Download Writing Equations Using the Distributive Property

Writing Equations Using the
Distributive Property
MAFS.3.OA.2.5
Lesson Opening
1. If you combined the arrays below, what multiplication equation
could represent it?
2×3
2×3
2. If the two equations below were combined, what multiplication
equation could represent it? (Use square tiles to model if needed)
2 × 5 = 10
2 × 5 = 10
Lesson Opening
1. If you combined the arrays below, what multiplication equation
could represent it?
2×3
2×3
2. If the two equations below were combined, what multiplication
equation could represent it? (Use square tiles to model if needed)
2 × 5 = 10
2 × 5 = 10
or
Yesterday, we learned…
3×2
3×2
3×4
can be broken apart
Yesterday, we learned…
3×2
3×2
3×4
can be broken apart
Here is how we would write it as an equation:
3 x 4 = (3 × 2) + (3 × 2)
3 x 4 = (3 x 2) + (3 x 2)
Put parentheses around each multiplication array to show
that it NAMES the array. Also, if we solve the equation we have
to do the operation inside the parentheses first!
3 x 4 = (3 x 2) + (3 x 2)
Then, put an addition sign in between the arrays to show
that you ADD the products of the array to find the TOTAL product.
Write the equation for this
array:
4 x 5 = (4 x 2) + (4 x 3)
Write the equation for this
array:
4 x 5 = (4 x 2) + (4 x 3)
2
3
The 5 was decomposed into 2 and 3.
Then each part was multiplied by 4.
Write the equation for this
array:
6 x 5 = (3 x 5) + (3 x 5) = 30
3
3
The 6 was decomposed into 3 and 3.
Then each part was multiplied by 5.
Here’s another way to think about it…
6
6
4
6 x 10
tens
2
This is a number bond that shows 6
decomposed into 4 and 2.
4
2
tens
tens
4 x 10
2 x 10
This is a number bond that shows 6 tens
decomposed into 4 tens and 2 tens.
6 x 10 = (4 x 10) + (2 x 10)
Let’s try another one.
7
7x4
This is a number bond that shows 7 fours
decomposed into 5 fours and 2 fours.
fours
7 x 4 = (5 x 4) + (2 x 4)
5
2
fours
fours
5x4
2x4
On your dry-erase board, write an equation
for the following:
8
8x3
threes
8 x 3 = (5 x 3) + (3 x 3) = 24
or
8 x 3 = (4 x 3) + (4 x 3) = 24
5
3
threes
threes
5x3
3x3
or
8 x 3 = (6 x 3) + (2 x 3) = 24
or
8 x 3 = (7 x 3) + (1 x 3) = 24
Use the Distributive Property to write an
equation (think of a number bond or an array).
6×6
(3 × 6) + (3 × 6) = 36
(4 × 6) + (2 × 6) = 36
(5 × 6) + (1 × 6) = 36
(6 × 3) + (6 × 3) = 36
(6 × 4) + (6 × 2) = 36
(6 × 5) + (6 × 1) = 36
Use the Distributive Property to write an
equation (think of a number bond or an array).
7×8
(5 × 8) + (2 × 8) = 56
(4 × 8) + (3 × 8) = 56
(6 × 8) + (1 × 8) = 56
(7 × 4) + (7 × 4) = 56
(7 × 5) + (7 × 3) = 56
(7 × 6) + (7 × 2) = 56
Your Turn
• Draw the array that represents the
multiplication expression.
• Use two different colors to
represent how you can break
apart the array.
• Write the equation that represents
how you broke apart the array.
• Don’t forget to write the product.
Bonus Questions
1. The following equation represents an array broken apart into 3
smaller arrays. What is the equation for the original array? How do
you know?
(5 × 3) + (5 × 3) + (5 × 2) = 40
2. Can you break apart this array into 3 smaller arrays? What would
the equation be?
3 × 12
Bonus Questions
1. The following equation represents an array broken apart into 3
smaller arrays. What is the equation for the original array? How do
you know?
rows
columns
rows
columns
rows
columns
(5 × 3) + (5 × 3) + (5 × 2) = 40
Since there are 5 rows in each of the arrays, I know the array has 5 rows. So then I add up
all the columns. 3 + 3 + 2 = 8. So the original array is 5 × 8.
2. Can you break apart this array into 3 smaller arrays? What would
the equation be?
3 × 12
Bonus Question #2 Answer
Choose to decompose either the
3 or the 12.
3 × 12
3
12
12
threes
threes
twelves
10
1
1
twelve
1
twelve
twelve
(1 x 12) + (1 x 12) + (1 x 12) = 36
threes
1
three
1 three
(10 x 3) + (1 x 3) + (1 x 3) = 36
4
4
threes
4
threes
threes
(4 x 3) + (4 x 3) + (4 x 3) = 36
Exit Ticket:
Which expressions could represent the array?
a) 6 × 4
b) 4 × 6
c) (6 × 4) + (6 × 4)
d) (3 × 4) + (3 × 4)
e) (6 × 2) + (6 × 2)
f) (6 × 4) × (6 × 2)