Study guide: Write Expressions and Analyze Paired Patterns
Use grouping symbols, translate instructions, compare expression structure, and generate paired rules.
Ideas to explain in your own words
- Parentheses specify which part of an expression is treated as one grouped quantity.
- Writing an expression records a calculation before doing it.
- Expression structure can show a size relationship directly.
- Two rules can create paired values when applied the same number of times.
Useful vocabulary
- expression
- A calculation without an equality claim.
- parentheses
- Grouping symbols that identify a part calculated together.
Watch your reasoning
- Do not ignore parentheses when multiplying a sum.
- A multiplier after a total needs grouping around the total.
- Times as large and more are different relationships.
- A different starting value can change a simple multiplier relationship.
A worked review example
For 4×(6+3), the group is nine, so the result is 36. Without parentheses, 4×6+3=24+3=27. The grouped expression multiplies the whole sum by four, while the ungrouped version multiplies only six and then adds three. Treat the grouped sum as one quantity. Do not ignore parentheses when multiplying a sum. Draw a box around each grouped quantity before calculating.
Make a practice plan
- Evaluate Expressions with Grouping Symbols: Evaluate (18−6)÷3 and 18−6÷3. Expected: 4 and 16.
- Translate Calculation Instructions into an Expression: Write subtract six from twenty, then divide that result by two. Expected: (20−6)÷2.
- Compare Expressions Without Unneeded Arithmetic: Compare 6×(408+27) with 2×(408+27). Expected: first is three times the second.
- Generate Paired Patterns and Explain a Relationship: A starts at zero adding five; B starts at zero adding ten. At step four: pair (20,40), with B twice A.