Order of Operations
31 - (7 + 2) x 3
31 - 9 x 3
31 - 27
4
Name the x-coordinate and y-coordinate for the ordered pair (7, 12)
The x-coordinate is 7 and the y-coordinate is 12
Solve 3,218 ÷ 2
The quotient is 1,609.
True or false: 43 is a composite number. Explain your reasoning.
What is false? 43 is a prime number because its only factors are 1 and itself.
Describe the pattern: 243, 81, 27, 9, 3
The pattern is Divide by 3
Insert parentheses to make this statement correct
6 x 5 - 3 + 10 ÷ 2 = 17
6 x (5 - 3) + 10 ÷ 2 = 17
Name the quotient, remainder, divisor, and dividend for the problem below.
543 ÷ 7 = 77 R 4
The dividend is 543
The divisor is 7
The quotient is 77
The remainder is 4
Basic facts and patterns can be used to help you divide. Which basic fact helps you to divide 42,000 ÷ 6. Explain why
The basic fact that can help you divide 42,000 by 6 is 42 ÷ 6 = 7. 42,000 is 1,000 times 42. If we know 42 ÷ 6 = 7, then we can multiply the quotient by 1,000 (three zeros at the end). 42,000 ÷ 6 = 7,000
Give three examples of odd composite numbers between 1 and 100.
Three examples of odd composite numbers between 1 and 100 (ex. 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99)
Name all the factors of 72.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The airport administration did a study and found that an additional 5 minutes of delay in the overall operation of the airport is caused for every 32 passengers that are late for their flights. What is the delay in the overall operation if there are 832 passengers late for their flights?
832 ÷ 32 x 5
26 x 5
130
There will be a delay of 130 minutes in the overall operation of the airport.
Name three prime numbers between 1-100 that are greater than 19.
What are (ex. 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)
A game costs $238.92. My five friends and I decide we want to buy it together. If we split the cost evenly, how much will we each need to pay to buy the game?
We would each need to pay $39.82 to buy the game.
Name are the factor pairs for 24
Examples:
1 x 24
2 x 12
3 x 8
4 x 6
Create a table of values for Divide by 2 plus 3; (n ÷ 2) + 3
Example:
n (n ÷ 2) + 3
16 11
8 7
20 13
54 30
Explain why 3 x 6 + 11 has a different value than 3 x (6 + 11)
3 x 6 + 11 has a different value than 3 x (6 + 11) because 3 x (6 + 11) has parenthesis which means you would need to solve that first, giving you 17, before multiplying by 3. 3 x 17 = 51.
In 3 x 6 + 11, since there is no parenthesis you would multiply 3 x 6 first and then add 11. 18 + 11 = 29.
The product of each equation is different based on the order of operations.
Create a factor tree for 56. Then write the prime factorization based on this factor tree, if exponents can be used, use them.
Refer to the white board for the factor tree.
Prime factorization 2 x 2 x 2 x 7
Prime factorization using exponents: 2³ x 7
Which is the most reasonable estimate for $54.34 ÷ 7 . Then explain how you estimated, if it is an overestimate or underestimate and why.
The most reasonable estimate for $54.34 ÷ 7 is $8. I can use compatible numbers to help me solve. I know that 56 ÷ 7 = 8, and since $54 is close to $56, $8 would be a reasonable estimate. It will be an overestimate because $56 > than $54.34.
True or False. 9,585 is divisible by 9 and 3, but not 6. Explain how you know.
What is true?
9,585 is divisible by 9 because the sum of the digits are divisible by 9 (9+5+8+5 =27 and 27/9 = 3)
9,585 is divisible by 3 because the sum of the digits are divisible by 3 (9+5+8+5 =27 and 27/3 = 9)
9,585 is not divisible by 6 because the number has to be divisible by 2 and 3, since 9,585 is an odd number it cannot be divisible by 2.
Find the ordered pair for F and I.
What point is at (-6, 3) and (4, 7)
The ordered pair for F is (-4, -2)
The ordered pair for I is (7, -2)
The point at (-6, 3) is A
The point at (3, 4) is E
Using the order of operations, explain step by step how to solve this problem.
14 ÷ (10 - 3) + 8 x (2 + 6) - 4
14 ÷ (10 - 3) + 8 x (2 + 6) - 4 {First check to see if there is anything in parentheses. In this problem there are two items in parenthesis (always solve from left to right). Since (10 - 3) is first, starting on the left, we solve for that. 10-3=7}
=14 ÷ 7 + 8 (2+6) - 4 {Now we solve the second problem in parentheses, 2 + 6= 8}
= 14 ÷ 7 + 8 x 8 - 4 {Next you look to see if there is any multiplication or division to complete, and solve from left to right. Since 14 ÷ 7 is before 8 x 8, we solve that first}
= 2 + 8 x 8 - 4 {Now we solve 8 x 8}
= 2 + 64 - 4 {Next you look to see if there is any addition or subtraction to complete and solve from left to right. Since there is both addition and subtraction, but 2 + 64 comes before - 4, we complete that, 2 + 64 = 66}
= 66 - 4 {Now we solve 66 - 4 = 62}
= 62
Write each number that 996 is divisible by and explain why.
996 is divisible by 2 because any number is divisible by 2 if the number is even.
996 is divisible by 3 because any number where the sum of the digits of the number is divisible by 3, it is divisible by 3. 9 + 9 + 6 = 24, and 24 ÷ 3 = 8
996 is divisible by 4 because if the last two digits are divisible by 4, then it is also divisible by 4. 96 ÷ 4 = 24
996 is divisible by 6 because if a number is divisible by 2 and 3 it is divisible by 6. Since it is an even number, it is divisible by 2, and since 9 + 9 + 6 = 24, and 24 ÷ 3 = 8, it is divisible by 3.
Solve the problem, then interpret the remainder. Ms. Idara has 983 paperback books. She wants to put her paperback books on storage shelves. Each shelf can hold 50 paperback books. How many storage shelves are needed?
983 ÷ 50 = 19 R 33
Ms. Idara will need 20 storage shelves to hold her books.
The quotient tells us that that are 19 storage shelves that will be completely filled with 50 books. The remainder tells us there are 33 extra paperback books. This means she will need an extra shelf to hold the leftover books, but this shelf will not be completely filled.
Without dividing, how would you determine if a number is divisible by 2, 3, 4, 5, and 6?
You can determine if a number is by 2, 3, 4, 5, and 6, by using divisibility rules.
The number would be divisible by 2 if it is an even number.
The number would be divisible by 3 if the sum of the digits of the number is divisible by 3.
The number would be divisible by 4 if the last two digits are divisible by 4.
The number would be divisible by 5 if the last digit is 0 or 5.
The number would be divisible by 6 if it is divisible by BOTH 2 and 3.
Explain how graphing (3, 5) is different from graphing (5, 3)
Graphing (3, 5) is different from graphing (5, 3) because they have different x and y coordinates. In (3, 5) the x-coordinate is 3, which means you go over 3 before going up to the y-coordinate 5. But in (5, 3) the x-coordinate is 5, which means you go over 5 before going up to the y-coordinate 3. The points would then be in two different locations, and so they are graphed differently.