RemeliaMaths Year 5 Addition & subtraction
Year 5 column addition and subtraction with large numbers
The objective: Add and subtract whole numbers with more than 4 digits, including formal columnar methods.
The explanation, example and questions are the ones Remelia uses in the app; the questions are not taken from any test paper.
The idea
Column method with 5 and 6 digits is identical to 4 digits. Only the length changes.
How to do it
- Line up the place values exactly, ones under ones.
- Work right to left.
- Exchange as needed, including across zeros.
A worked example
40,003 − 12,547 = 27,456. Check: 27,456 + 12,547 = 40,003.
Watch for
Misaligned columns when the two numbers have different lengths. Write them carefully or use squared paper.
Try four questions
-
Rosa says: 498,240 − 378,170 = 120,130.
Is Rosa right? Write the correct answer, not just yes or no.
Show the answer to question 1
Answer: 120,070 · "No, 120,070" is right too; "No" on its own scores nothing
Why:
Column method with six digits. Line up the ones carefully: a misaligned column is the most common way to lose this mark.
Rosa's answer was not right: the correct answer is 120070.
-
460,118 + 150,839 = ?
Show the answer to question 2
Answer: 610,957
Why:
Column method with six digits. Line up the ones carefully: a misaligned column is the most common way to lose this mark.
-
Ines used the column method for 624,938 − 32,054 and got 492,884.
That is not right. Working from the ones, which column has the first wrong digit?
- A the hundred thousands
- B the tens
- C the ones
- D the hundreds
Show the answer to question 3
Answer: A · the hundred thousands
Why:
624,938 − 32,054 = 592,884.
Compare from the ones: the first digit that differs is in the hundred thousands column. Everything is right up to the hundred thousands, and that digit is one out: 4 for 5.
-
Sana used the column method for 136,490 + 104,971 and got 240,461.
That is not right. Working from the ones, which column has the first wrong digit?
- A the hundreds
- B the ten thousands
- C the thousands
- D the ones
Show the answer to question 4
Answer: C · the thousands
Why:
136,490 + 104,971 = 241,461.
Compare from the ones: the first digit that differs is in the thousands column. The 1 exchanged into the thousands was forgotten.
Answers
- 1. 120,070 · "No, 120,070" is right too; "No" on its own scores nothing
- 2. 610,957
- 3. A · the hundred thousands
- 4. C · the thousands
The mistakes Remelia names
When a wrong answer to a question like these matches one of these mistakes, the app says what the child seems to have done before they try again.
- Question 1, the answer 120,130: It looks as if you took the smaller digit from the bigger one, even where the bigger one was at the bottom. Where the top digit is smaller, exchange first: take 1 from the next column to the left, which makes 10 more in this one, then subtract.
- Question 2, the answer 510,947: It looks as if a column came to 10 or more and nothing was exchanged. Write its ones digit, and exchange the ten for 1 in the next column to the left.