Common Mistakes with Arrays
Learn
Everyone makes mistakes when learning something new. In this lesson, we will look at common mistakes students make with arrays. Learning to spot these mistakes will help you avoid them!
Mistake 1: Confusing Rows and Columns
The Mistake
Some students mix up rows (going across) and columns (going up and down).
O O O O O
O O O O O
O O O O O
Wrong: "This shows 5 rows with 3 in each row."
Right: "This shows 3 rows with 5 in each row."
Tip: Rows go across like rows of seats. Count rows first (top to bottom), then count how many in one row (left to right).
Mistake 2: Adding Instead of Multiplying
The Mistake
When students see 3 rows and 4 in each row, they sometimes add 3 + 4 instead of multiplying.
Wrong: 3 + 4 = 7
Right: 3 x 4 = 12 (or 4 + 4 + 4 = 12)
Tip: Remember, multiplication means "groups of." 3 rows with 4 means 3 groups of 4.
Mistake 3: Counting Items Twice
The Mistake
When counting items in an array, some students count the same item more than once.
O O O
O O O
Wrong: Counting and getting 7 or 5
Right: 2 x 3 = 6 items
Tip: Point to each item as you count. Use multiplication to check your counting.
Mistake 4: Uneven Rows
The Mistake
Drawing arrays with rows that have different numbers of items.
O O O O
O O O
O O O O O
Wrong: This is NOT an array because rows are uneven.
Tip: Arrays must have the SAME number in every row. All rows must be equal!
Mistake 5: Forgetting to Answer the Question
The Mistake
Finding the right answer but not writing a complete answer to the question.
Question: "How many apples are there in all?"
Wrong: Writing just "12"
Right: Writing "There are 12 apples in all."
Tip: Read the question again after you solve. Make sure your answer matches what was asked.
Spot the Mistake
Look at these examples. Can you find what went wrong?
Example 1
Problem: A garden has 4 rows of flowers with 3 flowers in each row. How many flowers?
Student answer: 4 + 3 = 7 flowers
What went wrong? The student added instead of multiplied.
Correct answer: 4 x 3 = 12 flowers
Example 2
Student drew this array for 2 x 5:
O O O O O
O O O O O
O O O O O
What went wrong? The student drew 3 rows instead of 2 rows.
Correct array: Should have 2 rows with 5 in each row.
Example 3
Student said this array shows 6 x 2:
O O O O O O
O O O O O O
What went wrong? The student switched rows and columns. This shows 2 x 6.
Note: 2 x 6 and 6 x 2 both equal 12, but the arrays look different!
Practice Problems
Find and fix the mistakes in these problems.
Problem 1
Student drew this array for 3 x 4:
O O O
O O O
O O O
O O O
Is this correct? If not, what should the array look like?
Problem 2
Student wrote: "5 rows with 2 in each row equals 5 + 2 = 7"
Find the mistake and write the correct answer.
Problem 3
Is this a correct array? Why or why not?
O O O O
O O O
O O O O
Problem 4
A student counted this array and said there are 15 items:
O O O O
O O O O
O O O O
Is the student correct? What is the actual total?
Problem 5
Student answer: "The array shows 4 x 6 = 24"
O O O O O O
O O O O O O
O O O O O O
O O O O O O
Is this correct? Explain your thinking.
Problem 6
Draw the correct array for 5 x 3. Then draw the incorrect array someone might make if they confused rows and columns.
Problem 7
Circle the mistake: "There are 3 rows with 7 chairs in each row. 3 + 7 = 10 chairs."
Write the correct solution.
Problem 8
Which of these is NOT an array? Explain why.
A)
O O O O O O O O
B)
O O O O O O O O
C)
O O O O O O O O O O O O O O O
Problem 9
True or False: 2 x 8 and 8 x 2 show different arrays but have the same total.
Explain your answer with drawings.
Problem 10
A student solved this problem: "A bookshelf has 6 shelves with 4 books on each shelf. How many books?"
Student answer: "24"
Is the math correct? What is missing from the answer?
Check Your Understanding
Answer these questions to show what you learned about avoiding mistakes.
- What is the difference between rows and columns?
- Why do you multiply (not add) when working with arrays?
- What must be true about every row in an array?
- How can you check if your array answer is correct?
Click to see answers
- Rows go across (horizontal). Columns go up and down (vertical).
- We multiply because we are finding the total of equal groups. Adding rows + items per row does not give the total.
- Every row must have the same number of items.
- You can check by using repeated addition or by counting all the items one by one.
Next Steps
- Review any mistakes you have made in previous lessons
- Practice checking your work before turning it in
- Move on to the Unit Quiz to test everything you learned!