Distributive Detective
Fill in the blank: 4 x 6 = (2 x 6) + (___ x 6)
2
What is 3 × 6?
18
An array has 3 rows with 4 stars in each row.
How many stars are there?
3 × 4 = 12
There are 4 bags of candy.
Each bag contains 5 pieces.
How many pieces of candy are there?
4 × 5 = 20
True or False?
6 × 4 = 4 × 6
True
Both equal 24.
What is the product?
5 x 8 = (3 x 8) + (2 x 8)
40
What is 8 × 4?
32
An array has 5 rows and 6 columns.
Write a multiplication equation to find the total.
5 × 6 = 30
A toy store has 6 shelves.
Each shelf holds 8 toys.
How many toys are there altogether?
6 × 8 = 48
Find the missing number:
(3 × 5) + (___ × 5) = 40
Answer: 5
15 + 25 = 40
Which expression is equivalent to 7 x 6
A. (3 x 6) + (4 x 6)
B. (3 x 6) + (3 x 6)
C. (7 x 3) + (6 x 3)
A.
Find the product:
7 × 8 = ?
56
An array has 4 rows and 8 columns.
You split it into two arrays with 4 columns each.
Write an equation showing the two smaller arrays.
(4 × 4) + (4 × 4) = 32
A teacher has 7 tables.
There are 4 students sitting at each table.
If 3 more students join the class, how many students are there now?
7 × 4 = 28
28 + 3 = 31 students
Two students solve 6 × 8 differently.
Student A: (3 × 8) + (3 × 8)
Student B: (4 × 8) + (2 × 8)
Are both students correct? Explain.
Answer: Yes!
Student A: 24 + 24 = 48
Student B: 32 + 16 = 48
Both equal 6 × 8.
A student breaks 8 x 7 into : (5 x 7) + (3 x 7)
Find the value of each smaller multiplication problem and the total.
5 x 7 = 35
3 x 7 = 21
35+21= 56
Find the missing factor:
___ × 9 = 63
7
An array has 6 rows and 7 columns.
You separate it into two arrays:
How many objects are in the original array?
(6 × 5) + (6 × 2)
30 + 12 = 42
A farmer plants 9 rows of flowers.
Each row contains 6 flowers.
He picks 8 flowers to make a bouquet.
How many flowers are left?
9 × 6 = 54
54 − 8 = 46 flowers
A student writes:
(4 × 7) + (3 × 7) = 7 × ___
What number belongs in the blank?
Explain why.
Answer: 7
Because 4 + 3 = 7.
7 × 7 = 49
A student says:
"I can solve 9 × 8 by using (5 × 8) + (3 × 8)."
Is the student correct?
If not, explain the mistake and write a correct equation using the distributive property.
No! The student broke 9 into 5 + 3, which equals 8.
Correct equation:
9 × 8 = (5 × 8) + (4 × 8)
40 + 32 = 72
I'm thinking of a number.
What is my number? Explain how you know.
Answer: 8
8 × 6 = 48
8 × 7 = 56
8 × 9 = 72
An array has 8 rows and 9 columns.
A student divides the array into three smaller arrays.
The first array has 8 rows and 2 columns.
The second array has 8 rows and 3 columns.
How many columns must the third array have?
Then write a complete distributive property equation and solve.
9 − 2 − 3 = 4 columns
(8 × 2) + (8 × 3) + (8 × 4)
16 + 24 + 32 = 72
A school is preparing prizes for 3 classrooms.
Each classroom has 8 students.
Every student will receive 4 prizes.
The school already has 75 prizes.
Does the school have enough prizes? If not, how many more does it need?
3 × 8 = 24 students
24 × 4 = 96 prizes needed
96 − 75 = 21 more prizes needed
A teacher writes this equation on the board:
(4 × ___) + (5 × ___) = 81
Both blanks must contain the SAME number.
The missing number is 9.
(4 × 9) + (5 × 9)
36 + 45 = 81
Original equation:
9 × 9 = 81