)
- solve equations with one missing number (e.g., □ – 26 = 15, solving for □)
- solve equations with two missing numbers (e.g., □ - ▲ = 7 – 4)
- write an integer to represent a situation (e.g., Yordanos spent $75)
Good luck!
-Ms. Lewis.
Monday, September 21, 2009
Friday, September 18, 2009
Group Problem
Hi Grade 6s,
You will be solving a problem in your math groups next week. You should post your thoughts, ideas, and challenges on the blog so you are sharing with your group.
Each group will be answering the same question. On Monday, we will be solving the problem in class. I hope that the discussion we have here on the blog will help you come up with your solutions on Monday.
So, without further ado, here is your problem:
The famous Lewis School of Mathematics is building a new section as more families move into the fabulous city of Lewistown. The following numbers of families have moved into Lewistown over the past 4 years: 3 more families than the first year, then 8 more families the following year, then 13 more families the next year, and 18 more families the past year. If this pattern continues, in how many more years will a total of 43 families have moved into town?
Group 1 should post their comments here.
Group 2 should post their comments here.
Group 3 should post their comments here.
Group 4 should post their comments here.
Group 5 should post their comments here.
Good luck!
-Ms. Lewis.
You will be solving a problem in your math groups next week. You should post your thoughts, ideas, and challenges on the blog so you are sharing with your group.
Each group will be answering the same question. On Monday, we will be solving the problem in class. I hope that the discussion we have here on the blog will help you come up with your solutions on Monday.
So, without further ado, here is your problem:
The famous Lewis School of Mathematics is building a new section as more families move into the fabulous city of Lewistown. The following numbers of families have moved into Lewistown over the past 4 years: 3 more families than the first year, then 8 more families the following year, then 13 more families the next year, and 18 more families the past year. If this pattern continues, in how many more years will a total of 43 families have moved into town?
Group 1 should post their comments here.
Group 2 should post their comments here.
Group 3 should post their comments here.
Group 4 should post their comments here.
Group 5 should post their comments here.
Good luck!
-Ms. Lewis.
Wednesday, September 16, 2009
Solving Equations
Hello Grade 6s!
Our 2nd week is nearly done. I don't know about you, but our time together so far has flown by for me!
Today we talked about two strategies for finding a missing number in an equation.
We talked about guess and check. If our equation was 163 = ___ + 49, we might guess the missing number is 100. We check this by adding 100 to 49. 100 + 49 = 149. The answer is too low. Next, we could try 115 as the possible missing number. We check again: 115 + 49 = 164. This answer is 1 more than what we need, so we know that the missing number is 114 (we took 1 away from 115).
Our second strategy is using the inverse operation. If we're trying to solve ____ ÷ 6 = 144, we use the INVERSE (or opposite) operation. We know that divison and multiplication are INVERSE operations, just as addition and subtraction are inverse operations.
So we use the numbers we know: 144 x 6 = the missing number. 144 x 6 = 864, so 864 is the missing number.
Questions? Post them here, and I will reply!
-Ms. Lewis.
Our 2nd week is nearly done. I don't know about you, but our time together so far has flown by for me!
Today we talked about two strategies for finding a missing number in an equation.
We talked about guess and check. If our equation was 163 = ___ + 49, we might guess the missing number is 100. We check this by adding 100 to 49. 100 + 49 = 149. The answer is too low. Next, we could try 115 as the possible missing number. We check again: 115 + 49 = 164. This answer is 1 more than what we need, so we know that the missing number is 114 (we took 1 away from 115).
Our second strategy is using the inverse operation. If we're trying to solve ____ ÷ 6 = 144, we use the INVERSE (or opposite) operation. We know that divison and multiplication are INVERSE operations, just as addition and subtraction are inverse operations.
So we use the numbers we know: 144 x 6 = the missing number. 144 x 6 = 864, so 864 is the missing number.
Questions? Post them here, and I will reply!
-Ms. Lewis.
Monday, September 14, 2009
Patterns In Division
Happy Monday!
Today in class, we looked at patterns in division. We learned that there are tips and tricks to help us figure out if humongous numbers are divisible by 2, 3, 4, 5, 6, 8, 9, or 10.
USE THE GUIDE IN YOUR HOMEWORK BOOKS TO HELP YOU!
What I've noticed after marking your school notebooks is some of you are confusing how to solve for divisible by 4 with divisible by 5.
For numbers divisible by 3, the SUM of the digits will be divisible by 3.
Example: 1962 has a digit sum of 18 (1+9+6+2=18). We know that 18 divided by 3 equals 6, so 1962 is divisible by 3.
For numbers divisible by 4, the number represented by the tens and ones digits will be divisible by 4.
Example: 1962 has 62 as the number represented by the tens and ones digits. 62 cannot be divided by 4, therefore 1962 is not divisible by 4.
Questions? Post them here!
See you tomorrow, my little mathematicians!
Today in class, we looked at patterns in division. We learned that there are tips and tricks to help us figure out if humongous numbers are divisible by 2, 3, 4, 5, 6, 8, 9, or 10.
USE THE GUIDE IN YOUR HOMEWORK BOOKS TO HELP YOU!
What I've noticed after marking your school notebooks is some of you are confusing how to solve for divisible by 4 with divisible by 5.
For numbers divisible by 3, the SUM of the digits will be divisible by 3.
Example: 1962 has a digit sum of 18 (1+9+6+2=18). We know that 18 divided by 3 equals 6, so 1962 is divisible by 3.
For numbers divisible by 4, the number represented by the tens and ones digits will be divisible by 4.
Example: 1962 has 62 as the number represented by the tens and ones digits. 62 cannot be divided by 4, therefore 1962 is not divisible by 4.
Questions? Post them here!
See you tomorrow, my little mathematicians!
Friday, September 11, 2009
We Made It!
Happy Friday, everyone!
Thanks for a great math-filled week. You guys are awesome!
Remember, if you need help with your homework this week, post a comment on our math blog, and I will respond as soon as I can.
It's supposed to be sunny this weekend. Try to get outside and soak up some of those beautiful rays :).
See you Monday!
-Ms. Lewis.
Thanks for a great math-filled week. You guys are awesome!
Remember, if you need help with your homework this week, post a comment on our math blog, and I will respond as soon as I can.
It's supposed to be sunny this weekend. Try to get outside and soak up some of those beautiful rays :).
See you Monday!
-Ms. Lewis.
Thursday, September 10, 2009
Number Patterns
Good evening, Grade 6s!
Tonight's homework may be tricky for some of you, as the explanation was really quick.
Let's review:
Because we are looking at patterning, we want to see how the numbers are related to each other.
For example, let's say I have a number pattern the following 6 terms:
6, 18, 54, 162, 486, 1458
To figure out how these numbers are connected, let's start with what we know.
We know that 6 x 3 = 18. We also know that 6 + 12 = 18. Our next step is to check our choices against the rest of the terms in the pattern to see if the rule applies to all terms.
18 + 12 does not equal 54, so the pattern rule can't be +12 each time.
18 x 3 does equal 54. Let's check the next term to make sure it also follows the rule:
54 x 3 does equal 162.
Etc., etc.
So...we would write the pattern rule as follows:
Start at 6. Multiply by 3 each time.
Questions? Post 'em here!
See you tomorrow :).
-Ms. Lewis.
Tonight's homework may be tricky for some of you, as the explanation was really quick.
Let's review:
Because we are looking at patterning, we want to see how the numbers are related to each other.
For example, let's say I have a number pattern the following 6 terms:
6, 18, 54, 162, 486, 1458
To figure out how these numbers are connected, let's start with what we know.
We know that 6 x 3 = 18. We also know that 6 + 12 = 18. Our next step is to check our choices against the rest of the terms in the pattern to see if the rule applies to all terms.
18 + 12 does not equal 54, so the pattern rule can't be +12 each time.
18 x 3 does equal 54. Let's check the next term to make sure it also follows the rule:
54 x 3 does equal 162.
Etc., etc.
So...we would write the pattern rule as follows:
Start at 6. Multiply by 3 each time.
Questions? Post 'em here!
See you tomorrow :).
-Ms. Lewis.
Wednesday, September 9, 2009
Patterning
Hello my little bloggers!
Today we talked about patterning in math, specifically using an input/output machine. We discussed how to figure out what the operations are for a machine based on the input/output results, like the example below:
We figured out that if we start with what we know, we can see that the output numbers are increasing by 3 each time. Being the clever math students that we are, we know that if our numbers are increasing by 3 each time, the first operation of the input/output machine must be input x 3.
When we looked at the output numbers and compared them to the input numbers (1 and 1, for example), we know that 1 x 3 doesn't equal 1 (the number in the output column). The number is too small. We know the second operation is either going to be division or subtraction, as those are the two operations that make numbers smaller.
So...how do we get from 1 x 3=3, to 1 x 3=1?
We know that 3-2=1. Could the next operation be -2?
Let's check the other input/output data against our hypothesis.
2 x 3 = 6 - 2 = 4
3 x 3 = 9 - 2 = 7
4 x 3 = 12 - 2 = 10
5 x 3 = 15 - 2 = 13.
We've got it!
How did today's lesson go? Is anything in the land of patterning still a mystery? If so, post your questions here (especially if you need help with tonight's homework!).
Thanks for another great day. You guys are fabulous!
-Ms. Lewis.
Today we talked about patterning in math, specifically using an input/output machine. We discussed how to figure out what the operations are for a machine based on the input/output results, like the example below:
We figured out that if we start with what we know, we can see that the output numbers are increasing by 3 each time. Being the clever math students that we are, we know that if our numbers are increasing by 3 each time, the first operation of the input/output machine must be input x 3. When we looked at the output numbers and compared them to the input numbers (1 and 1, for example), we know that 1 x 3 doesn't equal 1 (the number in the output column). The number is too small. We know the second operation is either going to be division or subtraction, as those are the two operations that make numbers smaller.
So...how do we get from 1 x 3=3, to 1 x 3=1?
We know that 3-2=1. Could the next operation be -2?
Let's check the other input/output data against our hypothesis.
2 x 3 = 6 - 2 = 4
3 x 3 = 9 - 2 = 7
4 x 3 = 12 - 2 = 10
5 x 3 = 15 - 2 = 13.
We've got it!
How did today's lesson go? Is anything in the land of patterning still a mystery? If so, post your questions here (especially if you need help with tonight's homework!).
Thanks for another great day. You guys are fabulous!
-Ms. Lewis.
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