Algebraic Thinking & Patterns

5.G.1Write expressions01/04

Write simple expressions (no variables).

Step01of 04

An expression is a math phrase: numbers and operations, but no equals sign. Translate words into math directly.

"Sum of 12 and 7"	→12 + 7
"7 less than 12"	→12 − 7 (NOT 7 − 12)
"Twice 9"	→2 × 9
"Half of 20"	→20 ÷ 2 or 20/2
"3 added to 4 doubled"	→(4 × 2) + 3

5.G.1 — Write simple expressions (no variables).

Step 01 of 04

An expression is a math phrase: numbers and operations, but no equals sign. Translate words into math directly.

"Sum of 12 and 7"	→12 + 7
"7 less than 12"	→12 − 7 (NOT 7 − 12)
"Twice 9"	→2 × 9
"Half of 20"	→20 ÷ 2 or 20/2
"3 added to 4 doubled"	→(4 × 2) + 3

Step 02 of 04

Order matters. "7 less than 12" means start with 12 and subtract 7, not the other way around.

Be careful with grouping. "5 times the SUM of 3 and 4" requires parentheses: $5 \times (3 + 4) = 35$ . Without them you'd get $5 \times 3 + 4 = 19$ , a different answer.

Step 03 of 04

Worked example. "Twice the sum of 5 and 8."

2 \times (5 + 8) = 2 \times 13 = 26

Step 04 of 04

Don't compute, just write. The skill is the TRANSLATION; you can compute later.

Key insight

Words → math. Watch for "of," "less than," "sum of." Use parentheses to enforce grouping when the wording calls for it.

5.G.2 — Evaluate expressions (parentheses, brackets).

Step 01 of 04

Order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Step 02 of 04

Worked example. Evaluate $3 + 4 \times 5$ .

Multiplication first: $4 \times 5 = 20$ . Then add: $3 + 20 = 23$ .

NOT 35 (which would be left-to-right without PEMDAS).

Step 03 of 04

Parentheses override the order.

(3 + 4) \times 5 = 7 \times 5 = 35

Step 04 of 04

Brackets and braces work like extra parentheses. Innermost first, working outward.

[2 \times (3 + 5)] - 4 = [2 \times 8] - 4 = 16 - 4 = 12

Key insight

PEMDAS order: Parens → Exponents → ×/÷ → +/−. Within each level, work LEFT TO RIGHT. Innermost grouping symbols first.

5.G.3 — Number patterns from two rules.

Step 01 of 04

Two rules can generate two parallel sequences. Compare them to find patterns and relationships.

Step 02 of 04

Worked example. Rule A: "Add 3, starting at 0." Rule B: "Add 6, starting at 0."

Rule A	→0, 3, 6, 9, 12, 15, 18, ...
Rule B	→0, 6, 12, 18, 24, 30, 36, ...

Notice each B value is DOUBLE the corresponding A value.

Step 03 of 04

Plot pairs (A, B): (0, 0), (3, 6), (6, 12), (9, 18), ... All these lie on a straight line through the origin with slope 2 — $B = 2 A$ .

Step 04 of 04

The relationship comes from the rules: B's "add 6" is twice A's "add 3," so the multiplier between corresponding values is 2.

Key insight

Two parallel sequences from two rules. Compare term by term to find the relationship — often a constant ratio. Plotting pairs reveals patterns visually.

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5.G.1 – 5.G.3 · CCSS 5.OA.A / 5.OA.B · Full curriculum →