095r. Mental and Written Strategies for Addition and Subtraction
Learning Intentions
- To understand the commutative and associative laws for addition
- Use the mental strategies partitioning, compensating and doubling/halving to Calculate a sum or difference of whole numbers mentally
- use the addition and subtraction algorithms to Solve the sum and difference of whole numbers
Pre-requisite Summary
- Understand that addition combines quantities and subtraction finds the difference between quantities. See 003. Mental Strategies and Laws for Addition and Subtraction
- Know the place value of digits in whole numbers 002. Place Value and Comparing Numbers
- Be able to split numbers into tens, hundreds and ones 002. Place Value and Comparing Numbers
- Recall basic addition and subtraction facts
- Understand that an algorithm is a step-by-step written method. See 004. Written Algorithms for Addition and Subtraction and 005. Multiplication Laws and Algorithms
- Be able to line up numbers correctly by place value. See 002. Place Value and Comparing Numbers
Worked Examples
Worked Example 1
Use the commutative law to rewrite:
a)
b)
Worked Example 2
Use the associative law to make the addition easier:
a)
b)
Worked Example 3
Use partitioning to calculate mentally:
a)
b)
Worked Example 4
Use compensating to calculate mentally:
a)
b)
Worked Example 5
Use doubling/halving to calculate mentally:
a)
b)
Worked Example 6
Use the addition algorithm:
a)
b)
Worked Example 7
Use the subtraction algorithm:
a)
b)
Problems
Problem 1
Use the commutative law to rewrite:
a)
b)
Problem 2
Use the associative law to make the addition easier:
a)
b)
Problem 3
Use partitioning to calculate mentally:
a)
b)
Problem 4
Use compensating to calculate mentally:
a)
b)
Problem 5
Use doubling/halving to calculate mentally:
a)
b)
Problem 6
Use the addition algorithm:
a)
b)
Problem 7
Use the subtraction algorithm:
a)
b)
Exercises
Understanding and Fluency
Exercise 1.
Rewrite each addition Use the commutative law:
a)
b)
c)
Exercise 2.
Use the associative law to add more easily:
a)
b)
c)
Exercise 3.
Use partitioning to calculate mentally:
a)
b)
c)
Exercise 4.
Use compensating to calculate mentally:
a)
b)
c)
Exercise 5.
Use doubling/halving to calculate mentally:
a)
b)
c)
Exercise 6.
Use the addition algorithm:
a)
b)
c)
Exercise 7.
Use the subtraction algorithm:
a)
b)
c)
Exercise 8.
Choose a sensible mental strategy and calculate:
a)
b)
c)
d)
Reasoning
Exercise 9.
Explain why
Exercise 10.
Mia says the associative law means
Exercise 11.
Which mental strategy is most efficient for
Exercise 12.
A student solves
Describe the error.
Problem-solving
Exercise 13.
A shop sold
Exercise 14.
A stadium had
Exercise 15.
A teacher buys
Exercise 16.
At a fun run, Sam ran
Exercise 17.
A library had
Exercise 18.
Create two addition questions where:
a) the commutative law is useful
b) the associative law is useful
Potential Misunderstandings
- The commutative law applies to addition, but students may incorrectly assume it always applies to subtraction
- Students may confuse the commutative law with the associative law
- Students may think the associative law changes the order of numbers, when it actually changes the grouping of numbers
- In partitioning, students may split numbers incorrectly by place value
- In compensating, students may adjust one number but forget to compensate in the answer
- Students may overuse doubling/halving when it is not an efficient strategy
- In written algorithms, students may misalign digits and place values
- In subtraction with regrouping, students may subtract the smaller digit from the larger digit regardless of order
- Students may forget to regroup correctly across zeros
- Students may treat mental strategies and written algorithms as unrelated, rather than as different methods for the same operations
Next: 096r. Reviewing Multiplication and Division Strategies