Place Value
What is 875 rounded to the nearest ten?
880.
Draw an equal groups model to represent 24 ÷ 3.
Three circles with 8 tallies/dots in each circle.
Which number is the product?
2 x 4 = 8
8
What property of multiplication do you see here?
(6 x 2) x 5 = 6 x (2 x 5)
a. commutative property
b. associative property
c. distributive property
b. associative property
Bonus 100 points if you can write an expression and label the factors and product.
7 x 6 = 42.
7 and 6 are the factors. 42 is the product.
Write: What is the standard form represented by the expanded form of this number:
2000 + 40 + 3
Bonus 100 points if you can ALSO draw a math sketch of base 10 blocks to model this number (the ones cubes, tens sticks, hundreds flats, and the thousands cubes).
2,043
Bonus 200 points: Write a division problem for the array and solve.
5 x 4 = 20
The teacher will hand you a piece of paper with an array. Which way do the columns go? Which way do the rows go? Label using an arrow to show direction.
Rows are horizontal. Think of rows of seats in a movie theater--you'd probably want to sit in the same ROW as your friends, not the same COLUMN.
Columns are vertical. Think of the beautiful columns that support old buildings.
What property of multiplication allows you to swap the order of numbers around in an equation?
Example: 5 x 4 x 2 = 2 x 5 x 4
a. commutative property
b. associative property
c. distributive property
a. commutative property
Solve: 3 x 14.
Hint: Consider using the distributive property. It can take a lot of time to draw out an array, and it is easier to mess up your counting when using an array or equal groups if the numbers are larger.
3 x 14 = 42
Which number (or numbers) round to 400 as both the nearest ten AND hundred:
a. 376
b. 497
c. 402
d. 395
c. 402 AND d. 395
The teacher will hand you a piece of paper with a model of base ten blocks. What number does the model represent?
a. 3,239
b. 4,239
c. 31,239
d. 4,329
b. 4,239
No stealing on this question. Label the quotient, dividend, and divisor.
100 points added for each correct.
100 points deducted for each wrong.
Bonus 100 points if you label all 3 correctly for a potential total of 400 points.
15 ÷ 3 = 5
15 ÷ 3 = 5
15 = dividend
5 = divisor
3 = quotient
Solve this equation using the distributive property:
16 x 4 = __
You must be able to explain how what you did used the distributive property.
16 x 4 = 64
Split 16 into two smaller numbers that add up to 16. Could include: 10 and 6, 12 and 4, 8 and 8, etc.
Multiply those two numbers by 4. Example:
10 x 4 = 40
6 x 4 = 24
Find the sum of (add) the two products you found. Example:
40 + 24 = 64
Complete the equation: 16 x 4 = 64
Which equation is true?
a. 18 ÷ 3 = 6
b. 6 x 3 = 9
c. 3 x 6 = 21
d. 3 ÷ 6 = 18
a. 18 ÷ 3 = 6
The baseball park sold ice cream cones and recorded how much of each flavor they sold in a chart.
Ice Cream Flavor | Number of cones sold
Vanilla | 4,923
Chocolate | 4,802
Strawberry | 5,026
Sorbet | 4,997
Correctly order the FLAVORS from least to greatest amount sold.
Hint: You need to say the names of the flavors. Use the numbers to help you order, then use the flavors in that order as your answer.
Chocolate < Vanilla < Sorbet < Strawberry
Bonus 100 points: What do you think the < means?
Solve this division problem using a model of your choice: 27 ÷ 3
You MUST have a model that correctly shows how you solved the problem in order to earn the points AND you must be able to EXPLAIN how the model helped you solve the problem.
Models may vary (arrays, equal groups, etc.).
27 ÷ 3 = 9
What is the sum of 448 and 627?
1,075
Using the associative and commutative properties, write this expression a new way, then solve using any method.
(6 x 2) x 3
Answer: 36
Some potential expressions:
(6 x 3) x 2
(2 x 3) x 6
(3 x 2) x 6
6 x (3 x 2)
2 x (3 x 6)
3 x (2 x 6)
A comparison with a missing number is shown.
__ > 6,429
Select all values that make this comparison true.
a. 7,009
b. 6,208
c. 6,427
d. 6,492
e. 6,431
f. 5,989
__ > 6,429
a. 7,009
d. 6,492
e. 6,431
The baseball park sold ice cream cones and recorded how much of each flavor they sold in a chart.
Ice Cream Flavor | Number of cones sold
Vanilla | 4,923
Chocolate | 4,802
Strawberry | 5,026
Sorbet | 4,997
Correctly order the FLAVORS from greatest to least amount sold.
Hint: You need to say the names of the flavors. Use the numbers to help you order, then use the flavors in that order as your answer.
Strawberry > Sorbet > Vanilla > Chocolate
Bonus 100 points: What do you think the > means?
The teacher will give you a piece of paper with a box array model. Choose all correct expressions of the model.
a. 9 x 4
b. 4 + 9
c. 4 x 9
d. 4 + 4 + 4 + 4 + 4 + 4
e. 9 x 9 x 9 x 9
f. 9 + 9 + 9 + 9
a, c, and f
a. 9 x 4 CORRECT
b. 4 + 9 INCORRECT
c. 4 x 9 CORRECT
d. 4 + 4 + 4 + 4 + 4 + 4 INCORRECT
e. 9 x 9 x 9 x 9 INCORRECT
f. 9 + 9 + 9 + 9 CORRECT
What does = mean?
Hint: Think about how you would see it in different types of equations. For example:
15 ÷ 3 = 5
(4 x 2) x 3 = 4 x (2 x 3)
64 ÷ 8 = 2 x 4
Bonus 100 points if you can explain your answer using one or more of the example equations above.
= means that the expression on one side is the same as (or another way of writing) the expression on the other side.
= does NOT mean "The answer is ..."
(4 x 2) x 3 = 4 x (2 x 3) shows that the side on the left is going to be the same as the side on the right even though they are written differently.
15 ÷ 3 = 5 shows that "15 ÷ 3" is another way of writing "5"
64 ÷ 8 = 2 x 4 shows that both expressions are going to end up being the same answer when we solve them, meaning that even though they are very different, they are still equal to each other.
Explain and provide an example of each property of multiplication: commutative, associative, and distributive.
Associative: It does not matter what you multiply together first if there are more than two numbers in an expression. Example: (2 x 3) x 4 = 2 x (3 x 4)
Distributive: You can break larger numbers in an expression into smaller numbers that equal the sum of the larger number (ex: you can break 12 into 10 and 2 because 10 + 2 = 12), and use those smaller numbers to find the product through extra, but simpler steps.
Example: 12 x 4 can be broken into 10 x 4 = 40 and 2 x 4 = 8. Then you can add 40 + 8 to get 12 x 4 = 48.
The equation 24 ÷ ? = __
can be solved using the equation
? x __ = 24
In 24 ÷ ? = __, the ? can be replaced with:
a. 3 b. 4 c. 5
In ? x __ = 24, the ? can be replaced with:
a. 2 b. 3 c. 6
Hint: Remember, we can use the same numbers for multiplication and division problems, but the order of how we switch them up DOES matter when we do this.
In 24 ÷ ? = __, the ? can be replaced with:
a. 3
In ? x __ = 24, the ? can be replaced with:
b. 3
This is because the ? needs to be the same number if we want to find what __ is.
We can rewrite the expressions like this:
24 ÷ 3 = __
3 x __ = 24
This way, it is easier for us to find the other missing number now that we know that ? is 3 and we have plugged it in to our equations.