Operations and Algebraic Thinking
What you must understand
Grade 4 work here centers on using the four operations to solve multi-step word problems, interpreting multiplication as comparison ("4 times as many as 6"), finding factor pairs and recognizing prime and composite numbers up to 100, and generating and describing number patterns that follow a given rule. You should also be fluent with the idea that a symbol or letter can stand for an unknown quantity in an equation.
Traps to watch
- Comparison language. "Times as many" is multiplicative, not additive. If Ana has 5 stickers and Bo has 3 times as many, Bo has 15, not 8.
- Hidden steps. Multi-step problems often require an answer to an intermediate question first. Read the whole problem before computing.
- Left-to-right errors. In an expression with parentheses, do the grouped part first; otherwise multiply and divide before adding and subtracting.
- Pattern rules. A pattern may add, subtract, multiply, or alternate. Check the difference or ratio between consecutive terms before naming the rule.
Rule of thumb
For any word problem, write an equation with a symbol for the unknown before you calculate. For comparison problems, ask: "Which quantity is the larger, and how many times the smaller fits inside it?"
Worked example
A shelf holds 8 boxes with 6 markers each. Then 14 markers are removed. How many remain? Step 1: 8 x 6 = 48 markers total. Step 2: 48 - 14 = 34 markers remain. As one expression: (8 x 6) - 14 = 34. The parentheses show that the multiplication happens first.