Here is a video I made about the Order of Operations.
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I can't claim credit for this awesome song, but it is definitely a great way to remember the order of operations! The next few days, we'll be learning about the order of operations. Using the order of operations correctly is essential to getting the right answer on more complicated math problems.
Below are some useful links you can use to learn more about the Order of Operations. Start here: http://www.coolmath.com/prealgebra/05-order-of-operations/ http://www.mathsisfun.com/operation-order-pemdas.html This site has a short lesson on Order of Operations and some practice problems to try http://www.math-play.com/Order-of-Operations-Millionaire/order-of-operations-millionaire.html Order of Operations Millionaire http://www.mathplayground.com/howto_pemdas.html Video on Order of Operations http://www.mathplayground.com/order_of_operations.html Challenging game on Order of Operations http://www.ixl.com/math/grade-5/simplify-expressions-using-order-of-operations-and-parentheses Practice problems http://www.khanacademy.org/math/arithmetic/order-of-operations/v/introduction-to-order-of-operations Videos on Order of Operations-from basic to challenging http://www.funbrain.com/algebra/index.html Another game http://flocabulary.com/pemdas/ Rap about PEMDAS mrnussbaum.com/orderops This week we started our new math unit on even, odd, prime, and composite numbers. A lot of the kids were confused as to why we were going over even and odd again when most of them already knew it. I explained that the main reason is that a lot of people confuse even and odd numbers with prime and composite numbers. First, we did an activity to review even and odd numbers. We all took tiles and lined them up into two columns, then recorded them in a table. We talked about how odd numbers had one tile leftover without a partner and even numbers all had a partner to dance with. We then talked about "third wheels" and "odd man out" and related this activity to being at a school dance, the leftover person standing sad in the corner with no one to talk to or dance with. Of course, I had to take advantage of the opportunity to belt out the song "All By Myself." (A couple people walked past the room excited because they thought Celine Dion was at school, but alas, it was just me ;) j/k). Our next activity had the kids determining if certain rules could be applied to even and odd numbers. When E= even number and O= odd number, they had to test different numbers to see what was true in each situation (see below): To prove each one, they had to list at least two number sentences per question.
For example, for Is the product of two odd numbers even or odd? It would look like this: 3 x 7= 21 5 x 3 = 15, so the product of two odd numbers is ODD. They then had to complete an exit ticket that required them to look at the problems as equations and determine which statements were true: E + E = O E + E = E E + O = E E + O = O O + O = E O + O = O Afterward, we put the following in our notebooks. Here are a couple of songs I made up about prime and composite numbers:
"Prime and Composite" by Mrs. Wippich (Sung to the tune of the chorus in "Cool for the Summer" by Demi Lovato) Count each factor up one at a time Only two (one and itself) it's priiiiiiiiiiiime If of three or more it is comprised You'll realize It's a composite number "Prime or Composite?" by Mrs. Wippich (Sung to the tune of "Uma Thurman" by Fall Out Boy) I can take numbers and then factor them out, factor them out Wo oah Count up the factors tell whether it's prime or composite You want to know if it's prime or composite Factor it-DON'T JUST GUESS! You want to know if it's prime or composite Factor it- You'll pass the test Just factor numbers with the rainbow method or t-chart, it's your choice, just factor it divide it down to the factors that can be multiplied together and then you will see I can take numbers and then factor them out, factor them out Wo oah Count up the factors tell whether it's prime or composite You want to know if it's prime or composite Factor it-DON'T JUST GUESS! You want to know if it's prime or composite Factor it- You'll pass the test A number's prime if it only has two factors (one/itself), only two But what happens if a number's factors do count up to more than 2 (composite!) I can take numbers and then factor them out, factor them out Wo oah Count up the factors tell whether it's prime or composite Factor it out, and then count up the factors only one and itself, you'll know that you've found a prime Factor it out, and then count up the factors more than two factors, it's a composite number this time You want to know if it's prime or composite Factor it-DON'T JUST GUESS! You want to know if it's prime or composite Factor it- You'll pass the test I can take numbers and then factor them out, factor them out Wo oah Count up the factors tell whether it's prime or composite I can take numbers and then factor them out, factor them out Wo oah Count up the factors tell whether it's prime or composite Yesterday we learned some divisibility rules and played a game to help us with our prime and composite numbers.
The kids have learned what prime and composite numbers are: Prime numbers- have only two factors, one and itself EXAMPLE) 2- the only two factors that can be multiplied together to make 2 are 1 and 2 (itself) Composite numbers- have 3 or more unique factors (can also stated as "more than 2 unique factors") I am so impressed by how many kids know their math facts this year, however, since we have to learn about prime and composite numbers between 1 and 100, these facts don't always help. One way to figure out how many factors a number has is to just do the division, which could take forever... the student would have to do 89 divided by 2, 89 divided by 3...and so on until they got to 89 divided by 9. Ain't nobody got time for that! So, in order to make it easier to determine a number's factors, we started talking about divisibility rules yesterday. What are divisibility rules? They are rules that tell you if a number is evenly divisible by (can be divided by) a certain number. Here are the rules we follow: 2- A number is divisible by 2 if the number ends in an EVEN number: 0, 2, 4, 6, 8 Examples) 482 is divisible by 2 because the digit in the ones place is an even number. 891 is NOT divisible by 2 because the digit in the ones place is an odd number. 3- A number is divisible by 3 if, after adding up the digits in the number you end up with a sum that is evenly divisible by 3 Examples) 482: 4 + 8 + 2= 14. 14 is not divisible by 3 (when you divide 14 by 3 you have a remainder), so neither is 482. 891 is divisible by 3 because 8 + 9 + 1 = 18 and 18 is evenly divisible by 3 (when you divide 18 into 3 groups, you don't have a remainder). 5- If a number ends in 0 or 5 in the ones place, then the number is divisible by 5. Example) 615 is divisible by 5 because it ends in a 5. 892 is not divisible by 5 because it does not end in a 0 or 5, it ends in 2. 6- If a number is divisible by BOTH 2 and 3, it is also divisible by 6. Example) 624 is divisible by 2 because it ends in an even number in the ones place. 624 is also divisible by 3 because 6 + 2 + 4 = 12 and 12 is divisible by 3 with no remainder. Therefore, 624 is also divisible by 6 because it is divisible by both 2 and 3 (which are factors of 6). 7- Sorry, the rule takes longer to figure out than to just divide whatever number you have by 7 to see if it is a factor. Example) 57 divided by 7 is 8 remainder 1, so it is not divisible by 7. 91 divided by 7 is 13 remainder 0, so it IS divisible by 7, meaning 7 is a factor of 91. 9- Just like the threes rule, if you add up the digits of the number and it is divisible by 9, then the whole number is divisible by 9. Example) 711 added together is 7 + 1 + 1 = 9, and 9 is evenly divisible by 9, so 711 is as well. To find out how many factors a number has, start applying the rules from 2-9 until you find one that works. Once you've figured out even just one additional factor for a number other than 1 and itself, you can automatically stop and call it composite. Example: 93 We know that two factors for 93 are 1 x 93 because all numbers have the factors 1 and itself. Let's test the 2s rule: It is NOT divisible by 2 because it ends in an odd number. So we still only have 2 factors so far: 1 and 93. Let's try the 3s rule: 9 + 3 = 12. 12 is divisible by 3 with no remainder, so that means 93 is as well. Guess what! We don't even need to figure out what the other factor is that has to be multiplied times 3 to get 93- we now know that 3 is a factor because the rule worked, 93 has at least 3 factors- 1,3 and 93, so we know it is composite! We don't even need to go to the 4s rule because we know three factors already- 1, 3, and 93. Of course, it is a lot less work on paper to memorize the 25 prime numbers from 1-100, however, if you don't do this, you can just follow these rules or do all of the math. For those of you who want to memorize the primes from 1-100, here they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 Always remember that 0 and 1 are neither prime nor composite www.mathplayground.com/thinkingblocks.html
Hello, math friends :) In the first couple of weeks of school, we'll be starting on math SOL 5.4, creating and solving word problems. For step-by-step directions on how to create your own multi-step problem, scroll down. Math SOL 5.4The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. Here are the steps to creating your own multistep word problem. 1. Find a one-step word problem and solve it. Remember the problem solving steps we talked about in class.
Example) Sarah baked 3 trays of 12 cookies to bring to a party. How many cookies did she bake in all? I know that each tray has 12 cookies, so if I multiply 3 (trays) times 12 (cookies), I get 36 total cookies (or, instead of multiplying, I could also add 12 + 12 + 12, which is the same as 3 x 12.). 2. Use the answer from the first word problem to make a new problem. Example) My answer to the first question was 36 cookies. Here are some options I could use with my first word problem's answer.
3. Make a "hidden question" by writing a single combined problem. To do this, combine the original word problem and your new question from step number 2. Then, leave out the question from your first word problem- the question you are leaving out is the "hidden question." Example) Here are the two problems I need to combine.
I put them together, and then erase the first question.
Here is my final multistep word problem (yay!):
Hope this helps!!! Now that you've seen how to make a "hidden question" word problem, can you identify the hidden question in the following word problem? Figuring out the hidden question will help you solve the problem. Nicholas bought 4 dozen packs of eggs for $3 a dozen. How much change did Nicholas get back if he paid with a $20 bill? If you guessed the hidden question was "How much did Nicholas spend in all on the eggs?"... you are correct! Below are some helpful websites that allow the students to practice solving multi-step word problems. The more they practice solving them, the easier it will become to create their own. This website has practice multi-step problems and includes videos that walk you through how to solve each problem if you are stuck. Very useful! http://www.mathplayground.com/wp_2A.html Another mathplayground.com resource, "Word Problems with Katie" has two different levels. Each level starts out with simpler, single-step problems and moves on to more challenging multistep problems. http://www.mathplayground.com/WordProblemsWithKatie2.html Can you tell I love mathplayground.com? Here is another game that starts easy and gets more challenging as you move through the problems (and you get a chance to play basketball occasionally). http://www.mathplayground.com/mathhoops_Z1.html One of the best conceptual resources I know of online for teaching multistep word problems, "Thinking Blocks" has problems in all four operations. Students may want to start with the addition and subtraction Thinking Blocks and move on to multiplication and division. To access the word problems, scroll down until you see four boxes that say "Thinking Blocks-Model and Solve Word Problems" and click on the operations you want to practice. If you are unsure of what to do, watch the video tutorial before you "Start Modeling." http://www.mathplayground.com/thinkingblocks.html This site has practice problems. If you get an answer wrong, it gives a written explanation to show you how to solve the problem, step-by-step. http://www.ixl.com/math/grade-5/multi-step-word-problems So I just made several videos about some methods for solving multiplication and division problems and most of them didn't save- aaaaaaaaaa! Here are the ones that DID save. I'll try to redo the rest this weekend. We are doing some review of multiplication and division in class right now and I thought it would be useful to post a couple of sites I like for different ways to solve these problems. Click on the links below to explore!
Multiplication-Interactives Array multiplication Area model Standard Algorithm Lattice video Step-by-step tutorial (written) Division The Quotient Cafe - walks you through the steps of the partial products method of division Long division step-by-step interactive Long division interactive Long division interactive with help Long division mountain game |
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