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 Solve 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., ten = ones)

Worked Examples

Worked Example 1

Explain why a written algorithm is helpful, then Calculate:

a)

b)

Worked Example 2

Use the addition algorithm:

a)

b)

Worked Example 3

Use the subtraction algorithm:

a)

b)

Worked Example 4

Use subtraction with multiple regrouping:

a)

b)

Problems

Problem 1

a)

b)

Problem 2

a)

b)

Problem 3

a)

b)

Problem 4

a)

b)

Exercises

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Understanding and Fluency

Exercise 1.

Calculate Use the addition algorithm:

a)

b)

c)

Exercise 2.

Calculate using the addition algorithm:

a)

b)

c)

Exercise 3.

Calculate using the subtraction algorithm:

a)

b)

c)

Exercise 4.

Calculate using the subtraction algorithm:

a)

b)

c)

Exercise 5.

Calculate:

a)

b)

c)

Exercise 6.

Calculate:

a)

b)

c)

Reasoning

Exercise 7.

A student writes:

Explain the mistake.

Exercise 8.

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

Exercise 9.

Is regrouping needed for ? Justify your answer.

Exercise 10.

Which requires regrouping? Explain:

a)

b)

Problem-solving

Exercise 11.

A school collected cans in week 1 and cans in week 2. How many in total?

Exercise 12.

A library had books and removed . How many remain?

Exercise 13.

A stadium holds people. If attend, how many seats are empty?

Exercise 14.

A shop sold items on Monday and on Tuesday. How many items in total?

Exercise 15.

A warehouse stored boxes and shipped . 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
• 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 as preventing regrouping (e.g., difficulty with )
• Students may forget to include carried digits in the next column calculation

Next: 005. Multiplication Laws and Algorithms