Evaluating Expressions
Evaluate this expression:
5 x (13 x 2)
(5 x 2) x 13
(10) x 13
130
What is the volume of a rectangular prism that has these dimensions? Label your answer in the correct units.
length: 2 cubes
width: 3 cubes
height: 4 cubes
(2 x 3) x 4
(6) x 4
24 cubic units
Name the multiplication strategy being used:
When you divide one number by 2 and multiply the other number by 2, the overall value of the equation does not change.
Doubling and Halving
Define these three division words:
Dividend
Divisor
Quotient
Dividend: the number you're dividing
Divisor: the number you're dividing by
Quotient: the answer to a division problem
Write a numerical expression to represent each statement. Include parentheses.
To find 32 x 9, I find 32 x 10 and remove 1 group of 32.
32 x 9 = (32 x 10) - (1 x 32)
32 x 9 = (320) - (32)
32 x 9 = 288
Mrs. Mitchell counted the number of cubes on one layer of a rectangular prism and she got 25. The rectangular prism has 9 layers. What is the volume of the rectangular prism in cubic units?
25 x 9
(100 x 9) / 4
900 / 4
225 cubic units
Name the multiplication strategy being used:
To find 9 x 27, I can find 10 x 27 then take away 1 group of 27.
Over/Under Strategy
Four friends made 55 chocolate muffins and shared them equally. How many muffins did each friend get?
For this problem:
1. Write an expression to represent the problem.
2. Show your thinking and label your answer.
3. Deal with the remainder (if there is one) in the way that best fits the situation.
55 / 4 = 13 and 3/4 muffins
Write a numerical expression to represent each statement. Include parentheses.
To find 56 x 25, I double and halve.
56 x 25 = (56 / 2) x (25 x 2)
56 x 25 = (28 / 2) x (50 x 2)
56 x 25 = (14) x (100)
56 x 25 = 1,400
Find the volume of the rectangular prism Mrs. Mitchell is showing in front of the class.
You must include the full equation and the correct answer to receive points.
(2 x 3) x 5
(6) x 5
30 cubic units
Name the multiplication strategy being used:
To find 24 x 21, I can draw an array to find 20 x 21 and 4 x 21 then add them together to find the answer.
Partial Products Strategy
There are 76 fifth graders and 4 teachers going on buses to a field trip to the zoo. If each van can carry 6 people, how many vans will they need to get to the zoo?
For this problem:
1. Write an expression to represent the problem.
2. Show your thinking and label your answer.
3. Deal with the remainder (if there is one) in the way that best fits the situation.
(76 + 4) / 6 = 13 remainder 2.
They will need to get another van for the remaining 2 people.
So they will need 14 vans total.
Evaluate this expression:
(25 x 22) - (1 x 22)
(25 x 22) - (1 x 22)
((100 x 22)/4) - (22)
(2200/4) - (22)
(550) - (22)
528
Avery's dad is the head coach of the San Diego Padres. The team receives crates of new game baseballs at the beginning of every season that have 62 baseballs in each layer. If there are 5 layers of baseballs, how many baseballs are there in all.
You must write the equation, show your thinking, and correct answer for points.
(62) x 5
(62 x 10) / 2
620 / 2
310 baseballs
Name the multiplication strategy being used:
To find 50 x 26, I can find 100 times 26 and then divide the answer in 2.
To find 5 x 26, I can find 10 times 26 and then divide the answer in 2.
Half 10/Half 100 Strategy
Mrs. Mitchell's class held a fundraiser and raised $55.00. They donated all the money, splitting it evenly among 4 charities. How much did they donate to each charity?
For this problem:
1. Write an expression to represent the problem.
2. Show your thinking and label your answer.
3. Deal with the remainder (if there is one) in the way that best fits the situation.
55.00 / 4 = $13.75
2 x (4 x 6) + 2 x (2 x 5) + 2 x (7 x 2)
2 x (4 x 6) + 2 x (2 x 5) + 2 x (7 x 2)
2 x (24) + 2 x (10) + 2 x (14)
48 + 20 + 28
96
Find the volume of the composite rectangular prism Mrs. Mitchell is showing in front of the class.
You must include the FULL equation (with parenthesis) and the correct answer to receive points.
((3 x 3) x 4) + ((2 x 3) x 2)
(9 x 4) + (6 x 2)
(36) + (12)
48 cubic units
Name the multiplication strategy being used (you must name BOTH):
To help me solve (5 x 72) x 2, I can reorder the numbers OR regroup the numbers to make it simpler to solve.
For example, I could instead write (5 x 2) x 72, which is (10) x 72, which is 720.
Associative or Commutative Properties
Solve this problem. Show your work.
384 / 12
*You may use Base 10 pieces to help you solve!
384 / 12 = 32