Operations and Algebraic Thinking
What this domain covers
Operations and Algebraic Thinking on the Grade 4 test asks you to use the four operations to solve problems, interpret multiplication as comparison, find factors and multiples, and extend number patterns. Problems often combine skills, so read for the hidden question before computing.
Core rules to know
- Multiplicative comparison: '5 times as many as 9' means 5 × 9 = 45. '9 more than 45' means 45 + 9.
- Multi-step problems: solve in order, labeling each result. Check that the final answer matches what was asked.
- Factors and multiples: factors divide a number evenly; multiples are products of that number and whole numbers. 1, 2, 3, 4, 6, 8, 12, 24 are factors of 24. 24, 48, 72 are multiples of 24.
- Prime and composite: a prime has exactly two factors, 1 and itself; a composite has more than two. 1 is neither.
- Patterns: state the rule, then apply it consistently. A rule may use addition, subtraction, multiplication, or a combination.
Worked example
A red ribbon is 9 cm long. A blue ribbon is 5 times as long. How much longer is the blue ribbon?
- Find blue length: 5 × 9 = 45 cm.
- Compare lengths: 45 − 9 = 36 cm. Answer: 36 cm longer. The phrase 'times as long' gives the blue length; 'how much longer' asks for a difference, not the total.
Traps that cost marks
- Treating '3 times as many' as '3 more than.'
- Stopping after the first step when a second comparison is requested.
- Listing multiples when the question asks for factors, or including 1 and the number itself as the only factors of a composite.
- Applying a pattern rule to only one term instead of checking the next two terms.