004. Written Algorithms for Addition and Subtraction

Learning Intentions

• To understand that algorithms can be used to add or subtract numbers in cases where mental strategies are ineffective
• apply the addition algorithm to find the sum of positive integers
• apply the subtraction algorithm to find the difference of positive integers

Pre-requisite Summary

• Understanding place value in whole numbers (ones, tens, hundreds, thousands)
• Ability to align numbers vertically by place value
• Recall of basic addition facts to 20
• Recall of basic subtraction facts within 20
• Understanding regrouping/renaming (e.g., $1$ ten = $10$ ones)

Worked Examples

Worked Example 1

Explain why a written algorithm is helpful, then calculate:

a) $47+38$
b) $256+189$

Worked Example 2

Use the addition algorithm:

a) $3472+2685$
b) $9056+3178$

Worked Example 3

Use the subtraction algorithm:

a) $84-57$
b) $4203-1786$

Worked Example 4

Use subtraction with multiple regrouping:

a) $6000-2458$
b) $10002-3679$

Problems

Problem 1

a) $58+36$
b) $314+278$

Problem 2

a) $5283+1649$
b) $8907+2356$

Problem 3

a) $73-48$
b) $3504-1879$

Problem 4

a) $7000-3286$
b) $9001-4578$

Exercises

Understanding and Fluency

1. Calculate using the addition algorithm:
   a) $46+27$
   b) $358+246$
   c) $2487+3125$

2. Calculate using the addition algorithm:
   a) $75+19$
   b) $624+389$
   c) $6405+2876$

3. Calculate using the subtraction algorithm:
   a) $63-28$
   b) $504-276$
   c) $4200-1583$

4. Calculate using the subtraction algorithm:
   a) $92-57$
   b) $800-467$
   c) $5006-2489$

5. Calculate:
   a) $1278+3456$
   b) $7045+2388$
   c) $9999+1001$

6. Calculate:
   a) $6302-2145$
   b) $8000-3267$
   c) $10000-4758$

Reasoning

7. A student writes:

   $$\begin{array}{r}347\\ +58\\ 815\end{array}$$

   Explain the mistake.

8. Why must digits be aligned by place value when using written algorithms?

9. Is regrouping needed for $4512+2376$? Justify your answer.

10. Which requires regrouping? Explain:
    a) $6421-3210$
    b) $6421-3298$

Problem-solving

11. A school collected $2458$ cans in week 1 and $3679$ cans in week 2. How many in total?

12. A library had $7500$ books and removed $2864$. How many remain?

13. A stadium holds $9000$ people. If $6785$ attend, how many seats are empty?

14. A shop sold $3275$ items on Monday and $2486$ on Tuesday. How many items in total?

15. A warehouse stored $8004$ boxes and shipped $3589$. How many remain?

Potential Misunderstandings

• Students may not align digits according to place value before applying the algorithm
• Students may forget to carry when the sum of a column exceeds $9$
• Students may incorrectly regroup during subtraction (e.g., subtracting the smaller digit from the larger without borrowing)
• Students may regroup from the wrong place value column
• Students may treat $0$ as preventing regrouping (e.g., difficulty with $4000-1256$)
• Students may forget to include carried digits in the next column calculation

Next: 005. Multiplication Laws and Algorithms