Partition Rectangles Into Equal Squares - 2nd Grade Math

Carlos draws a rectangle and wants to make exactly 18 equal squares inside it. He decides to make 3 rows. How many squares will be in each row?
Answer: 6 squares in each row To find squares per row, divide total squares by number of rows: 18 ÷ 3 = 6 squares in each row. Choice A (5) would give only 15 total squares (5 × 3). Choice C (9) would give 27 total squares (9 × 3). Choice D (15) subtracts rows from total instead of dividing.
In the figure, Sam covered a rectangle with same-size square tiles arranged in equal rows. How many square tiles did Sam use?
Answer: 14 When you see a rectangle covered with equal rows of square tiles, you're really looking at an array—and arrays are just a picture of multiplication. To find the total, you multiply the number of rows by the number of tiles in each row (or you can add the rows repeatedly). In this figure, the rectangle is made of 2 rows with 7 tiles in each row. That gives you $2 \times 7 = 14$ tiles. You could also think of it as $7 + 7 = 14$ , which is the same idea shown as repeated addition. Now look at the wrong choices. Choice A (11) is what you'd get if you only counted the tiles along the outside edge instead of every tile filling the rectangle—a common mistake when students count the border and forget the inside. Choice B (20) is too many; you might land here if you miscounted a row as having more tiles than it does, like using $4 \times 5$ for a different-shaped array. Choice D (16) is close to the correct answer but happens if you accidentally count one tile in each row twice, or use $2 \times 8$ instead of $2 \times 7$ . Only C (14) matches the actual rows and columns. Tip: For any tile or array problem, first count how many tiles are in one row, then count how many rows there are, and multiply. Skip-counting by the row length (7, 14…) is a fast way to check your answer.
Sarah makes a rectangle with equal squares arranged in 4 rows and 6 columns. She then removes all squares from the middle 2 columns. How many squares remain in her rectangle?
Answer: 16 Removing 2 of the 6 columns leaves 4 columns, and 4 rows times 4 columns equals 16 squares. Choice B, 18, removes too few squares. Choice C, 20, only removes 1 column's worth. Choice D, 22, barely changes the original total.
Emma draws lines to make a grid of squares with 2 rows and 5 columns. Then she colors every square in the first column blue. How many blue squares are there?
Answer: 2 The first column has one square in each of the 2 rows, so coloring that column blue colors 2 squares. Choice B is the number of columns, not the number of squares in one column. Choice C mixes rows and columns in a way that does not match any single part of the grid. Choice D is the total number of squares in the whole grid, not just the first column.
Look at the rectangle below. Only part of the rectangle has been split into equal squares. If the whole rectangle were split into the same size squares, how many equal squares would it have in all?
Answer: $15$ The shaded corner shows a $2\times 3$ block of 6 equal squares. The whole rectangle is 3 rows tall and 5 columns wide when using the same size square, so $3\times 5=15$ squares in all.
Refer to the figure. Marta drew a rectangle and split it into equal squares. How many equal squares did she make?
Answer: 16 When a rectangle is split into equal squares arranged in rows and columns, you can find the total number of squares by multiplying the number of rows by the number of squares in each row. This is the same idea as an array in multiplication — rows × columns = total. For Marta's rectangle, the figure shows 4 rows with 4 squares in each row. So you calculate: $4 \times 4 = 16$ That means Marta made 16 equal squares, which matches choice A. Now look at why the others don't work. Choice B (20) would happen if you miscounted and thought there were 5 squares in one direction and 4 in the other ( $5 \times 4 = 20$ ) — a common error when you count grid lines instead of grid spaces. Choice C (9) is what you'd get from a $3 \times 3$ grid, so this answer represents undercounting a row and a column. Choice D (25) comes from a $5 \times 5$ grid, which means overcounting in both directions — again, often caused by counting the lines that form the squares rather than the squares themselves. A helpful tip: when counting squares in a grid, gently point to the inside of each square, not the lines. Better yet, count how many squares are in the top row, then count how many rows there are, and multiply. This turns a counting problem into a quick multiplication problem and helps you avoid off-by-one mistakes.
A rectangle is made of small squares arranged in 3 equal rows, with 4 squares in each row. How many squares are there in total?
Answer: 12 squares 3 rows with 4 squares in each row gives 3 times 4, or 12 squares in total. Choice B only counts the squares in one row. Choice C is 1 less than the correct total. Choice D comes from adding the row and column counts instead of multiplying.
Look at the rectangle below. How many equal squares are used to cover the whole rectangle?
Answer: $9$ The rectangle has 3 rows and 3 columns of equal squares. $3+3+3=9$ squares in all.
Refer to the rectangle below. Which sentence correctly describes it?
Answer: $2$ rows and $4$ columns, $8$ squares in all The rectangle has 2 rows going across and 4 columns going up and down. That makes $2\times 4=8$ equal squares in all.
An array has 3 rows with 3 squares in each row. Which number sentence shows the total number of squares?
Answer: $3+3+3$ The array has 3 rows with 3 squares in each row, so the total is 3 + 3 + 3, making Choice A correct. Choice B is wrong because it only shows two groups instead of three. Choice C is wrong because the two numbers being added are not equal, which does not match the array. Choice D is wrong because it uses four equal groups instead of three.
Refer to the figure. Which sentence correctly describes the rectangle?
Answer: It has 4 rows and 3 columns, for 12 squares in all. When you see a rectangle broken into equal squares, think of it like a grid or an array. Rows go across (left to right), and columns go up and down. To find the total number of squares, you multiply the number of rows by the number of columns — this is one of the earliest ways you learn multiplication. For this rectangle, counting across each row gives you 3 squares, and counting down each column gives you 4 squares. That means there are 4 rows and 3 columns. Multiplying gives $4 \times 3 = 12$ squares in all, which matches choice D. Choice A is wrong because a 3-by-3 grid would only have 9 squares and would look like a perfect square, not a taller rectangle. Choice B mixes up the counting — it also miscounts the total, since 3 rows and 4 columns would give $3 \times 4 = 12$ , not 7. Adding rows and columns instead of multiplying is a common slip. Choice C describes a bigger square shape (4 rows and 4 columns give 16), which is more squares than the figure shows. A helpful tip: always point with your finger and count the rows down the side first, then the columns across the top. Write both numbers down, then multiply. Watch out for answers that add rows and columns instead of multiplying — that's a trap the test uses often at this level.
Refer to the figure. A rectangle is divided into same-size squares. How many squares are in the rectangle?
Answer: 18 When a rectangle is divided into equal squares arranged in rows and columns, you can find the total number of squares by multiplying the number of rows by the number of squares in each row. This is the foundation of the array model for multiplication — a big idea in 2nd-grade math. For this rectangle, count the squares along one side to find the rows, then count along the other side to find the columns. The figure shows 3 rows with 6 squares in each row (or 6 rows with 3 in each). Multiplying gives $3 \times 6 = 18$ squares, which matches choice A. Choice B (24) is what you'd get if you miscounted and used a 4×6 array — a common mistake when you accidentally count an extra row. Choice C (20) suggests a 4×5 array, which happens if you miscount both dimensions. Choice D (12) is likely the result of only counting the squares along the border (the outside edge) instead of all the squares inside the rectangle, or mistakenly using a 3×4 grid. A helpful strategy: whenever you see a rectangle split into equal squares, don't try to count every single square one by one — that's slow and easy to mess up. Instead, count just one row and one column, then multiply. This connects your counting skills to multiplication and helps you check your answer quickly.
A rectangle is divided into a grid with 4 rows and 6 columns of equal squares (24 squares in all). If Anna covers the top 2 rows with paper, how many squares are still showing underneath?
Answer: 12 squares The grid has 4 rows of 6 squares, which is 24 squares in all. Covering the top 2 rows covers 2 times 6, or 12 squares, leaving 24 minus 12, which is 12 squares still showing. Getting 8 or 10 undercounts how many squares are in each covered row. Getting 15 overcounts how many squares remain after covering exactly 2 full rows.
Look at the rectangle below. How many equal squares are in the rectangle?
Answer: $14$ The rectangle has 2 rows and 7 columns of equal squares. $7+7=14$ squares in all.
The figure shows a rectangle partitioned into equal squares. How many equal squares are in the rectangle in all?
Answer: 20 When a rectangle is split into equal squares arranged in rows and columns, you can find the total number of squares by multiplying the number of rows by the number of squares in each row. This is your first taste of using multiplication (or repeated addition) to count arrays — a big idea in 2nd grade math. For a rectangle partitioned into 4 rows of 5 squares each, you can add $5 + 5 + 5 + 5 = 20$ or multiply $4 \times 5 = 20$ . Either way, there are 20 equal squares in all, which matches choice C. Choice A (25) is what you'd get if you miscounted the rectangle as a 5-by-5 square instead of a 4-by-5 rectangle — a trap when you rush and assume all sides are equal. Choice B (10) comes from adding the rows and columns ( $4 + 5 + 1 = 10$ or $5 + 5 = 10$ ) instead of multiplying them; adding only counts one row plus one column, not the whole grid. Choice D (15) happens if you miscount a row as having only 3 squares, giving $5 \times 3 = 15$ , or skip a full row when counting. A helpful strategy: when you see a grid of equal squares, count the squares in one row, count the number of rows, and multiply. Double-check by lightly touching each square as you count so you don't skip or repeat any. This "rows × columns" trick will prepare you for multiplication and area later on.
The figure shows a rectangle split into same-size squares. How many equal squares fill the rectangle?
Answer: 21 When a rectangle is split into equal squares arranged in neat rows and columns, you can find the total number of squares by multiplying the number of rows by the number of columns. This is the foundation of area and, later, multiplication — instead of counting each square one by one, you can skip-count or multiply. For this rectangle, the squares are arranged in 3 rows of 7 squares each (or 7 columns of 3). That gives you: $3 \times 7 = 21$ So the rectangle is filled with 21 equal squares, which matches choice D. Choice A (12) would come from a rectangle of 3 rows and 4 columns ( $3 \times 4$ ), so it likely reflects miscounting the columns. Choice B (10) suggests only adding rows and columns ( $3 + 7 = 10$ ) instead of multiplying — a common mix-up between adding and multiplying. Choice C (14) would happen if you counted only 2 rows of 7 ( $2 \times 7$ ), missing one full row of squares. A helpful strategy: whenever you see a grid of equal squares, count how many are in one row, then count how many rows there are, and multiply. Double-check by skip-counting: 7, 14, 21. If your answer matches both methods, you know it's right. Remember — with grids, multiply, don't add.
Look at the rectangle shown. Tom divides it into squares by making 5 equal columns. If each column has 3 squares, how many lines did Tom draw inside the rectangle?
Answer: 6 lines total inside the rectangle To make 5 columns, Tom needs 4 vertical lines inside the rectangle. To make 3 rows (since each column has 3 squares), he needs 2 horizontal lines inside. Total internal lines: 4 + 2 = 7 lines. Choice B (8) might count one extra line incorrectly. Choice C (9) adds columns plus rows incorrectly. Choice D (10) counts boundary lines or makes other errors.
In the diagram, two rectangles are each partitioned into same-size squares. Which rectangle has more equal squares, and how many more?
Answer: Rectangle B has 2 more squares. When a rectangle is partitioned into same-size squares, you can find the total number of squares by multiplying the number of rows by the number of columns — this is the foundation of arrays and early multiplication. To compare two rectangles, count the squares in each, then subtract to find the difference. Imagine Rectangle A is made of 3 rows and 4 columns, giving $3 \times 4 = 12$ squares. Rectangle B is made of 2 rows and 7 columns, giving $2 \times 7 = 14$ squares. Since $14 - 12 = 2$ , Rectangle B has 2 more squares than Rectangle A. Choice A is wrong because it reverses the comparison — Rectangle A actually has fewer squares, not more. Choice C overcounts the difference; a gap of 4 would only happen if one rectangle had 16 and the other 12, which isn't the case here. Choice D assumes the totals are equal, but even though the rectangles may look similar in size, the arrangement of rows and columns produces different totals — a common visual trap. A helpful strategy: whenever you see a rectangle split into squares, count carefully by rows and columns, then multiply. Don't judge by how "big" the rectangle looks — a long, skinny rectangle can hold more squares than a shorter, wider one. Always compute both totals before comparing.
Refer to the figure. A rectangle is partitioned into equal squares. How many squares are in one row?
Answer: 5 When a rectangle is partitioned (divided) into equal squares, you can figure out how many squares fit in a row by counting across just one row — you don't need to count every single square in the whole rectangle. Think of it like rows and columns in a grid: a "row" goes across (left to right), and a "column" goes up and down. For this figure, counting the squares that go across one horizontal row gives you 5 squares, making B the correct choice. You could also check this by dividing the total number of squares by the number of rows — if the rectangle has 15 squares total arranged in 3 rows, then $15 \div 3 = 5$ squares per row. Choice A (3) is the number of rows in the rectangle, not the number of squares in each row — a common mix-up between rows and columns. Choice C (15) is the total number of squares in the entire rectangle, not just one row. Choice D (8) doesn't match the figure at all; it might come from adding rows and columns ( $3 + 5 = 8$ ) instead of looking at one row by itself. A helpful tip: whenever a question asks about "a row" or "a column," point your finger and trace just that one line across or down. Don't count the whole shape. Remember — rows run across, columns go down (think of "rows of seats" in a theater going side to side).
The figure shows a rectangle broken into rows and columns of equal squares. How many squares are there in total?
Answer: 6 When a rectangle is divided into equal squares arranged in rows and columns, you can find the total number of squares by multiplying the number of rows by the number of columns. This is your first introduction to the idea behind multiplication as an array — instead of counting every square one by one, you can use the shape's structure. For this rectangle, there are 2 rows and 3 columns (or 3 rows and 2 columns, depending on orientation). Either way, the total is $2 \times 3 = 6$ squares. You can double-check by counting: top row has 3 squares, bottom row has 3 squares, and $3 + 3 = 6$ . That confirms B. Choice A (5) is a common mistake when you miscount and skip a square — perhaps counting one row as 2 instead of 3. Choice C (7) happens when you accidentally count a square twice, often one in the corner where rows and columns meet. Choice D (10) is the trap of adding rows and columns incorrectly or confusing this with a larger $2 \times 5$ arrangement — it doesn't match the figure shown. A helpful tip: whenever you see a grid of equal squares, look for the rows-times-columns shortcut instead of counting one at a time. This builds the foundation for multiplication you'll use in 3rd grade. If you're unsure, count one full row, then multiply by the number of rows — it's faster and less error-prone than counting every square.

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