2nd Grade · 2.G.A.2

Partitioning rectangles in 2nd grade

Partitioning rectangles means splitting a rectangle into rows and columns of squares that are all the same size, then counting the squares. In 2nd grade, your child draws these grids, counts the squares and starts to count them a row at a time.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

2.G.A.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

What it means, in plain words

To partition a shape is to split it into parts. A row is a line of squares that goes across, from left to right. A column is a line of squares that goes up and down. A rectangle split into 3 rows and 5 columns holds 15 squares.

The squares must all be the same size, with no gaps and no overlaps. Drawing that is harder than it looks, because uneven lines make some squares big and some small. Graph paper helps, because the squares are already there.

Your child can count the squares one by one, or count by rows: if each row has 5 squares, count 5, 10, 15. Partitioning rectangles in 2nd grade prepares for multiplication and area in 3rd grade, but for now your child only counts.

Your child should be able to:

Split a rectangle into rows and columns of same-size squares
Tell rows, which go across, from columns, which go up and down
Count the squares one by one or a row at a time
Spot a split where the squares are not all the same size

Example

A rectangle is split into 3 rows with 5 same-size squares in each row. How many squares are there in all?

Each row has 5 squares.
Count by rows: 5, 10, 15.
There are 3 rows, so the count stops at 15. There are 15 squares in all.

Example

How do you split a rectangle into 2 rows and 5 columns of same-size squares, and how many squares does it make?

Draw one line across the middle to make 2 rows.
Draw 4 lines up and down, evenly spaced, to make 5 columns.
Count: 5 squares in the top row and 5 in the bottom row. There are 10 squares in all.

Where children usually get stuck

Your child draws 3 lines across a rectangle to make 3 rows, then finds 4 rows.
Lines and rows are not the same thing. The edges of the rectangle close off the top and bottom rows, so 3 lines inside make 4 rows.
What helps. Draw 1 line across a rectangle and count the rows together: 2. Add one more line at a time and count again, until the pattern is clear.
Your child draws the lines one at a time, and the last row or column ends up squeezed and much smaller.
The spacing was not planned before drawing, so the space runs out at the end.
What helps. Fold a paper rectangle in half, then in half again, and open it. The creases make same-size parts. Draw over the creases together.
Counting the squares one by one, your child counts some twice and misses others.
Without a plan, the eye jumps around the grid and loses its place.
What helps. Count one row at a time, left to right. Cover each finished row with a strip of paper before starting the next.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Count the rows and columns in the grid. Type how many rows and how many columns.
Rows:
Columns:
Show the answer and how to solve it
The grid has $2$ rows and $3$ columns.
1. 1Look at the grid below. Rows go across, from left to right.
2. 2Count the rows from top to bottom. The grid has $2$ rows.
3. 3Now count the columns. Columns go up and down. The grid has $3$ columns.
4. 4Type $2$ in the Rows box and $3$ in the Columns box.
Common mistake. A common mistake is swapping the row count and the column count. Rows go across (like rows of seats in a theater), and columns go up and down (like columns holding up a roof).
The idea underneath. Rows go across (left to right) and columns go up and down. Counting in the right direction matches each number to the right box.
2On level
Carlos says this rectangle has 7 squares.
Select the statement that best describes Carlos's count.
A
Carlos's 7 comes from adding the rows and columns.
B
Carlos's 7 comes from counting only one column.
C
Carlos's 7 is correct.
D
Carlos's 7 comes from counting only one row.
Show the answer and how to solve it
Carlos's 7 comes from adding the rows and columns $(3 + 4 = 7)$ . The rectangle actually has 3 rows of 4 squares, so the total is 12 squares — not 7.
1. 1Look at the rectangle. It is split into rows and columns of small squares.
2. 2Count how many squares are in one row, and count how many rows there are. There are 4 squares in each row, and there are 3 rows.
3. 3Add the squares in each row to find the total: $4 + 4 + 4 = 12$ squares.
4. 4Carlos said the total is 7. Notice that $3 + 4 = 7$ . Carlos added the number of rows and the number of columns instead of counting all the squares.
Common mistake. A common mistake is adding the rows and columns: $3 + 4 = 7$ . The total is really 12 because there are 3 rows of 4 squares.
The idea underneath. When a rectangle is split into rows and columns of squares, find the total by counting all the squares. Adding rows and columns or counting just one row or column gives a different number that is not the total.
3On level
Maya says this grid has 4 rows. Which sentence best describes what Maya counted?
A
Maya counted the columns.
B
Maya counted every square.
C
Maya counted one too many rows.
D
Maya counted the rows correctly.
Show the answer and how to solve it
The answer is 'Maya counted the rows correctly.' The grid has 4 rows, and Maya said 4 — so her count matches the actual number of rows.
1. 1Look at the grid below. Count the rows going from top to bottom — there are 4 rows.
2. 2Now count the columns going from left to right — there are 2 columns.
3. 3Maya said the grid has 4 rows. The grid does have 4 rows, so 4 matches the actual row count.
4. 4Check the other values: columns = 2 (not 4), total squares $= 4 \times 2 = 8 (not 4)$ , one too many rows $= 4 + 1 = 5 (not 4)$ . Only the actual row count matches 4.
5. 5Maya counted the rows correctly.
Common mistake. A common mistake is picking 'Maya counted the columns' because students expect a wrong count and assume columns must be the cause. But there are only 2 columns, not 4. The number 4 matches the actual rows (4 rows), so Maya counted the rows correctly.
The idea underneath. When a count is wrong, look at what the count DOES match in the picture. If it matches rows × columns, every square was counted. If it matches the columns alone, columns were counted instead of rows.
4Stretch
Mia tried to split the rectangle below into same-size squares. Did she do it correctly?
A
Yes, all the parts are the same.
B
No, the rectangle is empty.
C
Yes, the rectangle is divided up.
D
No, the parts are not all the same.
Show the answer and how to solve it
Mia did not split the rectangle into same-size squares correctly. The parts are not all the same size — some strips are taller and some are shorter.
1. 1Look at the rectangle Mia made. It is split into 5 parts.
2. 2Compare the size of each part. Some parts are tall and some parts are short. The parts are NOT all the same size.
3. 3Same-size squares must all be equal. Because Mia's parts are different sizes, she did NOT split the rectangle into same-size squares correctly.
Common mistake. A common mistake is counting the parts (1, 2, 3, 4, 5) and stopping there, without comparing the sizes of the parts. Always check that every part is the same size, not just that there are several parts.
The idea underneath. Same-size squares need TWO things — same size AND square shape. Even if a rectangle is divided into many parts, it isn't same-size squares unless every part is equal.